Jose M Sasian
 Professor, Optical Sciences
 Professor, Astronomy
 Member of the Graduate Faculty
Contact
 (520) 6213733
 Meinel Optical Sciences, Rm. 532
 Tucson, AZ 85721
 jose.sasian@optics.arizona.edu
Bio
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Courses
202425 Courses

Advanced Lens Design
OPTI 696A (Fall 2024) 
Dissertation
OPTI 920 (Fall 2024) 
Lens Design
OPTI 517 (Fall 2024) 
Master's Report
OPTI 909 (Fall 2024) 
Thesis
OPTI 910 (Fall 2024)
202324 Courses

Independent Study
OPTI 599 (Summer I 2024) 
Directed Graduate Research
OPTI 792 (Spring 2024) 
Dissertation
OPTI 920 (Spring 2024) 
Independent Study
OPTI 599 (Spring 2024) 
Intro to Aberrations
OPTI 518 (Spring 2024) 
Master's Report
OPTI 909 (Spring 2024) 
Optical Shop Practices
OPTI 597A (Spring 2024) 
Optical Spec/Fab/Testing
OPTI 415 (Spring 2024) 
Research
OPTI 900 (Spring 2024) 
Advanced Lens Design
OPTI 696A (Fall 2023) 
Lens Design
OPTI 517 (Fall 2023) 
Master's Report
OPTI 909 (Fall 2023)
202223 Courses

Independent Study
OPTI 599 (Spring 2023) 
Intro to Aberrations
OPTI 518 (Spring 2023) 
Master's Report
OPTI 909 (Spring 2023) 
Optical Shop Practices
OPTI 597A (Spring 2023) 
Optical Spec/Fab/Testing
OPTI 415 (Spring 2023) 
Research
OPTI 900 (Spring 2023) 
Advanced Lens Design
OPTI 696A (Fall 2022) 
Independent Study
OPTI 599 (Fall 2022) 
Lens Design
OPTI 517 (Fall 2022) 
Master's Report
OPTI 909 (Fall 2022) 
Thesis
OPTI 910 (Fall 2022)
202122 Courses

Independent Study
OPTI 599 (Spring 2022) 
Intro to Aberrations
OPTI 518 (Spring 2022) 
Master's Report
OPTI 909 (Spring 2022) 
Optical Shop Practices
OPTI 597A (Spring 2022) 
Thesis
OPTI 910 (Spring 2022) 
Advanced Lens Design
OPTI 696A (Fall 2021) 
Independent Study
OPTI 599 (Fall 2021) 
Lens Design
OPTI 517 (Fall 2021) 
Master's Report
OPTI 909 (Fall 2021) 
Thesis
OPTI 910 (Fall 2021)
202021 Courses

Dissertation
OPTI 920 (Spring 2021) 
Independent Study
OPTI 599 (Spring 2021) 
Intro to Aberrations
OPTI 518 (Spring 2021) 
Master's Report
OPTI 909 (Spring 2021) 
Practical Optical System Dsgn
OPTI 617 (Spring 2021) 
Advanced Lens Design
OPTI 696A (Fall 2020) 
Dissertation
OPTI 920 (Fall 2020) 
Independent Study
OPTI 599 (Fall 2020) 
Lens Design
OPTI 517 (Fall 2020) 
Thesis
OPTI 910 (Fall 2020)
201920 Courses

Dissertation
OPTI 920 (Spring 2020) 
Intro to Aberrations
OPTI 518 (Spring 2020) 
Optical Shop Practices
OPTI 597A (Spring 2020) 
Thesis
OPTI 910 (Spring 2020) 
Advanced Lens Design
OPTI 696A (Fall 2019) 
Dissertation
OPTI 920 (Fall 2019) 
Independent Study
OPTI 499 (Fall 2019) 
Lens Design
OPTI 517 (Fall 2019) 
Thesis
OPTI 910 (Fall 2019)
201819 Courses

Internship
OPTI 493 (Summer I 2019) 
Thesis
OPTI 910 (Summer I 2019) 
Dissertation
OPTI 920 (Spring 2019) 
Intro to Aberrations
OPTI 518 (Spring 2019) 
Master's Report
OPTI 909 (Spring 2019) 
Optical Shop Practices
OPTI 597A (Spring 2019) 
Thesis
OPTI 910 (Spring 2019) 
Advanced Lens Design
OPTI 696A (Fall 2018) 
Dissertation
OPTI 920 (Fall 2018) 
Lens Design
OPTI 517 (Fall 2018) 
Thesis
OPTI 910 (Fall 2018)
201718 Courses

Dissertation
OPTI 920 (Summer I 2018) 
Thesis
OPTI 910 (Summer I 2018) 
Dissertation
OPTI 920 (Spring 2018) 
Independent Study
OPTI 499 (Spring 2018) 
Independent Study
OPTI 599 (Spring 2018) 
Intro to Aberrations
OPTI 518 (Spring 2018) 
Optical Shop Practices
OPTI 597A (Spring 2018) 
Research
OPTI 900 (Spring 2018) 
Thesis
OPTI 910 (Spring 2018) 
Advanced Lens Design
OPTI 696A (Fall 2017) 
Dissertation
OPTI 920 (Fall 2017) 
Independent Study
OPTI 599 (Fall 2017) 
Lens Design
OPTI 517 (Fall 2017) 
Master's Report
OPTI 909 (Fall 2017) 
Thesis
OPTI 910 (Fall 2017)
201617 Courses

Dissertation
OPTI 920 (Spring 2017) 
Intro to Aberrations
OPTI 518 (Spring 2017) 
Master's Report
OPTI 909 (Spring 2017) 
Optical Shop Practices
OPTI 597A (Spring 2017) 
Thesis
OPTI 910 (Spring 2017) 
Dissertation
OPTI 920 (Fall 2016) 
Lens Design
OPTI 517 (Fall 2016) 
Master's Report
OPTI 909 (Fall 2016) 
Thesis
OPTI 910 (Fall 2016)
201516 Courses

Master's Report
OPTI 909 (Summer I 2016) 
Thesis
OPTI 910 (Summer I 2016) 
Dissertation
OPTI 920 (Spring 2016) 
Intro to Aberrations
OPTI 518 (Spring 2016) 
Master's Report
OPTI 909 (Spring 2016) 
Optical Shop Practices
OPTI 597A (Spring 2016) 
Thesis
OPTI 910 (Spring 2016)
Scholarly Contributions
Journals/Publications
 Herman, E., & Sasian, J. (2014). Aberration considerations in lens tolerancing. Applied Optics, 53(3), 341346.More infoAbstract: © 2014 Optical Society of America.Often the tolerancing of an optical system is performed by treating the optical system as a black box in which the designer sets tolerances for perturbations and then runs a Monte Carlo analysis to determine the asbuilt performance. When the effects of the perturbations are not considered, the tolerances might result tighter than necessary, proper compensation might be missed, and manufacturing cost can be increased. By acquiring aberration sensitivity for each type of perturbation, an optical engineer can increase tolerances by ad hoc compensation. An aberration sensitivity evaluation can be performed quickly and can be incorporated into the initial lens design phase. A lens designer can find what surfaces or elements within the optical system will be problematic before any timeconsuming Monte Carlo run is performed. In this paper we use aberration theory of plane symmetric systems to remove, to some useful extent, the blackbox tolerancing approach and to provide some insights into tolerancing. The tolerance sensitivities that are analyzed are with respect to surface tilt, center thickness, index value, and radius. To analyze these perturbations, exact wavefront calculations are performed for the following aberrations: uniform astigmatism, uniform coma, linear astigmatism, distortion I, distortion II, spherical aberration, linear coma, quadratic astigmatism, and cubic distortion. We provide a discussion about how the aberration tolerancing analysis is useful.
 Li, C., & Sasián, J. (2014). Adaptive dispersion formula for index interpolation and chromatic aberration correction. Optics Express, 22(1), 11931202.More infoAbstract: This paper defines and discusses a glass dispersion formula that is adaptive. The formula exhibits superior convergence with a minimum number of coefficients. Using this formula we rationalize the correction of chromatic aberration per spectrum order. We compare the formula with the Sellmeier and Buchdahl formulas for glasses in the Schott catalogue. The six coefficient adaptive formula is found to be the most accurate with an average maximum index of refraction error of 2.91 × 106 within the visible band. © 2014 Optical Society of America.
 Sasian, J., & Acosta, E. (2014). Generation of spherical aberration with axially translating phase plates via extrinsic aberration. Optics Express, 22(1), 289294.More infoAbstract: We show that spherical aberration of all orders can be generated as an extrinsic aberration in a system of axially translating plates. Some practical examples are provided. In particular for two phase plates that are 10 mm in diameter it is possible to generate from 10 to 10 waves of fourthorder spherical aberration with an axial displacement of +/ 0.65 mm. We also apply the phenomenon of extrinsic aberration for the generation of a conical wavefront and other nonaxially symmetric wavefronts, in other words we propose what can be called a generalized zoom plate. © 2014 Optical Society of America.
 Sasián, J. (2014). Polarization fields and wavefronts of two sheets for understanding polarization aberrations in optical imaging systems. Optical Engineering, 53(3).More infoAbstract: Polarization aberrations by highlighting the concepts of polarization aberration fields and of wavefronts of two sheets are explained. The fields have a vector character and are derived from the aberration function of plane symmetric systems. It is shown that in the presence of retardance, an incoming optical field is split into two fields and therefore one can speak of wavefronts of two sheets. Both concepts, polarization aberration fields and wavefronts of two sheets, ease the understanding of polarization aberrations. © 2014 The Authors.
 Acosta, E., & Sasian, J. (2013). MicroAlvarez lenses for a variable dynamic range ShackHartmann wavefront sensor. Technical Digest of the 18th Microoptics Conference, MOC 2013.More infoAbstract: The wellknown Alvarez lenses consist of a pair of aspheric surfaces such that their relative lateral displacement results in an equivalent quadratic phase inducing lens that can be tuned from positive to negative powers by controlling the amount and direction of the displacements. In applications requiring a range of only positive powers, the use of the Alvarez lenses in their original design results in an inefficient use of plate size and equivalent lens aperture. We show formulas to shape the surfaces overcoming this inefficient problem. The design parameters to construct an array of microAlvarez lenses to compose a ShackHartmann wavefront sensor with variable dynamic range is given. © 2013 The Japan Society of Applied Physics.
 Chamadoira, S., Sasian, J., & Acosta, E. (2013). Modified point diffraction interferometer to evaluate tolerances in the design of progressive addition lenses. Proceedings of SPIE  The International Society for Optical Engineering, 8844.More infoAbstract: The main goal of this work is to show the principles, design and performance of a modified point diffraction interferometer to evaluate the local higher order aberrations of progressive addition lenses in order to analyze the tolerances in the design of these ophthalmic components for a reasonable level of comfort by the different users. We also present a detailed analysis of high order aberrations in circular regions within the four most relevant regions of interest of this kind of lenses. © 2013 SPIE.
