[1] Evans C J and Bryan J B 1999 “Structured”, “textured” or “engineered” surfaces CIRP Ann. 48 541-56

[2] Jiang X Q, Scott P and Whitehouse D 2007 Freeform surface characterisation—a fresh strategy CIRP Ann. 56 553-6

[3] Zhang B, Hou W, Jin G and Zhu J 2021 Simultaneous improvement of field-of-view and resolution in an imaging optical system Opt. Express 29 9346-62

[4] Moein S and Suleski T J 2021 Freeform optics for variable extended depth of field imaging Opt. Express 29 40524-37

[5] Davies M A, Dutterer B S, Swagler S, Lawing E and Horvath N 2021 Optomechanical design and fabrication of a wide field of view 250-mm-aperture freeform imaging system Proc. 22nd Advanced Maui Optical and Space Surveillance Technologies (AMOS) Conf. (Maui, HI)

[6] Zhan A L, Colburn S, Dodson C M and Majumdar A 2017 Metasurface freeform nanophotonics Sci. Rep. 7 1673

[7] Geyl R, Ruch E, Bourgois R, Mercier-Ythier R, Leplan H and Riguet F 2018 Freeform optics design, fabrication and testing technologies for space applications Proc. SPIE 11180 111800P

[8] Falaggis K, Rolland J, Duerr F and Sohn A 2022 Freeform optics: introduction Opt. Express 30 6450-5

[9] Vives S, Pascal S, Secroun A, Gray M, Le Mignant D, Cuby J G and Ferrari M 2011 Modeling highly aspherical optical surfaces using a new polynomial formalism into Zemax Proc. SPIE 8167 81670B

[10] Caron J and Baumer S 2021 Progress in freeform mirror design for space applications Proc. SPIE 11852 118521S

[11] Wang Y B, Wang C L, Xing Q R, Liu F, Li Y F, Chai L, Wang Q Y, Fang F Z and Zhang X D 2009 Periodic optical delay line based on a tilted parabolic generatrix helicoid reflective mirror Appl. Opt. 48 1998-2005

[12] Bentez P, Minano J C, Zamora P, Buljan M, Cvetkovic A, Hernandez M, Mohedano R, Chaves J and Dross O 2010 Free-form Kohler nonimaging optics for photovoltaic concentration Proc. SPIE 7849 78490K

[13] Hussein S, Hamilton B, Tutunea-Fatan O R and Bordatchev E 2016 Novel retroreflective micro-optical structure for automotive lighting applications SAE Int. J. Passeng. Cars—Mech. Syst. 9 497-506

[14] Cheng D W, Wang Y T, Hua H and Talha M M 2009 Design of an optical see-through head-mounted display with a low f -number and large field of view using a freeform prism Appl. Opt. 48 2655-68

[15] Tang Z Y and Gross H 2021 Improved correction by freeform surfaces in prism spectrometer concepts Appl. Opt. 60 333-41

[16] Ding Y, Liu X, Zheng Z R and Gu P F 2008 Freeform LED lens for uniform illumination Opt. Express 16 12958-66

[17] Feng Z X, Cheng D W and Wang Y T 2020 Iterative freeform lens design for prescribed irradiance on curved target Opto-Electron. Adv. 3 200010

[18] Wu R M, Feng Z X, Zheng Z R, Liang R G, Benitez P, Minano J C and Duerr F 2018 Design of freeform illumination optics Laser Photonics Rev. 12 1700310

[19] Su X, Ji P, Liu K, Walker D, Yu G Y, Li H Y, Li D and Wang B 2019 Combined processing chain for freeform optics based on atmospheric pressure plasma processing and bonnet polishing Opt. Express 27 17979-92

[20] Hofele M, Roth A, Schanz J, Neuer J, Harrison D K, De Silva A K M and Riegel H 2021 Laser polishing of additive manufactured aluminium parts by modulated laser power Micromachines 12 1332

[21] Tong Z, Zhong W B, To S and Zeng W H 2020 Fast-tool-servo micro-grooving freeform surfaces with embedded metrology CIRP Ann. 69 505-8

[22] Chen S Y, Xue S, Zhai D D and Tie G P 2020 Measurement of freeform optical surfaces: trade-off between accuracy and dynamic range Laser Photonics Rev. 14 1900365

[23] Fang F Z, Zhang X D, Weckenmann A, Zhang G X and Evans C 2013 Manufacturing and measurement of freeform optics CIRP Ann. 62 823-46

[24] Winston R, Minano J C, Benitez P, Shatz N and Bortz J C 2005 Nonimaging Optics (Burlington, MA: Elsevier Academic Press)

[25] Minano J C and Gonzalez J C 1992 New method of design of nonimaging concentrators Appl. Opt. 31 3051-60

[26] Minano J C, Gonzlez J C and Benitez P 1995 A high-gain, compact, nonimaging concentrator: RXI Appl. Opt. 34 7850-6

[27] Minano J C, Benitez P and Gonzalez J C 1995 RX: a nonimaging concentrator Appl. Opt. 34 2226-35

[28] Minano J C, Gonzalez J C and Zanesco I 1994 Flat high concentration devices Proc. IEEE 1st World Conf. on Photovoltaic Energy Conversion—WCPEC (A Joint Conf. PVSC, PVSEC and PSEC) (Waikoloa, HI: IEEE) pp 1123-6

