James H Burge

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Journals/Publications

• Butel, G. P., Smith, G. A., & Burge, J. H. (2015). Deflectometry using portable devices. Optical Engineering, 54, 025111--025111.
• Elazhary, T. T., Zhou, P., Zhao, C., & Burge, J. H. (2015). Generalized sine condition. Applied optics, 54, 5037--5049.
• Huang, R., Su, P., Burge, J. H., Huang, L., & Idir, M. (2015). High-accuracy aspheric x-ray mirror metrology using Software Configurable Optical Test System/deflectometry. Optical Engineering, 54, 084103--084103.
• Kim, D. W., Su, T., Su, P., Oh, C., Graves, L., & Burge, J. (2015). Accurate and rapid IR metrology for the manufacture of freeform optics. SPIE Newsroom.
• Smith, G. A., & Burge, J. H. (2015). Subaperture stitching tolerancing for annular ring geometry. Applied Optics, 54, 8080--8086.
• Su, T., Maldonado, A., Su, P., & Burge, J. H. (2015). Instrument transfer function of slope measuring deflectometry systems. Applied optics, 54, 2981--2990.
• Butel, G. P., Smith, G. A., & Burge, J. H. (2014). Binary pattern deflectometry. Applied Optics, 53(5), 923-930.
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  Abstract: © 2014 Optical Society of America.Deflectometry is widely used to accurately calculate the slopes of any specular reflective surface, ranging from car bodies to nanometer-level mirrors. This paper presents a new deflectometry technique using binary patterns of increasing frequency to retrieve the surface slopes. Binary Pattern Deflectom-etry allows almost instant, simple, and accurate slope retrieval, which is required for applications using mobile devices. The paper details the theory of this deflectometry method and the challenges of its implementation. Furthermore, the binary pattern method can also be combined with a classic phase-shifting method to eliminate the need of a complex unwrapping algorithm and retrieve the absolute phase, especially in cases like segmented optics, where spatial algorithms have difficulties. Finally, whether it is used as a stand-alone or combined with phase-shifting, the binary patterns can, within seconds, calculate the slopes of any specular reflective surface.
• Butel, G. P., Smith, G. A., & Burge, J. H. (2014). Binary pattern deflectometry. Applied optics, 53(5), 923--930.
• Cai, W., Zhou, P., Zhao, C., & Burge, J. H. (2014). Diffractive optics calibrator: measurement of etching variations for binary computer-generated holograms. Applied optics, 53(11), 2477--2486.
• Huang, R., Su, P., Horne, T., Brusa, G., & Burge, J. H. (2014). Optical metrology of a large deformable aspherical mirror using software configurable optical test system. Optical Engineering, 53(8), 085106--085106.
• Lampen, S., Dubin, M., & Burge, J. H. (2014). Alignment of a three-mirror anastigmat using the sine condition test. Applied Optics, 53(9), 1874-1888.
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  Abstract: © 2014 Optical Society of America.Continuing to develop the sine condition test (SCTest), we show how violations of the generalized sine condition can be used to align a three-mirror anastigmat (TMA). This paper shows how the linear aberrations measured using the sine condition, along with aberrations that have constant field dependence, can be used to align a system. We discuss the design of the test hardware needed to align a TMA and the procedure for alignment. Using simulation, we then investigate the behavior of the alignment SCTest for various levels of mirror misalignment, mirror fabrication errors, and misalignment of the test equipment. All of these tests show that the alignment SCTest can successfully align an optical system.
• Lampen, S., Dubin, M., & Burge, J. H. (2014). Alignment of a three-mirror anastigmat using the sine condition test. Applied optics, 53(9), 1874--1888.
• Maldonado, A. V., Su, P., & Burge, J. H. (2014). Development of a portable deflectometry system for high spatial resolution surface measurements. Applied optics, 53(18), 4023--4032.
• Morel, S., Dubin, M., Shiefman, J., & Burge, J. (2014). Application of a synthetic extended source for interferometry. Applied Optics, 53(33), 7903--7915.
• Peng, S. u., A., M., Tianquan, S. u., Huang, R., Dominguez, M. Z., Maldonado, A., Butel, G., Wang, Y., Parks, R. E., & Burge, J. H. (2014). Aspheric and freeform surfaces metrology with software configurable optical test system: A computerized reverse Hartmann test. Optical Engineering, 53(3).
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  Abstract: Abstract. A software configurable optical test system (SCOTS) based on deflectometry was developed at the University of Arizona for rapidly, robustly, and accurately measuring precision aspheric and freeform surfaces. SCOTS uses a camera with an external stop to realize a Hartmann test in reverse. With the external camera stop as the reference, a coordinate measuring machine can be used to calibrate the SCOTS test geometry to a high accuracy. Systematic errors from the camera are carefully investigated and controlled. Camera pupil imaging aberration is removed with the external aperture stop. Imaging aberration and other inherent errors are suppressed with an N-rotation test. The performance of the COTS test is demonstrated with the measurement results from a 5-mdiameter Large Synoptic Survey Telescope tertiary mirror and an 8.4-m diameter Giant Magellan Telescope primary mirror. The results show that SCOTS can be used as a large-dynamic-range, high-precision, and non-null test method for precision aspheric and freeform surfaces. The SCOTS test can achieve measurement accuracy comparable to traditional interferometric tests. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE).
• Cai, W., Zhou, P., Zhao, C., & Burge, J. H. (2013). Analysis of wavefront errors introduced by encoding computer-generated holograms. Applied Optics, 52(34), 8324-8331.
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  Abstract: The fabrication of computer-generated holograms (CGH) by e-beam or laser-writing machine specifically requires using polygon segments to approximate the continuously smooth fringe pattern of an ideal CGH. Wavefront phase errors introduced in this process depend on the size of the polygon segments and the shape of the fringes. In this paper, we propose a method for estimating the wavefront error and its spatial frequency, allowing optimization of the polygon sizes for required measurement accuracy. This method is validated with computer simulation and direct measurements from an interferometer. © 2013 Optical Society of America.
• Cai, W., Zhou, P., Zhao, C., & Burge, J. H. (2013). Diffractive optics calibrator: Design and construction. Optical Engineering, 52(12).
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  Abstract: Abstract. We present a new device, the diffractive optics calibrator, for measuring duty cycle and etching depth for computer-generated holograms (CGHs). The system scans the CGH with a collimated laser beam and collects the far-field diffraction pattern with a CCD array. The relative intensities of the various orders of diffraction are used to fit the phase shift from etching and the duty cycle of the binary pattern. The system is capable of measuring variations that cause 1-nm peakto- valley (PV) phase errors in the wavefront created by the CGH. The measurements will be used primarily for quality control CGHs, but the data can also be used to provide a lookup table for corrections that allow calibration of the lithography errors. Such calibrations may be necessary for us to achieve our goal of measuring freeform aspheric surfaces with 1-nm RMS accuracy. © 2013 Society of Photo-Optical Instrumentation Engineers (SPIE).
• Cai, W., Zhou, P., Zhao, C., & Burge, J. H. (2013). The diffractive optics calibrator: Design and construction. Proceedings of SPIE - The International Society for Optical Engineering, 8839.
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  Abstract: We present a new device, the Diffractive Optics Calibrator (DOC), for measuring duty-cycle and etching depth for computer generated holograms (CGH). The system scans the CGH with a collimated laser beam, and collects the far field diffraction pattern with a CCD array. The relative intensities of the various orders of diffraction are used to fit the phase shift from etching and the duty cycle of the binary pattern. The system is capable of measuring variations that cause 1 nm PV phase errors in the wavefront created by the CGH. The measurements will be used primarily for quality control CGHs, but the data can also be used to provide a lookup table for corrections that allow calibration of the lithography errors. Such calibration may be necessary for us to achieve our goal of measuring freeform aspheric surfaces with 1 nm RMS accuracy. © 2013 SPIE.
• Coyle, L. E., Dubin, M. B., & Burge, J. H. (2013). Design and analysis of an alignment procedure using computer-generated holograms. Optical Engineering, 52(8), 084104.
• Hoyo, J. D., Kim, D. W., & Burge, J. H. (2013). Super-smooth optical fabrication controlling high spatial frequency surface irregularity. Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: Modern advanced optical systems often require challenging high spatial frequency surface error control during their optical fabrication processes. While the large scale surface figure error can be controlled by directed material removal processes such as small tool figuring, surface finish (
• Huang, R., Peng, S. u., Burge, J. H., & Idir, M. (2013). X-ray mirror metrology using SCOTS/deflectometry. Proceedings of SPIE - The International Society for Optical Engineering, 8848.
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  Abstract: SCOTS is a high precision slope measurement technology based on deflectometry. Light pattern on a LCD display illuminates the test surface and its reflected image is used to calculate the surface slope. SCOTS provides a high dynamic range full field measurement of the optics without null optics required. We report SCOTS tests on X-ray mirrors to nm and even sub nm level with precise calibration of the test system. A LCD screen with dots/check board pattern was aligned into the system at the test mirror position to calibrate camera imaging distortion in-situ. System errors were further eliminated by testing and subtracting a reference flat which was also aligned at the same position as the test mirror. A virtual reference based on the ideal shape of the test surface was calculated and subtracted from the test raw data. This makes the test a 'virtual null' test. Two X-ray mirrors were tested with SCOTS. 0.1μrad (rms) slope precision and sub nm (rms) surface accuracy were achieved. © 2013 SPIE.
• Huang, R., Peng, S. u., Horne, T., Zappellini, G. B., & Burge, J. H. (2013). Measurement of a large deformable aspherical mirror using SCOTS (software configurable optical test system). Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: The software configurable optical test system (SCOTS) is an efficient metrology technology based on reflection deflectometry that uses only an LCD screen and a camera to measure surface slope. The surface slope is determined by triangulations using the coordinates of the display screen, camera and test mirror. We present our recent SCOTS test results concentrated on high dynamic range measurements of low order aberrations. The varying astigmatism in the 91 cm diameter aspheric deformable secondary mirror for the Large Binocular Telescope (LBT) was measured with SCOTS, requiring no null corrector. The SCOTS system was designed on axis with camera and screen aligned on the optical axis of the test mirror with the help of a 6 inch pellicle beam splitter. The on-axis design gives better control of the astigmatism in the test. The high dynamic range of slope provided a measurement of astigmatism with 0.2 μm rms accuracy in the presence of 231 μm peak-to-valley (PV) aspheric departure. The simplicity of the test allowed the measurements to be performed at multiple elevation angles. © 2013 SPIE.
• Kim, D. W., Kim, B. C., Zhao, C., Oh, C. J., & Burge, J. H. (2013). Algorithms for surface reconstruction from curvature data for freeform aspherics. Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: Increasing demand for highly accurate freeform aspheric surfaces requires accurate and efficient measurement techniques. One promising possibility uses a sub-aperture scanning system that measures local curvature variations across the part. In this paper, we develop and demonstrate two different data processing algorithms, a zonal approach using Southwell integration method and a modal approach leveraging Zernike curvature basis, that reconstruct the surface 3-dimensional profiles from the curvature data. The performance of suggested methods and the sensitivity to noise is diagnosed for various SNR (Signal-to-Noise Ratio) cases. © 2013 SPIE.
• Kim, D. W., Martin, H. M., & Burge, J. H. (2013). Optical surfacing process optimization using parametric smoothing model for mid-to-high spatial frequency error control. Proceedings of SPIE - The International Society for Optical Engineering, 8884.
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  Abstract: High performance optical systems aiming for very low background noise from scattering or a sharp point spread function with high encircled energy often specify their beam wavefront quality in terms of a structure function or power spectral density function, which requires a control of mid-to-high spatial frequency surface errors during the optics manufacturing process. Especially for fabrication of large aspheric optics, achieving the required surface figure irregularities over the mid-to-high spatial frequency range becomes a challenging task as the polishing lap needs to be compliant enough to conform to the varying local surface shapes under the lap. This compliance degrades the lap's smoothing capability, which relies on its rigidity. The smoothing effect corrects the mid-to-high spatial frequency errors as a polishing lap removes low spatial frequency (i.e. larger than the lap size) errors on the optical surface. Using a parametric smoothing model developed to quantitatively describe the smoothing effects during Computer Controlled Optical Surfacing (CCOS) processes, actual CCOS data from large aspheric optics fabrication projects have been analyzed and studied. The measured surface error maps were processed with the model to compare different polishing runs using various polishing parameters. The results showing the smoothing effects of mid-to-high spatial frequency surface irregularity will be presented to provide some insights for a CCOS process optimization in terms of smoothing efficiency. © 2013 SPIE.
• Lampen, S., Dubin, M., & Burge, J. H. (2013). Design and optimization of the sine condition test for measuring misaligned optical systems. Applied Optics, 52(29), 7099-7108.
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  PMID: 24217726;Abstract: By taking a new look at an old concept, we have shown in our previous work how the Abbe sine condition can be used to measure linearly field-dependent aberrations in order to verify the alignment of optical systems. In this paper, we expand on this method and discuss the design choices involved in implementing the sine condition test (SCTest). Specifically, we discuss the two illumination options for the test: point source with a grating or flat-panel display, and we discuss the tradeoffs of the two approaches. Additionally, experimental results are shown using a flat-panel display to measure linearly fielddependent aberrations. Last, we elaborate on how to implement the SCTest on more complex optical systems, such as a three-mirror anastigmat and a double Gauss imaging lens system. © 2013 Optical Society of America.
• Lampen, S., Dubin, M., & Burge, J. H. (2013). Erratum: Implementation of sine condition test to measure optical system misalignments (Applied Optics (2011) 50 (6391-6398)). Applied Optics, 52(35), 8518-.
• Oh, C. J., Frater, E. H., Coyle, L., Dubin, M., Lowman, A., Zhao, C., & Burge, J. H. (2013). Alignment of 4-mirror Wide Field Corrector for the Hobby-Eberly Telescope. Proceedings of SPIE - The International Society for Optical Engineering, 8844.
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  Abstract: The Hobby-Eberly Telescope (HET) Wide Field Corrector (WFC) is a four-mirror optical system which corrects for aberrations from the 10-m segmented spherical primary mirror. The WFC mirror alignments must meet particularly tight tolerances for the system to meet performance requirements. The system uses 1-m class highly aspheric mirrors, which precludes conventional alignment methods. For the WFC system alignment a "center reference fixture" has been used as the reference for each mirror's vertex and optical axis. The center reference fixtures have both a CGH and sphere mounted retroreflector (SMR) nests. The CGH is aligned to the mirror's optical axis to provide a reference for mirror decenter and tilt. The vertex of each mirror is registered to the SMR nests on the center reference fixtures using a laser tracker. The spacing between the mirror vertices is measured during the system alignment using these SMR nest locations to determine the vertex locations. In this paper the procedures and results from creating and characterizing these center reference fixtures are presented. As a verification of proposed alignment methods the results from their application in the WFC system alignment are also presented. © 2013 SPIE.
• Peng, S. u., Khreishi, M., Huang, R., Tianquan, S. u., & Burge, J. H. (2013). Precision aspheric optics testing with SCOTS: A deflectometry approach. Proceedings of SPIE - The International Society for Optical Engineering, 8788.
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  Abstract: Absolute measurement with SCOTS/deflectometry is a calibration problem. We use a laser tracker to calibrate the test geometry. The performance id demonstrated with the initial measurement results from the Large Synoptic Survey Telescope tertiary mirror. Systematic errors from the camera are carefully controlled. Camera pupil imaging aberration is removed with an external aperture stop. Imaging aberration and other inherent errors are suppressed with a rotation test. Results show that the SCOTS can act as a large dynamic range, high precision, non-null test method for precision aspheric optics. The SCOTS test can achieve measurement accuracy comparable with the traditional interferometric testing. © 2013 SPIE.
• Shu, Y., Kim, D. W., Martin, H. M., & Burge, J. H. (2013). Correlation-based smoothing model for optical polishing. Optics Express, 21(23), 28771-28782.
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  Abstract: A generalized model is developed to quantitatively describe the smoothing effects from different polishing tools used for optical surfaces. The smoothing effect naturally corrects mid-to-high spatial frequency errors that have features small compared to the size of the polishing lap. The original parametric smoothing model provided a convenient way to compare smoothing efficiency of different polishing tools for the case of sinusoidal surface irregularity, providing the ratio of surface improvement via smoothing to the bulk material removal. A new correlation-based smoothing model expands the capability to quantify smoothing using general surface data with complex irregularity. For this case, we define smoothing as a band-limited correlated component of the change in the surface and original surface. Various concepts and methods, such as correlation screening, have been developed and verified to manipulate the data for the calculation of smoothing factor. Data from two actual polishing runs from the Giant Magellan Telescope off-axis segment and the Large Synoptic Survey Telescope monolithic primary-tertiary mirror were processed, and a quantitative evaluation for the smoothing efficiency of a large pitch lap and a conformal lap with polishing pads is provided. © 2013 Optical Society of America.
• Smith, G. A., Zhao, C., Peng, S. u., & Burge, J. H. (2013). Subaperture stitching performance estimation. Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: Subaperture stitching extends measurements such as interferometry by combining several overlapping measurements into a single, high-accuracy estimate of the overall image. In designing a subaperture measurement regimen, there are several tradeoffs related to size, quantity and locations of subapertures within the full aperture of the test optic. Understanding how individual subaperture measurement noise couples through these parameters into errors in the final stitched map is important for estimating overall system performance. In this work, we explore parametric rules for estimating the accuracy of stitched results based on subaperture geometry parameters and noise characteristics for a self-calibrating system where both a test optic and reference optic are simultaneously determined. From these rules, we examine types of errors introduced by stitching which enables confidence estimates for the final stitched map surface quality. © 2013 SPIE.
• Taniguchi, K., Kim, D. W., Shimura, K., & Burge, J. H. (2013). Steerable diffraction limited line illumination system using deformable mirror. Proceedings of SPIE - The International Society for Optical Engineering, 8843.
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  Abstract: Many scientific and industrial applications often require high performance optical systems utilizing spatially shaped illumination patterns of laser beams. Precisely shaped line illumination can be used for various line scanning systems or surface inspection devices. In order to achieve the highest resolution or superior signal to noise ratio limited by the fundamental theory, a diffraction limited illumination optical system (e.g.
• Tayabaly, K., Stover, J. C., Parks, R. E., Dubin, M., & Burge, J. H. (2013). Use of the surface PSD and incident angle adjustments to investigate near specular scatter from smooth surfaces. Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: The Rayleigh Rice vector perturbation theory has been successfully used for several decades to relate the surface power spectrum of optically smooth reflectors to the angular resolved scatter resulting from light sources of known wavelength, incident angle and polarization. While measuring low frequency roughness is relatively easy, the corresponding near specular scatter can be difficult to measure. This paper discusses using high incident angle near specular measurements along with profile generated surface power spectrums as a means of checking a near specular scatter requirement. The specification in question, a BRDF of 1.0 sr-1 at 2 mrad from the specular direction and at a wavelength of 1μm, is very difficult to verify by conventional scatter measurements. In fact, it is impractical to directly measure surface scatter from uncoated Zerodur because of its high bulk scatter. This paper presents profilometer and scatterometer data obtained from coated and uncoated flats at several wavelengths and outlines the analysis technique used to check this tight specification. © 2013 SPIE.
• Tianquan, S. u., Wang, S., Parks, R. E., Peng, S. u., & Burge, J. H. (2013). Measuring rough optical surfaces using scanning long-wave optical test system. 1. Principle and implementation. Applied Optics, 52(29), 7117-7126.
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  PMID: 24217728;Abstract: Current metrology tools have limitations when measuring rough aspherical surfaces with 1-2 μm root mean square roughness; thus, the surface cannot be shaped accurately by grinding. To improve the accuracy of grinding, the scanning long-wave optical test system (SLOTS) has been developed to measure rough aspherical surfaces quickly and accurately with high spatial resolution and low cost. It is a longwave infrared deflectometry device consisting of a heated metal ribbon and an uncooled thermal imaging camera. A slope repeatability of 13.6 μrad and a root-mean-square surface accuracy of 31 nm have been achieved in the measurements of two 4 inch spherical surfaces. The shape of a rough surface ground with 44 μm grits was also measured, and the result matches that from a laser tracker measurement. With further calibration, SLOTS promises to provide robust guidance through the grinding of aspherics. © 2013 Optical Society of America.
• Valente, M., Lewis, B., Melena, N., Smith, M., Burge, J. H., & Zhao, C. (2013). Advanced surface metrology for meter-class optics. Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: Refinements in computer controlled optical surfacing allow efficient grinding and polishing of meterclass optics to accuracy limited only by the surface metrology. We present a categorization of metrology methods and their implementation for meter-class optical components. Interferometry with computer generated holograms provides nanometer accuracy for full surface measurements of a wide range of convex and concave aspheric surfaces. For measuring off-axis and freeform aspheric surfaces, the holograms include features that provide references for alignment. Very high spatial resolution is achieved with subaperture interferometric measurements which can be stitched together to provide a full-aperture map. Scanning systems complement the capabilities of interferometry by achieving larger dynamic range and providing independent corroboration. Optical coordinate measurement machines (CMMs) provide non-contact measurements of surfaces in their ground state to guide figuring, as well as highly accurate measurements of finished optics. Scanning systems for measuring flat mirrors provide excellent resolution and absolute accuracy. The performance and practical issues for this full array of measurement techniques are presented to show the relative strengths of each method. © 2013 SPIE.
• Zhao, C., & Burge, J. H. (2013). Optical testing with computer generated holograms: Comprehensive error analysis. Proceedings of SPIE - The International Society for Optical Engineering, 8838.
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  Abstract: Interferometry with computer generated holograms (CGHs) has become the industry standard for accurate measurements of aspheric optical surfaces. The CGH is a diffractive optical element that can be designed to create virtually any phase or amplitude distribution, and can be accurately manufactured using methods and equipment developed for integrated circuit production. Surface measurements with nanometer level precision can be performed using accurately wellcalibrated equipment. This paper provides a systematic analysis of all significant sources of error for CGH metrology, including encoding error, pattern distortion, substrate irregularity and calibration, and system alignment. © 2013 SPIE.
• Zhao, C., & Burge, J. H. (2013). Orthonormal curvature polynomials over a unit circle: Basis set derived from curvatures of Zernike polynomials. Optics Express, 21(25), 31430-31443.
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  Abstract: Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials. © 2013 Optical Society of America.
• Burge, J. H., & Kim, D. W. (2012). The thermal sieve: A diffractive baffle that provides thermal isolation of a cryogenic optical system from an ambient temperature collimator. Proceedings of SPIE - The International Society for Optical Engineering, 8442.
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  Abstract: We present the thermal sieve, which is a diffractive baffle that provides thermal isolation between an ambient collimator and a cryogenic optical system being measured. The baffle uses several parallel plates with holes in them. The holes are lined up to allow the collimated light to pass, but the view factor for thermal radiation is greatly reduced. A particular design is shown here that allows less than 0.25 W/m2 thermal transfer and degrades the test wavefront by only 3 nm rms. © 2012 SPIE.
• Burge, J. H., & Zhao, C. (2012). Applications of subaperture stitching interferometry for very large mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 8450.
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  Abstract: Full aperture interferometric metrology has enabled fabrication and verification of large primary mirrors with nm precision. The measurement of mirrors that are several meters in diameter with flat or convex aspheric surfaces can be performed using interferometric measurements of overlapping subaperture regions, then stitching the date from these measurements together to provide a full map. This paper explores the application of this measurement technique for very large mirrors, and discusses issues for measuring large flat or convex mirrors. © 2012 SPIE.
