Acta Optica Sinica, Volume. 43, Issue 8, 0822012(2023)

Design Methods and Applications of Freeform Surface Imaging Optical Systems

Menghui Wang, Gaoxing Zhao, Qiran Shi, Yilin Tan, and Jun Zhu*
Author Affiliations
  • Department of Precision Instrument, Tsinghua University, Beijing 100084, China
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    References(136)

    [1] Cui S F, Lyons N P, Diaz L R et al. Silicone optical elements for cost-effective freeform solar concentration[J]. Optics Express, 27, A572-A580(2019).

    [2] Wei L D, Li Y C, Jing J J et al. Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface[J]. Optics Express, 26, 8550-8565(2018).

    [3] Schiesser E M, Bauer A, Rolland J P. Effect of freeform surfaces on the volume and performance of unobscured three mirror imagers in comparison with off-axis rotationally symmetric polynomials[J]. Optics Express, 27, 21750-21765(2019).

    [4] Yoon C, Bauer A, Xu D et al. Absolute linear-in-k spectrometer designs enabled by freeform optics[J]. Optics Express, 27, 34593-34602(2019).

    [5] Rolland J P, Davies M A, Suleski T J et al. Freeform optics for imaging[J]. Optica, 8, 161-176(2021).

    [6] Fang F Z, Zhang X D, Weckenmann A et al. Manufacturing and measurement of freeform optics[J]. CIRP Annals, 62, 823-846(2013).

    [7] Jiang X, Scott P, Whitehouse D. Freeform surface characterisation-a fresh strategy[J]. CIRP Annals, 56, 553-556(2007).

    [8] Thompson K P, Rolland J P. Freeform optical surfaces: a revolution in imaging optical design[J]. Optics and Photonics News, 23, 30-35(2012).

    [9] Kingslake R, Johnson R B[M]. Lens design fundamentals(2010).

    [10] Shannon R R[M]. The art and science of optical design(1997).

    [11] Conrady A E[M]. Applied optics and optical design, part one(1991).

    [12] Hou W, Zhu J, Yang T et al. Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems[J]. Journal of Optics, 17, 055603(2015).

    [13] Yang T, Zhu J, Jin A G. Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface[J]. Chinese Optics Letters, 14, 60801-60805(2016).

    [14] Shack R V, Thompson K. Influence of alignment errors of a telescope system on its aberration field[J]. Proceedings of SPIE, 0251, 146-153(1980).

    [15] Thompson K P. Aberration fields in tilted and decentered optical systems[D](1980).

    [16] Thompson K. Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry[J]. Journal of the Optical Society of America A, 22, 1389-1401(2005).

    [17] Schmid T, Rolland J P, Rakich A et al. Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT)[J]. Optics Express, 18, 17433-17447(2010).

    [18] Fuerschbach K, Rolland J P, Thompson K P. Theory of aberration fields for general optical systems with freeform surfaces[J]. Optics Express, 22, 26585-26606(2014).

    [19] Bauer A, Schiesser E M, Rolland J P. Starting geometry creation and design method for freeform optics[J]. Nature Communications, 9, 1756(2018).

    [20] Sasian J M. How to approach the design of a bilateral symmetric optical system[J]. Optical Engineering, 33, 2045-2061(1994).

    [21] Reshidko D, Sasian J. Method for the design of nonaxially symmetric optical systems using free-form surfaces[J]. Optical Engineering, 57, 101704(2018).

    [22] Papa J C, Howard J M, Rolland J P. Starting point designs for freeform four-mirror systems[J]. Optical Engineering, 57, 101705(2018).

    [23] Papa J C, Howard J M, Rolland J P. Three-mirror freeform imagers[J]. Proceedings of SPIE, 1069, 106901D(2018).

    [24] Papa J C, Howard J M, Rolland J P. Automatic solution space exploration for freeform optical design[C], FM4B.1(2019).

    [25] Wassermann G D, Wolf E. On the theory of aplanatic aspheric systems[J]. Proceedings of the Physical Society Section B, 62, 2-8(1949).