[29] Barone G, Buonomano A, Forzano C and Palombo A 2019 Solar thermal collectors Solar Hydrogen Production ed F Calise, M D D’Accadia, M Santarelli, A Lanzini and D Ferrero (Amsterdam: Elsevier) ch 6, pp 151-78

[30] Muhammad-Sukki F, Ramirez-Iniguez R, McMeekin S G, Stewart B G and Clive B 2010 Solar concentrators Int. J. Appl. Sci. 1 1-15

[31] Vu N H and Shin S 2016 A concentrator photovoltaic system based on a combination of prism-compound parabolic concentrators Energies 9 645

[32] Li X, Dai Y J, Li Y and Wang R Z 2013 Performance investigation on a novel single-pass evacuated tube with a symmetrical compound parabolic concentrator Sol. Energy 98 275-89

[33] Ning X H, Winston R and O’Gallagher J 1987 Dielectric totally internally reflecting concentrators Appl. Opt. 26 300-5

[34] Benitez P, Minano J C, Blen J, Mohedano R, Chaves J, Dross O, Hernandez M, Alvarez J L and Falicoff W 2004 SMS design method in 3D geometry: examples and applications Proc. SPIE 5185 18-29

[35] Cvetkovic A 2009 Free-form optical systems for nonimaging applications PhD Thesis Universidad Politécnica De Madrid, Spain (available at: https://oa.upm.es/1782/)

[36] Wojtanowski J and Drozd T 2020 Simplified geometric approach to freeform beam shaper design Int. J. Opt. 2020 2896593

[37] Dickey F M and Lizotte T E 2017 Laser Beam Shaping Applications 2nd edn (Boca Raton, FL: CRC Press)

[38] Frieden B R 1965 Lossless conversion of a plane laser wave to a plane wave of uniform irradiance Appl. Opt. 4 1400-3

[39] Rhodes P W and Shealy D L 1980 Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis Appl. Opt. 19 3545-53

[40] Jiang W, Shealy D L and Martin J C 1993 Design and testing of a refractive reshaping system Proc. SPIE 2000 64-75

[41] Hoffnagle J A and Jefferson C M 2003 Beam shaping with a plano-aspheric lens pair Opt. Eng. 42 3090-9

[42] Alvarez L W 1967 Two-element variable-power spherical lens US Patent 3305294

[43] Zou Y C, Zhang W, Chau F S and Zhou G Y 2015 Miniature adjustable-focus endoscope with a solid electrically tunable lens Opt. Express 23 20582-92

[44] Zhou G Y, Yu H B and Chau F S 2013 Microelectromechanically-driven miniature adaptive Alvarez lens Opt. Express 21 1226-33

[45] Chaves J 2016 Introduction to Nonimaging Optics 2nd edn (Boca Raton, FL: CRC Press) p 786

[46] Feng Z X, Luo Y and Han Y J 2010 Design of LED freeform optical system for road lighting with high luminance/illuminance ratio Opt. Express 18 22020-31

[47] Luo Y, Feng Z X, Han Y J and Li H T 2010 Design of compact and smooth free-form optical system with uniform illuminance for LED source Opt. Express 18 9055-63

[48] Jiang J B, To S, Lee B W and Cheung B 2010 Optical design of a freeform TIR lens for LED streetlight Optik 121 1761-5

[49] Wu R M, Huang C Y, Zhu X Y, Cheng H N and Liang R G 2016 Direct three-dimensional design of compact and ultra-efficient freeform lenses for extended light sources Optica 3 840-3

[50] Wu R M, Zheng Z R, Li H F and Liu X 2011 Freeform lens for off-axis illumination in optical lithography system Opt. Commun. 284 2662-7

[51] Fournier F and Rolland J 2008 Optimization of freeform lightpipes for light-emitting-diode projectors Appl. Opt. 47 957-66

[52] Munoz F, Benitez P and Minano J 2008 High-order aspherics: the SMS nonimaging design method applied to imaging optics Proc. SPIE 7061 70610G

[53] Nie Y F, Mohedano R, Benitez P, Chaves J, Minano J C, Thienpont H and Duerr F 2016 Optical design of an ultrashort throw ratio projector with two freeform mirrors Proc. SPIE 9947 99470C

[54] Zheng Z R, Sun X T, Liu X and Gu P F 2008 Design of reflective projection lens with Zernike polynomials surfaces Displays 29 412-7

[55] Bian Y X, Li H F, Wang Y F, Zheng Z R and Liu X 2015 Method to design two aspheric surfaces for a wide field of view imaging system with low distortion Appl. Opt. 54 8241-7

[56] Zhuang Z F, Chen Y T, Yu F H and Sun X W 2014 Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface Appl. Opt. 53 E69-E76

[57] Rolland J P and Cakmakci O 2005 The past, present, and future of head-mounted display designs Proc. SPIE 5638 368-77

[58] Foote B and Melzer J 2015 A history of helmet mounted displays Proc. SPIE 9470 94700T

[59] Wang Y T, Cheng D W and Xu C 2017 Freeform optics for virtual and augmented reality Optical Design and Fabrication 2017 (Freeform, IODC, OFT) (Denver, CO: Optica Publishing Group) p JTu3A.1