• Burge, J., Johnson, J. B., Parks, R. E., & Burge, J. H. (2012). Surface stresses of mixed-mode grinding materials on borosilicate glass. Applied optics, 51(18).
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  Mixed-mode grinding occurs when a bound abrasive works in both brittle and ductile regimes simultaneously. Substrates ground in a mixed-mode behavior show reduced curvature induced by compressive surface forces than loose abrasives as demonstrated by observing the Twyman effect. This reduction in bending corresponds to reduced subsurface damage. This is verified by controlled acid etching, which shows the exponential decay of the compressive force per unit length. Loose abrasive particles, added to maintain pad wear due to low pressures, have no effect on the measured stresses. If loose abrasive wear ceases, the pads glaze. Glazing creates near-specular surfaces while reducing measurable stress. These effects for borosilicate glass and Trizact grinding pads are explored and quantified.
• Burge, J., Kim, D. W., Cai, W., & Burge, J. H. (2012). Use of thermal sieve to allow optical testing of cryogenic optical systems. Optics express, 20(11).
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  Full aperture testing of large cryogenic optical systems has been impractical due to the difficulty of operating a large collimator at cryogenic temperatures. The Thermal Sieve solves this problem by acting as a thermal barrier between an ambient temperature collimator and the cryogenic system under test. The Thermal Sieve uses a set of thermally controlled baffles with array of holes that are lined up to pass the light from the collimator without degrading the wavefront, while attenuating the thermal background by nearly 4 orders of magnitude. This paper provides the theory behind the Thermal Sieve system, evaluates the optimization for its optical and thermal performance, and presents the design and analysis for a specific system.
• Burge, J., Zhou, P., Shu, Y., Zhao, C., & Burge, J. H. (2012). Diffraction effects for interferometric measurements due to imaging aberrations. Optics express, 20(4).
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  Aspheric surfaces are often measured using interferometers with null correctors, either refractive or diffractive. The use of null correctors allows high accuracy in the measurement, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations couple with diffraction effects and limit the accuracy of the measurements, causing high frequency features in the surface under test to be filtered out and creating artifacts near boundaries, especially at edges. We provide a concise methodology for analyzing these effects using the astigmatic field curves to define the aberration, and showing how this couples with diffraction as represented by the Talbot effect and Fresnel edge diffraction. The resulting relationships are validated with both computer simulations and direct measurements from an interferometer with CGH null corrector.
• Butel, G. P., Smith, G. A., & Burge, J. H. (2012). Optimization of dynamic structured illumination for surface slope measurements. Proceedings of SPIE - The International Society for Optical Engineering, 8493.
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  Abstract: We present a fast and ambiguity-free method for slope measurement of reflective optical elements based on reflectometry. This novel reflectometric method applies triangulation to compute the slope based off projected patterns from an LCD screen, which are recorded by a camera. Accurate, ambiguity-free measurements can be obtained by displaying one pixel at a time on the screen and retrieving its unique image. This process is typically accelerated by scanning lines of pixels or encoding the information with phase using sinusoidal waves. Various measurement techniques exist, centroiding and phase-shifting being the most accepted, but their sensitivities vary with experimental conditions. This paper demonstrates solutions based on various parameters such as uncertainty or efficiency. The results are presented in a decision matrix and merit function. Additionally, we propose a new measurement technique - Binary squares screens - in an attempt to address system limitations and compare current systems to our solutions using the decision matrix. Several test conditions are proposed along with the best suited solution. © 2012 SPIE.
• Dominguez, M. Z., Armstrong, J., Peng, S. u., Parks, R. E., & Burge, J. H. (2012). SCOTS: A useful tool for specifying and testing optics in slope space. Proceedings of SPIE - The International Society for Optical Engineering, 8493.
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  Abstract: When defining surface irregularities more often than not it is useful to represent these as slope errors rather than surface errors. However, surface error specifications are more commonly used even though they do not accurately represent performance but simply physical characteristics. An example of slope measurement technique and specification is a method developed by the University of Arizona called SCOTS (Software Configurable Optical Test System) which has showed to be accurate, while very fast and easy to setup. It directly measures the transverse ray aberration/slope of an optical system using transmission deflectometry. © 2012 SPIE.
• Johnson, J. B., Parks, R. E., & Burge, J. H. (2012). Surface stresses of mixed-mode grinding materials on borosilicate glass. Applied Optics, 51(18), 4151-4156.
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  PMID: 22722292;Abstract: Mixed-mode grinding occurs when a bound abrasive works in both brittle and ductile regimes simultaneously. Substrates ground in a mixed-mode behavior show reduced curvature induced by compressive surface forces than loose abrasives as demonstrated by observing the Twyman effect. This reduction in bending corresponds to reduced subsurface damage. This is verified by controlled acid etching, which shows the exponential decay of the compressive force per unit length. Loose abrasive particles, added to maintain pad wear due to low pressures, have no effect on the measured stresses. If loose abrasive wear ceases, the pads glaze. Glazing creates near-specular surfaces while reducing measurable stress. These effects for borosilicate glass and Trizact grinding pads are explored and quantified. © 2012 Optical Society of America.
• Kim, D. W., Cai, W., & Burge, J. H. (2012). Use of Thermal Sieve to allow optical testing of cryogenic optical systems. Optics Express, 20(11), 12378-12392.
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  PMID: 22714225;Abstract: Full aperture testing of large cryogenic optical systems has been impractical due to the difficulty of operating a large collimator at cryogenic temperatures. The Thermal Sieve solves this problem by acting as a thermal barrier between an ambient temperature collimator and the cryogenic system under test. The Thermal Sieve uses a set of thermally controlled baffles with array of holes that are lined up to pass the light from the collimator without degrading the wavefront, while attenuating the thermal background by nearly 4 orders of magnitude. This paper provides the theory behind the Thermal Sieve system, evaluates the optimization for its optical and thermal performance, and presents the design and analysis for a specific system. © 2012 Optical Society of America.
• Kim, D. W., Martin, H. M., & Burge, J. H. (2012). Control of mid-spatial-frequency errors for large steep aspheric surfaces. Optics InfoBase Conference Papers.
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  Abstract: Control of mid-spatial-frequency errors on precision optical surfaces is very important for next-generation optical systems. We present results of smoothing experiments and of polishing runs utilizing figuring and smoothing for the 8.4m GMT off-axis segment. © 2012 OSA.
• Lampen, S., Dubin, M., & Burge, J. H. (2012). Use of a flat panel display for measurement of sine condition violations. Proceedings of SPIE - The International Society for Optical Engineering, 8491.
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  Abstract: Previous works have shown the viability of using the Sine Condition Test (SCTest) to verify the alignment of optical systems. The SCTest uses the Abbe sine condition to measure the mapping between the entrance and exit pupils of an optical system. From this pupil mapping, the linearly-field dependent aberrations can be measured and used to verify the alignment. Specifically, the linear astigmatism is used as a metric to determine how well the optical system is aligned. An advantage to using the sine condition to measure the off-axis performance is that the measurement equipment can be placed on-axis. By doing this, the uncertainty of the measurement is reduced, making this test especially useful for verifying systems with large inherent aberrations. In this paper, we expand the design space of the SCTest by exploring the two different source options: a point source with a grating or a flat-panel display. Additionally, we show experimental results of implementing the SCTest using a flat-panel display. Last, we explain how the SCTest can be implemented on more complex systems, such as a three-mirror anastigmat (TMA) and a double Gauss. By exploring the design space, we provide more design options for selecting the SCTest source, increasing the flexibility and utility of the SCTest. © 2012 SPIE.
• Lee, S., Parks, R., & Burge, J. H. (2012). Self-consistent way to determine relative distortion of axial symmetric lens systems. Applied Optics, 51(5), 588-593.
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  PMID: 22330290;Abstract: We present a simple method to determine the relative distortion of axially symmetric lens systems. This method uses graphs to determine every parametric value instead of nonlinear minimization computation and is composed of an LCD screen to display a square grid pattern of pixel-wide spots and a set of analyzing processes for the spots in the image. The two Cartesian components of the spot locations are processed by a two-step linear least-square fitting to third-order polynomials. The graphs for the coefficients enable us to determine the amount of decentering of the camera lens axis with respect to the center of the image array and the tip/tilt of the screen, which in turn gives the relative distortion coefficient. We present experimental results to demonstrate the utility of the method by comparing our results with the corresponding values determined by open source software available online. © 2012 Optical Society of America.
• Lewis, B., & Burge, J. H. (2012). Fitting high-order Zernike polynomials to finite data. Proceedings of SPIE - The International Society for Optical Engineering, 8493.
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  Abstract: While the use of Zernike polynomials to represent simulated or measured data on a grid of points is common, the accuracy of the coefficients can be limited by the non-orthogonality of the functions over the pixelated domains. The Zernike polynomials are defined to be analytically orthogonal over a circular domain, but this breaks down for discrete data. A simple correction is presented that uses a weighted scalar product to determine coefficients. This method preserves the meaning of the Zernike polynomials and allows efficient calculations using an inner product. The algorithm for defining the weighting function is provided, and simulations are included that demonstrate nearly an order of magnitude improvement in accuracy when the new weighted scalar product is used. © 2012 SPIE.
• Peng, S. u., Oh, C. J., Zhao, C., & Burge, J. H. (2012). Optical testing for meter size aspheric optics. Proceedings of SPIE - The International Society for Optical Engineering, 8466.
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  Abstract: Several meter size steep aspheric optics, with aspheric departure ranging from 100μm to 2mm, have been successfully fabricated at the College of Optical Sciences at University of Arizona. Optical metrology systems have been developed for measuring the optical surfaces efficiently and accurately. These systems include laser tracker surface profiler, swing arm optical CMM with different type of sensors, slope measurements with SCOTS, the Software Configurable Optical Test System (SCOTS) and interferometry with computer generated holograms. We summarize the test methods and provide comparison of the relative strengths and weaknesses. © 2012 SPIE.
• Peng, S. u., Parks, R. E., Wang, Y., Oh, C. J., & Burge, J. H. (2012). Swing-arm optical coordinate measuring machine: Modal estimation of systematic errors from dual probe shear measurements. Optical Engineering, 51(4).
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  Abstract: The swing-arm optical coordinate measuring machine (SOC), a profilometer with a distance-measuring interferometric probe for in situ measurement of the topography of aspheric surfaces,has been used for measuring highly aspheric mirrors with a performance rivaling full aperture interferometric tests. Recently, we implemented a dual probe, self-calibration mode for the SOC. Data from the dual probes can be used to calibrate the swing-arm air bearing errors since both probes see the same bearing errors while measuring different portions of the test surface. Bearing errors are reconstructed from modal estimation of the sheared signal. © 2012 Society of Photo-Optical Instrumentation Engineers.
• Peng, S. u., Wang, S., Khreishi, M., Wang, Y., Tianquan, S. u., Zhou, P., Parks, R. E., Law, K., Rascon, M., Zobrist, T., Martin, H., & Burge, J. H. (2012). SCOTS: A reverse Hartmann test with high dynamic range for Giant Magellan Telescope primary mirror segments. Proceedings of SPIE - The International Society for Optical Engineering, 8450.
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  Abstract: A software configurable optical test system (SCOTS) based on fringe reflection was implemented for measuring the primary mirror segments of the Giant Magellan Telescope (GMT). The system uses modulated fringe patterns on an LCD monitor as the source, and captures data with a CCD camera and calibrated imaging optics. The large dynamic range of SCOTS provides good measurement of regions with large slopes that cannot be captured reliably with interferometry. So the principal value of the SCOTS test for GMT is to provide accurate measurements that extend clear to the edge of the glass, even while the figure is in a rough state of figure, where the slopes are still high. Accurate calibration of the geometry and the mapping also enable the SCOTS test to achieve accuracy that is comparable measurement accuracy to the interferometric null test for the small- and middle- spatial scale errors in the GMT mirror. © 2012 SPIE.
• Peng, S. u., Wang, Y., Burge, J. H., Kaznatcheev, K., & Idir, M. (2012). Non-null full field X-ray mirror metrology using scots: A reflection deflectometry approach. Optics Express, 20(11), 12393-12406.
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  PMID: 22714226;Abstract: In a previous paper, the University of Arizona (UA) has developed a measurement technique called: Software Configurable Optical Test System (SCOTS) based on the principle of reflection deflectometry. In this paper, we present results of this very efficient optical metrology method applied to the metrology of X-ray mirrors. We used this technique to measure surface slope errors with precision and accuracy better than 100 nrad (rms) and ∼200 nrad (rms), respectively, with a lateral resolution of few mm or less. We present results of the calibration of the metrology systems, discuss their accuracy and address the precision in measuring a spherical mirror. © 2012 Optical Society of America.
• Smith, G. A., Lewis, B. J., Kim, D. W., Palmer, M., Loeff, A. R., & Burge, J. H. (2012). SAGUARO: Data analysis software for optical engineering. Optics InfoBase Conference Papers.
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  Abstract: SAGUARO software is written for the optical engineer and designed to simplify data analysis and visualization. SAGUARO is easy for the end-user processing optical test information as well as the developer adding new functionalities. © 2012 OSA.
• Smith, G. A., Lewis, B. J., Palmer, M., Kim, D. W., Loeff, A. R., & Burge, J. H. (2012). Open source data analysis and visualization software for optical engineering. Proceedings of SPIE - The International Society for Optical Engineering, 8487.
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  Abstract: SAGUARO is open-source software developed to simplify data assimilation, analysis, and visualization by providing a single framework for disparate data sources from raw hardware measurements to optical simulation output. Developed with a user-friendly graphical interface in the MATLAB™ environment, SAGUARO is intended to be easy for the enduser in search of useful optical information as well as the developer wanting to add new modules and functionalities. We present here the flexibility of the SAGUARO software and discuss how it can be applied to the wider optical engineering community. © 2012 SPIE.
• Tuell, M. T., Martin, H. M., Burge, J. H., Ketelsen, D. A., Law, K., Gressler, W. J., & Zhao, C. (2012). Fabrication of the LSST monolithic primary-tertiary mirror. Proceedings of SPIE - The International Society for Optical Engineering, 8450.
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  Abstract: As previously reported (at the SPIE Astronomical Instrumentation conference of 2010 in San Diego1), the Large Synoptic Survey Telescope (LSST) utilizes a three-mirror design in which the primary (M1) and tertiary (M3) mirrors are two concentric aspheric surfaces on one monolithic substrate. The substrate material is Ohara E6 borosilicate glass, in a honeycomb sandwich configuration, currently in production at The University of Arizona's Steward Observatory Mirror Lab. We will provide an update to the status of the mirrors and metrology systems, which have advanced from concepts to hardware in the past two years. In addition to the normal requirements for smooth surfaces of the appropriate prescriptions, the alignment of the two surfaces must be accurately measured and controlled in the production lab, reducing the degrees of freedom needed to be controlled in the telescope. The surface specification is described as a structure function, related to seeing in excellent conditions. Both the pointing and centration of the two optical axes are important parameters, in addition to the axial spacing of the two vertices. This paper details the manufacturing process and metrology systems for each surface, including the alignment of the two surfaces. M1 is a hyperboloid and can utilize a standard Offner null corrector, whereas M3 is an oblate ellipsoid, so it has positive spherical aberration. The null corrector is a phase-etched computer-generated hologram (CGH) between the mirror surface and the center-of-curvature. Laser trackers are relied upon to measure the alignment and spacing as well as rough-surface metrology during looseabrasive grinding. © 2012 SPIE.
• Wang, Y., Peng, S. u., Parks, R. E., Oh, C. J., & Burge, J. H. (2012). Swing arm optical coordinate-measuring machine: High precision measuring ground aspheric surfaces using a laser triangulation probe. Optical Engineering, 51(7).
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  Abstract: The swing arm optical coordinate-measuring machine (SOC), a profilometer with a distance measuring interferometric sensor for in situ measurement of the topography of aspheric surfaces, has shown a precision rivaling the full aperture interferometric test. To further increase optical manufacturing efficiency, we enhance the SOC with an optical laser triangulation sensor for measuring test surfaces in their ground state before polishing. The calibrated sensor has good linearity and is insensitive to the angular variations of the surfaces under testing. Sensor working parameters such as sensor tip location, projection beam angle, and measurement direction are calibrated and incorporated in the SOC data reduction software to relate the sensor readout with the test surface sag. Experimental results show that the SOC with the triangulation sensor can measure aspheric ground surfaces with an accuracy of 100 nm rms or better. © 2012 Society of Photo-Optical Instrumentation Engineers (SPIE).
• Zhou, P., Cai, W., Zhao, C., & Burge, J. H. (2012). Parametric definition for the CGH patterns and error analysis in interferometric measurements. Proceedings of SPIE - The International Society for Optical Engineering, 8415.
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  Abstract: Computer-generated holograms are often used to test aspheric surfaces. This paper provides a parametric model for the CGH phase function using the exact geometric model. The phase function is then used to derive the sensitivity functions to alignment errors in testing. When using the CGH to test aspheric surface, it is important to separate the diffraction orders and only allow the desired order to pass the system. This paper also provides a recipe for determining the amount of carriers needed to eliminate the ghost images. © 2012 SPIE.
• Zhou, P., Martin, H. M., Zhao, C., & Burge, J. H. (2012). Mapping distortion correction for GMT interferometric test. Optics InfoBase Conference Papers.
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  Abstract: The interferometric test for the 8.4m off-axis segment of the GMT primary mirror uses a complex null corrector that introduces a large amount of mapping distortion. This paper discusses the mapping correction for this test. © 2012 OSA.
• Zhou, P., Shu, Y., Zhao, C., & Burge, J. H. (2012). Diffraction effects for interferometric measurements due to imaging aberrations. Optics Express, 20(4), 4403-4418.
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  PMID: 22418200;Abstract: Aspheric surfaces are often measured using interferometers with null correctors, either refractive or diffractive. The use of null correctors allows high accuracy in the measurement, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations couple with diffraction effects and limit the accuracy of the measurements, causing high frequency features in the surface under test to be filtered out and creating artifacts near boundaries, especially at edges. We provide a concise methodology for analyzing these effects using the astigmatic field curves to define the aberration, and showing how this couples with diffraction as represented by the Talbot effect and Fresnel edge diffraction. The resulting relationships are validated with both computer simulations and direct measurements from an interferometer with CGH null corrector. © 2012 Optical Society of America.
• Zhou, P., Zhao, C., & Burge, J. (2012). Diffraction effects for interferometric measurements due to imaging aberrations. Proceedings of SPIE - The International Society for Optical Engineering, 8493.
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  Abstract: Aspheric surfaces are often measured using interferometers with null correctors. The null corrector creates a wavefront that matches the surface under test, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations cause high frequency features in the surface under test to be filtered out and create artifacts at edges. We provide a concise methodology for analyzing these effects using field curvatures, and showing how they couple with diffraction as represented by the Talbot effect and Fresnel edge diffraction. © 2012 SPIE.
• Burge, J. H., Fähnle, O. W., & Williamson, R. (2011). Introduction. Proceedings of SPIE - The International Society for Optical Engineering, 8126, xi.
• Burge, J. H., Zhao, C., Dubin, M., & Lampen, S. (2011). Determination of off-axis aberrations of imaging systems using on-axis measurements. Proceedings of SPIE - The International Society for Optical Engineering, 8129.
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  Abstract: Imaging aberrations that have linear dependence on field angle are caused by pupil aberrations that can be described using the Abbe sine condition. This well-known relationship is frequently used to guide the design of optical imaging systems. For example, the aberration of coma is eliminated in the design of axisymmetric systems by controlling the pupil distortion, as defined by a standard implementation of the sine condition. An optical system with misalignments of surface irregularities will suffer pupil distortions that are quantified using a more generalized form of the sine condition. Such pupil aberrations create image aberrations that have linear dependence on field angle. While it is possible to infer the state of alignment by measuring multiple field points, it may be more straightforward to perform a single on-axis measurement of the sine condition violations. This paper summarizes the generalized sine condition and relationship between violations of this condition and aberrations with linear field dependence. An application is discussed for measuring sine condition violations of a 4-mirror system, which allows determination of the off-axis aberrations. © 2011 SPIE.
• Burge, J., Lampen, S., Dubin, M., & Burge, J. H. (2011). Implementation of sine condition test to measure optical system misalignments. Applied optics, 50(34).
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  Rather than measuring aberrations across the field to quantify the alignment of an optical system, we show how a single, on-axis measurement of the pupil mapping can be used to measure the off-axis performance of the system and determine the state of alignment. In this paper we show how the Abbe sine condition can be used to relate the mapping between the entrance and exit pupils to image aberrations that have linear field dependence. This mapping error then can be used to measure the linear astigmatism caused by the misalignment. Additionally, we present experimental results from the sine condition test on a simple system.
• Cai, W., Cuerden, B., Parks, R. E., & Burge, J. H. (2011). Strength of glass from Hertzian line contact. Proceedings of SPIE - The International Society for Optical Engineering, 8125.
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  Abstract: In optical lens assembly, metal retaining rings are often used to hold the lens in place. If we mount a lens to a sharp metal edge using normal retention force, high compressive stress is loaded to the interface and the calculated tensile stress near the contact area from Hertzian contact appears higher than allowable. Therefore, conservative designs are used to ensure that glass will not fracture during assembly and operation. We demonstrate glass survival with very high levels of stress. This paper analyzes the high contact stress between glass lenses and metal mounts using finite element model and to predict its effect on the glass strength with experimental data. We show that even though contact damage may occur under high surface tensile stress, the stress region is shallow compared to the existing flaw depth. So that glass strength will not be degraded and the component can survive subsequent applied stresses. © 2011 SPIE.
• Champagne, J. A., Burge, J. H., & Crowther, B. G. (2011). Thermo-opto-mechanical analysis of a cubesat lens mount. Proceedings of SPIE - The International Society for Optical Engineering, 8125.
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  Abstract: A potential cubesat payload for low resolution study of planet Earth from space is an optical imaging system. Due to budget, space, and time constraints, commercial photographic lenses of the double Gauss type are prime candidates for limited duration cubesat optics. However, photographic objectives are not designed to operate in a space environment and modifications are usually necessary. One method of improving optical performance of the objective over large temperature variations is by replacing the stock lens mount with a different material. This paper describes the thermoopto-mechanical analysis of several lens mount materials for a double Gauss imaging system suitable for a cubesat. © 2011 SPIE.
• Chase, K. A., & Burge, J. H. (2011). Analysis of lens mount interfaces. Proceedings of SPIE - The International Society for Optical Engineering, 8125.
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  Abstract: Lenses are typically mounted into precision machined barrels and constrained with spacers and retaining rings. The details of the interfaces between the metal and the glass are chosen to balance the accuracy of centration and axial position, stress in the glass, and the cost for production. This paper presents a systematic study of sharp edge, toroidal, and conical interfaces and shows how to control accuracy, estimate stress, and limit production costs. Results are presented from computer models, finite element simulations, and experimental testing. © 2011 SPIE.
• Coyle, L. E., Dubin, M., & Burge, J. H. (2011). Low uncertainty alignment procedure using computer generated holograms. Proceedings of SPIE - The International Society for Optical Engineering, 8131.