    [26] Vaskas E M. Note on the wasserman-wolf method for designing aspheric surfaces[J]. Journal of the Optical Society of America, 47, 669-670(1957).

    [27] Knapp D J. Conformal optical design[D](2002).

    [28] Hicks R A. Direct methods for freeform surface design[J]. Proceedings of SPIE, 6668, 666802(2007).

    [29] Cheng D W, Wang Y T, Hua H. Free form optical system design with differential equations[J]. Proceedings of SPIE, 7849, 78490Q(2010).

    [30] Hicks R A. Controlling a ray bundle with a free-form reflector[J]. Optics Letters, 33, 1672-1674(2008).

    [31] Hicks R A, Croke C. Designing coupled free-form surfaces[J]. Journal of the Optical Society of America A, 27, 2132-2137(2010).

    [32] Volatier J B, Druart G. Differential method for freeform optics applied to two-mirror off-axis telescope design[J]. Optics Letters, 44, 1174-1177(2019).

    [33] Miñano J C, González J C. New method of design of nonimaging concentrators[J]. Applied Optics, 31, 3051-3060(1992).

    [34] Miñano J C, Benítez P, González J C. RX: a nonimaging concentrator[J]. Applied Optics, 34, 2226-2235(1995).

    [35] Miñano J C, Benítez P, Lin W et al. An application of the SMS method for imaging designs[J]. Optics Express, 17, 24036-24044(2009).

    [36] Duerr F, Benítez P, Miñano J C et al. Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles[J]. Optics Express, 20, 5576-5585(2012).

    [37] Duerr F, Benítez P, Miñano J C et al. Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces[J]. Optics Express, 20, 10839-10846(2012).

    [38] Nie Y F, Thienpont H, Duerr F. Multi-fields direct design approach in 3D: calculating a two-surface freeform lens with an entrance pupil for line imaging systems[J]. Optics Express, 23, 34042-34054(2015).

    [39] Benítez P, Nikolic M, Miñano J C et al. Second-order semi-aplanatic freeform optics as a limit case of the SMS 3D design method[J]. Optics Express, 30, 25985-25994(2022).

    [40] Zhu J, Yang T, Jin G F. Design method of surface contour for a freeform lens with wide linear field-of-view[J]. Optics Express, 21, 26080-26092(2013).

    [41] Yang T, Zhu J, Wu X F et al. Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method[J]. Optics Express, 23, 10233-10246(2015).

    [42] Yang T, Zhu J, Hou W et al. Design method of freeform off-axis reflective imaging systems with a direct construction process[J]. Optics Express, 22, 9193-9205(2014).

    [43] Zhu J, Wu X F, Yang T et al. Generating optical freeform surfaces considering both coordinates and normals of discrete data points[J]. Journal of the Optical Society of America A, 31, 2401-2408(2014).

    [44] Gong T T, Jin G F, Zhu J. Full-field point-by-point direct design method of off-axis aspheric imaging systems[J]. Optics Express, 24, 29417-29426(2016).

    [45] Gong T T, Jin G F, Zhu J. Point-by-point design method for mixed-surface-type off-axis reflective imaging systems with spherical, aspheric, and freeform surfaces[J]. Optics Express, 25, 10663-10676(2017).

    [46] Zhang B Q, Jin G F, Zhu J. Design method for freeform optical systems containing diffraction gratings[J]. Optics Express, 26, 20792-20801(2018).

    [47] Tang R R, Zhang B Q, Jin G F et al. Multiple surface expansion method for design of freeform imaging systems[J]. Optics Express, 26, 2983-2994(2018).

    [48] Wu W C, Jin G F, Zhu J. Optical design of the freeform reflective imaging system with wide rectangular FOV and low F-number[J]. Results in Physics, 15, 102688(2019).

    [49] Yang T, Zhu J, Jin G F. Starting configuration design method of freeform imaging and afocal systems with a real exit pupil[J]. Applied Optics, 55, 345-353(2016).