[60] Hua H, Hu X D, Gao C Y and Qin X 2014 Eyetracked optical see-through head-mounted display as an AAC device Proc. SPIE 9117 91170T

[61] Benitez P et al 2017 Advanced freeform optics enabling ultra-compact VR headsets Proc. SPIE 10335 103350I

[62] Hu X D and Hua H 2014 High-resolution optical see-through multi-focal-plane head-mounted display using freeform optics Opt. Express 22 13896-903

[63] National Aeronautics and Space Administration 2010 “Infrared waves” (NASA Science) (available at: http://science.nasa.gov/ems/07_infraredwaves)

[64] Gade R and Moeslund T B 2014 Thermal cameras and applications: a survey Mach. Vis. Appl. 25 245-62

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

[66] Chen J J, Su J H, Jin N, Li Z X, Zhang X D, Zhang H and Zhou L G 2017 Design and tests of a high-performance long-wave infrared refractive thermal imager: freeform lens in coaxial system Appl. Sci. 7 1195

[67] Zhu J, Hou W, Zhang X D and Jin G F 2015 Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view J. Opt. 17 015605

[68] Jiang X Q 2018 Freeform CIRP Encyclopedia of Production Engineering ed The International Academy for Production Engineering (Berlin: Springer) pp 1-7

[69] Duerr F, Benitez P, Minano J C, Meuret Y and Thienpont H 2012 Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces Opt. Express 20 10839-46

[70] Hicks R A 2007 Direct methods for freeform surface design Proc. SPIE 6668 666802

[71] Wassermann G D and Wolf E 1949 On the theory of aplanatic aspheric systems Proc. Phys. Soc. B 62 2-8

[72] Vaskas E M 1957 Note on the Wassermann-wolf method for designing aspheric surfaces J. Opt. Soc. Am. 47 669-70

[73] Volatier J B and Druart G 2019 Differential method for freeform optics applied to two-mirror off-axis telescope design Opt. Lett. 44 1174-7

[74] Knapp D J 2002 Conformal optical design PhD Thesis The University of Arizona, Tucson, Arizona (available at: http://hdl.handle.net/10150/289852)

[75] Ries H and Rabl A 1994 Edge-ray principle of nonimaging optics J. Opt. Soc. Am. A 11 2627-32

[76] Ries H R and Winston R 1994 Tailored edge-ray reflectors for illumination J. Opt. Soc. Am. A 11 1260-4

[77] Jenkins D and Winston R 1996 Tailored reflectors for illumination Appl. Opt. 35 1669-72

[78] Ong P T, Gordon J M and Rabl A 1996 Tailored edge-ray designs for illumination with tubular sources Appl. Opt. 35 4361-71

[79] Ries H and Muschaweck J 2002 Tailored freeform optical surfaces J. Opt. Soc. Am. A 19 590-5

[80] William A P 1998 Design of illumination lenses via extrinsic differential geometry Proc. SPIE 3428 154-62

[81] Fournier F R, Cassarly W J and Rolland J P 2010 Fast freeform reflector generation using source-target maps Opt. Express 18 5295-304

[82] Yang T, Jin G F and Zhu J 2017 Automated design of freeform imaging systems Light 6 e17081

[83] Benitez P and Minano J C 2007 The future of illumination design Opt. Photonics News 18 20-25

[84] Canavarro D, Chaves J and Collares-Pereira M 2019 Simultaneous multiple surface method for the design of new parabolic dish-type concentrator using a Cassegranian approach AIP Conf. Proc. 2126 050001

[85] Canavarro D 2014 Advances in the design of solar concentrators for thermal applications PhD Thesis Universidade de Evora, Portugal

[86] Gimenez-Benitez P, Minano J C, Blen J, Arroyo R M, Chaves J, Dross O, Hernandez M and Falicoff W 2004 Simultaneous multiple surface optical design method in three dimensions Opt. Eng. 43 1489-502

[87] Minano J C, Benitez P, Lin W, Infante J, Munoz F and Santamaria A 2009 An application of the SMS method for imaging designs Opt. Express 17 24036-44

[88] Valencia-Estrada J C and Garcia-Marquez J 2019 Freeform geometrical optics I: principles Appl. Opt. 58 9455-64

[89] Minano J C, Benitez P, Cvetkovic A and Mohedano R 2013 SMS 3D design method Illumination Engineering: Design with Nonimaging Optics ed R J Koshel (Piscataway, NJ: Wiley) pp 101-46

[90] Shack R V and Thompson K 1980 Influence of alignment errors of a telescope system on its aberration field Proc. SPIE 0251 146-53

[91] Thompson K 2005 Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry J. Opt. Soc. Am. A 22 1389-401

[92] Fuerschbach K, Rolland J P and Thompson K P 2014 Theory of aberration fields for general optical systems with freeform surfaces Opt. Express 22 26585-606

[93] Bauer A, Schiesser E M and Rolland J P 2018 Starting geometry creation and design method for freeform optics Nat. Commun. 9 1756

[94] Zheng X, Li Z X, Zhang X D and Fang F Z 2018 Manufacturing-constrained optical design methodology for cylindrical freeform reflective imaging system Opt. Express 26 22547-62

