Freeform optics for imaging

In the last 10 years, freeform optics has enabled compact and high-performance imaging systems. This article begins with a brief history of freeform optics, focusing on imaging systems, including marketplace emergence. The development of this technology is motivated by the clear opportunity to enable science across a wide range of applications, spanning from extreme ultraviolet lithography to space optics. Next, we define freeform optics and discuss concurrent engineering that brings together design, fabrication, testing, and assembly into one process. We then lay out the foundations of the aberration theory for freeform optics and emerging design methodologies. We describe fabrication methods, emphasizing deterministic computer numerical control grinding, polishing, and diamond machining. Next, we consider mid-spatial frequency errors that inherently result from freeform fabrication techniques. We realize that metrologies of freeform optics are simultaneously sparse in their existence but diverse in their potential. Thus, we focus on metrology techniques demonstrated for the measurement of freeform optics. We conclude this review with an outlook on the future of freeform optics.

[1]  John C. Lambropoulos,et al.  Use of magnetorheological finishing (MRF) to relieve residual stress and subsurface damage on lapped semiconductor silicon wafers , 2001, Optics + Photonics.

[2]  D. Golini,et al.  Twyman effect mechanics in grinding and microgrinding. , 1996, Applied optics.

[3]  Shanyong Chen,et al.  Adaptive wavefront interferometry for unknown free-form surfaces. , 2018, Optics express.

[4]  David M. Aikens,et al.  Derivation of preliminary specifications for transmitted wavefront and surface roughness for large optics used in inertial confinement fusion , 1995, Other Conferences.

[5]  David R. Shafer.  Design With Two-Axis Aspheric Surfaces , 1978, Optics & Photonics.

[6]  Jannick P. Rolland,et al.  Off-axis conics as base surfaces for freeform optics enable null testability. , 2020, Optics express.

[7]  Matthew A. Davies,et al.  Experimental characterization of variable output refractive beamshapers using freeform elements , 2014, Optics & Photonics - Optical Engineering + Applications.

[8]  Joseph M. Howard,et al.  Automatic Solution Space Exploration for Freeform Optical Design , 2019 .

[9]  Jannick P Rolland,et al.  How good is your lens? Assessing performance with MTF full-field displays. , 2017, Applied optics.

[10]  Sivan Salzman,et al.  Magnetorheological finishing of chemical-vapor deposited zinc sulfide via chemically and mechanically modified fluids. , 2016, Applied optics.

[11]  Liam Blunt,et al.  Development and Application of Interferometric On-Machine Surface Measurement for Ultraprecision Turning Process , 2018, Journal of Manufacturing Science and Engineering.

[12]  Moran Hf.  A new microtome with a diamond knife , 1957 .

[13]  Christopher J. Evans,et al.  Rapid post-polishing of diamond-turned optics , 1994 .

[14]  T. Suleski,et al.  The Minimum Modulation Curve as a tool for specifying optical performance: application to surfaces with mid-spatial frequency errors. , 2019, Optics express.

[15]  R. J. Benjamin.  Diamond Turning at a Large Optical Manufacturer , 1978 .

[16]  Kate Medicus,et al.  Current use and potential of additive manufacturing for optical applications , 2017, Optifab.

[17]  Pablo Benitez,et al.  Design in 3D geometry with the simultaneous multiple surface design method of nonimaging optics , 1999, Optics & Photonics.

[18]  Changsik Yoon,et al.  Absolute linear-in-k spectrometer designs enabled by freeform optics. , 2019, Optics express.

[19]  Markus C. Knauer,et al.  Phase measuring deflectometry: a new approach to measure specular free-form surfaces , 2004, SPIE Photonics Europe.

[20]  Weiyao Zou,et al.  Differential Shack-Hartmann curvature sensor: local principal curvature measurements. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[21]  Yoshiharu Namba,et al.  Title advances in optical fabrication for astronomy , 2018, Monthly Notices of the Royal Astronomical Society.

[22]  Angela Davies,et al.  Phase measuring deflectometry for determining 5 DOF misalignment of segmented mirrors , 2017, Optical Engineering + Applications.

[23]  Peter Kühnhold,et al.  Reduction of chromatic aberration influences in vertical scanning white-light interferometry , 2014 .