 Cristina, L., Sasian, J., Stefani, M. A., & Caiado, J. (2013). Twomirror telescope design with thirdorder coma insensitive to decenter misalignment. Optics Express, 21(6), 68516865.More infoPMID: 23546067;Abstract: Misalignments always occur in real optical systems. These misalignments do not generate new aberration forms, but they change the aberration field dependence. Twomirror telescopes have been used in several applications. We analyze a twomirror telescope configuration that has negligible sensitivity to decenter misalignments. By applying the wave aberration theory for planesymmetric optical systems it is shown that the asphericity in the secondary mirror, if properly chosen, can compensate for any decenter perturbation allowing thirdorder coma unchanged across the field of view. For any twomirror system it is possible to find a configuration in which decenter misalignments do not generate fielduniform coma. © 2013 Optical Society of America.
 Elazhary, T. T., Nakano, M., & Sasián, J. (2013). Hyper numerical aperture imaging lens using a thin multi reflection Catadioptric optical element. Optics Express, 21(13), 1580915814.More infoPMID: 23842366;Abstract: Several stateoftheart imaging applications require a large operational spectral band, a large field size, and a high numerical aperture (NA). The design of a lens that simultaneously meets these requirements is a challenging task. We present optical designs of hyper NA imaging systems that comprise a multi reflection optical element. Light entering this element reflects multiple times before exiting. The present lens designs are 1.65 NA imaging system that operate in the broad spectral band [486.1 ∼656.3 nm], have field size of 1.75 mm, and 20X magnification. © 2013 Optical Society of America.
 Herman, E., Sasián, J., & Youngworth, R. N. (2013). Optomechanical considerations for realistic tolerancing. Proceedings of SPIE  The International Society for Optical Engineering, 8844.More infoAbstract: Optical tolerancing simulation has improved so that the modeling of optomechanical accuracy can better predict asbuilt performance. A key refinement being proposed within this paper is monitoring formal interference fits and checking lens elements within their mechanical housings. Without proper checks, simulations may become physically unrealizable and pessimistic, thereby resulting in lower simulated yields. An improved simulation method has been defined and demonstrated in this paper with systems that do not have barrel constraints. The demonstration cases clearly show the trend of the beneficial impact with yield results, as a yield increase of 36.3% to 39.2% is garnered by one example. Considerations in simulating the realistic optomechanical system will assist in controlling cost and providing more accurate simulation results. © 2013 SPIE.
 Reshidko, D., & Sasián, J. (2013). Method of calculation and tables of optothermal coefficients and thermal diffusivities for glass. Proceedings of SPIE  The International Society for Optical Engineering, 8844.More infoAbstract: In a lens system a temperature change has the effect of changing the index of refraction and the geometry of the lens elements. In addition, after a temperature change the lens takes some time to stabilize. As a consequence the optical properties of the nominal lens system change. We review the concepts of the optothermal coefficient and of the thermal diffusivity, and provide a method for their rapid calculation in lens design software. We also provide tables of these coefficients that are needed in a lens tolerancing analysis. © 2013 SPIE.
 Sasian, J., Elazhary, T. T., Nakano, M., & Sasian, J. M. (2013). Hyper numerical aperture imaging lens using a thin multi reflection Catadioptric optical element. Optics express, 21(13).More infoSeveral stateoftheart imaging applications require a large operational spectral band, a large field size, and a high numerical aperture (NA). The design of a lens that simultaneously meets these requirements is a challenging task. We present optical designs of hyper NA imaging systems that comprise a multi reflection optical element. Light entering this element reflects multiple times before exiting. The present lens designs are 1.65 NA imaging system that operate in the broad spectral band [486.1 ~656.3 nm], have field size of 1.75 mm, and 20X magnification.
 Sasián, J. (2013). Polarization fields for understanding polarization aberrations in optical imaging systems. Proceedings of SPIE  The International Society for Optical Engineering, 8841.More infoAbstract: This paper provides a set of polarization aberration fields that are useful for understanding polarization aberrations in optical imaging systems. The aberration function of a plane symmetric system is used to build the polarization fields. Polarization aberration coefficients for a system of spherical surfaces are also given. © 2013 SPIE.
 H., R., Hillenbrand, M., Sinzinger, S., & Sasian, J. (2012). Optical performance of coherent and incoherent imaging systems in the presence of ghost images. Applied Optics, 51(30), 71347143.More infoPMID: 23089763;Abstract: Ghost image analysis is of interest for optical designers as ghost images may degrade image quality in imaging systems. In a previous paper by Abd ElMaksoud and Sasian [Appl. Opt. 50, 2305 (2011)], ghost image analysis for incoherent systems was evaluated using geometrical optics. Some criteria were presented to identify focused ghost images at the nominal image plane. The main goal of this paper is to provide a conceptual understanding of ghost image formation and its impact on the performance of imaging systems using wave theory and Fourier optics. To achieve this goal, a methodology is developed to model ghost images after considering diffraction effects. Expressions for the ghost diffraction point spread function and the ghost transfer function are presented. These functions are used to construct effective point spread and effective transfer functions. To provide insights on the developed theory, some simulation examples are provided and discussed. © 2012 Optical Society of America.
 Liao, L., C., F., Parks, R. E., & Sasian, J. M. (2012). Precision focallength measurement using imaging conjugates. Optical Engineering, 51(11).More infoAbstract: A method for effective focal length measurement using imaging conjugates is discussed and demonstrated. This method is used to determine the effective focal length of an objective lens with precision and without the need to know the exact position of the principal planes by measuring relative distances of imaging conjugates. Focal length determination was done with the aid of an interferometer and with a precision of ±0.054%. A discussion of the method is presented and an error analysis discussed. This method can be used for characterizing optical systems with a wide range of focal lengths because of its simple experimental configuration. © 2012 Society of PhotoOptical Instrumentation Engineers (SPIE).
 Sasián, J., & Youngworth, R. N. (2012). Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 8491, ixx.
 SánchezParedes, J., SilvaOrtigoza, G., CastroRamos, J., & Sasian, J. (2012). 1λ Ronchi tester to obtain the wave front aberration in converging optical systems using phase shifting interferometry. Optica Pura y Aplicada, 45(4), 461473.More infoAbstract: We implement a device to verify in a quantitative way the quality of any converging optical system by making an improvement to the source illumination of the Ronchi test and by implementing the phase shifting interferometry technique (PSI). We describe the design, implementation and verification of this specific device which has the capability to obtain the transversal aberration in two perpendicular directions. Illumination source was a set of LEDs powered with constant current to eliminate variations in the irradiance collected by the camera (CCD), and varying the voltage to increase the intensity of each different wavelength LED we test surfaces with different roughness. The PSI technique was developed by giving movements to the Ronchi ruling with step motors. The device has the capability to test any converging optical systems of either small or large f numbers, and working distances until 5000 mm. Aberrated wavefront with a precision of 1λ was computed when the light source is off axis for any rotationally symmetric mirror. © Sociedad Española de Óptica.
 Acosta, E., & Sasián, J. (2011). Phase plates for generation of variable amounts of primary spherical aberration. Optics Express, 19(14), 1317113178.More infoPMID: 21747471;Abstract: We discuss a set of phase platepairs for the generation of variable amounts of primary spherical aberration. The surface descriptions of these optical plates are provided, and their aberrationgenerating properties are verified with real raytracing. These platepairs are robust in that they allow large tolerances to spacing as well as errors in the relative displacement of the plates. Both primary spherical aberration (r4) and Zernike spherical aberration (6r4 6r2 + 1) can be generated. The amount of spherical aberration is proportional to the platepair displacement and in our example it reaches up to 48 waves (̃8 waves Zernike) for a clear aperture of 25 mm. © 2011 Optical Society of America.
 F.C., B., Liao, L., Montes, A. S., Luis, F., & Sasian, J. (2011). A multiobjective approach in the optimization of optical systems taking into account tolerancing. Proceedings of SPIE  The International Society for Optical Engineering, 8131.More infoAbstract: A MultiObjective approach for lens design optimization was verified. The optimization problem was approached by addressing simultaneously, but separately, image quality and system tolerancing. In contrast to other previous published methods, the error functions were not combined into a single merit function. As a result the method returns a set of nondominated solutions that generates a Pareto Front. Our method resulted in alternate and useful insights about the trade off solutions for a lens design problem. This Multiobjective optimization can conveniently be implemented with evolutionary methods of optimization that have established success in lens design. We provided an example of the insights and usefulness of our approach in the design of a Telephoto lens system using NSGAII, a popular multiobjective evolutionary optimization algorithm. © 2011 SPIE.
 H., R., & Sasian, J. (2011). Modeling and analyzing ghost images for incoherent optical systems. Applied Optics, 50(15), 23052315.More infoPMID: 21614126;Abstract: In a previous paper [Proc. SPIE 7428, 742807 (2009)], a methodology was developed to model and analyze incoherent ghosts that are formed by two reflections in the paraxial regime. In this paper, we extend the previously developed methodology to model and analyze ghost images that are formed by N (even) reflections. Rather than dealing with ghosts as spots of light, we apply the concept that each ghost has a structure in the nonparaxial regime that depends on the optical system parameters. A methodology to determine the fourthorder ghost aberration function is developed. We present new key parameters for ghost image formation, namely the ghost sagittal and tangential image surfaces. An expression for the paraxial ghost image irradiance distribution of the point object at the nominal image plane is derived. Since focused ghosts are the most bothersome ghosts, tools are proposed to identify potential problematic ghosts. Simulation examples are provided and are used to validate the developed methodology. © 2011 Optical Society of America.
 Hsueh, C., Elazhary, T., Nakano, M., & Sasian, J. (2011). Closedform sag solutions for Cartesian oval surfaces. Journal of Optics (India), 40(4), 168175.More infoAbstract: This paper presents a closedform solution to the sag of the Cartesian oval and an alternate iterative method for obtaining the sag. The emphasis is in providing a methodology for determining the sag and derivatives of a Cartesian surface for optical design, raytracing purposes. We verify our results by comparison of our solutions and by real ray tracing. © Optical Society of India 2011.
 Nakazawa, T., Sasian, J., & Abraham, F. K. (2011). Highspeed inline profiler using a modified Fourier transform method for measuring integrated circuit surface profiles. Optical Engineering, 50(5).More infoAbstract: We propose a highspeed surface profiler using a modified Fourier transform profilometry (FTP) approach. Our system geometry is different from a conventional profiler in that the fringeprojection lens and the imaging lens are at different heights from a reference plane. FTP computer simulation and experimental data are provided that supports our theoretical development. Our profiler provides a 1σ rms error of about 4 μm for an integrated circuit chip sample in an area of 14 mm × 6.5 mm with a 0.13 second data acquisition time. It is shown that our theoretical derivation is suitable for a micrometer scale object measurement. © 2011 Society of PhotoOptical Instrumentation Engineers (SPIE).