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  Abstract: We characterize the precision of a low uncertainty alignment procedure that uses computer generated holograms as center references to align optics in tilt and centration. This procedure was developed for the alignment of the Wide Field Corrector for the Hobby Eberly Telescope, which uses center references to provide the data for the system alignment. From previous experiments, we determined that using an alignment telescope or similar instrument would not achieve the required alignment uncertainty. We developed a new procedure that utilizes computer generated holograms to create multiple simultaneous images to perform the alignment. The center references are phase etched Fresnel zone plates that act like thin lenses. We use zero order reflections to measure tilt and first order imaging from the zone plates to measure centration. We performed multiple alignments with a prototype system consisting of two center references spaced one meter apart to characterize this method's performance. We scale the uncertainties for the prototype experiment to determine the expected alignment errors in the Wide Field Corrector. © 2011 SPIE.
• Dominguez, M. Z., Wang, L., Peng, S. u., Parks, R. E., & Burge, J. H. (2011). Software configurable optical test system for refractive optics. Proceedings of SPIE - The International Society for Optical Engineering, 8011.
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  Abstract: SCOTS (software configurable optical test system) is a useful tool that can provide lens manufacturers with the ability to evaluate the net performance of a lens system without the use of complex metrology systems and setups. This technique is based on measuring the transverse ray aberrations of rays to obtain wavefront information using transmission deflectometry, the refractive equivalent of reflection deflectometry. Some work using deflectometry on refractive surfaces has been briefly reported in the past, where the power of a single lens has been the measurement objective. Results showing the use of deflectometry on reflective optical surfaces, such as the primary mirror of the Giant Magellan Telescope (GMT) show that this method has a large dynamic range in which measurement accuracy is comparable with those of interferometric methods; generating interest on our part, to investigate deflectometry for refractive systems in more detail. In this paper, we focus on reporting initial tests using SCOTS by measuring simple refractive elements, such as 1" diameter biconvex BK7 lenses. Results indicate a good agreement when comparing them with equivalent MATLAB/ZEMAX wavefront measuring models, which include the measured lens parameters, where the estimated and measured wavefront RMS values and spherical aberration Zernike coefficient agree on average to within 10nm. We also investigate the effect of the chromatic aberration on the refractive optical system by collecting data using three different wavelengths: 620nm, 550nm and 450nm. The alignment of the test setup was done rapidly and we used an LCD screen with a pixel pitch of 0.1905mm. The camera used for the measurements was a simple digital CCD camera. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).
• Dominguez, M. Z., Wang, L., Peng, S. u., Parks, R. E., & Burge, J. H. (2011). Software configurable optical test system for refractive optics. Proceedings of SPIE - The International Society for Optical Engineering, 8082.
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  Abstract: SCOTS (software configurable optical test system) is a useful tool that can provide lens manufacturers with the ability to evaluate the net performance of a lens system without the use of complex metrology systems and setups. This technique is based on measuring the transverse ray aberrations of rays to obtain wavefront information using transmission deflectometry, the refractive equivalent of reflection deflectometry 3. Some work using deflectometry on refractive surfaces has been briefly reported in the past, where the power of a single lens has been the measurement objective4. Results showing the use of deflectometry on reflective optical surfaces, such as the primary mirror of the Giant Magellan Telescope (GMT) 1 show that this method has a large dynamic range in which measurement accuracy is comparable with those of interferometric methods; generating interest on our part, to investigate deflectometry for refractive systems in more detail. In this paper, we focus on reporting initial tests using SCOTS by measuring simple refractive elements, such as 1" diameter biconvex BK7 lenses. Results indicate a good agreement when comparing them with equivalent MATLAB/ZEMAX wavefront measuring models, which include the measured lens parameters, where the estimated and measured wavefront RMS values and spherical aberration Zernike coefficient agree on average to within 10nm. We also investigate the effect of the chromatic aberration on the refractive optical system by collecting data using three different wavelengths: 620nm, 550nm and 450nm. The alignment of the test setup was done rapidly and we used an LCD screen with a pixel pitch of 0.1905mm. The camera used for the measurements was a simple digital CCD camera. © 2011 SPIE.
• Dubin, M., Lampen, S., & Burge, J. H. (2011). Characterization of alignment using measurements of the sine condition. Proceedings of SPIE - The International Society for Optical Engineering, 8131.
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  Abstract: An experimental test for violations of the sine condition is presented. This test is particularly useful for identifying the state of alignment of an imaging system because it provides a direct measurement of the linear astigmatism (astigmatism that varies linearly with field) in a system using only on axis measurements. The concept of the test is explained from the perspective of both geometrical optics, using the sine condition, and wave optics. In addition, the results of an experimental proof of concept are presented. This experiment shows good agreement between the measured and predicted results. © 2011 SPIE.
• Hopkins, C. L., & Burge, J. H. (2011). Application of geometric dimensioning & tolerancing for sharp corner and tangent contact lens seats. Proceedings of SPIE - The International Society for Optical Engineering, 8131.
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  Abstract: This paper outlines methods for dimensioning and tolerancing lens seats that mate with spherical lens surfaces. The two types of seats investigated are sharp corner and tangent contact. The goal is to be able to identify which seat dimensions influence lens tilt and displacement and develop a quantifiable way to assign tolerances to those dimensions to meet tilt and displacement requirements. After looking at individual seats, methods are then applied to multiple lenses with examples. All geometric dimensioning and tolerancing is according to ASME Y14.5M - 1994. © 2011 SPIE.
• Johnson, J. B., Kim, D. W., Parks, R. E., & Burge, J. H. (2011). New approach for pre-polish grinding with low subsurface damage. Proceedings of SPIE - The International Society for Optical Engineering, 8126.
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  Abstract: For an optical surface to be properly prepared, the amount of material removed during polishing must be greater than the volume of grinding damage. An intermediate stage between loose abrasive grinding and polishing can reduce the total volume of subsurface damage. This results in less time and expense needed during the polishing phase. We have characterized the Prestos's coefficient and subsurface damage depth for 3M TrizactTM diamond tile pads and believe it can fit this intermediary role. Trizact shows a sizeable reduction in the overall subsurface damage compared to similar sized loose abrasives. This understanding of the abrasive behavior allows us to create a better grinding schedule that more efficiently removes material and finishing with less overall damage than traditional loose abrasives. © 2011 SPIE.
• Kim, D. W., Lewis, B. J., & Burge, J. H. (2011). Open-source data analysis and visualization software platform: SAGUARO. Proceedings of SPIE - The International Society for Optical Engineering, 8126.
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  Abstract: Optical engineering projects often require massive data processing with many steps in the course of design, simulation, fabrication, metrology, and evaluation. A MATLAB™-based data processing platform has been developed to provide a standard way to manipulate and visualize various types of data that are created from optical measurement equipment. The operation of this software platform via a graphical user interface is easy and powerful. Data processing is performed by running modules that use a proscribed format for sharing data. Complex operations are performed by stringing modules together using macros. While numerous modules have been developed to allow data processing without the need to write software, the greatest power of the platform is provided by its flexibility. A developer's toolkit is provided to allow development and customization of modules, and the program allows a real-time interface with the standard MATLAB environment. This software, developed by the Large Optics Fabrication and Testing group at the University of Arizona, is now publicly available.** We present the capabilities of the software and provide some demonstrations of its use for data analysis and visualization. Furthermore, we demonstrate the flexibility of the platform for solving new problems. © 2011 SPIE.
• Kim, D. W., Martin, H. M., & Burge, J. H. (2011). Calibration and optimization of computer-controlled optical surfacing for large optics. Proceedings of SPIE - The International Society for Optical Engineering, 8126.
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  Abstract: Precision optical surfaces can be efficiently manufactured using a computer-controlled optical surfacing (CCOS) process. Most CCOS processes are based on control of the dwell time of a tool on the workpiece, according to the desired removal and the tool influence function (TIF), which is the material wear function of the tool. Several major topics were investigated to improve current CCOS processes and provide new solutions for the next generation of CCOS processes. A rigid conformal (RC) lap using a visco-elastic non-Newtonian medium was invented. It conforms to the aspheric surface shape, yet maintains stiffness on short time scales to provide natural smoothing. The smoothing removes mid- to high-frequency errors while controlled dwell time removes low-frequency errors. A parametric smoothing model was also introduced to predict the smoothing effects. A parametric edge TIF model to represent measured edge TIFs was developed and demonstrated. This model covers the removal behavior as the tool overhangs the edge of the workpiece. These new tools and models were applied in a new process optimization technique called nonsequential optimization. The non-sequential approach performs a comprehensive optimization of dwell time using multiple TIFs (multiple tools) simultaneously. An overview of these newly implemented CCOS features** is presented along with some actual CCOS results. © 2011 SPIE.
• Lampen, S., Dubin, M., & Burge, J. H. (2011). Implementation of sine condition test to measure optical system misalignments. Applied Optics, 50(34), 6391-6398.
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  PMID: 22192991;Abstract: Rather than measuring aberrations across the field to quantify the alignment of an optical system, we show how a single, on-axis measurement of the pupil mapping can be used to measure the off-axis performance of the system and determine the state of alignment. In this paper we show how the Abbe sine condition can be used to relate the mapping between the entrance and exit pupils to image aberrations that have linear field dependence. This mapping error then can be used to measure the linear astigmatism caused by the misalignment. Additionally, we present experimental results from the sine condition test on a simple system. © 2011 Optical Society of America.
• Milby, E., & Burge, J. (2011). Centration of optical elements. Proceedings of SPIE - The International Society for Optical Engineering, 8126.
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  Abstract: Axisymmetric optical components such as lenses are frequently centered with the use of rotary air bearings, guided by optical instrumentation that use reflected or transmitted light. This report systematically explores methods of adjusting optical elements including wedged-shims, fine pitch screws, and positioning rods with a goal of defining the accuracy that can be expected. Analysis of the performance is supported with experimental data. A characterization and discussion of the merits of each positioning method is additionally presented. © 2011 SPIE.
• Parks, R. E., Su, P., Zobrist, T., Su, T., Park, W. H., Dominguez, M., Wang, L., Zhu, G., Butel, G., Lu, S. -., Wang, Y., Zhou, P., & Burge, J. H. (2011). Slope measuring metrology for precision free-form surfaces. Proceedings - ASPE 2011 Spring Topical Meeting: Structured and Freeform Surfaces, 51, 43-48.
• Peng, S. u., Wang, Y., Oh, C. J., Parks, R. E., & Burge, J. H. (2011). Swing arm optical CMM: Self calibration with dual probe shear test. Proceedings of SPIE - The International Society for Optical Engineering, 8126.
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  Abstract: Swing arm optical CMM (SOC), a profilometer with distance measuring interferometric probe for in situ measurement of the topography of aspheric has been used for measuring highly aspheric mirrors with a performance rivaling full aperture interferometric tests. Recently, we implemented a dual probe self calibration mode for the SOC. Data from the dual probes can be used to calibrate the swing-arm air bearing errors since both probes see the same bearing errors while measuring different portions of the test surface. Bearing errors are reconstructed from the shear signal with a modal estimation. © 2011 SPIE.
• Tianquan, S. u., Park, W. H., Parks, R. E., Peng, S. u., & Burge, J. H. (2011). Scanning long-wave optical test system - A new ground optical surface slope test system. Proceedings of SPIE - The International Society for Optical Engineering, 8126.
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  Abstract: The scanning long-wave optical test system (SLOTS) is under development at the University of Arizona to provide rapid and accurate measurements of aspherical optical surfaces during the grinding stage. It is based on the success of the software configurable optical test system (SCOTS) which uses visible light to measure surface slopes. Working at long wave infrared (LWIR, 7-14 um), SLOTS measures ground optical surface slopes by viewing the specular reflection of a scanning hot wire. A thermal imaging camera collects data while motorized stages scan the wire through the field. Current experiments show that the system can achieve a high precision at micro-radian level with fairly low cost equipment. The measured surface map is comparable with interferometer for slow optics. This IR system could be applied early in the grinding stage of fabrication of large telescope mirrors to minimize the surface shape error imparted during processing. This advantage combined with the simplicity of the optical system (no null optics, no high power carbon dioxide laser) would improve the efficiency and shorten the processing time. © 2011 SPIE.
• Allen, R., Peng, S. u., Burge, J. H., Cuerden, B., & Martin, H. M. (2010). Scanning pentaprism test for the GMT 8.4 m off-axis segments. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: The scanning pentaprism system for testing the 8.4 m off-axis segments for the Giant Magellan Telescope has recently been completed. The system uses a fiber source and a carriage mounted pentaprism to scan a 40 mm collimated beam across the surface of the segment under test. Since the scanning beam is parallel to the optical axis of the parent mirror, it comes to focus on a detector at the telescope's prime focus, where displacement of the spot is proportional to the slope error. A second collimated beam from a stationary reference pentaprism is used to compensate for any changes in the relative positions of the optical components during testing. The optical components are suspended over the mirror on a rail system that can be rotated so that scans can be made across any diameter of the segment. The test is capable of measuring wavefront slope errors to 1 μrad rms, adequate to verify that power, astigmatism, coma, and other low-order aberrations are small enough to be corrected easily at the telescope with the segment's active support system. © 2010 SPIE.
• Burge, J. H. (2010). Optical testing of mirrors for giant telescopes. Optics InfoBase Conference Papers.
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  Abstract: Today's giant telescopes use mirrors that require new methods of optical testing. This paper summarizes developments at University of Arizona for measuring off-axis primary mirror segments, large convex aspheric secondary mirrors, and giant turning flats. © 2010 OSA.
• Burge, J. H., Benjamin, S., Dubin, M., Manuel, A., Novak, M., Oh, C. J., Valente, M., Zhao, C., Booth, J. A., Good, J. M., Hill, G. J., Lee, H., MacQueen, P. J., Rafal, M., Savage, R., Smith, M. P., & Vattiat, B. (2010). Development of a wide field spherical aberration corrector for the Hobby Eberly Telescope. Proceedings of SPIE - The International Society for Optical Engineering, 7733(PART 1).
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  Abstract: A 4-mirror prime focus corrector is under development to provide seeing-limited images for the 10-m aperture Hobby-Eberly Telescope (HET) over a 22 arcminute wide field of view. The HET uses an 11-m fixed elevation segmented spherical primary mirror, with pointing and tracking performed by moving the prime focus instrument package (PFIP) such that it rotates about the virtual center of curvature of the spherical primary mirror. The images created by the spherical primary mirror are aberrated with 13 arcmin diameter point spread function. The University of Arizona is developing the 4-mirror wide field corrector to compensate the aberrations from the primary mirror and present seeing limited imaged to the pickoffs for the fiber-fed spectrographs. The requirements for this system pose several challenges, including optical fabrication of the aspheric mirrors, system alignment, and operational mechanical stability. © 2010 SPIE.
• Burge, J. H., Zhao, C., & Dubin, M. (2010). Measurement of aspheric mirror segments using Fizeau interferometry with CGH correction. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: Large aspheric primary mirrors are proposed that use hundreds segments that all must be aligned and phased to approximate the desired continuous mirror. We present a method of measuring these concave segments with a Fizeau interferometer where a spherical convex reference surface is held a few millimeters from the aspheric segment. The aspheric shape is accommodated by a small computer generated hologram (CGH). Different segments are measured by replacing the CGH. As a Fizeau test, nearly all of the optical elements and air spaces are common to both the measurement and reference wavefront, so the sensitivities are not tight. Also, since the reference surface of the test plate is common to all tests, this system achieves excellent control for the radius of curvature variation from one part to another. This paper describes the test system design and analysis for such a test, and presents data from a similar 1.4-m test performed at the University of Arizona. © 2010 SPIE.
• Burge, J. H., Zhao, C., & Dubin, M. (2010). Use of the abbe sine condition to quantify alignment aberrations in optical imaging systems. Optics InfoBase Conference Papers.
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  Abstract: Violation of Abbe's sine condition is well known to cause coma in axisymmetric imaging systems. We define non-symmetric violations, show how they come from misaligned optical systems, and how they causes image degradations. © OSA/IODC/OF&T 2010.
• Burge, J. H., Zhao, C., & Lu, S. H. (2010). Use of the Abbe sine condition to quantify alignment aberrations in optical imaging systems. Proceedings of SPIE - The International Society for Optical Engineering, 7652.
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  Abstract: Violation of Abbe's sine condition is well-known to cause coma in axisymmetric imaging systems, and generally any offense against the sine condition (OSC) will cause aberrations that have linear dependence on the field angle. A well-corrected imaging system must obey the Abbe sine condition. A misaligned optical system can have particular forms of the OSC which are evaluated here. The lowest order non-trivial effects of misalignment have quadratic pupil dependence which causes a combination of astigmatism and focus that have linear field dependence. Higher order terms can arise from complex systems, but the effects of misalignment are nearly always dominated by the lowest order effects which can be fully characterized by measuring images on axis and the on-axis offense against the sine condition. By understanding the form of the on-axis images and the OSC, the state of alignment can be determined. © 2010 Copyright SPIE - The International Society for Optical Engineering.
• Burge, J. H., Zhao, C., & Zhou, P. (2010). Imaging issues for interferometry with CGH null correctors. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: Aspheric surfaces, such as telescope mirrors, are commonly measured using interferometry with computer generated hologram (CGH) null correctors. The interferometers can be made with high precision and low noise, and CGHs can control wavefront errors to accuracy approaching 1 nm for difficult aspheric surfaces. However, such optical systems are typically poorly suited for high performance imaging. The aspheric surface must be viewed through a CGH that was intentionally designed to introduce many hundreds of waves of aberration. The imaging aberrations create difficulties for the measurements by coupling both geometric and diffraction effects into the measurement. These issues are explored here, and we show how the use of larger holograms can mitigate these effects. © 2010 SPIE.
• Burge, J., Kim, D. W., & Burge, J. H. (2010). Rigid conformal polishing tool using non-linear visco-elastic effect. Optics express, 18(3).
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  Computer controlled optical surfacing (CCOS) relies on a stable and predictable tool influence function (TIF), which is the shape of the wear function created by the machine. For a polishing lap, which is stroked on the surface, both the TIF stability and surface finish rely on the polishing interface maintaining intimate contact with the workpiece. Pitch tools serve this function for surfaces that are near spherical, where the curvature has small variation across the part. The rigidity of such tools provides natural smoothing of the surface, but limits the application for aspheric surfaces. Highly flexible tools, such as those created with an air bonnet or magnetorheological fluid, conform to the surface, but lack intrinsic stiffness, so they provide little natural smoothing. We present a rigid conformal polishing tool that uses a non-linear visco-elastic medium (i.e. non-Newtonian fluid) that conforms to the aspheric shape, yet maintains stability to provide natural smoothing. The analysis, design, and performance of such a polishing tool is presented, showing TIF stability of
• Burge, J., Kim, D. W., Park, W. H., An, H. K., & Burge, J. H. (2010). Parametric smoothing model for visco-elastic polishing tools. Optics express, 18(21).
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  A parametric smoothing model is developed to quantitatively describe the smoothing action of polishing tools that use visco-elastic materials. These materials flow to conform to the aspheric shape of the workpieces, yet behave as a rigid solid for short duration caused by tool motion over surface irregularities. The smoothing effect naturally corrects the mid-to-high frequency errors on the workpiece while a large polishing lap still removes large scale errors effectively in a short time. Quantifying the smoothing effect allows improvements in efficiency for finishing large precision optics. We define normalized smoothing factor SF which can be described with two parameters. A series of experiments using a conventional pitch tool and the rigid conformal (RC) lap was performed and compared to verify the parametric smoothing model. The linear trend of the SF function was clearly verified. Also, the limiting minimum ripple magnitude PVmin from the smoothing actions and SF function slope change due to the total compressive stiffness of the whole tool were measured. These data were successfully fit using the parametric smoothing model.
• Burge, J., Su, P., Parks, R. E., Wang, L., Angel, R. P., & Burge, J. H. (2010). Software configurable optical test system: a computerized reverse Hartmann test. Applied optics, 49(23).
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  A software configurable optical test system (SCOTS) based on the geometry of the fringe reflection or phase measuring deflectometry method was developed for rapidly, robustly, and accurately measuring large, highly aspherical shapes such as solar collectors and primary mirrors for astronomical telescopes. In addition to using phase shifting methods for data collection and reduction, we explore the test from the point view of performing traditional optical testing methods, such as Hartmann or Hartmann-Shack tests, in a reverse way. Using this concept, the slope data calculation and unwrapping in the test can also be done with centroiding and line-scanning methods. These concepts expand the test to work in more general situations where fringe illumination is not practical. Experimental results show that the test can be implemented without complex calibration for many applications by taking the geometric advantage of working near the center curvature of the test part. The results also show that the test has a large dynamic range, can achieve measurement accuracy comparable with interferometric methods, and can provide a good complement to interferometric tests in certain circumstances. A variation of this method is also useful for measuring refractive optics and optical systems. As such, SCOTS provides optical manufacturers with a new tool for performing quantitative full field system evaluation.
• Burge, J., Zhou, P., & Burge, J. H. (2010). Analysis of wavefront propagation using the Talbot effect. Applied optics, 49(28).
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  Talbot imaging is a well-known effect that causes sinusoidal patterns to be reimaged by diffraction with characteristic period that varies inversely with both wavelength and the square of the spatial frequency. This effect is treated using the Fresnel diffraction integral for fields with sinusoidal ripples in amplitude or phase. The periodic nature is demonstrated and explained, and a sinusoidal approximation is made for the case where the phase or amplitude ripples are small, which allows direct determination of the field for arbitrary propagation distance. Coupled with a straightforward method for calculating the effect in a diverging or converging beam, the Talbot method provides a useful approximation for a class of diffraction problems.
• Cai, W., Kim, D. W., Zhou, P., Parks, R. E., & Burge, J. H. (2010). Interferometer calibration using the random ball test. Optics InfoBase Conference Papers.
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  Abstract: Two different approaches (systematically and randomly rotating the CaliBallTM to calibrate a Fizeau interferometer transmission sphere) are demonstrated with similar calibration results. Thus, the random approach is preferred as a quicker and easier measurement procedure. © 2010 Optical Society of America.
• Coyle, L., Dubin, M., & Burge, J. H. (2010). Characterization of an alignment procedure using an air bearing and off-the-shelf optics. Proceedings of SPIE - The International Society for Optical Engineering, 7793.
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  Abstract: We characterize the precision of five approaches used to align a series of targets over a distance of two meters. For many applications, an alignment telescope provides the necessary precision for positioning targets. However, for systems with tight tolerances, we must have a measure of the uncertainties in the alignment telescope to determine if it can truly meet the system requirements. We develop a procedure to measure the precision of each alignment approach and compare their performances. We use a telescope constructed from off-the-shelf optics and mechanics to determine if we can obtain alignment precision comparable to an alignment telescope of superior optical quality. © 2010 SPIE.
• Dubin, M., Coyle, L. E., & Burge, J. H. (2010). Characterization of an alignment procedure using an air bearing and off-the-shelf optics. Optics InfoBase Conference Papers.
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  Abstract: We demonstrate that using a simple telescope mounted on a high quality bearing can yield comparable or lower uncertainty than an alignment telescope for the centering of elements in an optical system. © 2010 OSA.
• Hosoda, M., Parks, R. E., & Burge, J. H. (2010). Vacuum support for a large interferometric reference surface. Proceedings - ASPE Summer Topical Meeting on Precision Interferometric Metrology, ASPE 2010, 49, 97-102.