[24]  C Huang,et al.  Propagation errors in precision Fizeau interferometry. , 1993, Applied optics.

[25]  Thomas J. Suleski,et al.  Variable-diameter refractive beam shaping with freeform optical surfaces. , 2011, Optics letters.

[26]  Jose M. Sasian.  How to approach the design of a bilateral symmetric optical system , 1994 .

[27]  Kevin P Thompson,et al.  Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the astigmatic aberrations. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  Sheryl M. Gracewski,et al.  Contact mechanics models and algorithms for dome polishing with UltraForm Finishing (UFF) , 2007, SPIE Defense + Commercial Sensing.

[29]  R N Youngworth,et al.  Simple Estimates for the Effects of Mid-spatial-Frequency Surface Errors on Image Quality. , 2000, Applied optics.

[30]  Robert E. Parks.  Specifications: figure and finish are not enough , 2008, Optical Engineering + Applications.

[31]  Fritz Klocke,et al.  Material Removal Mechanisms in Lapping and Polishing , 2003 .

[32]  R. R. Donaldson,et al.  Design And Construction Of A Large, Vertical Axis Diamond Turning Machine , 1983, Optics & Photonics.

[33]  Matthew A. Davies,et al.  The mechanics of milling of germanium for IR applications , 2016 .

[34]  Zhen Cao,et al.  Design method of off-axis extreme ultraviolet lithographic objective system with a direct tilt process , 2015 .

[35]  Thomas J. Suleski,et al.  Characterization of hybrid molding and lithography for SU-8 micro-optical components , 2010 .

[36]  Pablo Benítez,et al.  Freeform aplanatic systems as a limiting case of SMS. , 2016, Optics express.

[37]  J. Qiao,et al.  Optimization of femtosecond laser processing of silicon via numerical modeling , 2016 .

[38]  Jannick P Rolland,et al.  Degeneracy in freeform surfaces described with orthogonal polynomials. , 2018, Applied optics.

[39]  J. B. Bryan,et al.  Design and construction of an ultraprecision 84 inch diamond turning machine , 1979 .

[40]  Hee Joo Choi,et al.  Pseudorandom orbiting stroke for freeform optics postprocessing , 2019 .

[41]  Robert A Norwood,et al.  Silicone optical elements for cost-effective freeform solar concentration. , 2019, Optics express.

[42]  Di Xu,et al.  Telecentric broadband objective lenses for optical coherence tomography (OCT) in the context of low uncertainty metrology of freeform optical components: from design to testing for wavefront and telecentricity. , 2019, Optics express.

[43]  Angela Davies,et al.  Optical surface characterization with the area structure function , 2013 .

[44]  Xuhui Xie,et al.  Algorithm for ion beam figuring of low-gradient mirrors , 2009 .

[45]  Tony Hull,et al.  Mid-spatial frequency matters: examples of the control of the power spectral density and what that means to the performance of imaging systems , 2012, Defense + Commercial Sensing.

[46]  R. A. Jones,et al.  Optimization of computer controlled polishing. , 1977, Applied optics.

[47]  Peter M. Harris,et al.  Evolution of the ‘Guide to the Expression of Uncertainty in Measurement’ , 2006 .

[48]  Qun Wei,et al.  Homodyne displacement measuring interferometer probe for optical coordinate measuring machine with tip and tilt sensitivity , 2015, SPIE Optifab.

[49]  Joseph M. Howard,et al.  Starting point designs for freeform four-mirror systems , 2018 .

[50]  Yayi Wei,et al.  Fast extreme ultraviolet lithography mask near-field calculation method based on machine learning. , 2020, Applied optics.

[51]  Bryan D. Stone,et al.  Foundations of second-order layout for asymmetric systems , 1992 .

[52]  Biswa Ranjan Swain,et al.  High-performance optical differentiation wavefront sensing towards freeform metrology. , 2019, Optics express.

[53]  François Blateyron,et al.  Chromatic Confocal Microscopy , 2011 .

[54]  Hong Hua,et al.  Design and demonstration of a vari-focal optical see-through head-mounted display using freeform Alvarez lenses. , 2019, Optics express.

[55]  Laurent Berthelot,et al.  Optimization of the optical performance of variable-power and astigmatism Alvarez lenses. , 2014, Applied optics.