    [50] Yang T, Jin G F, Zhu J. Design of image-side telecentric freeform imaging systems based on a point-by-point construction-iteration process[J]. Chinese Optics Letters, 15, 062202(2017).

    [51] Liu X Y, Zhu J. Design method of freeform off-axis multi-mirror optical systems[J]. Photonics, 9, 534(2022).

    [52] van Brunt B. Mathematical possibility of certain systems in geometrical optics[J]. Journal of the Optical Society of America A, 11, 2905-2914(1994).

    [53] Duerr F, Thienpont H. Freeform imaging systems: Fermat’s principle unlocks “first time right” design[J]. Light: Science & Applications, 10, 95(2021).

    [54] Nie Y F, Shafer D R, Ottevaere H et al. Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation[J]. Optics Express, 29, 17227-17245(2021).

    [55] Wuest T, Weimer D, Irgens C et al. Machine learning in manufacturing: advantages, challenges, and applications[J]. Production & Manufacturing Research, 4, 23-45(2016).

    [56] Koza J R, Bennett F H, Andre D et al. Automated design of both the topology and sizing of analog electrical circuits using genetic programming[M]. Gero J S, Sudweeks F. Artificial intelligence in design ’96, 151-170(1996).

    [57] Schmidhuber J. Deep learning in neural networks: an overview[J]. Neural Networks, 61, 85-117(2015).

    [58] LeCun Y, Bengio Y, Hinton G. Deep learning[J]. Nature, 521, 436-444(2015).

    [59] Yang T, Cheng D W, Wang Y T. Direct generation of starting points for freeform off-axis three-mirror imaging system design using neural network based deep-learning[J]. Optics Express, 27, 17228-17238(2019).

    [60] Fan C X, Yang B, Liu Y P et al. Using deep learning to automatically generate design starting points for free-form imaging optical systems[J]. Applied Optics, 61, 6241-6248(2022).

    [61] Chen W C, Yang T, Cheng D W et al. Generating starting points for designing freeform imaging optical systems based on deep learning[J]. Optics Express, 29, 27845-27870(2021).

    [62] Côté G, Lalonde J F, Thibault S. Deep learning-enabled framework for automatic lens design starting point generation[J]. Optics Express, 29, 3841-3854(2021).

    [63] Kaelbling L P, Littman M L, Moore A W. Reinforcement learning: a survey[J]. Journal of Artificial Intelligence Research, 4, 237-285(1996).

    [64] Yang T, Cheng D W, Wang Y T. Designing freeform imaging systems based on reinforcement learning[J]. Optics Express, 28, 30309-30323(2020).

    [65] Liu J, Wei H, Fan H J. A novel method for finding the initial structure parameters of optical systems via a genetic algorithm[J]. Optics Communications, 361, 28-35(2016).

    [66] Haupt R L, Haupt S E. Practical genetic algorithms[M]. Ahn C W. Advances in evolutionary algorithms: theory, design and practice, 7-22(2006).

    [67] Menke C. Application of particle swarm optimization to the automatic design of optical systems[J]. Proceedings of SPIE, 10690, 106901A(2018).

    [68] van Laarhoven P J M, Aarts E H L. Simulated annealing[M]. Van Laarhoven P J M, Aarts E H L. Simulated annealing: theory and applications, 7-15(1987).

    [69] Rutenbar R A. Simulated annealing algorithms: an overview[J]. IEEE Circuits and Devices Magazine, 5, 19-26(1989).

    [70] Ma J, Wang J S, Denker C et al. Optical design of multilayer achromatic waveplate by simulated annealing algorithm[J]. Chinese Journal of Astronomy and Astrophysics, 8, 349-361(2008).

    [71] Yang T, Jin G F, Zhu J. Automated design of freeform imaging systems[J]. Light: Science & Applications, 6, 17081(2017).

    [72] Wu W C, Wang H, Jin G F et al. Fast automatic design method for freeform imaging systems through system construction and correction[J]. Optics Letters, 45, 5140-5143(2020).