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  Abstract: This paper presents a vacuum support technique for a Fizeau type interferometer that uses a 1.1 m diameter reference surface. The interferometer uses Computer Generated Holograms (CGHs) for aspheric measurement, illumination optics and imaging optics. To reduce the effects of air turbulence and retrace error, the gap between the reference surface and Unit Under Test (UUT) is limited to 5 mm. The illumination optics consist of two lenses, one of which we call the test plate which includes the reference surface. The 1.1-m diameter illumination optics are quite heavy, 212 kg, and are prone to self-weight deflection problems. We solve this with a vacuum support of the test plate. A vacuum region is created between the two lenses in the illumination optics using a rubber seal. The upper lens of the illumination optics suffers extra deflection caused by vacuum. However, since this lens is in the common path of the interferometer this does not cause significant error in the interferogram. In this paper, a simple experiment on a small surface and analyses on a large model are discussed. In the simple experiment the deflection of flat surfaces having 100mm in diameter and 2.7mm in thickness was measured by a Wyko 6000 interferometer. The region between the two flat surfaces was sealed by an O-ring and a needle was inserted into the O-ring so that the sealed region could be evacuated. This experiment shows correspondence of less than 10 % between the simulation and the experiment. A finite element model simulation of the vacuum support for the 1.1-m test plate is also presented. The nominal surface slope irregularity caused by gravity at the reference surface is 26.88 nm/cm RMS. When a differential pressure is equal to 2300 Pa, the deflection is minimized to 0.75 nm/cm RMS. Based on an optical simulation of the system, this deflection introduces only 8.0 nm RMS into the measurement error. Therefore the vacuum support can be useful for reducing the effect of gravity on the reference surface.
• Kim, D. W., & Burge, J. H. (2010). Cryogenic thermal mask for space-cold optical testing for space optical systems. Optics InfoBase Conference Papers.
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  Abstract: An optical testing configuration utilizing the Cryogenic Thermal Mask (CTM) provides thermal decoupling between a cryogenic optical system under test and a collimator operating at ambient temperature, while passing the test wavefront without significant degradation. © 2010 Optical Society of America.
• Kim, D. W., & Burge, J. H. (2010). Rigid conformal polishing tool using non-linear visco-elastic effect. Optics Express, 18(3), 2242-2257.
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  PMID: 20174053;Abstract: Computer controlled optical surfacing (CCOS) relies on a stable and predictable tool influence function (TIF), which is the shape of the wear function created by the machine. For a polishing lap, which is stroked on the surface, both the TIF stability and surface finish rely on the polishing interface maintaining intimate contact with the workpiece. Pitch tools serve this function for surfaces that are near spherical, where the curvature has small variation across the part. The rigidity of such tools provides natural smoothing of the surface, but limits the application for aspheric surfaces. Highly flexible tools, such as those created with an air bonnet or magnetorheological fluid, conform to the surface, but lack intrinsic stiffness, so they provide little natural smoothing. We present a rigid conformal polishing tool that uses a non-linear visco-elastic medium (i.e. non-Newtonian fluid) that conforms to the aspheric shape, yet maintains stability to provide natural smoothing. The analysis, design, and performance of such a polishing tool is presented, showing TIF stability of
• Kim, D. W., Park, W. H., An, H. K., & Burge, J. H. (2010). Parametric smoothing model for visco-elastic polishing tools. Optics Express, 18(21), 22515-22526.
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  PMID: 20941150;Abstract: A parametric smoothing model is developed to quantitatively describe the smoothing action of polishing tools that use visco-elastic materials. These materials flow to conform to the aspheric shape of the workpieces, yet behave as a rigid solid for short duration caused by tool motion over surface irregularities. The smoothing effect naturally corrects the mid-to-high frequency errors on the workpiece while a large polishing lap still removes large scale errors effectively in a short time. Quantifying the smoothing effect allows improvements in efficiency for finishing large precision optics. We define normalized smoothing factor SF which can be described with two parameters. A series of experiments using a conventional pitch tool and the rigid conformal (RC) lap was performed and compared to verify the parametric smoothing model. The linear trend of the SF function was clearly verified. Also, the limiting minimum ripple magnitude PVmin from the smoothing actions and SF function slope change due to the total compressive stiffness of the whole tool were measured. These data were successfully fit using the parametric smoothing model. © 2010 Optical Society of America.
• Martin, H. M., Allen, R. G., Burge, J. H., Kim, D. W., Kingsley, J. S., Tuell, M. T., West, S. C., Zhao, C., & Zobrist, T. (2010). Fabrication and testing of the first 8.4 m off-axis segment for the Giant Magellan Telescope. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: The primary mirror of the Giant Magellan Telescope consists of seven 8.4 m segments which are borosilicate honeycomb sandwich mirrors. Fabrication and testing of the off-axis segments is challenging and has led to a number of innovations in manufacturing technology. The polishing system includes an actively stressed lap that follows the shape of the aspheric surface, used for large-scale figuring and smoothing, and a passive "rigid conformal lap" for small-scale figuring and smoothing. Four independent measurement systems support all stages of fabrication and provide redundant measurements of all critical parameters including mirror figure, radius of curvature, off-axis distance and clocking. The first measurement uses a laser tracker to scan the surface, with external references to compensate for rigid body displacements and refractive index variations. The main optical test is a full-aperture interferometric measurement, but it requires an asymmetric null corrector with three elements, including a 3.75 m mirror and a computer-generated hologram, to compensate for the surface's 14 mm departure from the best-fit sphere. Two additional optical tests measure large-scale and small-scale structure, with some overlap. Together these measurements provide high confidence that the segments meet all requirements. © 2010 SPIE.
• Park, W. H., Cuerden, B., Kim, S., & Burge, J. H. (2010). Parametric modeling of self-weighted distortion for plane optical mirrors. Proceedings - ASPE 2010 Annual Meeting, 50, 261-264.
• Parks, R. E., Peng, S. u., Oh, C. J., & Burge, J. H. (2010). Self-referenced surface profilometry. Proceedings - ASPE 2010 Annual Meeting, 50, 29-32.
• Peng, S. u., Burge, J. H., & Parks, R. E. (2010). Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors. Applied Optics, 49(1), 21-31.
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  PMID: 20062486;Abstract: Interferometers accurately measure the difference between two wavefronts, one from a reference surface and the other from an unknown surface. If the reference surface is near perfect or is accurately known from some other test, then the shape of the unknown surface can be determined.We investigate the case where neither the reference surface nor the surface under test is well known. By making multiple shear measurements where both surfaces are translated and/or rotated, we obtain sufficient information to reconstruct the figure of both surfaces with a maximum likelihood reconstruction method. The method is demonstrated for the measurement of a 1:6m flat mirror to 2nm rms, using a smaller reference mirror that had significant figure error. © 2009 Optical Society of America.
• Schwertz, K., & Burge, J. H. (2010). Cost and performance trade-offs for commercially available linear stages. Proceedings of SPIE - The International Society for Optical Engineering, 7793.
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  Abstract: The following paper provides the practicing engineer with guidelines on the relationships between cost and various performance factors for different types of linear stages. When multiple precise motions need to be made in a system, stages are typically the solution. A number of factors should be considered before choosing a stage: cost, load capacity, travel range, repeatability, resolution, encoding accuracy, errors in motion, stiffness, stability, velocity of motion, environmental sensitivity, and additional features like over-travel protection and locking mechanisms. There are a variety of different bearing types for linear stages, each with their own advantages and disadvantages. This paper presents charts that provide relationships between the cost, travel range, angular deviation, and load capacity of various types of manual one-axis linear stages. The stages considered were those that had less than a 2.5" travel range and sold by major optomechanical vendors. The bearing types investigated were dovetail, flexure, ball bearing, double row ball bearing, crossed roller bearing, and gothic arch ball bearing. Using the charts and general guidelines provided in this paper, a more informed decision may be made when selecting a linear stage. © 2010 SPIE.
• Schwertz, K., & Burge, J. H. (2010). Relating axial motion of optical elements to focal shift. Proceedings of SPIE - The International Society for Optical Engineering, 7793.
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  Abstract: In this paper, simple relationships are presented to determine the amount of focal shift that will result from the axial motion of a single element or group of elements in a system. These equations can simplify first-order optomechanical analysis of a system. Examples of how these equations are applied are shown for lenses, mirrors, and groups of optical elements. Limitations of these relationships are discussed and the accuracy is shown in relation to modeled systems. © 2010 SPIE.
• Tuell, M. T., Martin, H. M., Burge, J. H., Gressler, W. J., & Zhao, C. (2010). Optical testing of the LSST combined primary/tertiary mirror. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: The Large Synoptic Survey Telescope (LSST) utilizes a three-mirror design in which the primary (M1) and tertiary (M3) mirrors are two concentric aspheric surfaces on one monolithic substrate. The substrate material is Ohara E6 borosilicate glass, in a honeycomb sandwich configuration currently in production at The University of Arizona's Steward Observatory Mirror Lab. In addition to the normal requirements for smooth surfaces of the appropriate prescriptions, the alignment of the two surfaces must be accurately measured and controlled in the production lab. Both the pointing and centration of the two optical axes are important parameters, in addition to the axial spacing of the two vertices. This paper describes the basic metrology systems for each surface, with particular attention to the alignment of the two surfaces. These surfaces are aspheric enough to require null correctors for each wavefront. Both M1 and M3 are concave surfaces with both non-zero conic constants and higher-order terms (6th order for M1 and both 6th and 8th orders for M3). M1 is hyperboloidal and can utilize a standard Offner null corrector. M3 is an oblate ellipsoid, so has positive spherical aberration. We have chosen to place a phase-etched computer-generated hologram (CGH) between the mirror surface and the center-of-curvature (CoC), whereas the M1 null lens is beyond the CoC. One relatively new metrology tool is the laser tracker, which is relied upon to measure the alignment and spacings. A separate laser tracker system will be used to measure both surfaces during loose abrasive grinding and initial polishing. © 2010 SPIE.
• Valente, M. J., Kim, D. W., Oh, C. J., Novak, M. J., & Burge, J. H. (2010). Fabrication of 4-meter class astronomical optics. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: The 8-meter mirror production capacity at the University of Arizona is well known. As the Arizona Stadium facility is occupied with giant mirrors, we have developed capability for grinding, polishing, and testing 4-m mirrors in the large optics shop in the College of Optical Sciences. Several outstanding capabilities for optics up to 4.3 meters in diameter are in place: A 4.3-m computer controlled grinding and polishing machine allows efficient figuring of steeply aspheric and nonaxisymmetric surfaces. Interferometry (IR and visible wavelengths) and surface profilometry making novel use of a laser tracker allows quick, accurate in-process measurements from a movable platform on a 30-m vertical tower. A 2-meter class flat measured with a 1-m vibration insensitive Fizeau interferometer and scanning pentaprism system; stitching of 1-m sub-apertures provides complete surface data with the technology ready for extension to the 4 m level. These methods were proven successful by completion of several optics including the 4.3-m Discovery Channel Telescope primary mirror. The 10 cm thick ULE substrate was ground and polished to 16 nm rms accuracy, corresponding to 80% encircled energy in 0.073 arc-second, after removing low order bending modes. The successful completion of the DCT mirror demonstrates the engineering and performance of the support system, ability to finish large aspheric surfaces using computer controlled polishing, and accuracy verification of surface measurements. In addition to the DCT mirror, a 2-meter class flat was produced to an unprecedented accuracy of
• Wang, L., Peng, S. u., Parks, R. E., Sasian, J. M., & Burge, J. H. (2010). A low-cost, flexible, high dynamic range test for free-form illumination optics. Optics InfoBase Conference Papers.
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  Abstract: Software Configurable Optical Test System (SCOTS)[1], a computerized "reverse Hartmann test", can rapidly quantitatively measure complex 3D specular surfaces, for instance solar collectors, faceted automotive headlight or free-form surfaces without complex calibrations. © 2010 Optical Society of America.
• West, S. C., Bailey, S. H., Burge, J. H., Cuerden, B., Hagen, J., Martin, H. M., & Tuell, M. T. (2010). Wavefront control of the large optics test and integration site (LOTIS) 6.5 m Collimator. Applied Optics, 49(18), 3522-3537.
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  PMID: 20563205;Abstract: The LOTIS Collimator provides scene projection within a 6.5 m diameter collimated beam used for optical testing research in air and vacuum. Diffraction-limited performance (0.4 to 5 μm wavelength) requires active wavefront control of the alignment and primary mirror shape. A hexapod corrects secondary mirror alignment using measurements from collimated sources directed into the system with nine scanning pentaprisms. The primary mirror shape is controlled with 104 adjustable force actuators based on figure measurements from a center-of-curvature test. A variation of the Hartmann test measures slopes by monitoring the reflections from 36 small mirrors bonded to the optical surface of the primary mirror. The Hartmann source and detector are located at the f/15 Cassegrain focus. Initial operation has demonstrated a closed-loop 110 nm rms wavefront error in ambient air over the 6.5 m collimated beam. © 2010 Optical Society of America.
• West, S. C., Burge, J. H., Cuerden, B., Davison, W., Hagen, J., Martin, H. M., Tuell, M. T., Zhao, C., & Zobrist, T. (2010). Alignment and use of the optical test for the 8.4 m off-axis primary mirrors of the Giant Magellan Telescope. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: The Giant Magellan Telescope has a 25 meter f/0.7 near-parabolic primary mirror constructed from seven 8.4 meter diameter segments. Several aspects of the interferometric optical test used to guide polishing of the six off-axis segments go beyond the demonstrated state of the art in optical testing. The null corrector is created from two obliquelyilluminated spherical mirrors combined with a computer-generated hologram (the measurement hologram). The larger mirror is 3.75 m in diameter and is supported at the top of a test tower, 23.5 m above the GMT segment. Its size rules out a direct validation of the wavefront produced by the null corrector. We can, however, use a reference hologram placed at an intermediate focus between the two spherical mirrors to measure the wavefront produced by the measurement hologram and the first mirror. This reference hologram is aligned to match the wavefront and thereby becomes the alignment reference for the rest of the system. The position and orientation of the reference hologram, the 3.75 m mirror and the GMT segment are measured with a dedicated laser tracker, leading to an alignment accuracy of about 100 microns over the 24 m dimensions of the test. In addition to the interferometer that measures the GMT segment, a separate interferometer at the center of curvature of the 3.75 m sphere monitors its figure simultaneously with the GMT measurement, allowing active correction and compensation for residual errors. We describe the details of the design, alignment, and use of this unique off-axis optical test. © 2010 SPIE.
• Zhao, C., & Burge, J. H. (2010). Generalization of the Coddington equations to include hybrid diffractive surfaces. Proceedings of SPIE - The International Society for Optical Engineering, 7652.
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  Abstract: Coddington Equations are used to calculate the astigmatic images of a small bundle of rays centered on a ray commonly known as the principal ray. Some authors generalize it such that for a refractive or reflective surface of any shape to the 2nd order, and an incident wavefront of any shape to the 2nd order, the refracted or reflected wavefront can be calculated to the 2nd order. We extend it further such that it applies to the diffractive surface as well. The derivation is based on the general Snell's law and differential ray tracing approach. We present these generalized Coddington Equations in two forms: matrix formalism and explicit expressions. The equations are verified with explicit ray tracing using a commercial lens design program. The relations are applied to evaluate the imaging performance for null testing of aspheric surfaces using computer generated holograms. © 2010 Copyright SPIE - The International Society for Optical Engineering.
• Zhao, C., & Burge, J. H. (2010). Generalized coddington equations for refractive/diffractive hybrid surfaces. Optics InfoBase Conference Papers.
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  Abstract: We derived the generalized Coddington Equations for diffractive/refractive hybrid surfaces by using the general Snell's law and differential ray tracing approach. The Equations are given in two forms: matrix formalism and explicit expressions. © OSA / IODC/OF&T 2010.
• Zhou, P., & Burge, J. H. (2010). Analysis of wavefront propagation using the Talbot effect. Applied Optics, 49(28), 5351-5359.
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  PMID: 20885471;Abstract: Talbot imaging is a well-known effect that causes sinusoidal patterns to be reimaged by diffraction with characteristic period that varies inversely with both wavelength and the square of the spatial frequency. This effect is treated using the Fresnel diffraction integral for fields with sinusoidal ripples in amplitude or phase. The periodic nature is demonstrated and explained, and a sinusoidal approximation is made for the case where the phase or amplitude ripples are small, which allows direct determination of the field for arbitrary propagation distance. Coupled with a straightforward method for calculating the effect in a diverging or converging beam, the Talbot method provides a useful approximation for a class of diffraction problems. © 2010 Optical Society of America.
• Zhou, P., & Burge, J. H. (2010). Diffraction effects in interferometry. Optics InfoBase Conference Papers.
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  Abstract: Besides the geometrical errors, interferometry suffers errors due to diffraction, because the wavefront aberrations of the test and reference beams change as they propagate. This paper addresses errors due to diffraction effects in interferometry. © 2010 Optical Society of America.
• Zhou, P., Burge, J., & Zhao, C. (2010). Imaging issues for interferometric measurement of aspheric surfaces using CGH null correctors. Proceedings of SPIE - The International Society for Optical Engineering, 7790.
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  Abstract: Aspheric surfaces are measured using standard interferometers coupled with computer generated holograms (CGHs) that compensate the aspheric wavefronts. Such systems can measure complex aspheric shapes with accuracy of a few nanometers. However, the imaging properties of the interferometer-CGH combination can provide limitations for data mapping, resolution, and accuracy. These effects are explored, with an emphasis on the diffraction effects that are unique to interferometry. © 2010 SPIE.
• Zobrist, T. L., Burge, J. H., & Martin, H. M. (2010). Accuracy of laser tracker measurements of the GMT 8.4 m off-axis mirror segments. Proceedings of SPIE - The International Society for Optical Engineering, 7739.
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  Abstract: We have developed a metrology system that is capable of measuring rough ground and polished surfaces alike, has limited sensitivity to the nominal surface shape, and can accommodate surfaces up to 8.4 m in diameter. The system couples a commercial laser tracker with an advanced calibration technique and a system of stability references to mitigate numerous error sources. This system was built to guide loose abrasive grinding and initial polishing of the offaxis primary mirror segments for the Giant Magellan Telescope (GMT), and is also being used to guide the fabrication of the Large Synoptic Survey Telescope primary and tertiary mirrors. In addition to guiding fabrication, the system also works as a verification test for the GMT principal optical interferometric test of the polished mirror segment to corroborate the measurement in several low-order aberrations. A quantitative assessment of the system accuracy is presented, along with measurement results for GMT, including a comparison to the optical interferometric test of the polished surface. © 2010 SPIE.
• Burge, J. H., & Parks, R. (2009). Optomechanical engineering education at University of Arizona. Proceedings of SPIE - The International Society for Optical Engineering, 7424.
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  Abstract: The College of Optical Sciences at University of Arizona has established excellent programs for training BS, MS, and Ph.D. students in optical sciences and engineering. Research activities at the University of Arizona have also been closely coupled to developments in the field of optomechanical engineering. In response to request from the optics industry, we have recently expanded the educational opportunities for BS and MS students to follow engineering curricula that provide the right mix of optics and mechanical engineering. © 2009 SPIE.
• Burge, J. H., Benjamin, S., Caywood, D., Noble, C., Novak, M., Oh, C., Parks, R., Smith, B., Su, P., Valente, M., & Zhao, C. (2009). Fabrication and testing of 1.4-m convex off-axis aspheric optical surfaces. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: New developments in fabrication and testing techniques at the College of Optical Sciences, University of Arizona have allowed successful completion of 1.4-m diameter convex off-axis aspherics. The optics with up to 300 μm aspheric departure were finished using a new method of computer controlled polishing and measured with two new optical tests: the Swingarm Optical CMM (SOC) and a Fizeau interferometer using a spherical reference surface and CGH correction. This paper shows the methods and equipment used for manufacturing these surfaces. © 2009 SPIE.
• Burge, J. H., Fähnle, O. W., & Williamson, R. (2009). Proceedings of SPIE - The International Society for Optical Engineering: Introduction. Proceedings of SPIE - The International Society for Optical Engineering, 7426, ix.
• Burge, J., Kim, D. W., Kim, S., & Burge, J. H. (2009). Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions. Optics express, 17(24).
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  Optical surfaces can be accurately figured by computer controlled optical surfacing (CCOS) that uses well characterized sub-diameter polishing tools driven by numerically controlled (NC) machines. The motion of the polishing tool is optimized to vary the dwell time of the polisher on the workpiece according to the desired removal and the calibrated tool influence function (TIF). Operating CCOS with small and very well characterized TIF achieves excellent performance, but it takes a long time. This overall polishing time can be reduced by performing sequential polishing runs that start with large tools and finish with smaller tools. In this paper we present a variation of this technique that uses a set of different size TIFs, but the optimization is performed globally - i.e. simultaneously optimizing the dwell times and tool shapes for the entire set of polishing runs. So the actual polishing runs will be sequential, but the optimization is comprehensive. As the optimization is modified from the classical method to the comprehensive non-sequential algorithm, the performance improvement is significant. For representative polishing runs we show figuring efficiency improvement from approximately 88% to approximately 98% in terms of residual RMS (root-mean-square) surface error and from approximately 47% to approximately 89% in terms of residual RMS slope error.
• Burge, J., Kim, D. W., Park, W. H., Kim, S., & Burge, J. H. (2009). Parametric modeling of edge effects for polishing tool influence functions. Optics express, 17(7).
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  Computer controlled polishing requires accurate knowledge of the tool influence function (TIF) for the polishing tool (i.e. lap). While a linear Preston's model for material removal allows the TIF to be determined for most cases, nonlinear removal behavior as the tool runs over the edge of the part introduces a difficulty in modeling the edge TIF. We provide a new parametric model that fits 5 parameters to measured data to accurately predict the edge TIF for cases of a polishing tool that is either spinning or orbiting over the edge of the workpiece.
• Dubin, M. B., Su, P., & Burge, J. H. (2009). Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: Large, convex surfaces, such as secondary mirrors, have presented challenging metrology problems for many years. Over the years, new metrology approaches have been developed to keep pace with the ever changing definition of "large". The latest class of large secondary mirrors requires a new approach that is practical, scalable and can produce low uncertainty measurements. This paper presents a new configuration that uses a computer generated hologram based Fizeau interferometer to make sub-aperture measurements on large secondary mirrors. One of the key features of this system is that all of the surfaces used in the interferometer are spherical. Another key element is the ability to perform simultaneous phase shift interferometry which reduces sensitivity to vibration. An example system that is capable of measuring the Large Synoptic Survey Telescope secondary mirror is presented along with a sensitivity analysis. © 2009 SPIE.
• Kim, D. W., Kim, S., & Burge, J. H. (2009). Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions. Optics Express, 17(24), 21850-21866.