 Sasián, J., & Youngworth, R. N. (2011). Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 8131, ixx.
 Han, J., Sasian, J., & Gonzálezc, J. (2010). Conic constant tradeoff study in Cassegrain type telescopes with a field corrector. Proceedings of SPIE  The International Society for Optical Engineering, 7787.More infoAbstract: The fabrication and optical performance of a Cassegrain type telescope that employs a field corrector depends on the conic constant of the primary mirror. The design of the field corrector calls for different choices on mirror asphericity which imply a departure from the nominal Cassegrain or RitcheyChrétien solutions. This departure may not be acceptable given that the telescope would not operate properly without the field corrector. In this paper we present a study of the variation of mirror conic constant and field corrector choice of some existing telescopes. We also discuss some tradeoffs in the design of a telescope with a field corrector. © 2010 SPIE.
 Hsueh, C., Lin, P. D., & Sasian, J. (2010). Worstcasebased methodology for tolerance analysis and tolerance allocation of optical systems. Applied Optics, 49(31), 61796188.More infoAbstract: A methodology based on the worstcase approach is proposed for solving the tolerance analysis and tolerance allocation problems for optical systems. Compared with existing methods, the proposed tolerance allocation method has two principal advantages, namely, (1) it is based on an optical geometry gradient matrix and therefore provides means of obtaining the allowable tolerance limits, and (2) it yields the allowable tolerance limits of all the independent variables in the optical system simultaneously. The validity of the proposed methodology is demonstrated using a Dove prism for illustration purposes. © 2010 Optical Society of America.
 Liang, C., Ou, C., & Sasian, J. (2010). Phase shining gratingslit test with a cross slit. Optics Letters, 35(4), 496498.More infoPMID: 20160796;Abstract: A general graphical convolution method for fringe analysis of testing methods that use a spatially incoherent light source is presented. Results are shown for the gratingslit test using optical narrow and cross slits. The convolution method shows that phase shifting gratingslit test can be done with the cross slit at the expense of a reduced fringe contrast ratio. A phase shifting measurement with a crossslit modulator yields high measurement precision and validates our fringe contrast theory. © 2010 Optical Society of America.
 Nakazawa, T., Sasian, J., & Abraham, F. (2010). Fast optical profiler. Optics InfoBase Conference Papers.More infoAbstract: We present the optical design of a fast single shot profiler. A depth resolution of 0.6 micrometer RMS was achieved in an area of 1.2x0.9 mm with a 0.5 second data acquisition time. © 2010 Optical Society of America.
 Sasian, J. (2010). Sixthorder wavefront deformations: The coefficients and insights into wavefront propagation in optical systems. Optics InfoBase Conference Papers.More infoAbstract: The oral presentation of this paper provides historical remarks on the development of aberration theory and discusses the topic of sixthorder wavefront aberrations. We present some insights on wavefront propagation and deformation in optical systems. © Optical Society of America, 2010.
 Sasian, J. (2010). Sixthorder wavefront deformations: The coefficients and insights into wavefront propagation in optical systems. Proceedings of SPIE  The International Society for Optical Engineering, 7652.More infoAbstract: This paper provides a derivation of two key formulas for wavefront propagation and stop shifting to sixthorder of approximation. © 2010 Copyright SPIE  The International Society for Optical Engineering.
 Sasian, J., & Sasian, J. M. (2010). Theory of sixthorder wave aberrations. Applied optics, 49(16).More infoA sixthorder theory of wave aberrations for axially symmetric systems is developed. Specific formulas for the sixthorder extrinsic and intrinsic wave aberration coefficients are given, as well as relations between pupil and image aberrations. Equations are developed for the wavefront propagation to the sixth order of approximation. The concept of the irradiance function is developed, and the secondorder irradiance coefficients are found via conservation of flux at the pupils of the optical system and in terms of pupil aberrations. From purely geometrical considerations a generalized irradiance transport equation that describes irradiance changes in an optical system is derived. Confirming the aberration coefficients with real raytracing data was found to be indispensable.
 Sasian, J., Yuan, S., & Sasian, J. M. (2010). Aberrations of anamorphic optical systems III: the primary aberration theory for toroidal anamorphic systems. Applied optics, 49(35).More infoWe apply a new method for optical aberration derivation to anamorphic systems made from toroidal surfaces and obtain a complete set of primary aberration coefficients. This set is written in a form similar to the wellknown Seidel aberrations for rotationally symmetrical optical systems and includes firstorder quantities only, thus it can be easily applied to anamorphic lens design practice. By tracing four nonskew paraxial marginal and chief rays, the 16 anamorphic primary aberration coefficients can be easily calculated.
 Sasián, J. (2010). Erratum: Theory of sixthorder wave aberrations (Applied Optics (2010) 49 (D69)). Applied Optics, 49(33), 65026503.
 Sasián, J. (2010). Theory of sixthorder wave aberrations. Applied Optics, 49(16), D69D95.More infoPMID: 20517361;Abstract: A sixthorder theory of wave aberrations for axially symmetric systems is developed. Specific formulas for the sixthorder extrinsic and intrinsic wave aberration coefficients are given, as well as relations between pupil and image aberrations. Equations are developed for the wavefront propagation to the sixth order of approximation. The concept of the irradiance function is developed, and the secondorder irradiance coefficients are found via conservation of flux at the pupils of the optical system and in terms of pupil aberrations. From purely geometrical considerations a generalized irradiance transport equation that describes irradiance changes in an optical system is derived. Confirming the aberration coefficients with real raytracing data was found to be indispensable. © 2010 Optical Society of America.
 Sasián, J., & Youngworth, R. N. (2010). Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 7793, ix.
 Wang, L., & Sasian, J. M. (2010). Merit figures for fast estimating tolerance sensitivity in lens systems. Proceedings of SPIE  The International Society for Optical Engineering, 7652.More infoAbstract: We propose two parameters CS and AS for fast estimating sensitivities to constant coma and linear astigmatism in a misaligned lens system. We show that these figures correlate well with actual tolerancing of some lens systems. © 2010 Copyright SPIE  The International Society for Optical Engineering.
 Wang, L., & Sasian, J. M. (2010). Two figures of merit for fast estimating tolerance sensitivity in lens systems. Optics InfoBase Conference Papers.More infoAbstract: We propose two parameters CS and AS for fast estimating sensitivities to constant coma and linear astigmatism in misaligned lens system. We show that the figures correlate well with actual tolerancing of some lens systems. © 2010 Optical Society of America.
 Yuan, S., & Sasian, J. (2010). Aberrations of anamorphic optical systems III: The primary aberration theory for toroidal anamorphic systems. Applied Optics, 49(35), 68026807.More infoPMID: 21151238;Abstract: We apply a new method for optical aberration derivation to anamorphic systems made from toroidal surfaces and obtain a complete set of primary aberration coefficients. This set is written in a form similar to the wellknown Seidel aberrations for rotationally symmetrical optical systems and includes firstorder quantities only, thus it can be easily applied to anamorphic lens design practice. By tracing four nonskew paraxial marginal and chief rays, the 16 anamorphic primary aberration coefficients can be easily calculated. © 2010 Optical Society of America.
 H., R., & Sasian, J. M. (2009). Paraxial ghost image analysis. Proceedings of SPIE  The International Society for Optical Engineering, 7428.More infoAbstract: This paper develops a methodology to model ghost images that are formed by two reflections between the surfaces of a multielement lens system in the paraxial regime. An algorithm is presented to generate the ghost layouts from the nominal layout. For each possible ghost layout, paraxial ray tracing is performed to determine the ghost Gaussian cardinal points, the size of the ghost image at the nominal image plane, the location and diameter of the ghost entrance and exit pupils, and the location and diameter for the ghost entrance and exit windows. The paraxial ghost irradiance point spread function is obtained by adding up the irradiance contributions for all ghosts. Ghost simulation results for a simple lens system are provided. This approach provides a quick way to analyze ghost images in the paraxial regime. © 2009 Copyright SPIE  The International Society for Optical Engineering.
 H., R., Wang, L., Sasian, J. M., & Valencia, V. S. (2009). Depth of field estimation: Theory, experiment, and application. Proceedings of SPIE  The International Society for Optical Engineering, 7429.More infoAbstract: When a fingerprint image is acquired via contactless means, the depth of field must be measured. Due to the natural curvature of a finger, not all of the fingerprint will be in focus. Defocus introduced by such curvature may cause contrast reduction, loss of certain spatial frequencies, blurriness, and contrast reduction and reversal. We need to ensure that the imaging system has enough depth of field to compensate for the longitudinal displacement created by the finger curvature. This paper presents theoretical and experimental techniques to simulate and measure the depth of field of an imaging system. Experimentally, image contrast as a function of object position along the optical axis is measured for several spatial frequencies of interest, and the defocused modulation transfer function (MTF) is determined. The acceptable contrast range is defined by the system application and used to determine the corresponding depth of field. A diffraction image irradiance theoretical model is developed, and the Zemax optical design program is used to simulate depth of field. The experimental and simulated depthoffield results are presented and applied to a contactless fingerprint sensor. © 2009 Copyright SPIE  The International Society for Optical Engineering.
 Lee, S., & Sasian, J. (2009). Ronchigram quantification via a noncomplementary darkspace effect. Optics Express, 17(3), 18541858.More infoPMID: 19189015;Abstract: We observe a noncomplementary darkspace produced when two Ronchigrams, at zerophase and πphase, are overlapped and use these dark spaces to quantify Ronchigrams. Diffraction and multiple beam interference effects narrow the Ronchi fringes created with a coherent point source illumination and prevent accurate determination of the geometrical fringe edges. The dark spaces created when the intensity of two Ronchi grams is added allow assessing the geometrical edge at the dark space middle providing a way to reduce measurement errors. We reconstruct the wavefront deformation in a test beam with a 35term Zernike polynomial. Experimental results are presented. © 2009 Optical Society of America.
 Moore, L. B., Hvisc, A. M., & Sasian, J. (2009). Erratum: Aberration fields of a combination of plane symmetric systems (Optical Express (2008) 16 (1565515670)). Optics Express, 17(17), 1539015391.
 Sasian, J., & Youngworth, R. N. (2009). Proceedings of SPIE  The International Society for Optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 7433, ix.
 Sasian, J., Yuan, S., & Sasian, J. M. (2009). Aberrations of anamorphic optical systems. I: The firstorder foundation and method for deriving the anamorphic primary aberration coefficients. Applied optics, 48(13).More infoWe suggest that, in the paraxial region, a doubleplane symmetric optical system (anamorphic system) can be treated as two associated rotationally symmetric optical systems (RSOS). We find that paraxial quantities in the anamorphic system can be expressed as linear combinations of the paraxial marginal and chief rays traced in the two associated RSOS. As a result, we provide a set of equations that are key to derive the primary aberration coefficients for various anamorphic optical system types. By applying the generalized Aldis theorem to anamorphic optical systems, we build up the anamorphic total ray aberration equations. These equations can be reduced to thirdorder form, that is, the anamorphic primary ray aberration equations. We find that the terms in the anamorphic primary ray aberration equations can be expressed as paraxial marginal and chief raytrace data in the two associated RSOS, together with normalized object and stop coordinates. More importantly, we build up a novel method for deriving the anamorphic primary aberration coefficients for anamorphic optical systems of various types.