    [73] Zhang B Q, Jin G F, Zhu J. Towards automatic freeform optics design: coarse and fine search of the three-mirror solution space[J]. Light: Science & Applications, 10, 65(2021).

    [74] Zhang B Q, Men C, Zhu J. Design of a freeform imaging spectrometer based on a solution-diversified automatic design method[J]. Optics Express, 29, 37476-37488(2021).

    [75] Henri C. Anamorphotic lens system and method of making the same[P].

    [76] Kanolt C W. Multifocal ophthalmic lenses[P].

    [77] Alvarez L W. Two-element variable-power spherical lens[P].

    [78] Plummer W T. Unusual optics of the Polaroid SX-70 Land camera[J]. Applied Optics, 21, 196-208(1982).

    [79] Xie Y J, Mao X L, Li J P et al. Optical design and fabrication of an all-aluminum unobscured two-mirror freeform imaging telescope[J]. Applied Optics, 59, 833-840(2020).

    [80] Zhang X J, Xue D L, Li M et al. Designing, fabricating, and testing freeform surfaces for space optics[J]. Proceedings of SPIE, 8838, 88380N(2013).

    [81] Meng Q Y, Wang H Y, Wang K J et al. Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror[J]. Applied Optics, 55, 8962-8970(2016).

    [82] Meng Q Y, Wang H Y, Liang W J 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[J]. Applied Optics, 58, 609-615(2019).

    [83] Liu X Y, Zhu J. Automatic design method of starting points of freeform off-axis reflective imaging systems of small volume[J]. Optics Express, 30, 7954-7967(2022).

    [84] Liu C, Straif C, Flügel-Paul T et al. Comparison of hyperspectral imaging spectrometer designs and the improvement of system performance with freeform surfaces[J]. Applied Optics, 56, 6894-6901(2017).

    [85] Forbes G W. Characterizing the shape of freeform optics[J]. Optics Express, 20, 2483-2499(2012).

    [86] Reimers J, Bauer A, Thompson K P et al. Freeform spectrometer enabling increased compactness[J]. Light: Science & Applications, 6, 17026(2017).

    [87] Yang T, Cheng D W, Wang Y T. Freeform imaging spectrometer design using a point-by-point design method[J]. Applied Optics, 57, 4718-4727(2018).

    [88] Zhang B Q, Tan Y L, Jin G F et al. Imaging spectrometer with single component of freeform concave grating[J]. Optics Letters, 46, 3412-3415(2021).

    [89] Liu Y X, Bauer A, Viard T et al. Freeform hyperspectral imager design in a CubeSat format[J]. Optics Express, 29, 35915-35928(2021).

    [90] He T C. Coaxial ultra-short focus and large aperture projection lens design[D](2019).

    [91] Zhuang Z F, Chen Y T, Yu F H et al. Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface[J]. Applied Optics, 53, E69-E76(2014).

    [92] Gao Y, Cheng D W, Xu C et al. Design of an ultra-short throw catadioptric projection lens with a freeform mirror[J]. Proceedings of SPIE, 10154, 101540S(2016).

    [93] Yu B H, Tian Z H, Su D Q et al. Optical design of an ultra-short-focus projection system with low throw ratio based on a freeform surface mirror[J]. Chinese Journal of Optics, 13, 363-371(2020).

    [94] Graeupner P, Kuerz P, Stammler T et al. EUV optics: status, outlook and future[J]. Proceedings of SPIE, 12051, 1205102(2022).

    [95] Zahlten C, Gräupner P, van Schoot J et al. High-NA EUV lithography: pushing the limits[J]. Proceedings of SPIE, 11177, 111770B(2019).

    [96] Mao S S, Li Y Q, Liu K et al. Optical design of high numerical aperture extreme ultraviolet lithography objective with freeform surfaces[J]. Infrared and Laser Engineering, 48, 0814002(2019).