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  PMID: 19997430;Abstract: Optical surfaces can be accurately figured by computer controlled optical surfacing (CCOS) that uses well characterized subdiameter polishing tools driven by numerically controlled (NC) machines. The motion of the polishing tool is optimized to vary the dwell time of the polisher on the workpiece according to the desired removal and the calibrated tool influence function (TIF). Operating CCOS with small and very well characterized TIF achieves excellent performance, but it takes a long time. This overall polishing time can be reduced by performing sequential polishing runs that start with large tools and finish with smaller tools. In this paper we present a variation of this technique that uses a set of different size TIFs, but the optimization is performed globally-i.e. simultaneously optimizing the dwell times and tool shapes for the entire set of polishing runs. So the actual polishing runs will be sequential, but the optimization is comprehensive. As the optimization is modified from the classical method to the comprehensive non-sequential algorithm, the performance improvement is significant. For representative polishing runs we show figuring efficiency improvement from ̃88% to ̃98% in terms of residual RMS (root-mean-square) surface error and from ̃47% to ̃89% in terms of residual RMS slope error. © 2009 Optical Society of America.
• Kim, D. W., Park, W. H., Kim, S., & Burge, J. H. (2009). Edge tool influence function library using the parametric edge model for computer controlled optical surfacing. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: Computer controlled optical surfacing (CCOS) requires accurate knowledge of the tool influence function (TIF) for the polishing tool. The linear Preston's model for material removal has been used to determine the TIF for most cases. As the tool runs over the edge of the workpiece, however, nonlinear removal behavior needs to be considered to model the edge TIF. We reported a new parametric edge TIF model in a previous paper.* This model fits 5 parameters to measured data to accurately predict the edge TIF. We present material from the previous paper, and provide a library of the parametric edge TIFs for various tool shape and motion cases. The edge TIF library is a useful reference to design an edge figuring process using a CCOS technique. © 2009 SPIE.
• Kim, D. W., Park, W. H., Kim, S., & Burge, J. H. (2009). Parametric modeling of edge effects for polishing tool influence functions. Optics Express, 17(7), 5656-5665.
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  PMID: 19333334;Abstract: Computer controlled polishing requires accurate knowledge of the tool influence function (TIF) for the polishing tool (i.e. lap). While a linear Preston's model for material removal allows the TIF to be determined for most cases, nonlinear removal behavior as the tool runs over the edge of the part introduces a difficulty in modeling the edge TIF. We provide a new parametric model that fits 5 parameters to measured data to accurately predict the edge TIF for cases of a polishing tool that is either spinning or orbiting over the edge of the workpiece. © 2009 Optical Society of America.
• Manuel, A. M., & Burge, J. H. (2009). Alignment aberrations of the new solar telescope. Proceedings of SPIE - The International Society for Optical Engineering, 7433.
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  Abstract: The New Solar Telescope (NST) is an off-axis Gregorian telescope at Big Bear Solar Observatory (BBSO). This paper presents the expected aberrations due to misalignments of the secondary mirror for a general Gregorian telescope using an optical model of the on-axis "parent" telescope version of NST. The sensitivities of linear astigmatism and constant coma found by perturbing the axisymmetric model are presented and shown to match those predicted by the theory. Then we discuss how the actual aberrations are different due to the off-axis nature of the NST. Finally, we discuss the effect of the misalignments on the pointing of the telescope. © 2009 SPIE.
• Manuel, A. M., Burge, J. H., & Tessieres, R. (2009). Orthogonal field-dependent aberrations for misaligned optical systems. Optics InfoBase Conference Papers.
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  Abstract: We present a set of orthogonal field-dependent aberrations, useful for describing optical systems with tilted and decentered elements, derived from combinations of Zernike polynomials in both field space and pupil space. © 2009 Optical Society of America.
• Peng, S. u., Burge, J. H., Cuerden, B., Allen, R., & Martin, H. M. (2009). Scanning pentaprism measurements of off-axis aspherics II. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: The scanning pentaprism test has provided an important absolute test method for flat mirrors, parabolic mirrors and also collimation systems. We have developed a scanning pentaprism system to measure off-axis paraboloidal mirrors such as those for the Giant Magellan Telescope (GMT) primary mirror. Special characteristics of the pentaprism testing of an off-axis mirror are discussed in the paper. We provide performance results for the final measurement of a 1.7 m off-axis parabolic mirror and present a technique used to determine the radius of the parent, off-axis distance and the clocking of the mirror from the data from the scanning pentaprism system. © 2009 SPIE.
• Peng, S. u., Oh, C. J., Parks, R. E., & Burge, J. H. (2009). Swing arm optical CMM for aspherics. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: A profilometer for in situ measurement of the topography of aspheric mirrors called the Swing arm Optical CMM (SOC) was built, and has been used for measuring the figure of 1.4 m convex aspheric mirrors with a performance rivaling full aperture interferometric tests. Errors in the SOC that have odd symmetry are self-calibrated due to the test geometry. Even errors are calibrated against a full aperture interferometric test. © 2009 SPIE.
• Peng, S. u., Oh, C. J., Parks, R. E., & Burge, J. H. (2009). Swing arm optical CMM. Proceedings - ASPE Spring Topical Meeting on Mechanical Metrology and Measurement Uncertainty, ASPE 2009, 45, 20-25.
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  Abstract: A profilometer for in situ measurement of the topography of aspheric mirrors called the Swing arm Optical CMM (SOC) was built in the Optical Fabrication and Engineering Facility at the College of Optical Sciences, and has been used for measuring the figure of 1.4 m mirrors with a performance rivaling full aperture interferometric tests. The SOC uses a swing arm geometry as a means of supporting a distance measuring interferometric sensor a constant distance from, and pointed along a normal to, the center of curvature of a best fit spherical surface. Thus the sensor measures only the difference between the best fit sphere and the aspheric mirror profile. When the topography of the final mirror figure constructed from 64 profile scans is compared with the full aperture Fizeau test less than 5 nm accuracy is expected.
• Zhao, C., & Burge, J. H. (2009). Estimate of wavefront error introduced by encoding of computer generated holograms. Optics InfoBase Conference Papers.
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  Abstract: In testing aspheric optics with CGHs, errors introduced by the CGH must be budgeted. This paper presents a method for estimating the wavefront error introduced in the encoding process. Some results are shown. © 2009 IEEE.
• Zhao, C., & Burge, J. H. (2009). Estimate of wavefront error introduced by encoding of computer generated holograms. Pacific Rim Conference on Lasers and Electro-Optics, CLEO - Technical Digest.
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  Abstract: In testing aspheric optics with CGHs, errors introduced by the CGH must be budgeted. This paper presents a method for estimating the wavefront error introduced in the encoding process. Some results are shown. © 2009 IEEE.
• Zhao, C., & Burge, J. H. (2009). Orthonormal vector polynomials in a unit circle, application: Fitting mapping distortions in a null test. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: We developed a complete and orthonormal set of vector polynomials defined over a unit circle. One application of these vector polynomials is for fitting the mapping distortions in an interferometric null test. This paper discusses the source of the mapping distortions and the approach of fitting the mapping relations, and justifies why the set of vector polynomials is the appropriate choice for this purpose. Examples are given to show the excellent fitting results with the polynomials. © 2009 SPIE.
• Zhou, P., & Burge, J. H. (2009). Limits for interferometer calibration using the random ball test. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: The random ball test (RBT), also known as the CaliBall test, is often used to calibrate interferometer transmission spheres. This paper provides a way to estimate the total errors remaining after interferometer calibration using the RBT. Errors that cannot be removed by calibration include random errors due to measurement noise in the calibration, geometric errors, and errors due to diffraction. The random errors can be reduced by averaging multiple random ball tests. The geometric errors and diffraction errors are systematic, and arise when the radius of the CaliBall is different from that of the test optic. © 2009 SPIE.
• Zobrist, T. L., Burge, J. H., & Martin, H. M. (2009). Laser tracker surface measurements of the 8.4 m GMT primary mirror segment. Proceedings of SPIE - The International Society for Optical Engineering, 7426.
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  Abstract: We have developed a metrology system that is capable of measuring rough ground and polished surfaces alike, is nearly independent of the nominal surface shape, and can accommodate surfaces up to 8.4 m in diameter. The system couples a commercial laser tracker with an advanced calibration technique and a system of external references. This system was built to guide loose abrasive grinding and initial polishing of the off-axis primary mirror segments for the Giant Magellan Telescope, and will be used to guide the fabrication of the Large Synoptic Survey Telescope primary and tertiary mirrors as well. The results obtained using this system during the fabrication of the first segment of the Giant Magellan Telescope are presented along with an assessment of the expected system accuracy. © 2009 SPIE.
• Burge, J. H., Davison, W., Martin, H. M., & Zhao, C. (2008). Development of surface metrology for the Giant Magellan Telescope primary mirror. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: The Giant Magellan Telescope achieves 25 meter aperture and modest length using an f/0.7 primary mirror made from 8.4 meter diameter segments. The systems that will be used for measuring the aspheric optical surfaces of these mirrors are in the final phase of development. This paper discusses the overall metrology plan and shows details for the development of the principal test system - a system that uses mirrors and holograms to provide a null interferometric test of the surface. This system provides a full aperture interferometric measurement of the off-axis segments by compensating the 14.5 mm aspheric departure with a tilted 3.8-m diameter powered mirror, a 77 cm tilted mirror, and a computer generated hologram. The interferometric measurements are corroborated with a scanning slope measurement from a scanning pentaprism system and a direct measurement system based on a laser tracker.
• Burge, J. H., Su, P., & Zhao, C. (2008). Optical metrology for very large convex aspheres. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: Telescopes with very large diameter or with wide fields require convex secondary mirrors that may be many meters in diameter. The optical surfaces for these mirrors can be manufactured to the accuracy limited by the surface metrology. We have developed metrology systems that are specifically optimized for measuring very large convex aspheric surfaces. Large aperture vibration insensitive sub-aperture Fizeau interferometer combined with stitching software give high resolution surface measurements. The global shape is corroborated with a coordinate measuring machine based on the swing arm profilometer.
• Burge, J. H., Su, P., Yellowhair, J., & Zhao, C. (2008). Optical surface measurements for very large flat mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: Flat mirrors as large as 4 meters in diameter can be manufactured to high accuracy, limited by the surface metrology. We present metrology systems that are specifically optimized for measuring very large flats to high accuracy. A large aperture vibration insensitive Fizeau interferometer combined with stitching software provides high resolution surface measurements. Low order shape errors can be measured using scanning slope measurements from precision inclinometers or an autocollimator with scanning pentaprism.
• Burge, J., Zhao, C., & Burge, J. H. (2008). Orthonormal vector polynomials in a unit circle, Part II : Completing the basis set. Optics express, 16(9).
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  Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zernike polynomials. Here, we complete the basis by adding a complementary set of functions with zero divergence--those which are defined locally as a rotation or curl.
• Hvisc, A. M., & Burge, J. H. (2008). Alignment analysis of four-mirror spherical aberration correctors. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: Telescopes use primary mirrors with spherical shape to reduce the cost of the mirror fabrication and to allow the mirror to operate at fixed elevation. These advantages become significant as the size of the telescope grows. However, the disadvantage of the spherical primary is a large amount of spherical aberration which needs to be corrected. We present an analysis of alignment issues for four-mirror spherical aberration correctors for spherical primary mirror telescopes. The sensitivities of image quality across the field (in terms of spot size) to mirror misalignments are found. These sensitivities are useful in choosing the tolerances for the mechanical assembly holding the corrector. A singular value decomposition of the sensitivity matrix shows the combination of element motions that result in orthogonal aberration modes. Studying these combinations of modes and misalignments can lead to a conceptual understanding of the system, which aids in the initial and operational alignment of the spherical aberration corrector.
• Martin, H. M., Burge, J. H., Cuerden, B., Davison, W. B., Kingsley, J. S., Kittrell, W. C., Lutz, R. D., Miller, S. M., Zhao, C., & Zobrist, T. (2008). Progress in manufacturing the first 8.4 m off-axis segment for the Giant Magellan Telescope. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: The first of the 8.4 m off-axis segments for the primary mirror of the Giant Magellan Telescope is being manufactured at the Steward Observatory Mirror Lab. In addition to the manufacture of the segment, this project includes the development of a complete facility to make and measure all seven segments. We have installed a new 28 m test tower and designed a set of measurements to guide the fabrication and qualify the finished segments. The first test, a laser-tracker measurement of the ground surface, is operational. The principal optical test is a full-aperture interferometric test with a null corrector that includes a 3.75 m spherical mirror, a smaller sphere, and a computer-generated hologram. We have also designed a scanning pentaprism test to validate the measurement of low-order aberrations. The first segment has been cast and generated, and is in the process of loose-abrasive grinding.
• Martin, H. M., Burge, J. H., Cuerden, B., Davison, W. B., Kingsley, J. S., Lutz, R. D., Miller, S. M., & Tuell, M. (2008). Manufacture of a combined primary and tertiary mirror for the Large Synoptic Survey Telescope. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: The Large Synoptic Survey Telescope uses a unique optomechanical design that places the primary and tertiary mirrors on a single glass substrate. The honeycomb sandwich mirror blank was formed in March 2008 by spin-casting. The surface is currently a paraboloid with a 9.9 m focal length matching the primary. The deeper curve of the tertiary mirror will be produced when the surfaces are generated. Both mirrors will be lapped and polished using stressed laps and other tools on an 8.4 m polishing machine. The highly aspheric primary mirror will be measured through a refractive null lens, and a computer-generated hologram will be used to validate the null lens. The tertiary mirror will be measured through a diffractive null corrector, also validated with a separate hologram. The holograms for the two tests provide alignment references that will be used to make the axes of the two surfaces coincide.
• Novak, M., Zhao, C., & Burge, J. H. (2008). Distortion mapping correction in aspheric null testing. Proceedings of SPIE - The International Society for Optical Engineering, 7063.
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  Abstract: We describe methods to correct both symmetric and asymmetric distortion mapping errors induced by null testing elements such as holograms or null lenses. We show experimental results for direct measurement and correction of symmetric mapping distortion, as well as an example result for analytical mapping performed using an orthogonal set of vector polynomials for asymmetric correction. The empirical determination of symmetric distortion is made via calculation from predicted and measured changes to aberrations induced via known changes to the testing point.
• Peng, S. u., Burge, J. H., Cuerden, B., Sasian, J., & Martin, H. M. (2008). Scanning pentaprism measurements of off-axis aspherics. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: The pentaprism test is based on the property of a paraboloidal surface where all rays parallel to the optical axis will go through its focal point. We have developed a scanning pentaprism system that exploits this geometry to measure off-axis paraboloidal mirrors such as those for the Giant Magellan Telescope primary mirror. Extension of the pentaprism test to off-axis mirrors requires special attention to field effects that can be ignored in the measurement of an axisymmetric mirror. The test was demonstrated on a 1. -m diameter off-axis mirror and proved to have about 50nm rms surface accuracy. This paper gives detailed performance results for the measurement of the 1.7 m mirror, and designs and analysis for the test of the GMT segments.
• Zhao, C., & Burge, J. H. (2008). Orthonormal vector polynomials in a unit circle, Part II: Completing the basis set. Optics Express, 16(9), 6586-6591.
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  PMID: 18545361;Abstract: Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zernike polynomials. Here, we complete the basis by adding a complementary set of functions with zero divergence - those which are defined locally as a rotation or curl. © 2008 Optical Society of America.
• Zhao, C., & Burge, J. H. (2008). Stitching of off-axis sub-aperture null measurements of an aspheric surface. Proceedings of SPIE - The International Society for Optical Engineering, 7063.
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  Abstract: Optical testing of a large convex aspheric surface, such as the secondary of a Ritchey-Chretien telescope, can be performed with a Fizeau interferometer that utilizes subaperture aspheric reference plates, each providing a null test of a subaperture of the larger mirror. The subaperture data can be combined or stitched together to create a map of the full surface. The region of the secondary mirror surface under test in each sub-aperture is an off-axis segment of the parent aspheric surface, therefore, the Fizeau reference requires a non-axi-symmetric aspheric surface to match it. Misalignment of the Fizeau reference relative to the parent in each sub-aperture will then result in aberrations in the measurements other than the ordinary terms of piston and tilt. When stitching sub-aperture measurements together, the apparent aberrations due to the null lens misalignment need to be fitted and subtracted. This paper presents an algorithm to perform this particular type of stitching.
• Zobrist, T. L., Burge, J. H., Davison, W. B., & Martin, H. M. (2008). Measurements of large optical surfaces with a laser tracker. Proceedings of SPIE - The International Society for Optical Engineering, 7018.
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  Abstract: Surface measurements represent a significant part of the cost for manufacturing large aspheric optics. Both polished and rough ground surfaces must be measured with high precision and spatial resolution. We have developed a system that couples a commercial laser tracker with an advanced calibration technique and a system of external references. This system was built to measure the off-axis primary mirror segments for the Giant Magellan Telescope where it will guide loose abrasive grinding and initial polishing. The system is further expected to corroborate the optical interferometric tests of the completed mirrors, in several low-order aberrations. The design, analysis, calibration, and measured performance of this system will be presented.
• Burge, J. H., Peng, S. u., Zhao, C., & Zobrist, T. (2007). Use of a commercial laser tracker for optical alignment. Proceedings of SPIE - The International Society for Optical Engineering, 6676.
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  Abstract: Laser trackers have been developed that project laser beams and use optical systems to provide three dimensional coordinate measurements. The laser trackers incorporate a servo system to steer a laser beam so that it tracks a retro-reflector, such as a corner cube. The line of sight gimbal angles and the radial distance to the retroreflector are used to determine the coordinates of the retroreflector relative to the tracker. In this paper, we explore the use of the laser tracker to define the metrology for aligning optical systems, including the use of mirrors and windows. We discuss how to optimize the geometry to take advantage of the tracker's most accurate measurements. We show how to use the tracker for measuring angles as well as points.
• Burge, J. H., Zehnder, R., & Zhao, C. (2007). Optical alignment with computer generated holograms. Proceedings of SPIE - The International Society for Optical Engineering, 6676.
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  Abstract: Computer generated holograms (CGHs) have been successfully used for wavefront correction for measuring aspheric surfaces. Features on the CGHs have assisted the alignment of the optical test equipment. CGHs can also be used to provide alignment references for other complex optical systems. This paper discusses the types of CGHs that can be used for optical alignment and gives some examples.
• Burge, J., Zhao, C., & Burge, J. H. (2007). Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials. Optics express, 15(26).
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  Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonormal using the Gram- Schmidt technique. This set provides a complete basis for representing vector fields that can be defined as a gradient of some scalar function. It is then efficient to transform from the coefficients of the vector functions to the scalar Zernike polynomials that represent the function whose gradient was fit. These new vector functions have immediate application for fitting data from a Shack-Hartmann wavefront sensor or for fitting mapping distortion for optical testing. A subsequent paper gives an additional set of vector functions consisting only of rotational terms with zero divergence. The two sets together provide a complete basis that can represent all vector distributions in a circular domain.
• Burge, J., Zhou, P., & Burge, J. H. (2007). Coupling of surface roughness to the performance of computer-generated holograms. Applied optics, 46(26).
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  Computer-generated holograms (CGHs), such as those used in optical testing, are created by etching patterns into an optical substrate. Imperfections in the etching can cause small scale surface roughness that varies across the pattern. The variation in this roughness affects the phase and amplitude of the wavefronts in the various diffraction orders. A simplified model is developed and validated that treats the scattering loss from the roughness as an amplitude effect. We demonstrate the use of this model for engineering analysis and provide a graphical method for understanding the application. Furthermore, we investigate the magnitude of this effect for the application of optical testing and show that the effect on measurement accuracy is limited to 1 nm for typical CGHs.
• Burge, J., Zhou, P., & Burge, J. H. (2007). Fabrication error analysis and experimental demonstration for computer-generated holograms. Applied optics, 46(5).
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  Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm.
• C., P., Zehnder, R., Burge, J. H., & Poleshchuk, A. (2007). Absolute calibration of null correctors using dual computer-generated holograms. Proceedings of SPIE - The International Society for Optical Engineering, 6721.
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  Abstract: There is an increasing need for precision large aspheric optics with small focal ratios for astronomical and space applications. However, testing such optics presents a challenge. Interferometric testing of aspheric surfaces often requires the use of null lenses. Many of these null lenses are tested using a certification computer-generated hologram (CGH) for better error calibration. We present a method that will measure large aspheres to a greater level of accuracy than is presently possible. We use segmented and superposed CGH elements to certify and calibrate null lens errors absolutely to a high degree of accuracy. In such holograms two different phase functions are encoded on the CGH by means of aperture division. One subaperture generates a spherical wavefront that is used to determine the pattern errors of the hologram while the second subaperture reconstructs an aspherical wavefront used to calibrate the wavefront errors of the null lens. This careful calibration process involves the removal of both axisymmetric and non-axisymmetric errors in the null test. Once this is accomplished, the null lens may be used to test the asphere to a high degree of accuracy. Our initial results show that we can test 4-meter class aspheric mirrors to better than 1nm rms surface error. In current experiments we have set a goal of measuring such mirrors to better than lnm rms surface error.
• Hvisc, A. M., & Burge, J. H. (2007). Structure function analysis of mirror fabrication and support errors. Proceedings of SPIE - The International Society for Optical Engineering, 6671.
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  Abstract: Telescopes are ultimately limited by atmospheric turbulence, which is commonly characterized by a structure function. The telescope optics will not further degrade the performance if their errors are small compared to the atmospheric effects. Any further improvement to the mirrors is not economical since there is no increased benefit to performance. Typically the telescope specification is written in terms of an image size or encircled energy and is derived from the best seeing that is expected at the site. Ideally, the fabrication and support errors should never exceed atmospheric turbulence at any spatial scale, so it is instructive to look at how these errors affect the structure function of the telescope. The fabrication and support errors are most naturally described by Zernike polynomials or by bending modes for the active mirrors. This paper illustrates an efficient technique for relating this modal analysis to wavefront structure functions. Data is provided for efficient calculation of structure function given coefficients for Zernike annular polynomials. An example of this procedure for the Giant Magellan Telescope primary mirror is described.
• Mallik, P. C., Zhao, C., & Burge, J. H. (2007). Measurement of a 2-meter flat using a pentaprism scanning system. Optical Engineering, 46(2).
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  Abstract: Precise manufacturing of optical flats requires precise characterization of the surface. A scanning pentaprism system is ideal for use as an absolute and precise test for an optical flat. Such a system was built and used to test a 2-m diameter flat mirror. This system uses light from an autocollimator that is reflected from two pentaprisms to project reference beams of light onto the flat mirror. The light reflected from the mirror back through the pentaprisms provides information on low order optical aberrations in the flat mirror. We report results of the test on a 2-m flat, characterizing the errors and their sources. There is enormous potential for our system to be used to test larger flats and even curved surfaces, made of either a glass or a liquid. © 2007 Society of Photo-Optical Instrumentation Engineers.
• Peng, S. u., Burge, J. H., & Sasian, J. (2007). Shear test of the off-axis surface with an axis-symmetric parent. Proceedings of SPIE - The International Society for Optical Engineering, 6671.
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  Abstract: Interferometers with additional test optics are frequently used for measuring aspherical optical surfaces. In optical testing it is desirable to separate the figure measurement errors due to the test surface from figure errors that arise in the test equipment. For axially symmetric optics this is accomplished by rotating the surface being measured with respect to the test system. The data can then be processed to separate the non-axially symmetric errors that are fixed in the test system and those that rotate with the part. The axially symmetric errors cannot be distinguished with this technique. In this paper we present a variation of this technique for off-axis aspheric optics. The rotation is performed by rotating the test surface about the optical axis of its parent asphere, which may be outside the physical boundary of the test surface. As these rotations cannot be large, this motion is better described as a shear of the optical surface with respect to the test optics. By taking multiple measurements with different amounts of rotational shear and using maximum likelihood estimation methods, one can separate the errors in the test optics from the irregularity in the optical surface.