[95] Duerr F and Thienpont H 2021 Freeform imaging systems: Fermat’s principle unlocks “first time right” design Light 10 95

[96] Sasian J M 1994 How to approach the design of a bilateral symmetric optical system Opt. Eng. 33 2045-61

[97] Reshidko D and Sasian J 2018 Method for the design of nonaxially symmetric optical systems using free-form surfaces Opt. Eng. 57 101704

[98] Sasian J 2019 Method of confocal mirror design Opt. Eng. 58 015101

[99] Nikolov D K, Bauer A, Cheng F, Kato H, Vamivakas A N and Rolland J P 2021 Metaform optics: bridging nanophotonics and freeform optics Sci. Adv. 7 eabe5112

[100] Hazra L and Banerjee S 1999 Genetic algorithm in the structural design of Cooke triplet lenses Proc. SPIE 3737 172-9

[101] Trumper I L, Marrone D P and Kim D W 2019 Utilizing freeform optics in dynamic optical configuration designs J. Astron. Telesc. Instrum. Syst. 5 035005

[102] Zhuang Z F, Surman P and Yu F H 2016 A freeform optics design with limited data for extended LED light sources J. Mod. Opt. 63 2151-8

[103] Davies M A, Evans C J, Vohra R R, Bergner B C and Patterson S R 2003 Application of precision diamond machining to the manufacture of microphotonics components Proc. SPIE 5183 94-108

[104] Ikawa N, Donaldson R R, Komanduri R, Konig W, Aachen T H, McKeown P A, Moriwaki T and Stowers I F 1991 Ultraprecision metal cutting—the past, the present and the future CIRP Ann. 40 587-94

[105] Doetz M, Dambon O, Klocke F, Vogt C, Rascher R and Fahnle O 2018 Ductile mode single point diamond turning (SPDT) of binderless tungsten carbide molds Proc. SPIE 10742 107420E

[106] Pizani P S, Jasinevicius R, Duduch J G and Porto A J V 1999 Ductile and brittle modes in single-point-diamond-turning of silicon probed by Raman scattering J. Mater. Sci. Lett. 18 1185-7

[107] Shore P 1995 Machining of Optical Surfaces in Brittle Materials Using an Ultra-Precision Machine Tool Cranfield University, Cranfield (available at: http://hdl.handle.net/1826/3610)

[108] Yin Z Q, Dai Y F, Li S Y, Guan C L and Tie G P 2011 Fabrication of off-axis aspheric surfaces using a slow tool servo Int. J. Mach. Tools Manuf. 51 404-10

[109] Davis G E, Roblee J W and Hedges A R 2009 Comparison of freeform manufacturing techniques in the production of monolithic lens arrays Proc. SPIE 7426 742605

[110] Karpat Y 2019 Influence of diamond tool chamfer angle on surface integrity in ultra-precision turning of singe crystal silicon Int. J. Adv. Manuf. Technol. 101 1565-72

[111] Fang F Z, Zhang X D and Hu X T 2008 Cylindrical coordinate machining of optical freeform surfaces Opt. Express 16 7323-9

[112] Chen X, Kang M, Wang X S, Hassan M and Yang J 2017 Tool path optimal design for slow tool servo turning of complex optical surface Proc. Inst. Mech. Eng. B 231 825-37

[113] Wang D F, Sui Y X, Yang H J and Li D 2019 Adaptive spiral tool path generation for diamond turning of large aperture freeform optics Materials 12 810

[114] Patterson S R and Magrab E B 1985 Design and testing of a fast tool servo for diamond turning Precis. Eng. 7 123-8

[115] Trumper D L and Lu X D 2007 Fast tool servos: advances in precision, acceleration, and bandwidth Towards Synthesis of Micro-/Nano-systems ed F Kimura and K Horio (London: Springer) pp 11-19

[116] Patten J 2015 Micro laser assisted machining US Patent 20100065536

[117] Takeuchi Y, Suzukawa H, Kawai T and Sakaida Y 2006 Creation of ultra-precision microstructures with high aspect ratios CIRP Ann. 55 107-10

[118] Zhu Z W, To S, Tong Z, Zhuang Z X and Jiang X Q 2019 Modulated diamond cutting for the generation of complicated micro/nanofluidic channels Precis. Eng. 56 136-42

[119] Cheng M N, Cheung C F, Lee W B and To S 2007 A study of factors affecting surface quality in ultra-precision raster milling Key Eng. Mater. 339 400-6

[120] Li L and Yi A Y 2012 Design and fabrication of a freeform microlens array for a compact large-field-of-view compound-eye camera Appl. Opt. 51 1843-52

[121] Schonemann L et al 2020 Synergistic approaches to ultra-precision high performance cutting CIRP J. Manuf. Sci. Technol. 28 38-51

[122] Owen J D, Davies M A, Schmidt D and Urruti E H 2015 On the ultra-precision diamond machining of chalcogenide glass CIRP Ann. 64 113-6

[123] Owen J D, Shultz J A, Suleski T J and Davies M A 2017 Error correction methodology for ultra-precision three-axis milling of freeform optics CIRP Ann. 66 97-100