 Sasian, J., Yuan, S., & Sasian, J. M. (2009). Aberrations of anamorphic optical systems. II. Primary aberration theory for cylindrical anamorphic systems. Applied optics, 48(15).More infoBy applying a new method for aberration derivation to anamorphic systems made from cylindrical surfaces, we obtain a complete set of primary aberration coefficients. This set is in a form similar to the wellknown Seidel aberrations for rotationally symmetrical optical systems (RSOS). The aberration coefficients include firstorder quantities only. By tracing four nonskew paraxial marginal and chief rays in the two associated RSOS of the anamorphic system, the aberration coefficients can be derived.
 Wang, L., H., R., Sasian, J. M., & Valencia, V. S. (2009). Illumination scheme for highcontrast, contactless fingerprint images. Proceedings of SPIE  The International Society for Optical Engineering, 7429.More infoAbstract: Illumination is critical to achieve highcontrast, contactless fingerprint images. In this paper, we report results of fingerprint imaging experiments performed under different illumination conditions. We studied how polarization states, illumination wavelength, detection wavelength, and illumination direction influence the contrast of fingerprint images. Our research findings provide a selection rule for optimum illumination and a basis for us to construct an illuminator that generates uniform illumination and highcontrast contactless fingerprint images. © 2009 Copyright SPIE  The International Society for Optical Engineering.
 Wang, L., H., R., Sasian, J. M., Kuhn, W. P., Gee, K., & Valencia, V. S. (2009). A novel contactless alivenesstesting (CAT) fingerprint sensor. Proceedings of SPIE  The International Society for Optical Engineering, 7429.More infoAbstract: A contactless fingerprint sensor provides deformationfree, highquality fingerprint images and offers users a cleaner and more comfortable measurement environment. Here we propose and design an innovative prototype optical, contactless, compact, fingerprint sensor that quickly produces highquality, highcontrast interoperable fingerprint images. A proofof concept contactless, alivenesstesting (CAT) fingerprint sensor, which is connected to a PC via a firewire cable, was constructed and is currently operating in our laboratory. The CAT sensor affords a more userfriendly interface compared to existing contactless fingerprint sensors and also provides robust aliveness testing and spoof detection. In this paper, we present the imaging system design concepts, finger aliveness detection techniques, and the userfriendly interface approach. Various fingerprint matching results using the CAT sensor device are also presented and discussed. © 2009 Copyright SPIE  The International Society for Optical Engineering.
 Wang, L., Sasián, J. M., Peng, S. u., & Koshel, R. J. (2009). Generation of uniform illumination using faceted reflectors. Proceedings of SPIE  The International Society for Optical Engineering, 7423.More infoAbstract: Faceted reflectors are widely used for providing uniform illumination in many commercial lighting products. In this paper, some approaches of constructing faceted reflectors in commercial software are discussed. Two new methods for generating nonrotationally symmetric patterns such as square/rectangular illumination patterns using curvedfaceted reflectors are proposed and also explored in commercial software. The performances of various reflectors are compared using Monte Carlo raytracing. © 2009 Copyright SPIE  The International Society for Optical Engineering.
 Yang, B., Wang, Y., Liu, Y., Sasian, J., & Koshel, J. (2009). Efficient raytracing for freeform reflectors. Optik, 120(1), 4044.More infoAbstract: Efficient raytracing is the basis for computeraided design and analysis of illumination optical systems, which requires the sampling of hundreds of thousands of rays to achieve accurate results of illumination analysis. One type of most widely used illumination systems is freeform segmented reflectors with Bspline surfaces. An iterative method is used to calculate the coordinates of the intersection point of an incident ray with a Bspline surface in 3D space. Formulae are given to calculate the direction cosines of the surface normal at the intersection point, so that the direction cosines of the reflected ray can be obtained. For segmented reflectors, a method is presented to rapidly determine the segment with which the incident ray strikes. Experimental results show that the scheme proposed in this paper can perform raytracing through freeform reflectors with excellent efficiency, and is suitable for use in CAD software for vehicle headlights, for example. © 2007 Elsevier GmbH. All rights reserved.
 Yuan, S., & Sasian, J. (2009). Aberrations of anamorphic optical systems. I: The firstorder foundation and method for deriving the anamorphic primary aberration coefficients. Applied Optics, 48(13), 25742584.More infoPMID: 19412218;Abstract: We suggest that, in the paraxial region, a doubleplane symmetric optical system (anamorphic system) can be treated as two associated rotationally symmetric optical systems (RSOS). We find that paraxial quantities in the anamorphic system can be expressed as linear combinations of the paraxial marginal and chief rays traced in the two associated RSOS. As a result, we provide a set of equations that are key to derive the primary aberration coefficients for various anamorphic optical system types. By applying the generalized Aldis theorem to anamorphic optical systems, we build up the anamorphic total ray aberration equations. These equations can be reduced to thirdorder form, that is, the anamorphic primary ray aberration equations. We find that the terms in the anamorphic primary ray aberration equations can be expressed as paraxial marginal and chief raytrace data in the two associated RSOS, together with normalized object and stop coordinates. More importantly, we build up a novel method for deriving the anamorphic primary aberration coefficients for anamorphic optical systems of various types. © 2009 Optical Society of America.
 Yuan, S., & Sasian, J. (2009). Aberrations of anamorphic optical systems. II. primary aberration theory for cylindrical anamorphic systems. Applied Optics, 48(15), 28362841.More infoPMID: 19458731;Abstract: By applying a new method for aberration derivation to anamorphic systems made from cylindrical surfaces, we obtain a complete set of primary aberration coefficients. This set is in a form similar to the wellknown Seidel aberrations for rotationally symmetrical optical systems (RSOS). The aberration coefficients include firstorder quantities only. By tracing four nonskew paraxial marginal and chief rays in the two associated RSOS of the anamorphic system, the aberration coefficients can be derived. © 2009 Optical Society of America.
 Moore, L. B., Hvisc, A. M., & Sasian, J. (2008). Aberration fields of a combination of plane symmetric systems. Optics Express, 16(20), 1565515670.More infoPMID: 18825204;Abstract: By generalizing the wave aberration function to include plane symmetric systems, we describe the aberration fields for a combination of plane symmetric systems. The combined system aberration coefficients for the fields of spherical aberration, coma, astigmatism, defocus and distortion depend on the individual aberration coefficients and the orientations of the individual plane symmetric component systems. The aberration coefficients can be used to calculate the locations of the field nodes for the different types of aberration, including coma, astigmatism, defocus and distortion. This work provides an alternate view for combining aberrations in optical systems. © 2008 Optical Society of America.
 Sasian, J. (2008). Optical design of reflective widefield cameras. Proceedings of SPIE  The International Society for Optical Engineering, 7060.More infoAbstract: This paper discusses some methodologies that apply to the optical design of reflective widefield cameras. Among the methods considered are offaxis and eccentric pupil systems, concatenation of systems, tilted component systems, aberration theory, and confocal systems. The goal of the paper is to review design methods. In particular some systems are shown to illustrate two methodologies. © 2008 Copyright SPIE  The International Society for Optical Engineering.
 Sasian, J. M., & Youngworth, R. N. (2008). Optical System Alignment and Tolerancing II: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 7068, ix.
 Sasian, J., Moore, L. B., Hvisc, A. M., & Sasian, J. M. (2008). Aberration fields of a combination of plane symmetric systems. Optics express, 16(20).More infoBy generalizing the wave aberration function to include plane symmetric systems, we describe the aberration fields for a combination of plane symmetric systems. The combined system aberration coefficients for the fields of spherical aberration, coma, astigmatism, defocus and distortion depend on the individual aberration coefficients and the orientations of the individual plane symmetric component systems. The aberration coefficients can be used to calculate the locations of the field nodes for the different types of aberration, including coma, astigmatism, defocus and distortion. This work provides an alternate view for combining aberrations in optical systems.
 Liang, C., & Sasian, J. (2007). Geometrical optics modeling of the gratingslit test. Optics Express, 15(4), 17381744.More infoPMID: 19532411;Abstract: A novel optical testing method termed the gratingslit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the gratingslit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometricaloptics model for the gratingslit test is presented and the fringe contrast ratio with respect to the slit width and objectgrating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio. © 2007 Optical Society of America.
 Sasian, J. M., & Ruda, M. C. (2007). Proceedings of SPIE  The International Society for Optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 6676, vii.
 Sasian, J., Quick, J., Sheffield, J., Caudill, J., & Yantzer, P. (2007). Evaluation of brilliance, fire, and scintillation in round brilliant gemstones. Optical Engineering, 46(9).More infoAbstract: We discuss several illumination effects in gemstones and present maps to evaluate them. The matrices and tilt views of these maps permit one to find the stones that perform best in terms of illumination properties. By using the concepts of the main cutter's line, and the anticutter's line, the problem of finding the best stones is reduced by one dimension in the cutter's space. For the first time it is clearly shown why the Tolkowsky cut, and other cuts adjacent to it along the main cutter's line, is one of the best round brilliant cuts. The maps we introduce are a valuable educational tool, provide a basis for gemstone grading, and are useful in the jewelry industry to assess gemstone performance. © 2007 Society of PhotoOptical Instrumentation Engineers.
 Martin, H. M., Allen, R. G., Cuerden, B., Hill, J. M., Ketelsen, D. A., Miller, S. M., Sasian, J. M., Tuell, M. T., & Warner, S. (2006). Manufacture of the second 8.4 m primary mirror for the Large Binocular Telescope. Proceedings of SPIE  The International Society for Optical Engineering, 6273 I.More infoAbstract: The second 8.4 m primary mirror and its active support system were delivered to the Large Binocular Telescope in September 2005. The mirror was figured to an accuracy of 15 nm rms surface after subtraction of loworder aberrations that will be controlled by the active support. The mirror was installed into its operational support cell in the lab, and support forces were optimized to produce a figure accurate to 20 nm rms surface with no synthetic correction. The mirror was polished on a new 8.4 m polishing machine that gives the Mirror Lab the capacity to process up to four 8.4 m mirrors simultaneously, with each mirror going through a sequence of stations: casting furnace, generating machine, polishing machine, and integration with its support cell. The new polishing machine has two carriages for polishing tools, allowing use of two 1.2 m stressed laps during looseabrasive grinding and early polishing, followed by final figuring with a stressed lap and a small tool for local figuring.