[56]  Kai Xin,et al.  Correlation of mid-spatial features to image performance in aspheric mirrors , 2013, Optics & Photonics - Optical Engineering + Applications.

[57]  Jannick P Rolland,et al.  On-the-fly surface manufacturability constraints for freeform optical design enabled by orthogonal polynomials. , 2019, Optics express.

[58]  Guo-Fan Jin,et al.  Automated design of freeform imaging systems , 2017, Light: Science & Applications.

[59]  Takayuki Nakano,et al.  Configuration of an off-axis three-mirror system focused on compactness and brightness. , 2005, Applied optics.

[60]  Kevin Liang,et al.  Understanding the effects of groove structures on the MTF. , 2017, Optics express.

[61]  Christopher J. Evans,et al.  Concurrent engineering of a next-generation freeform telescope: metrology and test , 2019, Defense + Commercial Sensing.

[62]  W. Plummer,et al.  Photographic optical systems with nonrotational aspheric surfaces. , 1999, Applied optics.

[63]  William Kordonski,et al.  Magnetorheological Jet (MR JetTM) Finishing Technology , 2006 .

[64]  Mourad Idir,et al.  Non-null full field X-ray mirror metrology using SCOTS: a reflection deflectometry approach. , 2012, Optics express.

[65]  Kevin W. Thompson,et al.  Influence Of Alignment Errors Of A Telescope System On Its Aberration Field , 1980, Optics & Photonics.

[66]  Hamidreza Aryan,et al.  Simple methods for estimating the performance and specification of optical components with anisotropic mid-spatial frequency surface errors. , 2019, Optics express.

[67]  Matthew A. Davies,et al.  Machining and Metrology of a Chalcogenide Glass Freeform Lens Pair , 2016 .

[68]  E. B. Magrab,et al.  Design and testing of a fast tool servo for diamond turning , 1985 .

[69]  J. Bennett,et al.  Calculation of the power spectral density from surface profile data. , 1995, Applied optics.

[70]  John M Tamkin,et al.  Theory of point-spread function artifacts due to structured mid-spatial frequency surface errors. , 2010, Applied optics.

[71]  Linlin Zhu,et al.  Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment. , 2018, Optics express.

[72]  Lu Chen,et al.  Review of optical freeform surface representation technique and its application , 2017 .

[73]  Yao Hu,et al.  Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements. , 2016, Applied optics.

[74]  Zhou Jinsong,et al.  Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface. , 2018 .

[75]  W. Plummer.  Unusual optics of the Polaroid SX-70 Land camera. , 1982, Applied optics.

[76]  Paul Morantz,et al.  Rapid optical surface figuring using reactive atom plasma , 2012 .

[77]  David M. Aikens,et al.  Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems , 2008 .

[78]  David D Walker,et al.  Pseudo-random tool paths for CNC sub-aperture polishing and other applications. , 2008, Optics express.

[79]  Christopher J. Evans,et al.  Observations on the effect of retrace error in scanning white light interferometry of smooth optical surfaces , 2019, Optical Design and Fabrication 2019 (Freeform, OFT).

[80]  M. Alonso,et al.  Validity of the perturbation model for the propagation of MSF structure in 2D. , 2019, Optics express.

[81]  Christof Pruss,et al.  Fast and Flexible Non-Null Testing of Aspheres and Free-Form Surfaces with the Tilted-Wave-Interferometer , 2014 .

[82]  K. Thompson.  Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[83]  Christoph von Kopylow,et al.  Measuring deformations with deflectometry , 2014, Optics & Photonics - Optical Engineering + Applications.

[84]  Anand Asundi,et al.  Review of phase measuring deflectometry , 2018, Optics and Lasers in Engineering.

[85]  John M Tamkin,et al.  Effects of structured mid-spatial frequency surface errors on image performance. , 2010, Applied optics.

[86]  Jannick P. Rolland,et al.  Design for metrology for freeform optics manufacturing , 2019 .

[87]  Herbert Gross,et al.  Simulation and analysis of optical imaging systems including real freeform components , 2019 .

[88]  Tayyab I. Suratwala,et al.  Materials Science and Technology of Optical Fabrication , 2018 .

[89]  OxmanNeri,et al.  Additive Manufacturing of Optically Transparent Glass , 2015 .