[124] Zhang S J, To S, Zhu Z W and Zhang G Q 2016 A review of fly cutting applied to surface generation in ultra-precision machining Int. J. Mach. Tools Manuf. 103 13-27

[125] Sun Z W, To S and Yu K M 2019 An investigation in the ultra-precision fly cutting of freeform surfaces on brittle materials with high machining efficiency and low tool wear Int. J. Adv. Manuf. Technol. 101 1583-93

[126] Steinkopf R, Scheiding S, Gebhardt A, Risse S, Eberhardt R and Tünnermann A 2012 Fly-cutting and testing of freeform optics with sub-μm shape deviations Proc. SPIE 8486 84860K

[127] Brinksmeier E, Riemer O and Osmer J 2008 Tool path generation for ultra-precision machining of free-form surfaces Prod. Eng. 2 241-6

[128] Sun Z W, To S and Zhang S J 2018 A novel ductile machining model of single-crystal silicon for freeform surfaces with large azimuthal height variation by ultra-precision fly cutting Int. J. Mach. Tools Manuf. 135 1-11

[129] Brinksmeier E, Mutlugünes Y, Klocke F, Aurich J C, Shore P and Ohmori H 2010 Ultra-precision grinding CIRP Ann. 59 652-71

[130] Inasaki I 1987 Grinding of hard and brittle materials CIRP Ann. 36 463-71

[131] Bifano T G, Dow T A and Scattergood R O 1991 Ductile-regime grinding: a new technology for machining brittle materials J. Eng. Ind. 113 184-9

[132] Chen B, Guo B and Zhao Q L 2015 An investigation into parallel and cross grinding of aspheric surface on monocrystal silicon Int. J. Adv. Manuf. Technol. 80 737-46

[133] Wang S, Zhao Q L, Pan Y C and Guo B 2021 Ultra-precision raster grinding biconical optics with a novel profile error compensation technique based on on-machine measurement and wavelet decomposition J. Manuf. Process. 67 128-40

[134] Sun X, Stephenson D J, Ohnishi O and Baldwin A 2006 An investigation into parallel and cross grinding of BK7 glass Precis. Eng. 30 145-53

[135] Zhang Z Y, Yang X, Zheng L G and Xue D L 2017 High-performance grinding of a 2-m scale silicon carbide mirror blank for the space-based telescope Int. J. Adv. Manuf. Technol. 89 463-73

[136] Jiang W D and Tse B 2007 Freeform optics fabrication by diamond turning Proc. SPIE 10316 103161J

[137] Jiang W D 2007 Diamond turning aspheric projector mirrors Proc. SPIE 6722 672207

[138] Barkman M L, Dutterer B S, Davies M A and Suleski T J 2008 Free-form machining for micro-imaging systems Proc. SPIE 6883 68830G

[139] Stoebenau S and Sinzinger S 2009 Ultraprecision machining techniques for the fabrication of freeform surfaces in highly integrated optical microsystems Proc. SPIE 7426 742608

[140] Li L K and Yi A Y 2011 Design and fabrication of a freeform microlens array for uniform beam shaping Microsyst. Technol. 17 1713-20

[141] Chen Y and Yi A Y 2011 Design and fabrication of freeform glass concentrating mirrors using a high volume thermal slumping process Sol. Energy Mater. Sol. Cells 95 1654-64

[142] Stoebenau S, Kleindienst R, Hofmann M and Sinzinger S 2011 Computer-aided manufacturing for freeform optical elements by ultraprecision micromilling Proc. SPIE 8126 812614

[143] Joo J Y, Kim W H, Park S S and Song S B 2012 Design and manufacturing of LED primary optics for road lighting engine Proc. SPIE 8550 85502O

[144] Cheng Y, Zhang X D and Zhang G X 2013 Design and machining of Fresnel solar concentrator surfaces Int. J. Precis. Technol. 3 354-69

[145] Li Z X, Fang F Z, Chen J J and Zhang X D 2017 Machining approach of freeform optics on infrared materials via ultra-precision turning Opt. Express 25 2051-62

[146] Li D, Qiao Z, Walton K, Liu Y T, Xue J D, Wang B and Jiang X Q 2018 Theoretical and experimental investigation of surface topography generation in slow tool servo ultra-precision machining of freeform surfaces Materials 11 2566

[147] Zhang X D, Fang F Z, Wang H B, Wei G S and Hu X T 2009 Ultra-precision machining of sinusoidal surfaces using the cylindrical coordinate method J. Micromech. Microeng. 19 054004

[148] Wei L D, Li Y C, Jing J J, Feng L and Zhou J S 2018 Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface Opt. Express 26 8550-65

[149] Bauer A M 2016 Optical design with freeform surfaces, with applications in head-worn display design PhD Thesis University of Rochester, Rochestor, NY (available at: http://hdl.handle.net/1802/31694)

[150] Yan G P and Fang F Z 2019 Fabrication of optical freeform molds using slow tool servo with wheel normal grinding CIRP Ann. 68 341-4

[151] Kong L B, Ma Y G, Ren M J, Xu M and Cheung C 2020 Generation and characterization of ultra-precision compound freeform surfaces Sci. Prog. 103 1-21