 Sasian, J. (2006). Interpretation of pupil aberrations in imaging systems. Proceedings of SPIE  The International Society for Optical Engineering, 6342 I.More infoAbstract: We show that thirdorder pupil aberrations in an axially symmetric imaging system represent the basic stretches or deformations that the cross section of a beam can have at the exit pupil. © 2006 SPIEOSA.
 Sasian, J. M., & Turner, M. G. (2006). Proceedings of SPIE  The International Society for Optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 6289, xi.
 Cheng, X., Wang, Y., Hao, Q., & Sasian, J. M. (2005). Expert system for generating initial layouts of zoom systems with multiple moving lens groups. Optical Engineering, 44(1), 18.More infoAbstract: An expert system is developed for the automatic generation of initial layouts for the design of zoom systems with multiple moving lens groups. The Gaussian parameters of the zoom system are optimized using the dampedleastsquares method to achieve smooth zoom cam curves, with the fnumber of each lens group in the zoom system constrained to a rational value. Then each lens group is selected automatically from a database according to its range of fnumber, field of view, and magnification ratio as it is used in the zoom system. The lens group database is established from the results of analyzing thousands of zoom lens patents. Design examples are given, which show that the scheme is a practical approach to generate starting points for zoom lens design. © 2005 Society of PhotoOptical Instrumentation Engineers.
 DeBoo, B. J., Sasian, J. M., & Chipman, R. A. (2005). Depolarization of diffusely reflecting manmade objects. Applied Optics, 44(26), 54345445.More infoPMID: 16161657;Abstract: The polarization properties of light scattered or diffusely reflected from seven different manmade samples are studied. For each diffusely reflecting sample an inplane Mueller matrix bidirectional reflectance distribution function is measured at a fixed bistatic angle using a Mueller matrix imaging polarimeter. The measured profile of depolarization index with changing scattering geometry for most samples is well approximated by an inverted Gaussian function. Depolarization is minimum for specular reflection and increases asymptotically in a Gaussian fashion as the angles of incidence and scatter increase. Parameters of the Gaussian profiles fitted to the depolarization data are used to compare samples. The dependence of depolarization on the incident polarization state is compared for each Stokes basis vector: horizontal, vertical, 45°, 135°, and right and leftcircular polarized light. Linear states exhibit similar depolarization profiles that typically differ in value by less than 0.06 (where 1.0 indicates complete depolarization). Circular polarization states are depolarized more than linear states for all samples tested, with the output degree of polarization reduced from that of linear states by as much as 0.15. The depolarization difference between linear and circular states varies significantly between samples. © 2005 Optical Society of America.
 Peng, S. u., Hudman, J., Sasian, J. M., & Dallas, W. J. (2005). Dual beam generation at a ray caustic by a multiplexing computergenerated hologram. Optics Express, 13(13), 48434847.More infoPMID: 19498469;Abstract: Computer generated holograms (CGHs) are used for testing aspherical surfaces. They are also used for certifying null lens systems that are in turn used to test large aspheric mirrors. We demonstrate that, in order to minimize size, a nullcorrectorcertifying CGH can be located at a ray caustic. This placement minimizes the required size of the CGH and so makes it possible to certify some null correctors that otherwise, due to current size limitations of highprecision CGHs, could not be certified. Fabrication limits of precision CGHs are in the size range of 200250 mm and one part in 105 in feature placement. Our proof of principle involves a CGH that is about 20mm in diameter with a fabrication tolerance of one part in 104. ©2005 Optical Society of America.
 Sasian, J. (2005). From the landscape lens to the planar lens: A reflection on teaching lens design. Proceedings of SPIE  The International Society for Optical Engineering, 5865, 111.More infoAbstract: We review how optical aberration correction principles were applied in the design of classical photographic lenses. This makes the teaching of lens design more meaningful and interesting since a logical approach to understanding the increasing complexity of objective lenses is used.
 Sasián, J. M., Koshel, R. J., & Juergens, R. C. (2005). Proceedings of SPIE  The International Society for Optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 5875, ixx.
 CastroRamos, J., & Sasian, J. (2004). Automatic phase shifting Ronchi tester with a square Ronchi ruling. Proceedings of SPIE  The International Society for Optical Engineering, 5532, 199210.More infoAbstract: The Ronchi test is one of the simplest and most effective methods used for evaluating and measuring aberrations. Employed in optical shops, its use is limited to qualitative analysis. Few methods in use today produce quantitative results. What follows are explained both the development and the guidelines for manufacturing a Ronchi tester based on quantitative analysis which also has the advantage to receive automatic input and output of data. In order to achieve this goal, phase shifting interferometry and a square Ronchi ruling with a variable intensity LED were used. It is important to note that with the set up described only one movement of the motor which supports the square ruling is needed to simultaneously obtain both the X and Y components of the wave front aberration.
 DeBoo, B., Sasian, J., & Chipman, R. (2004). Degree of polarization surfaces and maps for analysis of depolarization. Optics Express, 12(20), 49414958.More infoPMID: 19484049;Abstract: The concept of degree of polarization surfaces is introduced as an aid to classifying the depolarization properties of Mueller matrices. Degree of polarization surfaces provide a visualization of the dependence of depolarization on incident polarization state. The surfaces result from a nonuniform contraction of the Poincaré sphere corresponding to the depolarization properties encoded in a Mueller matrix. For a given Mueller matrix, the degree of polarization surface is defined by moving each point on the unit Poincaré sphere radially inward until its distance from the origin equals the output state degree of polarization for the corresponding input state. Of the sixteen elements in a Mueller matrix, twelve contribute to the shape of the degree of polarization surface, yielding a complex family of surfaces. The surface shapes associated with the numerator and denominator of the degree of polarization function are analyzed separately. Protrusion of the numerator surface through the denominator surface at any point indicates nonphysical Mueller matrices. Degree of polarization maps are plots of the degree of polarization on flat projections of the sphere. These maps reveal depolarization patterns in a manner well suited for quantifying the degree of polarization variations, making degree of polarization surfaces and maps valuable tools for categorizing and classifying the depolarization properties of Mueller matrices. © 2004 Optical Society of America.
 Palusinski, I. A., & Sasián, J. M. (2004). Sag and phase descriptions for null corrector certifiers. Optical Engineering, 43(3), 697701.More infoAbstract: Null correctors are important in the fabrication of aspheric optics. Although null correctors simplify testing of aspheric surfaces, they can increase the risk of fabricating aspheric surfaces. Undetected errors in the null corrector will result in an aspheric surface that does not meet design specifications. To prevent such problems, a null corrector is certified prior to using it to test an aspheric surface during fabrication. Certification verifies that the null corrector has been produced properly. Current methods of certification that include computergenerated holograms and diamondturned mirrors require a mathematical description of the certifier. We provide sag and phase formulas for describing such certifiers. The formulas can be used to define certifiers for a broad range of aspheric surfaces. For each aspheric test surface, the specific certifier parameters are found through optimization using default merit functions. Via two different aspheric surfaces, we demonstrate the usefulness and simplicity of our truncatedseries sag and phase formulas to define certifiers. © 2004 Society of PhotoOptical Instrumentation Engineers.
 Sasián, J. M., Koshel, R. J., Manhart, P. K., & Juergens, R. C. (2004). Proceedings of SPIE  The Internationl Society for optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 5524, xixii.
 Cheng, X., Wang, Y., Hao, Q., & Sasian, J. (2003). Automatic element addition and deletion in lens optimization. Applied Optics, 42(7), 13091317.More infoPMID: 12638887;Abstract: A mechanism is established for the automatic addition and deletion of optical elements during the course of lens optimization. Two lensform parameters, quantifying the symmetry of the optical system and the opticalpower distribution among the individual lens elements, are used as criteria in this automatic procedure. Design examples are provided that demonstrate the practicability of the scheme. © 2003 Optical Society of America.
 DeBoo, B., & Sasian, J. (2003). Precise focallength measurement technique with a reflective Fresnelzone hologram. Applied Optics, 42(19), 39033909.More infoPMID: 12868829;Abstract: A new technique for precise focallength measurements with a hologram is presented. This technique is widely applicable and is particularly useful for measuring large, slow lenses. In diffraction, the Fresnelzone plate hologram emulates the reflective properties of a convex spherical mirror for use during transmission null tests of an optic by use of a phaseshifting interferometer. The hologram is written lithographically and therefore offers a higher degree of precision at a lower cost than its spherical mirror counterpart. A hologram offers the additional benefit of easy characterization by use of the same interferometer employed in examining the test optic. Better than ±0.01% precision is achieved during measurement of a 9m focallength lens by use of a 150mm aperture interferometer. © 2003 Optical Society of America.
 Sasian, J., DeBoo, B., & Sasian, J. M. (2003). Precise focallength measurement technique with a reflective Fresnelzone hologram. Applied optics, 42(19).More infoA new technique for precise focallength measurement with a hologram is presented. This technique is widely applicable and is particularly useful for measuring large, slow lenses. In diffraction, the Fresnelzone plate hologram emulates the reflective properties of a convex spherical mirror for use during transmission null tests of an optic by use of a phaseshifting interferometer. The hologram is written lithographically and therefore offers a higher degree of precision at a lower cost than its spherical mirror counterpart. A hologram offers the additional benefit of easy characterization by use of the same interferometer employed in examining the test optic. Better than +/0.01% precision is achieved during measurement of a 9m focallength lens by use of a 150mm aperture interferometer.
 Sasián, J. M., Koshel, R. J., & Manhart, P. K. (2003). Proceedings of SPIE  The International Society for Optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 5174, ix.
 Sasián, J. M., Yantzes, P., & Tivol, T. (2003). The Optical Design of Gemstones. Optics and Photonics News, 14(4), 2429.More infoAbstract: The role of optics in gemstone design along with related trends in the gemstone industry is discussed. The article describes how advanced optical design software is being used to optimize gemstones by modeling light propagation through stones. A device called the Firescope which is used to test gemstones is also discussed.
 DeBoo, B. J., & Sasian, J. M. (2002). Novel method for precise focal length measurement. Proceedings of SPIE  The International Society for Optical Engineering, 4832, 114121.More infoAbstract: A new technique for precise focal length measurements by use of a hologram is presented. The hologram is used in first order diffraction to emulate the reflective properties of a convex spherical mirror when performing null tests with a phaseshifting interferometer. The hologram, comprised of concentric reflective rings (much like a Fresnel zone plate), is written lithographically and offers a higher degree of precision, at lower cost, than its spherical mirror counterpart and many other potential measurement techniques.
 Kremer, R. M., DeBoo, B., & Sasián, J. M. (2002). Null corrector design for white light scatterplate interferometry on a large conic surface. Optical Engineering, 41(11), 28692875.More infoAbstract: A novel null corrector design for use with a white light scatterplate interferometer on a large conic surface is presented. In this design, an aspheric diamondturned mirror (DTM), hereafter called the nullcorrecting mirror (NCM), exactly cancels out the spherical aberration of the mirror under test. Lowpower refractive elements correct field aberrations over the finite aperture of the scatterplate. The null corrector maintains a phase difference between the test and reference beams of less than 1/2 wave over the finite field size of the scatterplate for optimal fringe visibility. The null corrector can be certified using another smaller DTM and/or a computergenerated hologram. The design has the significant advantages of being small in size, less expensive than designs using spherical surfaces (due to the small size of the NCM), and useable with other interferometers. We include discussions on the calculation of the surface profile for the NCM and certifying mirror, field correction, and achromatization. © 2002 Society of PhotoOptical Instrumentation Engineers.