• Yellowhair, J., & Burge, J. H. (2007). Analysis of a scanning pentaprism system for measurements of large flat mirrors. Applied Optics, 46(35), 8466-8474.
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  PMID: 18071377;Abstract: The optical surface of a large optical flat can be measured using an autocollimator and scanning pentaprism system. The autocollimator measures the slope difference between a point on the mirror and a reference point. Such a system was built and previously operated at the University of Arizona. We discuss refinements that were made to the hardware, the alignment procedure, and the error analysis. The improved system was demonstrated with a 1.6 m flat mirror, which was measured to be flat to 12 nm rms. The uncertainty in the measurement is only 9 nm rms. © 2007 Optical Society of America.
• Yellowhair, J., Peng, S. u., Novak, M., & Burge, J. (2007). Fabrication and testing of large flats. Proceedings of SPIE - The International Society for Optical Engineering, 6671.
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  Abstract: Flat mirrors of around 1 meter are efficiently manufactured with large piano polishers and measured with Fizeau interferometry. We have developed technologies and hardware that allow fabrication and testing of flat mirrors that are much larger. The grinding and polishing of the large surfaces uses conventional laps driven under computer control for accurate and systematic control of the surface figure. The measurements are provided by a combination of a scanning pentaprism test, capable of measuring power and low order irregularity over diameters up to 8 meters, and subaperture Fizeau interferometry. We have developed a vibration insensitive Fizeau interferometer with 1 meter aperture and software to optimally combine the data from the subaperture tests. These methods were proven on a 1.6 m flat mirror that was finished to 6 nm rms irregularity and 11 nm rms power.
• Zhao, C., & Burge, J. H. (2007). Imaging aberrations from null correctors. Proceedings of SPIE - The International Society for Optical Engineering, 6723.
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  Abstract: To test an aspheric surface, usually a null lens is designed to create an aspheric wavefront that matches the surface. The null lens also relays the image of the surface under test to the interferometer. The effect of image distortion from the null lens is well known, and is accommodated by remapping the data. Imaging aberrations created by the null lens also affect the measurement by smoothing out wavefront errors which correspond to ripples in the surface. This leads to data that does not faithfully represent the surface. We characterize this smoothing using a measurement transfer function, which is analogous to the modulation transfer function used to quantify the performance of imaging systems. In this paper we present a technique and tools for predicting the transfer function for a null test.
• Zhao, C., & Burge, J. H. (2007). Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials. Optics Express, 15(26), 18014-18024.
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  PMID: 19551099;Abstract: Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonormal using the GramSchmidt technique. This set provides a complete basis for representing vector fields that can be defined as a gradient of some scalar function. It is then efficient to transform from the coefficients of the vector functions to the scalar Zernike polynomials that represent the function whose gradient was fit. These new vector functions have immediate application for fitting data from a Shack-Hartmann wavefront sensor or for fitting mapping distortion for optical testing. A subsequent paper gives an additional set of vector functions consisting only of rotational terms with zero divergence. The two sets together provide a complete basis that can represent all vector distributions in a circular domain. © 2007 Optical Society of America.
• Zhou, P., & Burge, J. (2007). Coupling of surface roughness to the performance of computer-generated holograms. Applied Optics, 46(26), 6572-6576.
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  PMID: 17846652;Abstract: Computer-generated holograms (CGHs), such as those used in optical testing, are created by etching patterns into an optical substrate. Imperfections in the etching can cause small scale surface roughness that varies across the pattern. The variation in this roughness affects the phase and amplitude of the wavefronts in the various diffraction orders. A simplified model is developed and validated that treats the scattering loss from the roughness as an amplitude effect. We demonstrate the use of this model for engineering analysis and provide a graphical method for understanding the application. Furthermore, we investigate the magnitude of this effect for the application of optical testing and show that the effect on measurement accuracy is limited to 1 nm for typical CGHs. © 2007 Optical Society of America.
• Zhou, P., & Burge, J. H. (2007). Fabrication error analysis and experimental demonstration for computer-generated holograms. Applied Optics, 46(5), 657-663.
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  PMID: 17279150;Abstract: Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm. © 2007 Optical Society of America.
• Zhou, P., & Burge, J. H. (2007). Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors. Optics Express, 15(23), 15410-15417.
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  PMID: 19550826;Abstract: Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). The etching of the CGH pattern must be highly accurate to create desired wavefronts. Variations of line width, etching depth, and surface roughness cause unwanted wavefront errors. The sensitivity to these manufacturing errors is studied using scalar diffraction analysis. We provide a parametric model that can be used for optimizing the CGH design to give good diffraction efficiency and limited sensitivity to manufacturing errors. © 2007 Optical Society of America.
• Burge, J. H. (2006). An easy way to relate optical element motion to system pointing stability. Proceedings of SPIE - The International Society for Optical Engineering, 6288.
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  Abstract: The optomechanical engineering for mounting lenses and mirrors in imaging systems is frequently driven by the pointing or jitter requirements for the system. A simple set of rules was developed that allow the engineer to quickly determine the coupling between motion of an optical element and a change in the system line of sight. Examples are shown for cases of lenses, mirrors, and optical subsystems. The derivation of the stationary point for rotation is also provided. Small rotation of the system about this point does not cause image motion.
• Burge, J. H., Kot, L. B., Martin, H. M., Zehnder, R., & Zhao, C. (2006). Design and analysis for interferometric measurements of the GMT primary mirror segments. Proceedings of SPIE - The International Society for Optical Engineering, 6273 I.
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  Abstract: The Giant Magellan Telescope (GMT) uses seven 8.4-m diameter segments to create a giant primary mirror, 25 meters across with focal ratio f/0.7. The off-axis segments will be difficult to measure accurately, as they have 14.5 mm departure from the nearest fitting sphere! The test configuration adopted uses a large 3.75-m powered mirror to fold the light path and provide most of the aspheric correction, with a smaller mirror and computer generated hologram (CGH) providing the additional correction. These optics will be aligned to a vibration-insensitive interferometer using a combination of optical references created by the CGH and metrology with a laser tracker. Some key challenges for this system are presented here including, the system alignment, the large fold mirror, and the mechanical structure. Analysis of the optical test shows that it will meet GMT specifications, including the difficult requirement that the separate segments have matching radius of curvature. Additional corroborative testing will be performed to assure that the mirror segments are correctly figured.
• Burge, J. H., Kot, L. B., Martin, H. M., Zhao, C., & Zobrist, T. (2006). Alternate surface measurements for GMT primary mirror segments. Proceedings of SPIE - The International Society for Optical Engineering, 6273 II.
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  Abstract: The primary mirror for the 25-m Giant Magellan Telescope is made of seven circular segments, each of 8.4-m diameter. The lack of axisymmetry and the steep aspheric departure present significant technical challenges for the metrology. These segments will be measured interferometrically using a complex system of mirrors and holograms to give a null test with high spatial resolution. While analysis predicts this system will meet requirements, an additional set of measurements will be used to corroborate the principal interferometric measurement. The set of tests, including these alternate surface measurements, assures that all aspects of the mirror surface are measured completely and redundantly. The corroboration tests discussed in this paper are: Direct surface profile using metrology system based on a laser tracker, measuring low order shape errors Shear testing with full aperture interferometer, separating small scale errors in the null test from those in the mirror Slope testing with scanning pentaprism, measuring low order shape errors and sampling small scale errors.
• C., P., Zehnder, R., Burge, J. H., & Poleshchuk, A. (2006). Absolute calibration of null correctors using twin computer-generated holograms. Proceedings of SPIE - The International Society for Optical Engineering, 6292.
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  Abstract: We present a method for a cascading null test using twin computer-generated holograms to calibrate errors in null correctors. This will allow us to test large aspheres an order of magnitude better than current limits. We discuss various sources of CGH errors and how to calibrate them. We also mention some ways to measure and calibrate the errors in the test optics.
• Chang, Y., Zhou, P., & Burge, J. H. (2006). Analysis of phase sensitivity for binary computer-generated holograms. Applied Optics, 45(18), 4223-4234.
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  PMID: 16778930;Abstract: A binary diffraction model is introduced to study the sensitivity of the wavefront phase of binary computer-generated holograms on groove depth and duty-cycle variations. Analytical solutions to diffraction efficiency, diffracted wavefront phase functions, and wavefront sensitivity functions are derived. The derivation of these relationships is obtained by using the Fourier method. Results from experimental data confirm the analysis. Several phase anomalies were discovered, and a simple graphical model of the complex fields is applied to explain these phenomena. © 2006 Optical Society of America.
• Martin, H. M., Burge, J. H., Miller, S. M., Smith, B. K., Zehnder, R., & Zhao, C. (2006). Manufacture of a 1.7 m prototype of the GMT primary mirror segments. Proceedings of SPIE - The International Society for Optical Engineering, 6273 I.
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  Abstract: We have nearly completed the manufacture of a 1.7 m off-axis mirror as part of the technology development for the Giant Magellan Telescope. The mirror is an off-axis section of a 5.3 m f/0.73 parent paraboloid, making it roughly a 1:5 model of the outer 8.4 m GMT segment. The 1.7 m mirror will be the primary mirror of the New Solar Telescope at Big Bear Solar Observatory. It has a 2.7 mm peak-to-valley departure from the best-fit sphere, presenting a serious challenge in terms of both polishing and measurement. The mirror was polished with a stressed lap, which bends actively to match the local curvature at each point on the mirror surface, and works for asymmetric mirrors as well as symmetric aspheres. It was measured using a hybrid reflective-diffractive null corrector to compensate for the mirror's asphericity. Both techniques will be applied in scaled-up versions to the GMT segments.
• Peng, S. u., Burge, J., Sprowl, R. A., & Sasian, J. (2006). Maximum likelihood estimation as a general method of combining sub-aperture data for interferometric testing. Proceedings of SPIE - The International Society for Optical Engineering, 6342 II.
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  Abstract: Interferometers accurately measure the difference between two wavefronts, one from a reference surface and the other from an unknown surface. If the reference surface is near-perfect or is accurately known from some other test, then the shape of the unknown surface can be determined. We investigate the case where neither the reference surface nor the surface under test is known. By making multiple modulated measurements where both surfaces are translated and rotated, we obtain sufficient information to reconstruct the figure of both surfaces. We have developed software that provides a maximum likelihood estimation of both surfaces, as well as an assessment of the quality of the reconstruction. This was demonstrated for the measurement of a large flat mirror, using a smaller reference mirror that has significant shape errors. © 2006 SPIE-OSA.
• Zehnder, R., Burge, J. H., & Zhao, C. (2006). Use of computer generated holograms for alignment of complex null correctors. Proceedings of SPIE - The International Society for Optical Engineering, 6273 II.
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  Abstract: Large diameter, non-axisymmetric aspheric mirrors can be measured interferometrically using null correctors that employ computer generated holograms (CGHs). The testing of off axis segments for the new class of giant telescopes pose requirements that beyond the state of the an for CGHs alone. The long radius of curvature and the magnitude of the aspheric departure require other lenses and mirrors to be used along with the CGH. The alignment of these systems is very sensitive and the absolute accuracy of the alignment is critical to the system performance. We have developed techniques that use diffracted light from patterns on the CGH to accurately define the alignment of multi-element null correctors. We will present results from the null test of the 1.7-m New Solar Telescope primary mirror. The optical shape of this mirrors is an off-axis paraboloid from an f/0.7 parent.
• Zhao, C., Sprowl, R. A., Bray, M., & Burge, J. H. (2006). Figure measurement of a large optical flat with a Fizeau interferometer and stitching technique. Proceedings of SPIE - The International Society for Optical Engineering, 6293.
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  Abstract: Large flat mirrors can be measured by using subaperture Fizeau interferometer and stitching the data. We have implemented such a system that can efficiently and accurately measure flat mirrors several meters in diameter using a 1 meter sub-aperture instantaneous Fizeau interferometer, coupled with sophisticated analysis software. The 1-m aperture optical system uses a fused silica test plate, reflective collimator, and commercial instantaneous interferometer. Collimator errors, mapping distortion, surface errors in the test plate, and other systematic effects were measured and compensated for individual measurements. Numerous individual maps were stitched together to determine the global shape of a 2-m class flat.
• Burge, J., Zhao, C., Kang, D., & Burge, J. H. (2005). Effects of birefringence on Fizeau interferometry that uses a polarization phase-shifting technique. Applied optics, 44(35).
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  Interferometers that use different states of polarization for the reference and the test beams can modulate the relative phase shift by using polarization optics in the imaging system. Thus the interferometer can capture simultaneous images that have a fixed phase shift, which can be used for phase-shifting interferometry. As all measurements are made simultaneously, the interferometer is not sensitive to vibration. Fizeau interferometers of this type have an advantage compared with Twyman-Green-type systems because they are common-path interferometers. However, a polarization Fizeau interferometer is not strictly common path when both wavefronts are transmitted by an optic that suffers from birefringence. The two polarized beams see different phases owing to birefringence; as a result, an error can be introduced in the measurement. We study the effect of birefringence on measurement accuracy when different polarization techniques are used in Fizeau interferometers. We demonstrate that measurement error is reduced dramatically and can be eliminated if the reference and test beams are circularly polarized rather than linearly polarized.
• C., P., Zhao, C., & Burge, J. H. (2005). Measurement of a 2-meter flat using a pentaprism scanning system. Proceedings of SPIE - The International Society for Optical Engineering, 5869, 1-11.
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  Abstract: A scanning pentaprism system may be used as an absolute test for an optical flat. Such a system was built and used to test a 2-meter flat mirror. This system uses light from an autocollimator that is reflected from 2 pentaprisms to project reference beams of light onto the flat mirror. The light reflected from the mirror back through the pentaprisms provides information on low order optical aberrations in the flat mirror. We report results of the test on a 2-meter flat.
• Sabatke, E., Burge, J., & Sabatke, D. (2005). Analytic diffraction analysis of a 32-m telescope with hexagonal segments for high-contrast imaging. Applied Optics, 44(8), 1360-1365.
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  PMID: 15796232;Abstract: Large segmented telescopes cannot be modeled accurately with fast-Fourier-transform techniques since small features such as gaps between the segments will be inadequately sampled. An analytic Fourier-transform method can be used to model any pupil configuration with straight edges, including tolerance analysis and some types of apodization. We analytically investigated a 32-m segmented primary with 18 hexagonal segments for high-contrast imaging. There are significant regions in the image in which extrasolar planets could be detected. However, the hexagonal profile of the pupil was not as useful as expected. The gaps between the segments, the secondary obscuration, and the secondary spiders must be as small as possible and their edges must be apodized. Apodizing the edges of the individual segments reduced the useful regions in the image since the gaps appeared to be wider. © 2005 Optical Society of America.
• Zhao, C., Kang, D., & Burge, J. H. (2005). Effects of birefringence on Fizeau interferometry that uses a polarization phase-shifting technique. Applied Optics, 44(35), 7548-7553.
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  PMID: 16363779;Abstract: Interferometers that use different states of polarization for the reference and the test beams can modulate the relative phase shift by using polarization optics in the imaging system. Thus the interferometer can capture simultaneous images that have a fixed phase shift, which can be used for phase-shifting interferometry. As all measurements are made simultaneously, the interferometer is not sensitive to vibration. Fizeau interferometers of this type have an advantage compared with Twyman-Green-type systems because they are common-path interferometers. However, a polarization Fizeau interferometer is not strictly common path when both wavefronts are transmitted by an optic that suffers from birefringence. The two polarized beams see different phases owing to birefringence; as a result, an error can be introduced in the measurement. We study the effect of birefringence on measurement accuracy when different polarization techniques are used in Fizeau interferometers. We demonstrate that measurement error is reduced dramatically and can be eliminated if the reference and test beams are circularly polarized rather than linearly polarized. © 2005 Optical Society of America.
• Zhao, C., Kang, D., & Burge, J. H. (2005). Effects of birefringence on Fizeau interferometry that uses polarization phase shifting technique. Proceedings of SPIE - The International Society for Optical Engineering, 5869, 1-12.
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  Abstract: Interferometers that use different states of polarization for the reference and test beams can modulate the relative phase shift using polarization optics in the imaging system. This allows the interferometer to capture simultaneous images that have a fixed phase shift, which can be used for phase shifting interferometry. Since all measurements are made simultaneously, the interferometer is not sensitive to vibration. Fizeau interferometers of this type have advantage over Twyman-Green type systems because the optics are in the common path of both the reference and test wavefronts, therefore errors in these optics affect both wavefronts equally and do not limit the system accuracy. However, this is not strictly true for the polarization interferometer when both wavefronts are transmitted an optic that suffers from birefringence. If some of the components in the common path of the reference and test beams have residual birefringence, the two beams see different phases. Therefore, the interferometer is not strictly common path. As a result, an error can be introduced in the measurement. In this paper, we study the effect of birefringence on measurement accuracy when different polarization techniques are used in Fizeau interferometers. We demonstrate that measurement error is reduced dramatically for small amount of birefringence if the reference and test beams are circularly polarized rather than linearly polarized.
• Zhao, C., Zehnder, R., & Burge, J. H. (2005). Measuring the radius of curvature of a spherical mirror with an interferometer and a laser tracker. Optical Engineering, 44(9).
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  Abstract: We present a method to accurately measure the radius of curvature of a concave spherical mirror with a phase-measuring interferometer and a laser tracker. Use of a laser tracker eases the alignment of the testing system, eliminates the need to move the test piece during the measurement, and improves the accuracy of the distance measurement. Using this method, we measured the radius of curvature of a spherical mirror 0.5 m in diameter and about 2.5 m in radius of curvature. The accuracy of the measurement is better than ±20 μm. © 2005 Society of Photo-Optical Instrumentation Engineers.
• Zhao, C., Zehnder, R., Burge, J. H., & Martin, H. M. (2005). Testing an off-axis parabola with a CGH and a spherical mirror as null lens. Proceedings of SPIE - The International Society for Optical Engineering, 5869, 1-12.
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  Abstract: Steward Observatory Mirror Lab is currently polishing an off-axis parabola which will be the primary mirror of the New Solar Telescope. To test this mirror, we built a test equipment to combine a spherical mirror and a Computer Generated Hologram (CGH) as null lens. The spherical mirror is tilted to compensate much of the astigmatism and some coma. And the CGH compensates rest of aberrations. The combination of a spherical mirror and a CGH makes the test system compact. The technology developed here will be used to test the Giant Magellan Telescope's primary mirror segment - a five times larger off-axis parabola.
• Baiocchi, D., & Burge, J. H. (2004). Optimized active, lightweight space mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 5166, 49-57.
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  Abstract: Since 1996, a team at the University of Arizona has been designing and fabricating lightweight, active space mirrors. These glass/composite mirrors use a thin flexible substrate for the optical surface and an actuated composite structure for support. We present a design method that yields the best figure correction for the lightest mass by assuming that the substrate's material properties are the limiting parameters. The results are such that the designer decides on a total mass budget and an aperture area, and the algorithm provides the substrate thickness, number of support points, and the mass distribution between the substrate and actuators.
• Kim, T., Burge, J. H., Lee, Y., & Kim, S. (2004). Null test for a highly paraboloidal mirror. Applied Optics, 43(18), 3617-3618.
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  PMID: 15218600;Abstract: A circular null computer-generated hologram (CGH) was used to test a highly paraboloidal mirror (diameter, 90 mm; f number, 0.76). To verify the null CGH test a classic autocollimation test with a flat mirror was performed. Comparing the results, we show that the results of the null CGH test show good agreement with results of the autocollimation test. © 2004 Optical Society of America.
• Koudelka, P. D., & Burge, J. H. (2004). Fabrication of Cube Beamsplitters for White Light Interferometry. Proceedings of SPIE - The International Society for Optical Engineering, 5252, 17-25.
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  Abstract: Interferometric applications utilizing short coherence length sources, such as white light interferometry, require precise matching of optical path lengths for the two arms of the interferometer. If a cube beamsplitter element is utilized, the added dispersive material in the optical path could introduce undesirable optical path difference (OPD) effects and a consequent degradation in fringe visibility. For this reason a cube beamsplitter must be well matched for equal geometric path length in glass during the fabrication process. Two degrees of freedom must be controlled; the lateral position and relative rotation of the two prisms that comprise the beamsplitter. A method is described for efficiently assembling cubed beamsplitters utilizing a kinematic mount to adjust the relative position of the beamsplitter prisms with sub-micron precision for both degrees of freedom. The OPD is monitored simultaneously at three separate wavelengths during assembly by exploiting the color separation capabilities of a spatially congruent 3-CCD color camera. Once positioned to minimize the OPD, the prisms are bonded together with UV curing adhesive and any residual aberrations are quantified. The technique was proven by aligning prisms to 0.1 μm accuracy and measuring the OPD error to 0.05μm accuracy.
• Martin, H. M., Burge, J. H., Cuerden, B., Miller, S. M., Smith, B., & Zhao, C. (2004). Manufacture of 8.4 m off-axis segments: A 1/5 scale demonstration. Proceedings of SPIE - The International Society for Optical Engineering, 5494, 62-70.
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  Abstract: We describe the requirements for manufacturing and maintaining alignment of the 8.4 m off-axis segments of the Giant Magellan Telescope's primary mirror, and a demonstration of the manufacturing techniques on the 1.7 m off-axis primary mirror of the New Solar Telescope. This mirror is approximately a 1/5 scale model of a GMT segment. We show that the stressed lap polishing system developed for highly aspheric primary and secondary mirrors is capable of figuring the GMT segments and the NST mirror. We describe an optical test with a null corrector consisting of a tilted spherical mirror and a computer-generated hologram, and derive accuracy requirements for the test. The criterion for accuracy of low-order aberrations is that the active support system can correct any figure errors due to the laboratory measurement, with acceptably small forces and residual errors.
• Pan, F. Y., & Burge, J. (2004). Efficient testing of segmented aspherical mirrors by use of reference plate and computer-generated holograms. I. theory and system optimization. Applied Optics, 43(28), 5303-5312.
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  PMID: 15495420;Abstract: Telescopes with large aspherical primary mirrors collect more light and are therefore sought after by astronomers. Instead of large mirrors as a single piece, they can be made by use of numerous smaller segments. Because the segments must fit together to create the effect of a single mirror, segmented optics present unique challenges to fabrication and testing that are absent for monolithic optics. We have developed a new method for measuring large quantities of segments accurately, quickly, and economically using an interferometric test plate and computer-generated hologram (CGH). In this test, the aspheric mirror segments are interferometrically measured by use of a test plate with a best-fit spherical surface. The aspherical departure is accommodated with a small CGH that is imaged onto the test plates. The radius of curvature is tightly controlled by maintaining the gap between the test plate and the segment. We present a summary of the test and give the basic design tradeoffs for using a single system to measure all of the segments of a large aspheric mirror. © 2004 Optical Society of America.
• Pan, F. Y., Burge, J. H., Zehnder, R., & Wang, Y. (2004). Fabrication and alignment issues for segmented mirror telescopes. Applied Optics, 43(13), 2632-2642.