[152] Wei Y, Zhai P, Chen X Y and He L 2020 Study on design and diamond turning of optical freeform surface for progressive addition lenses Math. Problems Eng. 2020 2850606

[153] Kang M, Yang J, Wang X S and Chen X 2018 Study on the variational-difference-based design and slow tool servo turning of progressive addition lenses Adv. Mech. Eng. 10 1-12

[154] Kong L B, Cheung C, To S, Wang B and Ho L 2014 A theoretical and experimental investigation of design and slow tool servo machining of freeform progressive addition lenses (PALs) for optometric applications Int. J. Adv. Manuf. Technol. 72 33-40

[155] Feng H H, Xia R S, Li Y Y, Chen J J, Yuan Y M, Zhu D X, Chen S Y and Chen H 2017 Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo Int. J. Adv. Manuf. Technol. 91 3799-806

[156] Cai H B, Xu J L, Xiao J G, Zhang Y F and Shi G Q 2017 Study on optical freeform surface manufacturing of progressive addition lens based on fast tool servo IOP Conf. Ser.: Earth Environ. Sci. 69 012130

[157] Li Y Y, Chen J J, Feng H H, Li C H, Qu J and Chen H 2014 Freeform manufacturing of a progressive addition lens by use of a voice coil fast tool servo Proc. SPIE 9281 92810Q

[158] International Organization for Standardization (ISO) 2019 Optics and photonics—preparation of drawings for optical elements and systems—part 8: surface texture (available at: www.iso.org/standard/69532.html)

[159] Walker D D, Brooks D, Freeman R, King A, McCavana G, Morton R, Riley D and Simms J 2001 First aspheric form and texture results from a production machine embodying the precession process Proc. SPIE 4451 267-76

[160] Ri P, Wang Z Z, Wang C J, Xie Y H, Zhang D X and Guo Y B 2014 Research on control optimization for bonnet polishing system Int. J. Precis. Eng. Manuf. 15 483-8

[161] Walker D D, Beaucamp A T H, Doubrovski V, Dunn C, Freeman R, McCavana G, Morton R, Riley D, Simms J and Wei X 2005 New results extending the Precessions process to smoothing ground aspheres and producing freeform parts Proc. SPIE 5869 58690E

[162] Walker D D et al 2006 New developments in the precessions process for manufacturing free-form, large-optical, and precision-mechanical surfaces Proc. SPIE 6148 614805

[163] Kordonski W, Gorodkin S and Zhuravski N 2001 Static yield stress in magnetorheological fluid Int. J. Mod. Phys. B 15 1078-84

[164] Gorana V K, Jain V K and Lal G K 2004 Experimental investigation into cutting forces and active grain density during abrasive flow machining Int. J. Mach. Tools Manuf. 44 201-11

[165] Kordonski W I and Jacobs S D 1996 Magnetorheological finishing Int. J. Mod. Phys. B 10 2837-48

[166] Harris D C 2011 History of magnetorheological finishing Proc. SPIE 8016 80160N

[167] Kumar S and Singh A K 2018 Magnetorheological nanofinishing of BK7 glass for lens manufacturing Mater. Manuf. Process 33 1188-96

[168] Supranowitz C and Jones A 2021 Magnetorheological finishing of freeform optics using a spiral toolpath Proc. SPIE 11889 118891B

[169] Faehnle O, Rascher R, Vogt C and Kim D W 2018 Closed-loop laser polishing using in-process surface finish metrology Appl. Opt. 57 834-8

[170] Chao C L, Chou W C, Ma K J, Chen T T, Liu Y M, Kuo Y S and Chen Y T 2005 Investigation of laser ablation of CVD diamond film Proc. SPIE 5713 21-28

[171] Lednev V N, Pershin S M, Ionin A A, Kudryashov S I, Makarov S V, Ligachev A E, Rudenko A A, Chmelnitsky R A and Bunkin A F 2013 Laser ablation of polished and nanostructured titanium surfaces by nanosecond laser pulses Spectrochim. Acta B 88 15-19

[172] Becker H, Czerner S, Ostendorf A, Stippler P and Matteazzi P 2005 Technology improvements for microscale laser sintering Proc. SPIE 5827 467-74

[173] Bordatchev E V, Hafiz A M K and Tutunea-Fatan O R 2014 Performance of laser polishing in finishing of metallic surfaces Int. J. Adv. Manuf. Technol. 73 35-52

[174] Weingarten C, Schmickler A, Willenborg E, Wissenbach K and Poprawe R 2017 Laser polishing and laser shape correction of optical glass J. Laser Appl. 29 011702

[175] Hecht K, Bliedtner J, Rost M, Müller H and Schmidt T 2015 Carbon-dioxide laser beam polishing of fused silica surfaces—process development and optimization Adv. Eng. Mater. 17 240-6

[176] Heidrich S, Willenborg E, Weingarten C and Temmler A 2015 Laser polishing and laser form correction of fused silica optics Mater. Sci. Eng. Technol. 46 668-74

[177] Yamada I 2014 Historical milestones and future prospects of cluster ion beam technology Appl. Surf. Sci. 310 77-88

[178] Grogan D F, Zhao T, Bovard B G and Macleod H A 1992 Planarizing technique for ion-beam polishing of diamond films Appl. Opt. 31 1483-7