[90]  John C. Lambropoulos,et al.  Twyman effects in thin curved optics , 2017, Optifab.

[91]  Matthew A. Davies,et al.  On the ultra-precision diamond machining of chalcogenide glass , 2015 .

[92]  Andreas Tünnermann,et al.  Angular resolved power spectral density analysis for improving mirror manufacturing. , 2018, Applied optics.

[93]  G W Forbes,et al.  Strehl ratio as the Fourier transform of a probability density of error differences. , 2016, Optics letters.

[94]  Hamidreza Aryan,et al.  Predictive models for the Strehl ratio of diamond-machined optics. , 2019, Applied optics.

[95]  Matthew A. Davies,et al.  Design and characterization of an infrared Alvarez lens , 2012 .

[96]  Jay Kumler.  Designing and specifying aspheres for manufacturability; Technical Digest , 2005, Optifab.

[97]  Andreas Beutler.  Strategy for a flexible and noncontact measuring process for freeforms , 2016 .

[98]  H. Giessen,et al.  Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres , 2016, Nature Communications.

[99]  Stephan Stuerwald.  Error compensation in computer generated hologram-based form testing of aspheres. , 2014, Applied optics.

[100]  Andreas Tünnermann,et al.  Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope , 2015 .

[101]  Guoyu Yu,et al.  Machine Acceleration Effects on Computer Controlled Polishing , 2017 .

[102]  Jannick P Rolland,et al.  Starting geometry creation and design method for freeform optics , 2018, Nature Communications.

[103]  Juan C. Miñano,et al.  Freeform optics for Virtual Reality applications , 2017 .

[104]  H. Nouira,et al.  Characterization of the main error sources of chromatic confocal probes for dimensional measurement , 2014 .

[105]  Shai N. Shafrir,et al.  Subsurface damage and microstructure development in precision microground hard ceramics using magnetorheological finishing spots. , 2007, Applied optics.

[106]  J M Zavada,et al.  Residual surface roughness of diamond-turned optics. , 1975, Applied optics.

[107]  Guoyu Yu,et al.  Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface. , 2012, Optics express.

[108]  James C. Ross,et al.  New advancements in freeform optical metrology , 2017, Defense + Security.

[109]  David R. Lide,et al.  Three Dimensional Metrology , 2018 .

[110]  Chris J. Evans,et al.  Precision engineering: an evolutionary perspective , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[111]  James R Fienup,et al.  Verification of transverse translation diverse phase retrieval for concave optical metrology. , 2018, Optics letters.

[112]  R A Buchroeder,et al.  Wide-field tilted-component telescope: a leonard extended yolo all-reflecting system. , 1972, Applied optics.

[113]  von F. Zernike.  Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode , 1934 .

[114]  Bo Gao,et al.  Modal phase measuring deflectometry. , 2016, Optics express.

[115]  Liangyu He,et al.  Two-quadrant area structure function analysis for optical surface characterization. , 2012, Optics express.

[116]  D. C. Harris,et al.  History of magnetorheological finishing , 2011, Defense + Commercial Sensing.

[117]  Christian Brecher,et al.  Thermal issues in machine tools , 2012 .

[118]  Jannick P Rolland,et al.  Design of a freeform electronic viewfinder coupled to aberration fields of freeform optics. , 2015, Optics express.

[119]  K. Thompson,et al.  Freeform spectrometer enabling increased compactness , 2017, Light: Science & Applications.

[120]  Yongtian Wang,et al.  Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics. , 2014, Optics express.

[121]  James R. Fienup,et al.  Development of a concave freeform surface measurement using transverse translation-diverse phase retrieval , 2020, Optical Engineering.

[122]  Kyle Fuerschbach,et al.  Interferometric measurement of a concave, φ-polynomial, Zernike mirror. , 2014, Optics letters.

[123]  Effect of figure and waviness on image quality (A) , 1983 .

[124]  Jannick P Rolland,et al.  System design of a single-shot reconfigurable null test using a spatial light modulator for freeform metrology. , 2019, Optics letters.

[125]  Christoph Menke,et al.  Optical design with orthogonal representations of rotationally symmetric and freeform aspheres , 2013 .

[126]  J. Rolland,et al.  Optimal local shape description for rotationally non-symmetric optical surface design and analysis. , 2008, Optics express.