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  PMID: 15130002;Abstract: There is a great demand for new telescopes that use larger primary mirrors to collect more light. Because of the difficulty in the fabrication of mirrors larger than 8 m as a single piece, they must be made with numerous smaller segments. The segments must fit together to create the effect of a single mirror, which presents unique challenges for fabrication and testing that are absent for monolithic optics. This is especially true for the case of a highly aspheric mirror required to make a short two-mirror telescope. We develop the relationship between optical performance of the telescope and errors in the manufacture and operation of the individual segments. © 2004 Optical Society of America.
• Pan, F. Y., Burge, J., Anderson, D., & Poleshchuk, A. (2004). Efficient testing of segmented aspherical mirrors by use of a reference plate and computer-generated holograms. II. Case study, error analysis, and experimental validation. Applied Optics, 43(28), 5313-5322.
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  PMID: 15495421;Abstract: Segmented mirrors present unique challenges to fabrication and testing that are absent for monolithic optics. Since traditional asphere tests do not address segmented optics adequately, we validate a previously developed method to test large quantities of segments accurately, quickly, and economically. In this test, the aspheric shape of each segment is controlled to high accuracy by use of computergenerated holograms, and the radius of curvature is tightly controlled by use of the reference plate. In an adjoining paper [Appl Opt 43, 5303 (2004)] we developed the theory for this test, and now we present a complete system design and optimization for measuring the 1.4-m segments from a 30-m F/1 primary. A complete tolerance analysis predicts a test accuracy of 4.8-nm rms surface and excellent accuracy for controlling the geometry of the segment. In addition, a laboratory demonstration using 30-cm optics is presented that demonstrated 3.9-nm rms surface accuracy. © 2004 Optical Society of America.
• Baiocchi, D., Burge, J. H., & Cuerden, B. (2003). Metrology results and lessons learned from the Univ. of Arizona NGST mirror system demonstrator. Proceedings of SPIE - The International Society for Optical Engineering, 5180, 220-227.
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  Abstract: The University of Arizona has built a 2-m lightweight active mirror prototype for the next generation of space telescopes. This paper briefly reviews the mirror's opto-mechanical design, and its describes the three different metrology systems that were used to measure it during the actuation process. We also present a list of lessons learned while working on this project. We conclude by discussing one of the successful projects that has come out of this technology.
• Stamper, B. L., Burge, J. H., & Dallas, W. J. (2003). Three dimensional bulk index inhomogeneity measurement using computed tomography. Proceedings of SPIE - The International Society for Optical Engineering, 5180, 413-420.
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  Abstract: Manufacturers of optical glass strive to make a product that is homogeneous, isotropic, and free of any bubbles or mechanical strain. Glass used in forming images is very good, but the process of mixing the constituent materials, and melting them into a glass is limited. As uniform as the mixtures are, they are not perfect, and the effects can be seen anytime light must propagate through several centimeters of glass. One method for measuring the three dimensional inhomogeneities in a piece of glass will be shown. Interferometry and computed tomography will be used to map the bulk refractive index variations. Having three dimensional information on the refractive index is the first step in compensating for errors in an imaging system.
• Burge, J. H., & Martin, H. M. (2002). Optical issues for giant telescopes with extremely fast primary mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 4840, 226-237.
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  Abstract: Existing design rules break down as we plan for a new generation of giant optical telescopes of 20, 30, 50, even 100 meters in diameter. One might expect these telescopes to converge on the design universally accepted for similarly sized radio telescopes, with their highly aspheric, ∼ f/0.4, primary dish. But most of the optical design concepts now under consideration have favored spherical or relatively slow paraboloidal surfaces, leading to a much larger telescope, more subject to wind buffeting, and requiring gargantuan enclosures for protection. This paper explores issues and limitations for building and operating telescopes as the primary focal ratio is reduced to a value as small as f/0.4. Such compactness will be particularly important for mechanical stability, cost control and for large telescopes that must move continuously on a track, as in the 20/20 concept. We find that fabrication and alignment methods for telescopes using numerous small (1-m class) segments are driven to long focal ratios, while those using few large, actively controlled segments can be made as fast as f/0.5.
• Burge, J., Zhao, C., & Burge, J. H. (2002). Application of the pupil astigmatism criteria in optical design. Applied optics, 41(34).
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  We developed the pupil astigmatism criteria for correcting the quadratic field-dependent aberrations. These criteria provide an elegant way to determine and correct aberrations that have quadratic field dependence and arbitrary pupil dependence in the same way that the Abbe sine condition is used for aberrations with linear field dependence. Like the sine condition, the pupil astigmatism criteria involve only the properties of the rays originating from the on-axis object point, so it is convenient to implement them in optical design. We introduce an algorithm to apply the criteria in designing new well-corrected optical systems. Some example designs are presented.
• Burge, J., Zhao, C., & Burge, J. H. (2002). Comparison of exact pupil astigmatism conditions with Seidel approximations. Applied optics, 41(34).
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  The aberrations of axisymmetric imaging systems can be calculated to third order by use of the Seidel formula. The Coddington equations give aberrations that have quadratic dependence on the pupil, for all field points. The pupil astigmatism conditions were recently developed to predict and control aberrations that have quadratic field dependence and arbitrary pupil dependence. We investigate the relationship between the exact pupil astigmatism conditions and the classical Seidel treatment of pupil aberration.
• Burge, J., Zhao, C., & Burge, J. H. (2002). Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems. Journal of the Optical Society of America. A, Optics, image science, and vision, 19(12).
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  The Abbe sine condition and the recently developed pupil astigmatism conditions provide a powerful set of relationships for describing imaging systems that are free from aberrations that have linear and quadratic dependence on field, to all orders in the pupil. We have proved both of these conditions and applied them to axisymmetric imaging systems. We now extend our approach to plane-symmetric systems. Still using Hamilton's characteristic functions, we derive the general sine conditions and the pupil astigmatism conditions that describe plane-symmetric systems that are free of all aberrations with linear and quadratic field dependence.
• Burge, J., Zhao, C., & Burge, J. H. (2002). Criteria for correction of quadratic field-dependent aberrations. Journal of the Optical Society of America. A, Optics, image science, and vision, 19(11).
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  Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton's characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs.
• Kim, T., Burge, J. H., & Lee, Y. (2002). Measurement of highly parabolic mirror using computer generated hologram. Proceedings of SPIE - The International Society for Optical Engineering, 4778, 119-126.
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  Abstract: For evaluating the surface of parabolic mirror (90 mm, F/0.76), two different null test have been discussed. After designing, encoding, and fabricating the CGH(computer generated hologram), the null CGH test was performed. An autocollimation test with a flat mirror was also performed and these testing result were compared.
• Martin, H. M., Allen, R. G., Burge, J. H., Dettmann, L. R., Ketelsen, D. A., Miller, S. M., & Sasian, J. M. (2002). Fabrication of mirrors for the Magellan telescopes and the large binocular telescope. Proceedings of SPIE - The International Society for Optical Engineering, 4837(2), 609-618.
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  Abstract: We describe the fabrication and testing of the 6.5 m f/1.25 primary mirrors for the Magellan telescopes and the 8.4 m f/1.14 primary mirrors for the Large Binocular Telescope (LET). These mirrors, along with the 6.5 m MMT primary, are the fastest and most aspheric large mirrors made. Steward Observatory developed special methods to polish and measure these and other, fast mirrors. We use a stressed-lap polishing tool to fit the aspheric surface while providing strong passive smoothing, and computer-generated holograms to verify the measurement of up to 1.4 mm peak-to-valley asphericity to an accuracy of 0.01%. The Magellan mirrors are diffraction-limited at visible wavelengths, with surface accuracies of about 20 nm rms on active supports. We are currently polishing the first LET primary mirror and preparing to make the thin shells for the LET adaptive secondary mirrors.
• Morgan, R. M., Burge, J. H., & Woolf, N. (2002). Final laboratory results of visible nulling with dielectric plates. Proceedings of SPIE - The International Society for Optical Engineering, 4838(1), 644-655.
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  Abstract: Nullng stellar interferometry may enable the discovery of earth-like planets around other stars. In nulling mode, the zero order fringe is destructive and on axis, thus cancelling light form a bright source and allowing detection of dimer off-axis features. To create a deep on-axis null, the phase must be shifted half a wave achromatically over a broad band. The phase shift is created by adding optical path thickness with dielectric plates. Plates of different materials can balance dispersion. The nulling solutions found for TPF (infrared) and SIM (visible)are promising. This paper presents the final results of a dissertation that developed a nulling beam combiner testbed. The deepest null achieved over the spectral region of 600 to 800 nm was 7×10-3. The test bed revealed the extreme challenges of this technique and provided very valuable lessons to enable further implementations. The testbed first achromatized the null by actively controlling the optical thicknesses of the plates. The phase as a function of wavelength was measured by PSI on a spectrally dispersed fringe. The phase was fit to a model to determine the optical thicknesses. The eigenfunctions of the model were nearly collinear and consequently the dynamic range required of the phase data was very high and not supported by the hardware. The testbed then searched for the null fringe and locked on the null using a 300 Hz servo loop and on a grey fringe. The OPD was stabilized to 6 nm peak-to valley.
• Sabatke, E. M., & Burge, J. H. (2002). Basic principles in the optical design of imaging multiple aperture systems. Proceedings of SPIE - The International Society for Optical Engineering, 4832, 236-248.
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  Abstract: We discuss the basic concepts that have been useful in our work designing multiple aperture telescopes with wide fields of view. We examine combining errors at zero field and errors that are linear as a function of field. An easy optimization for satisfying the sine condition to eliminate linear piston errors is given. Methods for estimating the RMS wavefront errors for the lower-order combining errors are given.
• Sabatke, E. M., & Burge, J. H. (2002). Imaging interferometers using flat primary segments. Proceedings of SPIE - The International Society for Optical Engineering, 4849, 365-371.
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  Abstract: Gossamer mirrors have the potential to reach 100 meter baselines in space because of their very light weight. We explore a type of system that uses an array of flat gossamer mirrors as a primary mirror. Using wavefront reconstruction, we can easily estimate the fields of view for these systems. We report the fields of view as a function of the free parameters for these systems.
• Stamper, B., & Burge, J. (2002). Index inhomogeneity effects on imaging systems. Proceedings of SPIE - The International Society for Optical Engineering, 4832, 96-.
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  Abstract: Large field of view, high power, lithography, and laser fusion systems are all limited by refractive index variations of their constituent glass elements. To estimate how the image degrades, a model of the bulk index inhomogeneity must be formed.
• Tuell, M. T., Burge, J. H., & Anderson, B. (2002). Aspheric optics: Smoothing the ripples with semi-flexible tools. Optical Engineering, 41(7), 1473-1474.
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  Abstract: A well-known fabrication problem with aspheric optical surfaces lies in high-frequency surface irregularities inherent in the figuring process. Optical grinding and polishing tools can smooth these ripples, yet retain the flexibility required to fit the aspheric surface. An f/0.52, paraboloidal, 17-in. convex surface is produced with conventional rigid tools. A transmission ronchigram is obtained showing high-spatial-frequency errors of large magnitude. After four hours of grinding with a semi-flexible multiple-segment ring tool, almost all high-frequency error is removed. This shows good potential for smoothing finished aspheric optics. Flexible tools can also be involved in the figuring process itself.
• Zhao, C., & Burge, J. (2002). Criteria for correction of all aberrations with quadratic field dependence. Proceedings of SPIE - The International Society for Optical Engineering, 4832, 226-235.
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  Abstract: Aberrations of imaging systems can be described using a polynomial expansion of the dependence on field position. Aberrations on axis and those with linear field dependence can be calculated and controlled using Fermat's principle and the Abbe Sine Condition. We now present a powerful new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations, derived using Hamilton's characteristic functions, which we call the Pupil Astigmatism Criteria, use on-axis behavior to evaluate and control all aberrations with quadratic field dependence and arbitrary dependence on the pupil. These relations are explained, validated, and applied to design optical systems that are free of all quadratic field dependent aberrations.
• Zhao, C., & Burge, J. H. (2002). Application of the pupil astigmatism criteria in optical design. Applied Optics, 41(34), 7288-7293.
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  PMID: 12477120;Abstract: We developed the pupil astigmatism criteria for correcting the quadratic field-dependent aberrations. These criteria provide an elegant way to determine and correct aberrations that have quadratic field dependence and arbitrary pupil dependence in the same way that the Abbe sine condition is used for aberrations with linear field dependence. Like the sine condition, the pupil astigmatism criteria involve only the properties of the rays originating from the on-axis object point, so it is convenient to implement them in optical design. We introduce an algorithm to apply the criteria in designing new well-corrected optical systems. Some example designs are presented. © 2002 Optical Society of America.
• Zhao, C., & Burge, J. H. (2002). Comparison of exact pupil astigmatism conditions with Seidel approximations. Applied Optics, 41(34), 7284-7287.
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  PMID: 12477119;Abstract: The aberrations of axisymmetric imaging systems can be calculated to third order by use of the Seidel formulas. The Coddington equations give aberrations that have quadratic dependence on the pupil, for all field points. The pupil astigmatism conditions were recently developed to predict and control aberrations that have quadratic field dependence and arbitrary pupil dependence. We investigate the relationship between the exact pupil astigmatism conditions and the classical Seidel treatment of pupil aberrations. © 2002 Optical Society of America.
• Zhao, C., & Burge, J. H. (2002). Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 19(12), 2467-2472.
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  PMID: 12469742;Abstract: The Abbe sine condition and the recently developed pupil astigmatism conditions provide a powerful set of relationships for describing imaging systems that are free from aberrations that have linear and quadratic dependence on field, to all orders in the pupil. We have proved both of these conditions and applied them to axisymmetric imaging systems. We now extend our approach to plane-symmetric systems. Still using Hamilton's characteristic functions, we derive the general sine conditions and the pupil astigmatism conditions that describe plane-symmetric systems that are free of all aberrations with linear and quadratic field dependence. © 2002 Optical Society of America.
• Zhao, C., & Burge, J. H. (2002). Criteria for correction of quadratic field-dependent aberrations. Journal of the Optical Society of America A: Optics and Image Science, and Vision, 19(11), 2313-2321.
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  PMID: 12413132;Abstract: Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton's characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs. © 2002 Optical Society of America.
• Baiocchi, D., Burge, J. H., & Cuerden, B. (2001). Demonstration of a 0.5-m ultralightweight mirror for use at geosynchronous orbit. Proceedings of SPIE - The International Society for Optical Engineering, 4451, 86-95.
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  Abstract: Future space telescopes will require apertures that are larger than the current state of the art, yet fit within the exiting launch restrictions on size and mass. The mass can be reduced by using a thin flexible substrate for the optical surface and a rigid, lightweight frame with actuators for support. The accuracy of the optical surface is actively maintained by adjusting the actuators using feedback from wavefront measurements. We have designed, built and tested a 0.5-m demonstration mirror for use in geosynchronous Earth-imaging systems. The mirror has an areal density of 5 kg/m2 and is the lightest mirror we have made using the thin substrate design. This paper discusses the design, fabrication and performance of the 0.5-m mirror.
• Burge, J. H., Anderson, B., Benjamin, S., Cho, M., Smith, K., & Valente, M. (2001). Development of optimal grinding and polishing tools for aspheric surfaces. Proceedings of SPIE - The International Society for Optical Engineering, 4451, 153-164.
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  Abstract: The ability to grind and polish steep aspheric surfaces to high quality is limited by the tools used for working the surface. The optician prefers to use large, stiff tools to get good natural smoothing, avoiding small scale surface errors. This is difficult for steep aspheres because the tools must have sufficient compliance to fit the aspheric surface, yet we wish the tools to be stiff so they wear down high regions on the surface. This paper presents a toolkit for designing optimal tools that provide large scale compliance to fit the aspheric surface, yet maintain small scale stiffness for efficient polishing.
• Burge, J. H., Baiocchi, D., & Cuerden, B. (2001). Ultralightweight active mirror technology at the University of Arizona. Proceedings of SPIE - The International Society for Optical Engineering, 4198, 230-241.
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  Abstract: Lightweight mirrors for space can be made using a thin flexible substrate for the optical surface and a rigid lightweight frame with actuators for support. The accuracy of the optical surface is actively maintained by adjusting the actuators using feedback from wavefront measurements. The University of Arizona is now is the final stages of fabricating two such mirrors. A 2-m NGST Mirror System Demonstrator, with an areal density of 13 kg/m2, is being built for NASA and will be tested at cryogenic temperatures. A 50 cm development mirror, with an areal density of only 5 kg/m2, is also being fabricated. This paper discusses the fabrication processes involved with both of these mirrors.
• Poleshchuk, A., Korolkov, V., Cherkashin, V., Reichelt, S., & Burge, J. (2001). Polar coordinate laser writing systems: Error analysis of fabricated DOEs. Proceedings of SPIE - The International Society for Optical Engineering, 4440, 161-172.
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  Abstract: Diffractive optics is a field where the progress is defined by fabrication technology. Diffractive optical elements (DOEs) are generally planar structures, typically fabricated using X-Y image generators designed for semiconductor industry. However there are some kinds of DOEs for which the polar scanning geometry, where the optic rotates under a writing beam, is more preferable. In some cases polar coordinate machines provide the only practical method of fabricating DOEs with the required accuracy. It is necessary to take into account the DOE specification when choosing the fabrication method. The present paper considers peculiarities of polar coordinate laser systems for large size and high precision DOEs fabrication. The specific error sources for these systems are described and compared with those of X-Y systems. An optimal writing strategy is discussed. The wavefront aberrations of rotationally symmetric DOEs caused by fabrication errors were measured interferometrically. Different types of aberrations were identified and can be referred to certain writing errors. Interferometric measurements of the wavefront errors for binary zone plates with a 64 mm diameter and 0.45 numerical aperture have shown that the wavefront root-mean-square error does not exceed 0.009λ.
• Valente, M., Burge, J., DiCenso, R., Abusafieh, A., & Federico, D. (2001). Suitability of igneous rock for precision tooling. Proceedings of SPIE - The International Society for Optical Engineering, 4451, 174-180.
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  Abstract: Surface plates and blocking tools are commonly made of granite because of its good stability. But how stable is the granite, and which type of material is optimal? We have explored several materials manufacturing processes for a 4-m aspheric reference surface that would serve as a tool for laying up composite optics. In this paper, we discuss the materials selection, stability to thermal and moisture effects, and parameters for processing the surface to give sub-micron accuracy and stability.
• Zhao, C., & Burge, J. H. (2001). Vibration-compensated interferometer for surface metrology. Applied Optics, 40(34), 6215-6222.
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  PMID: 18364924;Abstract: An advanced interferometer was built for surface metrology in environments with severe vibration. This instrument uses active control to compensate for effects of vibration to allow surface measurement with high-resolution phase-shifting interferometry. A digital signal processor and high-speed phase control from an electro-optic modulator allows phase measurements at 4000 Hz. These measurements are fed back into a real-time servo in the digital signal processor that provides a vibration-corrected phase ramp for the surface measurements taken at video rates. Unlike fringe locking, which compensates vibration to keep the phase constant, we show a true phase servo that allows the phase to be stabilized while it is ramped, enabling surface measurements using phase-shifting interferometry that requires multiple images with controlled phase shifts. © 2001 Optical Society of America.
• Baiocchi, D., & Burge, J. H. (2000). Radius of curvature metrology for segmented mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 4093, 58-67.
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  Abstract: Future space and ground telescopes will have apertures that are increasingly larger in size. The primary mirrors for these telescopes will be so large that they cannot be fabricated, transported, and/or launched as a single entity. One solution is to build a large mirror out of smaller segments. The biggest challenge in fabricating segmented mirrors is matching the individual pieces so they form a single, continuous surface. This requirement means that the radii of curvature must all match. We present a technique for matching the relative radii of curvature for segmented mirrors, and we include an error analysis of this method.
• Catanzaro, B., Keane, D., Connell, S., Baiocchi, D., Burge, J., Maji, A., & Powers, M. (2000). UltraLITE glass/composite hybrid mirror. Proceedings of SPIE - The International Society for Optical Engineering, 4013, 663-671.
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  Abstract: The mass of the primary mirror has dominated the mass of larger aperture (>1 m class) telescopes. Spaceborne telescopes have much to gain from a significant reduction in areal density. Areal density is often limited by the stiffness to weight ratio of the primary mirror. Two key factors drive this criteria: telescope structural characteristics (launch and deployment) and fabrication requirements. A new class of hybrid composite mirrors has been designed, prototyped, and fabricated to demonstrate the advantage of the high stiffness to weight ratio of carbon fiber composite materials and the superior optical fabrication for low expansion glasses. This hybrid mirror utilizes a unique `set and forget' fabrication technique. A thin meniscus of glass is mounted to a stiff composite support structure using composite flexure rods. The meniscus is lightweighted using waterjet pocket milling and is conventionally polished to a precise radius of curvature. This meniscus is then supported on the flexures and actuated to a precise figure. The flexures are fixed and the actuators are removed. The substrate is then ion figured to achieve the final figure. The areal density of this mirror is 10 kg/m2. Surface figure on a 0.25 m aperture prototype was demonstrated at better than λ/4 (visible) prior to ion figuring. Two 0.6 m mirrors are under fabrication. The design of the mirror and results of the fabrication and testing will be discussed.
• Keski-Kuha, R., Bely, P., Burg, R., Burge, J., Davila, P., Geary, J., Hagopian, J., Jacobson, D., Lowman, A., Macenka, S., Mangus, J., Perrygo, C., Redding, D., Saif, B., Smith, S., & Wyant, J. (2000). NGST OTA optical metrology instrumentation and conceptual approaches. Proceedings of SPIE - The International Society for Optical Engineering, 4013, 826-835.
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  Abstract: An Integrated Product Team (IPT) was formed to develop a detailed concept for optical test methodology for testing of the NGST individual primary, secondary and tertiary mirrors and the full telescope system on the ground. The large, lightweight, deployable primary mirror, and the cryogenic operating environment make optical testing of NGST OTA (Optical Telescope Assembly) extremely challenging. A telescope of the complexity of NGST has never been built and tested on the ground in 1-g environment. A brief summary of the preliminary metrology test plan at the mirror component and telescope system level is presented.
• Martin, H. M., Burge, J. H., Vecchio, C. D., Dettmann, L. R., Miller, S. M., Smith, B., & Wildi, F. (2000). Optical fabrication of the MMT adaptive secondary mirror. Proceedings of SPIE - The International Society for Optical Engineering, 4007, I/-.
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  Abstract: We describe the optical fabrication of the adaptive secondary mirror for the MMT. The 640 mm f/15 secondary consists of a flexible glass shell, 1.8 mm thick, whose shape is controlled by 336 electromagnetic actuators. It is designed to give diffraction-limited images at a wavelength of 1 micron. For generating and polishing, the shell was supported by attaching it to a rigid glass blocking body with a thin layer of pitch. It could then be figured and measured using techniques developed for rigid secondaries. The highly aspheric surface was polished with a 30 cm stressed lap and small passive tools, and measured using a swing-arm profilometer and a holographic test plate. The goal for fabrication was to produce diffraction-limited images in the visible, after simulated adaptive correction using only a small fraction of the typical actuator forces. This translates into a surface accuracy of less than 19 nm rms with correction forces of less than 0.05 N rms. We achieved a surface accuracy of 8 nm rms after simulated correction with forces of 0.02 N rms.
• Morgan, R. M., Burge, J., & Woolf, N. (2000). Nulling interferometric beam combiner utilizing dielectric plates: Experimental results in the visible broadband. Proceedings of SPIE - The International Society for Optical Engineering, 4006, I/-.