[179] Insepov Z, Hassanein A, Norem J and Swenson D R 2007 Advanced surface polishing using gas cluster ion beams Nucl. Instrum. Methods Phys. Res. B 261 664-8

[180] Zou J, Zhong Y, Zhang J Z, Ekelund M and Shen Z J 2015 Separating macrostresses from microstresses in Al2O3-15vol%SiC particulate reinforced composites Scr. Mater. 109 84-88

[181] Sun G B, Jiang S L and Zhang J 2021 Research on Ion beam polishing efficiency with changing different beam diameters Proc. SPIE 11761 1176123

[182] Chkhalo N I, Churin S A, Pestov A E, Salashchenko N N, Vainer Y A and Zorina M V 2014 Roughness measurement and ion-beam polishing of super-smooth optical surfaces of fused quartz and optical ceramics Opt. Express 22 20094-106

[183] Bauer J, Frost F, Lehmann A, Ulitschka M, Li Y G and Arnold T 2019 Finishing of metal optics by ion beam technologies Opt. Eng. 58 092612

[184] de Schipper R 2012 Injection molding of optics for high volume consumer products Adv. Opt. Technol. 1 31-37

[185] Walther T 2010 Production of optical components using plastic injection molding technology Handbook of Plastic Optics 2nd edn, ed S Baumer (Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA) pp 197-217

[186] Fang F Z, Zhang N and Zhang X D 2016 Precision injection molding of freeform optics Adv. Opt. Technol. 5 303-24

[187] Dick L, Risse S and Tünnermann A 2016 Process influences and correction possibilities for high precision injection molded freeform optics Adv. Opt. Technol. 5 277-87

[188] Bensingh R J, Machavaram R, Boopathy S R and Jebaraj C 2019 Injection molding process optimization of a bi-aspheric lens using hybrid artificial neural networks (ANNs) and particle swarm optimization (PSO) Measurement 134 359-74

[189] Li L K, Raasch T W, Sieber I, Beckert E, Steinkopf R, Gengenbach U and Yi A Y 2014 Fabrication of microinjection-molded miniature freeform Alvarez lenses Appl. Opt. 53 4248-55

[190] Zhang H Y, Zhang N, Han W, Gilchrist M D and Fang F Z 2021 Precision replication of microlens arrays using variotherm-assisted microinjection moulding Precis. Eng. 67 248-61

[191] Lu Y J, Luo W, Wu X Y, Xu B, Wang C J, Li J J and Li L J 2020 Fabrication of micro-structured LED diffusion plate using efficient micro injection molding and micro-ground mold core Polymers 12 1307

[192] Zhang Y Y, Liang R G, Spires O J, Yin S H, Yi A and Milster T D 2020 Precision glass molding of diffractive optical elements with high surface quality Opt. Lett. 45 6438-41

[193] Schaub M, Schwiegerling J, Fest E C, Symmons A and Shepard R H 2011 Molded Optics: Design and Manufacture (Boca Raton, FL: CRC Press)

[194] He P, Li L K, Li H, Yu J F, Lee L J and Yi A Y 2014 Compression molding of glass freeform optics using diamond machined silicon mold Manuf. Lett. 2 17-20

[195] Gurganus D, Owen J D, Dutterer B S, Novak S, Symmons A and Davies M A 2018 Precision glass molding of freeform optics Proc. SPIE 10742 107420Q

[196] Gurganus D, Novak S, Symmons A and Davies M A 2019 Precision glass molding of freeform optics Optical Design and Fabrication 2019 (Freeform, OFT) (Washington, DC: Optica Publishing Group) p JW1A.4

[197] Zhang L C and Liu W D 2017 Precision glass molding: toward an optimal fabrication of optical lenses Front. Mech. Eng. 12 3-17

[198] Ristok S, Flad P and Giessen H 2022 Atomic layer deposition of conformal anti-reflective coatings on complex 3D printed micro-optical systems Opt. Mater. Express 12 2063-71

[199] Bielawny A 2019 Reflectors in lighting design: reflector-based non-imaging optics for lighting applications Adv. Opt. Technol. 8 469-81

[200] Thetford A 1969 A method of designing three-layer anti-reflection coatings Opt. Acta 16 37-43

[201] Piegari A and Flory F 2018 Optical Thin Films and Coatings: From Materials to Applications 2nd edn (Duxford: Woodhead Publishing, an imprint of Elsevier)

[202] Aitchison B and Cumbo M J 2017 Novel optical coating technology for freeform and conformal optics Optical Design and Fabrication 2017 (Freeform, IODC, OFT) (Denver, CO: Optica Publishing Group) p FTh3B.5

[203] Paul P, Pfeiffer K and Szeghalmi A 2020 Antireflection coating on PMMA substrates by atomic layer deposition Coatings 10 64

[204] Whitehouse D J 1994 Handbook of Surface Metrology (Bristol: Institute of Physics Publishing)

[205] International Organization for Standardization (ISO) 1996 Geometrical product specifications (GPS)—surface texture: profile method—nominal characteristics of contact (stylus) instruments (available at: www.iso.org/ obp/ui/#iso:std:iso:3274:ed-2:v1:en)