    [97] Liu Y, Li Y Q, Cao Z. Design method of off-axis extreme ultraviolet lithographic objective system with a direct tilt process[J]. Optical Engineering, 54, 075102(2015).

    [98] Wu Y, Wang L P, Zhang X et al. Design method for an off-axis reflective anamorphic optical system with aberration balance and constraint control[J]. Applied Optics, 60, 4557-4566(2021).

    [99] Yan X, Li Y Q, Liu L H et al. Grouping design method dependence on an illumination system and large off-axis distance for an anamorphic extreme ultraviolet lithography objective[J]. Applied Optics, 61, 806-811(2022).

    [100] Zhu J, Hou W, Zhang X D et al. Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view[J]. Journal of Optics, 17, 015605(2015).

    [101] Beier M, Hartung J, Peschel T et al. Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope[J]. Applied Optics, 54, 3530-3542(2015).

    [102] Tan Y L, Zhu J. Spatial three-mirror off-axis freeform optical system without any symmetry[J]. Photonics, 9, 326(2022).

    [103] Fuerschbach K, Rolland J P, Thompson K P. A new family of optical systems employing φ‑polynomial surfaces[J]. Optics Express, 19, 21919-21928(2011).

    [104] Cheng D W, Wang Y T, Hua H et al. Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism[J]. Applied Optics, 48, 2655-2668(2009).

    [105] Hua H, Hu X D, Gao C Y. A high-resolution optical see-through head-mounted display with eyetracking capability[J]. Optics Express, 21, 30993-30998(2013).

    [106] Cheng D W, Wang Y T, Hua H et al. Design of a wide-angle, lightweight head-mounted display using free-form optics tiling[J]. Optics Letters, 36, 2098-2100(2011).

    [107] Pan J W, Chiang C W, Huang K D et al. Demonstration of a broad band spectral head-mounted display with freeform mirrors[J]. Optics Express, 22, 12785-12798(2014).

    [108] Cheng D W, Duan J X, Chen H L et al. Freeform OST-HMD system with large exit pupil diameter and vision correction capability[J]. Photonics Research, 10, 21-32(2022).

    [109] Wilson A, Hua H. Design and demonstration of a vari-focal optical see-through head-mounted display using freeform Alvarez lenses[J]. Optics Express, 27, 15627-15637(2019).

    [110] Wei S L, Fan Z C, Zhu Z B et al. Design of a head-up display based on freeform reflective systems for automotive applications[J]. Applied Optics, 58, 1675-1681(2019).

    [111] Qin Z, Lin S M, Luo K T et al. Dual-focal-plane augmented reality head-up display using a single picture generation unit and a single freeform mirror[J]. Applied Optics, 58, 5366-5374(2019).

    [112] Lee J H, Yanusik I, Choi Y et al. Automotive augmented reality 3D head-up display based on light-field rendering with eye-tracking[J]. Optics Express, 28, 29788-29804(2020).

    [113] Gu L, Cheng D W, Liu Y et al. Design and fabrication of an off-axis four-mirror system for head-up displays[J]. Applied Optics, 59, 4893-4900(2020).

    [114] Bauer A, Rolland J P. Design of a freeform electronic viewfinder coupled to aberration fields of freeform optics[J]. Optics Express, 23, 28141-28153(2015).

    [115] Bauer A, Pesch M, Muschaweck J et al. All-reflective electronic viewfinder enabled by freeform optics[J]. Optics Express, 27, 30597-30605(2019).

    [116] Zhu J, Zhang B Q, Hou W et al. Design of an oblique camera based on a field-dependent parameter[J]. Applied Optics, 58, 5650-5655(2019).

    [117] Zhang B Q, Hou W, Jin G F et al. Simultaneous improvement of field-of-view and resolution in an imaging optical system[J]. Optics Express, 29, 9346-9362(2021).

    [118] Wu W C, Zhang B Q, Zhu J. Freeform imaging system with resolution that varies with the field angle in two dimensions[J]. Optics Express, 29, 37354-37367(2021).