[127]  Karsten Urban,et al.  B-spline representation of optical surfaces and its accuracy in a ray trace algorithm. , 2011, Applied optics.

[128]  J. B. Bryan,et al.  Compensation for Errors Introduced by Nonzero Fringe Densities in Phase-Measuring Interferometers , 1993 .

[129]  Julius Muschaweck,et al.  All-reflective electronic viewfinder enabled by freeform optics. , 2019, Optics express.

[130]  K. Thompson,et al.  A new family of optical systems employing φ-polynomial surfaces. , 2011, Optics express.

[131]  K. Falaggis,et al.  Absolute metrology by phase and frequency modulation for multiwavelength interferometry. , 2011, Optics letters.

[132]  Matthew A. Davies,et al.  Concurrent engineering of a next-generation freeform telescope: mechanical design and manufacture , 2019, Defense + Commercial Sensing.

[133]  Jessica DeGroote Nelson,et al.  Incorporating VIBE into the precision optics manufacturing process , 2011, Optical Engineering + Applications.

[134]  Jannick P. Rolland,et al.  Effect of freeform surfaces on the volume and performance of unobscured three mirror imagers in comparison with off-axis rotationally symmetric polynomials. , 2019, Optics express.

[135]  Cristina Canavesi,et al.  Target flux estimation by calculating intersections between neighboring conic reflector patches. , 2013, Optics letters.

[136]  Peter de Groot,et al.  Instantaneous measurement Fizeau interferometer with high spatial resolution , 2011, Optical Engineering + Applications.

[137]  Leslie L. Deck.  High precision interferometer for measuring mid-spatial frequency departure in free form optics , 2007, Optifab.

[138]  MODELING OF VIBRATION IN SINGLE-POINT DIAMOND TURNING , 2006 .

[139]  Ozan Cakmakci,et al.  Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[140]  José Sasián.  Method of confocal mirror design , 2019 .

[141]  Fengzhou Fang,et al.  Manufacturing and measurement of freeform optics , 2013 .

[142]  Todd Blalock,et al.  Measurement of mid-spatial frequency errors on freeform optics using deflectometry , 2019, Optical Metrology.

[143]  M. J. Cumbo,et al.  Surface microroughness of optical glasses under deterministic microgrinding. , 1996, Applied optics.

[144]  D. Gauthier,et al.  High-dimensional quantum cryptography with twisted light , 2014, 1402.7113.

[145]  W. Southwell.  Wave-front estimation from wave-front slope measurements , 1980 .

[146]  Jose Sasian,et al.  Method for the design of nonaxially symmetric optical systems using free-form surfaces , 2018 .

[147]  David Schaefer.  Basics of ion beam figuring and challenges for real optics treatment , 2018, Precision Optics Manufacturing.

[148]  Berge Tatian,et al.  Aberration balancing in rotationally symmetric lenses , 1974 .

[149]  R. Noll.  Effect of mid- and high-spatial frequencies on optical performance. [surface error effects on reflecting telescopes] , 1979 .

[150]  Paul E. Murphy,et al.  Freeform testability considerations for subaperture stitching interferometry , 2019, Optifab.

[151]  K. Thompson,et al.  Theory of aberration fields for general optical systems with freeform surfaces. , 2014, Optics express.

[152]  A. Tünnermann,et al.  Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo. , 2011, Optics express.

[153]  Harald Ries,et al.  Tailored freeform optical surfaces. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[154]  Y. Altintas,et al.  Generalized kinematics of five-axis serial machines with non-singular tool path generation , 2013 .

[155]  Jannick P. Rolland,et al.  Hybrid RBF and local ϕ-polynomial freeform surfaces , 2013 .

[156]  Fengzhou Fang,et al.  Review on fast tool servo machining of optical freeform surfaces , 2018 .

[157]  Luke A. DeMars,et al.  Super Sensitive Phase Measurement Deflectometry with effective fringe periods beyond the MTF limit , 2019, Optical Design and Fabrication 2019 (Freeform, OFT).

[158]  G. Forbes,et al.  Stitching Interferometry: A Flexible Solution for Surface Metrology , 2003 .

[159]  Julio Chaves,et al.  Introduction to Nonimaging Optics, Second Edition , 2015 .