 Laughlin, L., & Sasian, J. M. (2002). Source modeling and calculation of mask illumination during extreme ultraviolet lithography condenser design. Proceedings of SPIE  The International Society for Optical Engineering, 4832, 283292.More infoAbstract: Lithography condensers must create very uniform illumination at the mask plane. The nonuniformity in the illumination is required to be less than 1%. To meet this requirement a designer must use a method for determining the illumination created on the mask plane during the design of the condenser system. This paper describes a method for calculating the illumination at a plane in a lithography condenser system. This method is a general one that is applicable to many systems besides those for extreme ultraviolet lithography (EUVL). Our methodology uses reverse ray tracing to accurately and efficiently determine illumination in a system during the design phase. The technique is used with a standard optical design software package. This enables the system designer to test the illumination uniformity of the design with the same software that is used for the design work itself. Therefore, the user is not required to use illumination specific software to model the illumination properties for the design. Implementation of this new methodology necessitates accurate modeling of a source in the optical software. The technique for modeling sources using apodization files is described. Results are shown for point sources, multiple point source configurations, and finite sources that have nontrivial surface radiance distributions. In some cases, the results of our method are compared to those found using a traditional technique of calculating illumination.
 Sasian, J. M., & Koshel, R. J. (2002). Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 4768, vii.
 Kremer, R. M., DeBoo, B. J., & Sasian, J. M. (2001). Null corrector design for white light scatterplate interferometry on a large conic surface. Proceedings of SPIE  The International Society for Optical Engineering, 4442, 2633.More infoAbstract: We present a method for designing and testing a null corrector for use with scatterplate interferometry on a large conic mirror. The null corrector in a scatterplate interferometer must maintain OPD of less than 1/2 wave over a finite field size for optimal fringe visibility. Our design uses an aspheric diamondturned mirror (DTM) to exactly cancel out the spherical aberration of the surface under test. The DTM has the additional benefit of being useable in other types of interferometers for testing of the conic surface in a null condition. Low power refractive elements correct field aberrations over the finite aperture of the scatterplate. The null corrector can be certified using another smaller DTM or a computer generated hologram (CGH). This design has the advantages of being small in size, less expensive than designs using spherical surfaces (due to the small size of the nullcorrecting mirror), useable with other interferometers, and easy to align.
 Lerner, S., & Sasian, J. (2001). Parametrically defined surfaces reduce error. Laser Focus World, 37(5), 165168.More infoAbstract: Aspheric optical surfaces defined parametrically can have vastly lower residual errors than traditional polynomial representations, and can take less time to design.
 Liang, C., Descour, M. R., Sasian, J. M., & Lerner, S. A. (2001). Multilayercoatinginduced aberrations in extremeultraviolet lithography optics. Applied Optics, 40(1), 129135.More infoPMID: 18356983;Abstract: A multilayer coating alters the amplitude and phase of a reflected wave front. The amplitude effects are multiplicative and well understood. We present a mathematical formalism that can be used to describe the phase effects of coating in a general case. On the basis of this formalism we have developed an analytical method of estimating the wavefront aberrations introduced by the multilayer coating. For the case of fieldindependent aberrations, we studied both uniform and graded multilayer coatings. For the case of fielddependent aberrations, we studied only the effects of a uniform multilayer coating. Our analysis is based on a coated plane mirror tilted with respect to an incident converging beam. Altogether we have found, up to the second order, the following aberrations: a fielddependent piston, a fieldsquareddependent piston, defocus, fieldindependent tilt, fieldindependent astigmatism, and anamorphic magnification. To obtain numerical results we apply our analysis to the specific case of a plane mirror tilted 8.2 deg with respect to an incident converging beam with a numerical aperture of 0.1. We find that the magnitudes of the fieldindependent aberration coefficients for the graded coating are approximately ten times smaller than those for the uniform coating. We show that a coating can introduce anamorphic magnification. © 2001 Optical Society of America.
 Sasian, J. M. (2001). Trends in teaching lens design. Proceedings of SPIE  The International Society for Optical Engineering, 4588, 5658.More infoAbstract: Lens design is a widely spread field of optical engineering and virtually all opticaldevices that are manufactured involve some lens design. Lens design is considered at the University of Arizona as an important discipline and courses are offered at the Master's and Ph. D. levels. Although lens design involves simple geometrical concepts, the grasp by students of this discipline is not easy. It takes time, repetition of concepts, and homework exercises for students to grasp and then master the subject. Therefore, we have carefully chosen our approach to teaching lens design so that students, after two courses are prepared to do useful work at the industry level. In this paper we present our approach to teaching lens design.
 Sasian, J. M., & Manhart, P. K. (2001). Erratum: (Novel Optical Systems Design and Optimization IV (12 August 2001)). Proceedings of SPIE  The International Society for Optical Engineering, 4442, 157.
 Sasian, J. M., & Manhart, P. K. (2001). Proceedings of SPIE  The International Society for Optical Engineering: Introduction. Proceedings of SPIE  The International Society for Optical Engineering, 4442, vii.
 Sasián, J. M., Lerner, S. A., Lin, T. Y., & Laughlin, L. (2001). Ray and van CittertZernike characterization of spatial coherence. Applied Optics, 40(7), 10371043.More infoPMID: 18357087;Abstract: We discuss a ray and a van CittertZernike characterization of spatial coherence in condensers for projection systems. We present a rule of thumb with which to estimate the modulus of the coherence function at a given point of the illuminated object and a raytracing methodology with which to determine this modulus. For uniform illumination of the pupil we relate the modulus of the coherence function and the pupilfilling factor. We suggest that the rms of the angular ray spread at a given object point is an appropriate metric with which to characterize local coherence properties. © 2001 Optical Society of America.
 Lerner, S. A., & Sasian, J. M. (2000). Novel aspheric surfaces for optical design. Proceedings of SPIE  The International Society for Optical Engineering, 4092, 1725.More infoAbstract: New functional representations are needed for describing aspheric surfaces that can compensate for a high degree of wavefront asphericity and represent steeply sloped surfaces as the surface normal becomes perpendicular to the optical axis. The explicit definition of the standard aspheric surface limits the range of surfaces that it can properly describe. This paper presents both a parametrically defined surface approach and an implicitly defined surface approach. The utility of these novel approaches is demonstrated using examples of current interest. Additionally, this work shows that a Fourier series is not a useful optical surface.
 Lerner, S. A., & Sasian, J. M. (2000). Optical design with parametrically defined aspheric surfaces. Applied Optics, 39(28), 52055213.More infoPMID: 18354517;Abstract: The standard aspheric surface definition has been used successfully to correct aberrations in a wide variety of systems. However, in some current applications a more general surface definition is needed. We present a more general approach that uses parametrically defined optical surfaces for the optical design of imaging and illumination systems. © 2000 Optical Society of America.
 Lerner, S. A., & Sasian, J. M. (2000). Use of implicitly defined optical surfaces for the design of imaging and illumination systems. Optical Engineering, 39(7), 17961801.More infoAbstract: This paper presents an approach that uses implicitly defined optical surfaces for designing imaging and illumination systems. In the standard aspheric optical surface, consisting of a conic with an evenorder polynomial, the surface sagitta (sag), z, is defined explicitly as a function of the coordinates x and y. This standard aspheric surface is deemed useful for describing surfaces with small departures from a conic surface. However, optical surfaces with large departures from a conic are sometimes useful for current applications, such as null certification, conformal domes and windows, luminaires, and condenser design. The approach in this paper, which uses implicitly defined surfaces to describe highly aspheric surfaces, can be more general and easier to use for some situations. The sag z of an implicit surface is not defined directly, as it is in an explicit surface. Instead, it is defined indirectly in a more general form, as a function of x, y, and z. Because implicit functions have a more general form than explicit functions, they can better describe a variety of surfaces that cannot be easily described using the standard explicit aspheric surface. We show some examples of current interest.
 Lerner, S. A., Sasian, J. M., & Descour, M. R. (2000). Design approach and comparison of projection cameras for EUV lithography. Optical Engineering, 39(3), 792802.More infoAbstract: This paper presents an approach to designing allreflective, projection cameras for EUV lithography. We make a comparison of fourmirror cameras with numerical apertures ranging from 0.1 to 0.2 and ringfield widths from 1.0 to 3.6 mm. Additionally, we present two theoretical models that allow for the phase change introduced by multilayer coatings.
 Sabatke, E. M., & Sasian, J. M. (2000). Phase theory for multiple aperture systems. Proceedings of SPIE  The International Society for Optical Engineering, 4091, 617.More infoAbstract: We establish the groundwork for a phase theory applicable to multipleaperture systems. To do this, we define ideal behavior as the phase behavior of an offaxis system that has inherent rotational symmetry. Then we examine the phase behavior of a more general system that has only a single plane of symmetry. This system represents a branch of an actual synthetic aperture system. The comparison of the two systems leads to conditions for which the plane symmetric system has ideal behavior. As a result of this comparison, design rules that are commonly applied to multiple aperture systems appear naturally, including the wellknown requirement that the exit pupil is a scaled copy of the entrance pupil. The theory also shows that in reflective synthetic telescopes, fewer mirrors are required to achieve ideal behavior if the minors are offaxis sections of an axiallysymmetric parent system, rather than onaxis mirrors. The phase theory that we present is cohesive, provides useful design guidelines, and can be considered an addition to wave aberration theory.
 Sabatke, E. M., & Sasian, J. M. (2000). Secondorder phase theory in multiple aperture systems. Proceedings of SPIE  The International Society for Optical Engineering, 4006, II/.More infoAbstract: We establish the groundwork for a phase theory applicable to multipleaperture systems. We examine the phase behavior of a reference system with rotational symmetry, and then examine the phase behavior of a system with only a single plane of symmetry assumed. A comparison of the two systems leads to the mathematical conditions for which one branch of a multipleaperture system has ideal behavior.
 Sasian, J., Lerner, S. A., & Sasian, J. M. (2000). Optical design with parametrically defined aspheric surfaces. Applied optics, 39(28).More infoThe standard aspheric surface definition has been used successfully to correct aberrations in a wide variety of systems. However, in some current applications a more general surface definition is needed. We present a more general approach that uses parametrically defined optical surfaces for the optical design of imaging and illumination systems.
 Sasián, J. M. (2000). Aberrations from a prism and a grating. Applied Optics, 39(1), 3439.More infoPMID: 18337867;Abstract: Formulas for the wave aberrations introduced into a beam by a prism or a plane grating are derived from the theory of plane symmetric systems. Emphasis is made on the fielddependent aberrations. © 2000 Optical Society of America.