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  Abstract: A laboratory experiment was performed on the achromatic nulling in the visible to SIM requirements. The experiment employed phase shifting interferometry techniques on a spectrally-dispersed fringe to measure the phase as a function of wavelength. The phase was then used by a control system which adjusts the tilt of the plates and the air path difference until a satisfactory level of the null was achieved. A fast servo adjusted the air path difference to stabilize the phase to the nanometer level. The design issue and the experimental measure of phase versus wavelength are discussed. A description of the control system and a preliminary measure of the null are presented.
• Burge, J. H. (1999). Efficient testing of off-axis aspheres with test plates and computer-generated holograms. Proceedings of SPIE - The International Society for Optical Engineering, 3782, 348-357.
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  Abstract: Off axis aspheric surfaces, such as individual segments for a telescope mirror, and surfaces that do not have any optical axis are traditionally difficult to test. In addition to difficulties controlling the aspheric shape, mirror segments have tight on radius of curvature and optical axis position. This paper presents a new method of measuring these surfaces that uses a test plate with a spherical reference surface, in combination with a small computer generated hologram to compensate the aspheric departure. The example for measuring 1.8-m segments of a 10-m primary mirror is given.
• Burge, J. H. (1999). Ultra-lightweight, actively controlled mirrors for space. Proceedings of SPIE - The International Society for Optical Engineering, 3749, 84-85.
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  Abstract: Advanced technology mirrors for large space telescopes are being developed that use thin facesheets controlled by actuators. This concept was proven with a 50 cm prototype and is now being implemented for a 2 m cryogenic mirror that weighs only 40 kg. The reflective surface is provided by a glass facesheet, typically 2 mm thick, which is attached to a stiff lightweight support structure through a set of screw-type actuators. This system allows periodic adjustments with the actuators to maintain the surface figure as measured from a wavefront sensor. The optical surface accuracy and stability are maintained by the active system, which can be made using lightweight carbon fiber laminates that economically provide stiffness.
• Burge, J. H., Peper, T., & Jacobs, S. F. (1999). Thermal expansion of borosilicate glass, Zerodur, Zerodur M, and unceramized Zerodur at low temperatures. Optics and Photonics News, 10(5), XII-XIII.
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  Abstract: Current plans for space exploration are calling for more information about materials - at ever lower temperatures. The University of Arizona is making a 2-m prototype mirror for the Next Generation Space Telescope (NGST) to operate at 35 K.1 Previous low temperature measurements of thermal expansion have been limited to temperatures down to 77 K, except for the very low temperature studies of White et al.2,3,4.
• Burge, J., Cuerden, B., Miller, S., Crawford, B., Dorth, H., Sandler, D., & Wortley, R. (1999). Manufacture of a 2-m mirror with glass membrane facesheet and active rigid support. Proceedings of SPIE - The International Society for Optical Engineering, 3782, 123-133.
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  Abstract: A 2-m diameter mirror is being manufactured as a demonstrations for NASA's Next Generation Space Telescope (NGST). This mirror meets the challenging requirements of cryogenic operation and very low mass using an active control system. The mirror system consists of an aluminized glass membrane, 2 mm thick. This membrane is supported and controlled based on wavefront measurements with 169 remotely driven actuators. The system rigidity is provided by a lightweight carbon fiber composite structure. This entire mirror system, 2 meters across weighs less than 40 kg, and will demonstrate 20 nm surface quality in a cryogenic test facility at 35 K.
• Chang, Y., & Burge, J. (1999). Error analysis for CGH optical testing. Proceedings of SPIE - The International Society for Optical Engineering, 3782, 358-366.
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  Abstract: Computer generated holograms are widely used in optical testing and metrology. The primary role of the CGHs is to generate reference wavefront with any desired shape. Optical or electron-beam writers are commonly used for CGH fabrication. Limitations from the hologram fabrication processes cause errors in the reproduced wavefront. Errors in duty-cycle and etching depth have direct impact on both the amplitude and phase functions of the reproduced wavefront. A study using scalar diffraction model to simulate CGH fabrication errors and their effects on wavefront amplitude and phase functions are presented. Experimental analysis confirms the theoretical model. An example is given at the end to demonstrate one of the many applications of the wavefront sensitivity functions in CGH error budgeting for optical metrology.
• Martin, H. M., Allen, R. G., Burge, J. H., Dettmann, L. R., Ketelsen, D. A., Kittrell, W. C., & Miller, S. M. (1999). Polishing of a 6.5 m f/1.25 mirror for the first Magellan telescope. Proceedings of SPIE - The International Society for Optical Engineering, 3739, 47-55.
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  Abstract: We describe the optical fabrication and testing of the 6.5 m f/1.25 primary mirror for the first Magellan telescope. Figuring was performed with a 1.2 m stressed lap, which bends under active control to match the local curvature of the optical surface, and a variety of small passive tools. The figure was measured with IR and visible interferometers, using refractive null correctors to compensate 810 microns of aspheric departure. After subtraction of Seidel astigmatism and spherical aberration, the finished mirror is accurate to 14 nm rms surface error, and has an encircled energy of 80% in 0.06″ diameter at 500 nm.
• Sarlot, R. J., Bresloff, C. J., Burge, J. H., Fitz-Patrick, B. C., McGuire, P. C., Stamper, B. L., & Zhao, C. Y. (1999). Progress report on the optical system for closed-loop testing of the Multiple Mirror Telescope adaptive secondary mirror. Proceedings of SPIE - The International Society for Optical Engineering, 3779, 110-117.
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  Abstract: Steward Observatory is completing the manufacture of a deformable f/15 secondary mirror for the 6.5 m Multiple Mirror Telescope conversion that will, along with the wavefront sensing system, compensate for atmospheric turbulence. A potential difficulty of an adaptive secondary mirror is the ability to verify the commanded mirror shapes of a large convex deformable surface. An optical design is presently being implemented to test the deformable mirror's closed loop control system by optically projecting an artificial star to simulate starlight in the actual telescope. The test system has been designed to verify the control system by fitting into both a laboratory test structure as well as the telescope support structure itself. The optical design relies on two wavelength computer generated holograms used to remove spherical aberration as well as aid in the alignment of the test system optics by projecting alignment patterns.
• Sasian, J. M., Lerner, S. A., & Burge, J. (1999). Certification of a null corrector via a diamond turned asphere: Design and implementation. Proceedings of SPIE - The International Society for Optical Engineering, 3749, 284-285.
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  Abstract: One well-known problem of null correctors used to test astronomical optics is the potential error that they can introduce in the surface under test. This error results from the fabrication or assembly errors of the null corrector itself. One solution to this problem is to certify the null corrector using a computer generated hologram. The holograms are manufactured with a circular laser writing machine, and have demonstrated accuracy of 0.01 waves rms for mirrors as fast as f/1.1. The holograms are designed and manufactured independent from the null correctors, so when the null corrector and the hologram agree, they are assumed to be both correct.
• Sasian, J. M., Lerner, S. A., Burge, J. H., & Martin, H. M. (1999). Design, tolerancing, and certification of a null corrector to test 8.4 meter mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 3739, 444-448.
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  Abstract: A null corrector to test 8.4 m paraboloidal mirrors is presented. A diamond turned aspheric mirror that in conjunction with a hologram provides null corrector certifying redundancy. Introducing redundancy in certification approach permit null corrector to be properly adjusted despite tight tolerances.
• Zhao, C., & Burge, J. H. (1999). Vibration-compensated interferometer for measuring cryogenic mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 3782, 399-406.
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  Abstract: An advanced interferometer was built for measuring large mirrors at cryogenic temperatures. This instrument uses active control to compensate the effects of vibration to allow high resolution phase shift interferometry. A digital signal processor and high speed phase control from an electro-optic modulator allow phase measurements at 4000 Hz. These measurements are fed back to a real time servo in the DSP that provides a vibration-corrected phase ramp for the surface measurements taken at video rates. This instrument is planned to be integrated at NASA Marshall Space Flight Center's X-ray Calibration Facility for measuring NGST mirrors at 40 K.
• Sarlot, R. J., & Burge, J. H. (1998). Optical system for closed-loop testing of adaptive optic convex mirror. Proceedings of SPIE - The International Society for Optical Engineering, 3430, 126-135.
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  Abstract: Steward Observatory is building a deformable f/15 secondary mirror for the 6.5 m Multiple Mirror Telescope conversion that will compensate for atmospheric turbulence. A potential difficulty of an adaptive secondary mirror is the ability to verify the commanded mirror shapes of a large convex deformable surface. A new optical design is presented to test the deformable mirror's closed loop control system by optically projecting an artificial star to simulate starlight in the actual telescope. An optical fiber fed interferometer has been incorporated into the design to measure the deformable mirror's ability to compensate for atmospheric turbulence by measuring the wavefront through an atmospheric turbulence generator. The test system has been designed to verify the control system by fitting into both a laboratory test structure as well as the telescope support structure itself. The optical design relies on two wavelength computer generated holograms used to remove spherical aberration as well as aid in the alignment of the test system optics by projecting alignment patterns.
• Burge, J. H. (1997). Measurement of large convex aspheres. Proceedings of SPIE - The International Society for Optical Engineering, 2871, 362-373.
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  Abstract: Large convex aspheres are notoriously difficult to fabricate because of the tremendous cost and difficulty of making accurate measurements of the optical surfaces. The new 6.5- and 8-m-class telescopes require convex secondary mirrors that are larger, more aspheric, and more accurately figured than those for existing telescopes. Two powerful measurement techniques have been implemented at the Mirror Lab and demonstrated to be accurate and economical. The polished surfaces are interferometrically measured using holographic test plates. This measurement technique uses full-aperture test plates with computer-generated holograms (CGH) fabricated onto spherical reference surfaces. When supported a few millimeters from the secondary and properly illuminated with laser light, an interference pattern is formed that shows the secondary surface errors. The hologram consists of annular rings of metal drawn onto the curved test plate surface using a custom-built writing machine. This test has been implemented for secondaries up to 1.15-m diameter, with 4 nm rms surface measurement accuracy. In addition to this test, a swing arm profilometer was built to measure the rough surface during aspherization and loose abrasive grinding. The machine uses simple motions and high quality components to achieve 50 nm rms measurement accuracy over 1.8-m mirrors.
• Burge, J. H., Fehniger, M. J., & Cole, G. C. (1997). Demonstration of accuracy and flexibility of using CGH test plates for measuring aspheric surfaces. Proceedings of SPIE - The International Society for Optical Engineering, 3134, 379-389.
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  Abstract: A method of interferometrically measuring large convex aspheres using test plates with computer generated holograms was developed at the University of Arizona. We present the results from a set of experiments that demonstrate the accuracy, flexibility, and the simplicity of performing the holographic test. A low-cost stand-alone setup as built for implementing this test on a 38-cm convex hyperboloid. A direct comparison of the CGH measurement with results from a classical Hindle test shows excellent agreement. We also demonstrate the unique attribute of this test to measure bare glass surfaces and highly reflective surfaces without making any modifications to the test equipment. ©2004 Copyright SPIE - The International Society for Optical Engineering.
• Cherkashin, V. V., Churin, E. G., Korol'kov, V. P., Koronkevich, V. P., Kharissov, A. A., Poleshchuk, A. G., & Burge, J. H. (1997). Processing parameter optimization for thermochemical writing of DOEs on chromium films. Proceedings of SPIE - The International Society for Optical Engineering, 3010, 168-179.
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  Abstract: Computer-generated holograms are limited by conventional lithographic fabrication capabilities which rely on accurate deposition, exposure, and developing of photosensitive chemicals. We present an alternate fabrication technology that uses a focused laser beam to write patterns by inducing a thermochemical change in a bare metal film. The patterns are developed using a single etching step that dissolves the non- exposed metal. The thermochemical writing method allows holograms to be directly written onto large-diameter, thick, and non-flat substrates, requiring no intermediate steps that compromise the ultimate accuracy. Circular patterns for optical testing were written using a polar-coordinate laser writer. The laser power and control requirements are shown to be modest and the etching is shown to be tolerant of temperature and concentration variations. The technology is demonstrated with the fabrication of CGHs up to 136 mm in diameter used for optical testing.
• Cole, G. C., Burge, J. H., & Dettmann, L. R. (1997). Vibration stabilization of a phase shifting interferometer for large optics. Proceedings of SPIE - The International Society for Optical Engineering, 3134, 438-446.
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  Abstract: Phase shifting interferometry requires an intentional shifting of the relative phase between the reference arm and the test arm of fan interferometry. Vibration can lead to uncertainty in the relative phase difference with respect to time and result in erroneous surface measurements. We have developed a method for actively compensating for vibration using a closed-loop phase servo system. An essential feature of this is a high frequency phase measurement. The phase is modulated and the intensity variations are measured with a high sped photodiode and digitized. This information is processed by a DSP and a five step algorithm is used to determine the instantaneous phase. These high speed phase measurements are used in a closed loop phase servo to compensate for vibration and also allow for phase shifting interferometry. Test results with and without the vibration compensation will be presented. ©2004 Copyright SPIE - The International Society for Optical Engineering.
• Martin, H. M., Burge, J. H., Ketelsen, D. A., & West, S. C. (1997). Fabrication of the 6.5-m primary mirror for the Multiple Mirror Telescope Conversion. Proceedings of SPIE - The International Society for Optical Engineering, 2871, 399-404.
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  Abstract: The Steward Observatory Mirror Lab is in the process of fabricating the 6.5 m mirror for the conversion of the multiple mirror telescope (MMT) to a single primary mirror. For this purpose the lab has developed a versatile polishing system built around the stressed lap polishing tool. The system must produce an f/1.25 parabolic surface with an accuracy corresponding to 0.09 arcsecond FWHM seeing and 1.5% scattering loss at 500 nm wavelength.
• Smith, B. K., Burge, J. H., & Martin, H. M. (1997). Fabrication of large secondary mirrors for astronomical telescopes. Proceedings of SPIE - The International Society for Optical Engineering, 3134, 51-61.
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  Abstract: A new class of telescope is being built with primary mirrors as large as 8.4 meters in diameter and as fast as f/1. Fabricating the secondary mirrors for these telescopes has presented tough challenges because of their large sizes, up to 1.7 meter diameter; their aspheric departure of more than 300 microns; the required figure accuracy of a few tens of nanometers; and the fact that they are typically convex and difficult to measure. We have developed tools and techniques to meet these demands to produce secondary mirrors efficiently and accurately. A dedicated facility was constructed in the mirror lab that integrates a 1.8-m stressed-lap polishing machine with interferometric and mechanical measuring systems. This paper presents data from a 1.15-m secondary that was finished in our shop, and from two other large mirrors that are currently being fabricated. ©2004 Copyright SPIE - The International Society for Optical Engineering.
• Anderson, D. S., & Burge, J. H. (1995). Swing-arm profilometry of aspherics. Proceedings of SPIE - The International Society for Optical Engineering, 2536, 169-179.
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  Abstract: A profilometer is described that utilizes the swing-arm geometry to provide surface profile measurements of large, highly aspheric surfaces. The profilometer measurement is shown to be robust against stiffness and alignment induced errors in the probe motion.
• Burge, J. H. (1995). Applications of computer-generated holograms for interferometric measurement of large aspheric optics. Proceedings of SPIE - The International Society for Optical Engineering, 2576, 258-269.
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  Abstract: Interferometric optical testing using computer-generated holograms (CGH's) has proven to give highly accurate measurements of aspheric surfaces. New applications of CGH interferometry were developed to support the fabrication of the large, steep mirrors required by the next generation ground-based telescopes. A new test to certify null correctors was designed and implemented that uses small CGH's fabricated onto flat surfaces. This test solves the difficult problem of verifying the accuracy of the null correctors that are used for measuring primary mirrors. Several new techniques for hologram fabrication have been explored for this application. A second new use of CGH's was developed for measuring convex secondary mirrors using test plates with holograms fabricated onto concave spherical reference surfaces. This test provides efficient and accurate measurement of large aspheric convex mirrors. A polar coordinate laser writing machine was built for fabricating these patterns onto curved optical surfaces up to 1.8 meters in diameter and as fast as f/1. These powerful new techniques have been implemented and optimized at the Steward Observatory Mirror Laboratory to guide mirror polishing for large telescope projects. They can also be readily applied for measuring small aspheres to high accuracy.
• Burge, J. H. (1995). Fizeau interferometry for large convex surfaces. Proceedings of SPIE - The International Society for Optical Engineering, 2536, 127-138.
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  Abstract: Measurements of large convex surfaces are notoriously difficult because they require auxiliary optics that are larger than the surface being tested. Fizeau interferometry is well suited for these surfaces because the only surface required to be made to high accuracy is the concave reference surface, which is only slightly larger than the surface being measured. Convex surfaces which are spherical or aspheric can be measured using spherical, aspherical, or holographic test plates. The reference surfaces for these tests must be of good quality and measured to high accuracy. The optical systems that provide illumination and create an image of the interference pattern do not have to be made to high quality. The illumination systems can typically have errors several orders of magnitude larger than the allowable surface measurement errors, so these systems can be made at low cost. Several such systems using low cost aspheric mirrors and lenses for measuring convex spherical and aspherical surfaces are presented.
• Anderson, D. S., Burge, J. H., Ketelsen, D. A., Martin, B., West, S. C., Poczulp, G. A., Richardson, J. H., & Wong, W. (1994). Fabrication and testing of the 3.5-m, f/1.75, WIYN primary mirror. Proceedings of SPIE - The International Society for Optical Engineering, 1994, 193-207.
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  Abstract: The continuing development of rapid fabrication methods for large optics at the Steward Observatory Mirror Lab has resulted in the completion of the WIYN 3.5 m primary mirror in only five months. The use of these methods, though rapid, also resulted in one of the best surface figures we have produced (16 nm rms), excellent microroughness (8 angstroms rms), and very smooth small-scale figure error as determined by the structure function of the surface errors. In this paper, we review the important techniques in the grinding, polishing, and testing of the mirror used to achieve these results.
• Burge, J. H. (1994). Certification of null correctors for primary mirrors. Proceedings of SPIE - The International Society for Optical Engineering, 1994, 248-259.
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  Abstract: An optical test for measuring null correctors has been developed that uses a rotationally symmetric computer-generated hologram (CGH) to synthesize the wavefront that would be reflected by a perfect primary mirror. The test of a null lens is performed by measuring the CGH through the null corrector. Agreement between the null lens and the CGH indicates a high probability that both the null lens and the CGH are correct. This paper presents results that confirm the ease and accuracy of the test. Three null correctors for 3.5-m primary mirrors were measured at the Steward Observatory Mirror Lab using this test. Two of the null correctors were shown to have the correct conic constants within the measurement uncertainty of ± 78 ppm. The test of the third null corrector was limited by gross flaws in the holograms caused by a fabrication error. A proposed solution to the fabrication problem is presented.

Proceedings Publications

• Burge, J. H., & Lewis, B. (2015). Simultaneous Measurement of Both Surfaces of Conformal Windows using Flexible Optical Ray Metrology. In Freeform Optics.
• Huang, R., Su, P., & Burge, J. H. (2015). Deflectometry measurement of Daniel K. Inouye Solar Telescope primary mirror. In SPIE Optical Engineering+ Applications.
• Kim, D. W., Su, P., Oh, C. J., & Burge, J. H. (2015). Extremely Large Freeform Optics Manufacturing and Testing. In Conference on Lasers and Electro-Optics/Pacific Rim.
• Smith, G. A., & Burge, J. H. (2015). Subaperture stitching surface errors due to noise. In SPIE Optical Engineering+ Applications.
• Burge, J. H. (2014). Large optics fabrication and testing at the College of Optical Sciences. In SPIE Optical Engineering+ Applications, 918608--918608.
• Burge, J. H., Kim, D. W., & Martin, H. M. (2014). Process optimization for polishing large aspheric mirrors. In SPIE Astronomical Telescopes+ Instrumentation, 91512R--91512R.
• Burge, J., Su, P., Butel, G., Huang, R., Maldonado, A., & Su, T. (2014). Measuring large mirrors using SCOTS: the software configurable optical test system. In SPIE Astronomical Telescopes+ Instrumentation, 91510Z--91510Z.
• Dominguez, M. Z., Li, J., Zhou, P., & Burge, J. H. (2014). Vertex radius calculation and sensitivity analysis for measuring paraboloidal surfaces with a three-ball spherometer. In Optical Fabrication and Testing, OM3C--5.
• Elazhary, T. T., Zhou, P., Zhao, C., & Burge, J. H. (2014). Analytic Optical Design of Generally Non Axi-Symmetric Optical Systems. In International Optical Design Conference, ITh2A--3.
• Huang, R., Su, P., Su, T., Zhao, Y., Zhao, W., & Burge, J. H. (2014). Study of camera lens effects for a deflectometry surface measurement system: SCOTS. In Optical Fabrication and Testing, JTu5A--7.
• Kim, D. W., Oh, C. J., Su, P., & Burge, J. H. (2014). Advanced Technology Solar Telescope 4.2 m Off-axis Primary Mirror Fabrication. In Optical Fabrication and Testing, OTh2B--3.
• Maldonado, A., Kim, D. W., Su, P., & Burge, J. H. (2014). New Phase Measuring Deflectometry Device for Mid-to-High Spatial Frequency Surface Metrology. In Optical Fabrication and Testing, OW1B--2.
• Martin, H., Allen, R., Burge, J., Cuerden, B., Gressler, W., Hubler, W., Ketelsen, D., Kim, D., Kingsley, J., Law, K., & others, . (2014). Manufacture of the combined primary and tertiary mirrors of the Large Synoptic Survey Telescope. In SPIE Astronomical Telescopes+ Instrumentation, 915125--915125.
• Martin, H., Allen, R., Burge, J., Davis, J., Davison, W., Johns, M., Kim, D., Kingsley, J., Law, K., Lutz, R., & others, . (2014). Production of primary mirror segments for the Giant Magellan Telescope. In SPIE Astronomical Telescopes+ Instrumentation, 91510J--91510J.
• Oh, C., Frater, E., Zhao, C., Burge, J., Lee, H., & Hill, G. (2014). System alignment and performance test of a wide field corrector for the Hobby-Eberly telescope. In Proc. SPIE, 9145, 8.
• Tuell, M. T., Burge, J. H., Cuerden, B., Gressler, W., Martin, H. M., West, S. C., & Zhao, C. (2014). Final acceptance testing of the LSST monolithic primary/tertiary mirror. In SPIE Astronomical Telescopes+ Instrumentation, 91510W--91510W.
• Zhou, P., Burge, J. H., Zhao, C., Benjamin, S., Cuerden, B., & Bouchez, A. (2014). Design of adaptive optics calibration source for the Giant Magellan Telescope. In SPIE Astronomical Telescopes+ Instrumentation, 91484Z--91484Z.
• Zhou, P., Li, J., & Burge, J. H. (2014). An Alternative Approach to Measure the Interferometer Transfer Function. In Optical Fabrication and Testing, OM3C--2.
• Fan, B., Burge, J. H., Martin, H., Zeng, Z., Li, X., & Zhou, J. (2012). Dwell time calculation for computer controlled large tool. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 8515.

Others

• Parks, R. E., Smythe, R. A., Su, P., Burge, J. H., & Angel, R. (2015). System and method for non-contact metrology of surfaces.