[160]  Mohammed Hassan,et al.  Fiber-based tools: material removal and mid-spatial frequency error reduction. , 2017, Applied optics.

[161]  Bisrat G. Assefa,et al.  Imaging-quality 3D-printed centimeter-scale lens. , 2019, Optics express.

[162]  G W Forbes.  Fitting freeform shapes with orthogonal bases. , 2013, Optics express.

[163]  Hassan Foroosh,et al.  Application of radial basis functions to shape description in a dual-element off-axis magnifier. , 2008, Optics letters.

[164]  T. Cruz,et al.  Measurement of the Nanoscale Roughness by Atomic Force Microscopy: Basic Principles and Applications , 2012 .

[165]  Angela Davies,et al.  Characterization of the interpolation bias in the analysis of deflectometry measurement data , 2018, Optical Engineering + Applications.

[166]  Fritz Klocke,et al.  Precision molding of optics: a review of its development and applications , 2016 .

[167]  Ian J. Saunders,et al.  Fabrication and metrology of freeform aluminum mirrors for the SCUBA-2 instrument , 2005, SPIE Optics + Photonics.

[168]  Silvia M. Booij,et al.  Shaping with fluid jet polishing by footprint optimization. , 2004, Applied optics.

[169]  Gregg E. Davis,et al.  Assembly of a freeform off-axis optical system employing three φ-polynomial Zernike mirrors. , 2014, Optics letters.

[170]  A. Küng,et al.  Ultra-high precision CMMs and their associated tactile or/and optical scanning probes , 2014 .

[171]  Kevin P Thompson,et al.  Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[172]  Roland Geyl,et al.  Freeform optics design, fabrication and testing technologies for Space applications , 2019, International Conference on Space Optics.

[173]  Juan Carlos Miñano,et al.  Compact illumination optic with three freeform surfaces for improved beam control. , 2017, Optics express.

[174]  M. Pohl,et al.  Simulation of mid-spatials from the grinding process , 2016 .

[175]  Wolfgang Osten,et al.  Evaluation of absolute form measurements using a tilted-wave interferometer. , 2016, Optics express.

[176]  Matthew A. Davies,et al.  Error correction methodology for ultra-precision three-axis milling of freeform optics , 2017 .

[177]  Theodore T. Saito.  Diamond Turning of Optics , 1976 .

[178]  J. Stover,et al.  Roughness characterization of smooth machined surfaces by light scattering. , 1975, Applied optics.

[179]  Jianing Yao,et al.  Point-cloud noncontact metrology of freeform optical surfaces. , 2018, Optics express.

[180]  Atsushi Okuyama,et al.  Off-axial HMD optical system consisting of aspherical surfaces without rotational symmetry , 1996, Electronic Imaging.

[181]  Stefan Sinzinger,et al.  Subaperture stitching for measurement of freeform wavefront. , 2015, Applied optics.

[182]  Stefan Rakuff,et al.  Thermally induced errors in diamond turning of optical structured surfaces , 2007 .

[183]  G W Forbes,et al.  Characterizing the shape of freeform optics. , 2012, Optics express.

[184]  T. Suleski,et al.  Fabrication and characterization of a biomimetic polarization selective lens. , 2012, Optics letters.

[185]  Thomas R. Smith,et al.  Femtosecond laser polishing of germanium [Invited] , 2019, Optical Materials Express.

[186]  Wenjing Liang,et al.  Design of off-axis three-mirror systems with ultrawide field of view based on an expansion process of surface freeform and field of view. , 2019, Applied optics.

[187]  Herbert Gross,et al.  Description and reimplementation of real freeform surfaces. , 2017, Applied optics.

[188]  James H. Burge,et al.  Modal Data Processing for High Resolution Deflectometry , 2019 .

[189]  James E. Harvey,et al.  Scattering effects from residual optical fabrication errors , 1995, Other Conferences.

[190]  Konstantinos Falaggis,et al.  Multiwavelength interferometry: extended range metrology. , 2009, Optics letters.

[191]  Matthew A. Davies,et al.  Process evaluation and optimization for freeform precision glass molding , 2020, Optical Engineering + Applications.

[192]  Steven M. Arnold.  How To Test An Asphere With A Computer Generated Hologram , 1989, Photonics West - Lasers and Applications in Science and Engineering.