 Descour, M. R., Willer, M. R., Clarke, D. S., & Sasian, J. M. (1999). EUVL projectioncamera alignment methods. Proceedings of SPIE  The International Society for Optical Engineering, 3676(II), 663668.More infoAbstract: Comparison of misalignment modes associated with metrology data and projectioncamera performance can be used to increase the sensitivity of metrology measurements to specific cameraperformance specifications such as chiefray distortion. Selection of measurable misalignment modes in the case of metrology and interesting misalignment modes in the case of camera performance is based on a determination of whether a mode can `fit' into a projection camera given actuatorstroke and mirror tilt bounds. Measurement and interest subspaces are next compared using distance between subspaces. As an example of this type of analysis, we find that exitpupil wavefront measurements can be made more sensitive to chiefray distortion if these measurements are collected at field positions outside the ring field of view of an EUVL projection camera.
 Mitchell, T. A., & Sasian, J. M. (1999). Variable aberration correction using axially translating phase plates. Proceedings of SPIE  The International Society for Optical Engineering, 3705, 209220.More infoAbstract: Aerodynamic requirements on airborne optical systems have brought about the need to develop lower drag conformal domes. Because these domes typically deviate greatly from spherical surface descriptions, large amounts of aberrations are induced which vary with line of sight through the dome. Several solutions to this problem have been investigated, one of which is the use of translating phase plates to dynamically dial in the appropriate amount of aberration correction. Axially translating phase plates can be described as two nominally plane parallel phase plates with matched aspheric surfaces on their inner surfaces. When placed in contact, they behave as a single plane parallel plate, but when an axial separation is introduced, the optical ray passing through the first plate intersects the second plate at a different location resulting in both a change in optical path length and a set of induced aberrations. A mathematical derivation of the aberrations generated is performed for Zernike polynomial surfaces in the presence of both converging and collimated beams. Code V is used to verify the derived expressions and the theory is used to describe the results of a previous conformal optics aberration correction technique.
 Sasian, J. (1999). Nonrotationally symmetric optics proliferate. Laser Focus World, 35(7), S5X.
 Sasián, J. M., & Mansuripur, M. (1999). Design approaches with a lenslet array and a single, highnumericalaperture annularfield objective lens for optical data storage systems that incorporate large numbers of parallel readwriteerase channels. Applied Optics, 38(7), 11631168.More infoPMID: 18305727;Abstract: To achieve very high data rates (>109 bits/s) in optical data storage systems it is necessary to employ a large number of laser beams for parallel readwriteerase operations. Bringing all these beams to diffractionlimited focus with a highnumericalaperture objective lens (while maintaining focus and tracking) requires techniques that are fundamentally different from those that are currently practiced in the field of optical data storage. We present two possible solutions to the problem of designing an objective lens for such systems, one involving an array of highquality lenslets and the other based on a single, highnumericalaperture annularfieldofview conventional lens. Both approaches have advantages and disadvantages, on which we elaborate in the course of our discussions. © 1999 Optical Society of America.
 Sasian, J. M., & Descour, M. R. (1998). Power distribution and symmetry in lens systems. Optical Engineering, 37(3), 10011004.More infoAbstract: Two parameters for quantifying optical power distribution and lens symmetry are proposed as a tool to aid the lens designer in the search of optimum configurations. © 1998 Society of PhotoOptical Instrumentation Engineers.
 Chang, M. T., & Sasian, J. (1997). Variable spherical aberration generators. Proceedings of SPIE  The International Society for Optical Engineering, 3129, 217228.More infoAbstract: Most variable spherical aberration generators have differential moving components or floating elements, much like a regular zoom lens but with insignificantly small overall magnification change over the "zoom" range. The main purpose of the differential movements is to generate a variable amount of spherical aberration (SA). Such aberration generators can be used as standalone systems for aberration control or as subsystems for aberration compensation. The theory can also be applied to macro focusing mechanism as well as softfocus mechanism. This paper presents a survey of different variable SA generation mechanisms. Examples of some applications of the theory are presented.
 Gerber, R. E., Mansuripur, M., & Sasián, J. M. (1997). Versatile objective lens with adjustable correction for different wavelengths and substrate thicknesses for testing optical disks. Applied Optics, 36(11), 24142420.More infoPMID: 18253221;Abstract: A typical aspheric singlet used as the objective lens in opticaldisk datastorage systems will not work at different wavelengths or with different substrate thicknesses because of spherochromatism. Using two microscope objectives with adjustable collars and a pair of relay lenses, we have constructed a system in which a diffractionlimited spot of any wavelength in the range of 0.40.7 μm can be moved by as much as ±100 μm both the focusing and tracking directions. We accomplished this by simply moving an aspheric singlet mounted in an offtheshelf optical head. The system uses the adjustable collars of the microscope objectives to correct for the spherochromatism of the singlet and to accommodate the various thicknesses of the substrates. © 1997 Optical Society of America.
 Lentine, A. L., Reiley, D. J., Novotny, R. A., Morrison, R. L., Sasian, J. M., Beckman, M. G., Buchholz, D. B., Hinterlong, S. J., Cloonan, T. J., Richards, G. W., & McCormick, F. B. (1997). Asynchronous transfer mode distribution network by use of an optoelectronic VLSI switching chip. Applied Optics, 36(8), 18041814.More infoPMID: 18250868;Abstract: We describe a new optoelectronic switching system demonstration that implements part of the distribution fabric for a large asynchronous transfer mode (ATM) switch. The system uses a single optoelectronic VLSI modulatorbased switching chip with more than 4000 optical inputoutputs. The optical system images the input fibers from a twodimensional fiber bundle onto this chip. A new optomechanical design allows the system to be mounted in a standard electronic equipment frame. A large section of the switch was operated as a 208Mbits/s timemultiplexed space switch, which can serve as part of an ATM switch by use of an appropriate outofband controller. A larger section with 896 input light beams and 256 output beams was operated at 160 Mbits/s as a slowly reconfigurable space switch. © 1997 Optical Society of America.
 Reiley, D. J., & Sasian, J. M. (1997). Optical design of a freespace photonic switching system. Applied Optics, 36(19), 44974504.More infoPMID: 18259241;Abstract: The optical design of a photonic switching system is described in detail. The system is a 4f imaging system with one lens design based on a Petzval lens and the second lens design based on a double Gauss lens. The assembled system is 60 mm × 70 mm × 370 mm and features a single imaging stage, pupil division for beam combination, and a single fiber bundle for both input and output. A brief description of the system requirements is provided, and the implication of some of these requirements for the paraxial design is explained. The choice of design forms for the lenses is explained, the design process is outlined, and the final lens designs are provided. Lens tolerancing is outlined and the final lens tolerances are provided. Finally, the assembly and the alignment processes are described. © 1997 Optical Society of America.
 Sasian, J. M. (1997). Annular surfaces in annular field systems. Optical Engineering, 36(12), 34013403.More infoAbstract: We present an optical surface description that is more suitable for designing annular field systems than the standard aspheric surface representation. The use of this novel surface description leads to shorter design times and improved systems. © 1997 Society of PhotoOptical Instrumentation Engineers.
 Sasian, J. M. (1997). Doublecurvature surfaces in mirror system design. Optical Engineering, 36(1), 183188.More infoAbstract: The use in mirror system design of doublecurvature surfaces such as sections of toroids or ellipsoids is discussed. Four design examples are presented that illustrate how doublecurvature surfaces could be used to advantage in mirror system design. © 1997 society of PhotoOptical Instrumentation Engineers.
 Hinterlong, S. J., Lentine, A. L., Reiley, D. J., Sasian, J. M., Morrison, R. L., Novotny, R. A., Beckman, M. G., Buchholz, D. B., Cloonan, T. J., & Richards, G. W. (1996). ATM switching system demonstration using a 40Gb/s throughput smart pixel optoelectronic VLSI chip. LEOS Summer Topical Meeting, 2pp.More infoAbstract: A 155 Mb/s per channel demonstration of an ATM switching fabric was constructed using a 4096 optical input and 256 optical output chip. The construction of the demonstration was achieved with minimal of optical hardware. Quickly reconfigurable optoelectronic VLSI permitted switching at ATM cell boundaries.
 Lentine, A. L., Reiley, D. J., Novotny, R. A., Morrison, R. L., Sasian, J. M., Beckman, M. G., Buchholz, D. B., Hinterlong, S. J., Cloonan, T. J., Richards, G. W., & McCormick Jr., F. B. (1996). Optoelectronic ATM switch employing hybrid silicon CMOS/GaAs FETSEEDs. Proceedings of SPIE  The International Society for Optical Engineering, 2692, 100108.More infoAbstract: In the past few years, the demand for telecommunications services beyond voice telephony has skyrocketed. For the growth of these services to continue at this rate, cost effective means of transporting and switching large amounts of information must be found. Although fiber optic transmission has significantly reduced the cost of transmission, switching high bandwidth signals remains expensive. While all electronic switching systems are certainly possible for these high bandwidth systems, considerable effort has been expended to reduce the cost of fiber optic connections between frames or racks of equipment separated by several meters. As an example, one can envision fiberoptic data links connecting the line units that receive and transmit data from the outside world with an electronic switching fabric. Optical data links, ODLs, can perform the optical to electrical conversions. Several of these optical data links can be electrically connected with electronic switching chips on a printed circuit board. As the demand for bandwidth increases, several hundred to several thousand optical fibers might be incident on the switching fabric. Discrete optical data links and parallel data links with up to 32 fibers per data link remain an expensive solution to transporting this information due to their perlink cost, physical size, and power dissipation. Power dissipation on the switching chips is high because of the need for electronic drivers for the high speed electrical interconnections between the switching chips and the data links. By integrating the O/E conversions directly onto the switching chips, lower cost and higher density systems can be built. In this paper, we describe preliminary results of an experimental optoelectronic switching network based on this lower cost solution. The network is designed to be part of an asynchronous transfer mode (ATM) network based on the Growable Packet Architecture. The switching chip consists of GaAs/AlGaAs multiple quantum well modulators and detectors flip chip bonded to silicon VLSI circuitry. The optical system images the inputs from a two dimensional fiber bundle onto the switching chip, provides optical fanout of the signals from the fibers to the switching chip, and images the outputs from the chip onto the fiber bundle.
 Reiley, D. J., Sasian, J. M., & Beckman, M. G. (1996). Optomechanical design of a robust freespace optical switching system. Proceedings of SPIE  The International Society for Optical Engineering, 2691, 8490.More infoAbstract: To be competitive with electronic switching technologies, photonic switching systems must have stability that rivals that of electronic systems, requiring little or no intervention over time scales of years. This paper describes progress towards the goal of stable optical interconnects. We have built an extraordinarily stable freespace optical interconnect mounted in a standard electronics frame; the system operated successfully over a wide temperature range for three days and required no realignment after shipping. Robust optomechanical design played an important role in the successful operation of the system. The role of kinematic mounting principles, selfcentering lens mounts, materials selection, and longlever arm adjustments are described. Vigorous shaking of the system did not affect its biterror rate  measured to be less than 10E12 on a single channel.