    [119] Wu X F, Zhu J, Yang T et al. Transverse image translation using an optical freeform single lens[J]. Applied Optics, 54, E55-E62(2015).

    [120] Tang R R, Jin G F, Zhu J. Freeform off-axis optical system with multiple sets of performance integrations[J]. Optics Letters, 44, 3362-3365(2019).

    [121] Jahn W, Ferrari M, Hugot E. Innovative focal plane design for large space telescope using freeform mirrors[J]. Optica, 4, 1188-1195(2017).

    [122] Ma T, Yu J C, Liang P et al. Design of a freeform varifocal panoramic optical system with specified annular center of field of view[J]. Optics Express, 19, 3843-3853(2011).

    [123] Chen J J, Su J H, Jin N et al. Design and tests of a high-performance long-wave infrared refractive thermal imager: freeform lens in coaxial system[J]. Applied Sciences, 7, 1195(2017).

    [124] Zhu D Y, Hu Z J, Yan J H et al. Design of a compact off-axis freeform three-mirror system in a circular configuration[J]. Applied Optics, 61, 7078-7083(2022).

    [125] Sun Y H, Sun Y Q, Chen X Y et al. Design of a free-form off-axis three-mirror optical system with a low f-number based on the same substrate[J]. Applied Optics, 61, 7033-7040(2022).

    [126] Yang T, Zhou L J, Cheng D W et al. Designing reflective imaging systems with multiple-surfaces-integrated elements using a Gaussian function freeform surface[J]. Applied Optics, 61, 5215-5225(2022).

    [127] Yang T, Wang Y D, Ni D W et al. Design of off-axis reflective imaging systems based on freeform holographic elements[J]. Optics Express, 30, 20117-20134(2022).

    [128] Cheng D W, Chen H L, Yao C et al. Design, stray light analysis, and fabrication of a compact head-mounted display using freeform prisms[J]. Optics Express, 30, 36931-36948(2022).

    [129] Li M X, Xiao X S, Yu Q H et al. Design of integrated searching and tracking optical systems based on freeform mirrors[J]. Optics Express, 30, 286-295(2022).

    [130] Yu J, Shen Z X, Wang Z S. Compact dual band/dual FOV infrared imaging system with freeform prism[J]. Optics Letters, 46, 829-832(2021).

    [131] Toulouse A, Drozella J, Motzfeld P et al. Ultra-compact 3D-printed wide-angle cameras realized by multi-aperture freeform optical design[J]. Optics Express, 30, 707-720(2022).

    [132] Zhuang Z F, Parent J, Roulet P et al. Freeform wide-angle camera lens enabling mitigable distortion[J]. Applied Optics, 61, 5449-5456(2022).

    [133] Liu Y P, Yang B, Zhuang S L. Optimal focal length search and design of a compact zoom lens based on a telecentric intermediate image[J]. Applied Optics, 61, 7366-7372(2022).

    [134] Liu Y P, Yang B, Zhuang S L. Automated design of a slim catadioptric system combining freeform surface and zoom lens[J]. Optics Express, 30, 13372-13390(2022).

    [135] Moein S, Suleski T J. Freeform optics for variable extended depth of field imaging[J]. Optics Express, 29, 40524-40537(2021).

    [136] Cheng D W, Chen H L, Yang T et al. Optical design of a compact and high-transmittance compressive sensing imaging system enabled by freeform optics[J]. Chinese Optics Letters, 19, 112202(2021).

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    Menghui Wang, Gaoxing Zhao, Qiran Shi, Yilin Tan, Jun Zhu. Design Methods and Applications of Freeform Surface Imaging Optical Systems[J]. Acta Optica Sinica, 2023, 43(8): 0822012

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    Paper Information

    Category: Optical Design and Fabrication

    Received: Nov. 2, 2022

    Accepted: Dec. 30, 2022

    Published Online: Apr. 6, 2023

    The Author Email: Zhu Jun (j_zhu@tsinghua.edu.cn)

    DOI:10.3788/AOS221925

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