 Cloonan, T. J., Richards, G. W., Morrison, R. L., Lentine, A. L., Sasian, J. M., McCormick, F. B., Hinterlong, S. J., & Hinton, H. (1994). Shuffleequivalent interconnection topologies based on computergenerated binaryphase gratings. Applied Optics, 33(8), 14051431.More infoAbstract: Various shuffleequivalent interconnection topologies are analyzed, that are computer generated binary phase gratings to route the beams of light between the planar device arrays. The work also studies power requirements of these different interconnection patterns, in which the use of interconnections in the optical implementation of a new class of networks known as extended generalized shuffle networks is assumed.
 McCormick, F. B., Cloonan, T. J., Lentine, A. L., Sasian, J. M., Morrison, R. L., Beckman, M. G., Walker, S. L., Wojcik, M. J., Hinterlong, S. J., Crisci, R. J., Novotny, R. A., & Hinton, H. (1994). Fivestage freespace optical switching network with fieldeffect transistor selfelectroopticeffectdevice smartpixel arrays. Applied Optics, 33(8), 16011618.More infoAbstract: Using several pixel (2,1,1) optoelectronic switching nodes, a fivestage fully interconnected 32×16 switching fabric is designed and constructed. The system uses a highresolution optical chiptochip imaging system, 2D fiber bundles, and custom optomechanical packaging that uses modular kinematic component positioning. Two preliminary system experiments are described.
 McCormick, F. B., Cloonan, T. J., Lentine, A. L., Sasian, J. M., Morrison, R. L., Novotny, R. A., Beckman, M. G., Walker, S. L., Wojcik, M. J., Hinterlong, S. J., Crisci, R. J., & Hinton, H. S. (1994). Smart pixelbased switching fabric demonstration. Conference Proceedings  Lasers and ElectroOptics Society Annual Meeting, 8, 373374.More infoAbstract: The smart pixel device arrays which integrates electronics processing technology with the interconnection and communication features of optics. Prototypes of GaAs FETSEED smart pixels have been integrated with computer produced holograms, 2D fiber bundles, frequency stabilized lasers and a new optomechanical packaging to set up a fivestage, 32 × 16 freespace optical switching fabric. Recently, this system has been further developed rendering the fivestage operation effective at 155 Mbit/s.
 McCormick, F. B., Lentine, A. L., Morrison, R. L., Sasian, J. M., Cloonan, T. J., Novotny, R. A., Beckman, M. G., Wojcik, M. J., Hinterlong, S. J., & Buchholz, D. B. (1994). 155 Mb/s operation of a FETSEED freespace switching network. IEEE Photonics Technology Letters, 6(12), 14791481.More infoAbstract: The interconnection problems present in many highperformance digital systems may be alleviated through the use of surface normal optical interconnections using optoelectronic smart pixels. We present recent results of highspeed operation of a fivestage experimental freespace switching network using embedded control techniques for network control. The smart pixels consist of buffered GaAs FET logic with MQW SEED detectors and modulators. The system also incorporates external cavity lasers, bulk, micro, and diffractive optics, twodimensional fiber bundles, and novel optomechanics. At 155 Mb/s, 77 of the 80 total pixels in the system and 31 of the 32 input fibers were functional. Two of the network paths have carried digital video at 105 Mb/s for over four months without readjustment. Error rate measurements on these paths have shown a shortterm BER of 1010.
 Sasian, J. M., Novotny, R. A., Beckman, M. G., Walker, S. L., Wojcik, M. J., & Hinterlong, S. J. (1994). Fabrication of fiber bundle arrays for freespace photonic switching systems. Optical Engineering, 33(9), 29792985.More infoAbstract: We describe a technique for assembling fiber bundle arrays as needed in optical computing and phonic switching systems. Two 4 × 4 arrays with singlemode and multimode optical fibers were manufactured. Fiber ends were located to within 3 μm of their ideal position and to a pointing precision of 30 arcmin. A third 4 × 8 array was manufactured with singlemode fibers, and fiber ends were located to within 1.5 μm of their ideal position.
 Cloonan, T. J., McCormick, F. B., Lentine, A. L., Sasian, J. M., Morrison, R. L., Beckman, M. G., Walker, S. L., Wojcik, M. J., Hinterlong, S. J., Crisci, R. J., Novotny, R. A., & Hinton, H. S. (1993). System 5: a smart pixel based switching fabric. Conference Proceedings  Lasers and ElectroOptics Society Annual Meeting, 670671.More infoAbstract: A 5 stage, fully interconnected 32×16 switching network using smart pixel 2×1 switching nodes is demonstrated. The system was designed to operate with 150Mbps data rates.
 McCormick, F. B., Cloonan, T. J., Tooley, F. A., Lentine, A. L., Sasian, J. M., Brubaker, J. L., Morrison, R. L., Walker, S. L., Crisci, R. J., Novotny, R. A., Hinterlong, S. J., Hinton, H. S., & Kerbis, E. (1993). Sixstage digital freespace optical switching network using symmetric selfelectroopticeffect devices. Applied Optics, 32(26), 51535171.More infoPMID: 20856323;Abstract: We describe the design and demonstration of an extended generalized shuffle interconnection network, centrally controlled by a personal computer. A banyan interconnection pattern is implemented by use of computergenerated Fourier holograms and custom metallization at each 32 x 32 switching node array. Each array of electrically controlled tristate symmetric selfelectroopticeffect devices has 10,240 optical pinouts and 32 electrical pinouts, and the sixstage system occupies a 9 in. X 12.5 in. (22.9 cm x 31.7 cm) area. Details of the architecture, optical and mechanical design, and system alignment and tolerancing are presented. © 1993 Optical Society of America.
 Sasian, J. M., & Chipman, R. A. (1993). Staircase lens: A binary and diffractive field curvature corrector. Applied Optics, 32(1), 6066.More infoPMID: 20802662;Abstract: The optical characteristics of a family of diffractive lenses, called staircase lenses, are discussed. These lenses contribute no optical power and the fourthorder wave aberrations Petzval field curvature, distortion, and chromatic aberrations when collimated illumination is used. A diamondturned staircase lens comprising 150 steps was manufactured. The test results verify the generation of field curvature and longitudinal chromatic aberration. © 1993 Optical Society of America.
 Sasian, J. M., McCormick, F. B., Webb, R., Crisci, R. J., Mersereau, K. O., & Stawicki, R. P. (1993). Design, assembly, and testing of an objective lens for a freespace photonic switching system. Optical Engineering, 32(8), 18711878.More infoAbstract: An objective lens is designed, assembled and tested in this article. This lens is used in a freespace photonic switching system. Lens research, lens design and lens requirements. Lens specifications, and the variation of distortion and focal length are shown in the form of tables. Lens tolerancing, lens ordering, lens barrel and lens forms are discussed.
 McCormick, F. B., Tooley, F. A., Cloonan, T. J., Sasian, J. M., Hinton, H. S., Mersereau, K. O., & Feldblum, A. Y. (1992). Corrigendum: 'Optical interconnections using microlens arrays'. Optical and Quantum Electronics, 24(10), 12091212.
 McCormick, F. B., Tooley, F. A., Cloonan, T. J., Sasian, J. M., Hinton, H. S., Mersereau, K. O., & Feldblum, A. Y. (1992). Optical interconnections using microlens arrays. Optical and Quantum Electronics, 24(4), S465S477.More infoAbstract: Freespace interconnection of widely spaced pixels may be implemented using microlenses, rather than conventional imaging. Advantages, problems, and studies of system capacity are discussed. © 1992 Chapman & Hall.
 McCormick, F. B., Tooley, F. A., Sasian, J. M., Brubaker, J. L., Lentine, A. L., Cloonan, T. J., Morrison, R. L., Walker, S. L., & Crisci, R. J. (1991). Parallel interconnection of two 64 × 32 symmetric selfelectrooptic effect device arrays. Electronics Letters, 27(20), 18691871.More infoAbstract: The cascaded, parallel operation of two 2dimensional arrays of 2048 symmetric selfelectrooptic effect devices (SSEEDs) is demonstrated. Bistable operation of both arrays and cascading of information from each array to the other are shown. The system is compact, tolerant to misalignment, stable, and extensible.
 Sasian, J. M. (1991). Review of methods for the design of unsymmetrical optical systems. Proceedings of SPIE  The International Society for Optical Engineering, 1396, 453466.More infoAbstract: Methods for the design of unsymmetrical optical systems depend on the development of optical imaging theories. There is not a general theory of optical systems; instead, a number of theories or methods may be used for the design of unsymmetrical optics. There are currently three relevant concepts to gain insight about the behavior of unsymmetrical systems. These are: 1. Abbe's ideal model of imagery that is used to understand firstorder properties in imaging systems. 2. The concept of aberration expansion about an optical axis ray originated by Hamilton. An expansion of the wavefront deformation in polar form is particularly useful. 3. The concept of aberration field and the associated vector analysis that show aberration distribution over the field of view.
 Sasian, J. M. (1990). Design of a Schwarzschild flatfield, anastigmatic, unobstructed, widefield telescope. Optical Engineering, 29(1), 15.More infoAbstract: A recent development in the theory of bilateral symmetrical optical systems is applied to design the remarkable twomirror, unobstructed Schwarzschild telescope. We illustrate how this development was used to simplify the fabrication and testing of such a system.
 Sasian, J. M. (1990). Fourmirror optical system for large telescopes. Optical Engineering, 29(10), 11811185.More infoAbstract: The analysis of a plane symmetric, fourmirror optical system that has a real pupil to accomplish passive or active wavefront correction is presented. Several system solutions are possible, but the emphasis of the analysis is given to those that might simplify the fabrication of a large telescope.
 Sasian, J. M. (1987). FLATFIELD, ANASTIGMATIC, FOURMIRROR OPTICAL SYSTEM FOR LARGE TELESCOPES.. Optical Engineering, 26(12), 11971199.More infoAbstract: A largeaperture, flatfield, fourmirror optical system for large telescopes has been designed. Its main virtue is that it uses spherical surfaces for the primary and secondary mirrors, providing good imagery. Thirdorder theory and the optimization process are discussed for this optical system.
 Noble, R., Cobos, F., Diego, F., & Sasian, J. (1982). OPTICAL CHARACTERISTICS OF THE UNAM 2m RITCHEYCHRETIEN TELESCOPE.. Applied Optics, 21(17), 31813183.More infoPMID: 20396199;Abstract: Measurements made on the components and on two assembled systems of a 2m RitcheyChretien telescope have been employed to determine the actual characteristics of the telescope. Sufficient precision has been obtained so that other focal ratio systems can be designed.