[206] Taylor Hobson 2020 Form talysurf PGI freeform (available at: www.taylor-hobson.com/products/surfaceprofilers/optics-pgi/pgi-freeform)

[207] Wang Y M, Li Z X, Fu Z, Fang F Z and Zhang X D 2019 Radial scan form measurement for freeform surfaces with a large curvature using stylus profilometry Meas. Sci. Technol. 30 045010

[208] Spaan H, Donker R and Widdershoven I 2010 Isara 400: enabling ultra-precision coordinate metrology for large parts Proc. Euspen Int. Conf. (Delft: IBS Precision Engineering) pp 231-4

[209] Beutler A 2016 Strategy for a flexible and noncontact measuring process for freeforms Opt. Eng. 55 071206

[210] Scheiding S, Yi A Y, Gebhardt A, Li L, Risse S, Eberhardt R and Tünnermann A 2011 Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo Opt. Express 19 23938-51

[211] Sykora D M and de Groot P 2011 Instantaneous measurement Fizeau interferometer with high spatial resolution Proc. SPIE 8126 812610

[212] Arnold S M 1989 How to test an asphere with a computer generated hologram Proc. SIPE 1052 191-7

[213] Huang L, Wang T Y, Nicolas J, Vivo A, Polack F, Thomasset M, Zuo C, Tayabaly K, Kim D W and Idir M 2019 Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors Opt. Express 27 26940-56

[214] Ghim Y S, Rhee H G, Davies A, Yang H S and Lee Y W 2014 3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry Opt. Express 22 5098-105

[215] Fortmeier I, Stavridis M, Wiegmann A, Schulz M, Osten W and Elster C 2016 Evaluation of absolute form measurements using a tilted-wave interferometer Opt. Express 24 3393-404

[216] Ryle M 1972 The 5-km radio telescope at cambridge Nature 239 435-8

[217] Jackson N 2008 Principles of interferometry Jets from Young Stars II: Clues from High Angular Resolution Observations ed F Bacciotti, L Testi and E Whelan (Berlin: Springer) pp 193-218

[218] Jiang X Q, Wang K W, Gao F and Muhamedsalih H 2010 Fast surface measurement using wavelength scanning interferometry with compensation of environmental noise Appl. Opt. 49 2903-9

[219] Huang L, Idir M, Zuo C and Asundi A 2018 Review of phase measuring deflectometry Opt. Lasers Eng. 107 247-57

[220] Kim D W et al 2021 Advances in reconfigurable optical design, metrology, characterization, and data analysis J. Phys. Photon. 3 022003

[221] Huang L, Xue J P, Gao B, McPherson C, Beverage J and Idir M 2016 Modal phase measuring deflectometry Opt. Express 24 24649-64

[222] Maldonado A V, Su P and Burge J H 2014 Development of a portable deflectometry system for high spatial resolution surface measurements Appl. Opt. 53 4023-32

[223] Davies A, Vann T, Evans C and Butkiewicz M 2017 Phase measuring deflectometry for determining 5 DOF misalignment of segmented mirrors Proc. SPIE 10373 103730H

[224] Su P, Parks R E, Wang L R, Angel R P and Burge J H 2010 Software configurable optical test system: a computerized reverse Hartmann test Appl. Opt. 49 4404-12

[225] Su P et al 2012 SCOTS: a reverse Hartmann test with high dynamic range for giant Magellan telescope primary mirror segments Proc. SPIE 8450 84500W

[226] Yin J F, Bai Q and Zhang B 2018 Methods for detection of subsurface damage: a review Chin. J. Mech. Eng. 31 41

[227] Stover J C 2012 Optical Scattering: Measurement and Analysis 3rd edn (Bellingham, WA: SPIE Press)

[228] Liao Z M, Cohen S J and Taylor J R 1994 Total internal reflection microscopy (TIRM) as a nondestructive subsurface damage assessment tool Proc. SPIE 2428 43-53

[229] Sheehan L M, Kozlowski M R and Camp D W 1998 Application of total internal reflection microscopy for laser damage studies on fused silica Proc. SPIE 3244 282-95

[230] Lee Y 2011 Evaluating subsurface damage in optical glasses J. Eur. Opt. Soc. 6 11001

[231] Li D, Tong Z, Jiang X Q, Blunt L and Gao F 2018 Calibration of an interferometric on-machine probing system on an ultra-precision turning machine Measurement 118 96-104

[232] Li D, Jiang X Q, Tong Z and Blunt L 2018 Kinematics error compensation for a surface measurement probe on an ultra-precision turning machine Micromachines 9 334

[233] Li D, Jiang X Q, Tong Z and Blunt L 2019 Development and application of interferometric on-machine surface measurement for ultraprecision turning process J. Manuf. Sci. Eng. 141 014502

[234] Tong Z, Zhong W B, Zeng W H and Jiang X Q 2021 Closed-loop form error measurement and compensation for FTS freeform machining CIRP Ann. 70 455-8

[235] Tong Z, Zeng W H, Zhong W B and Jiang X Q 2021 A closed-loop feature-based FTS patterning and characterisation of functional structured surfaces Surf. Topogr.: Metrol. Prop. 9 025012

[236] Zhou W C 2020 Fabrication and metrology of freeform optical elements PhD Thesis The Ohio State University, Columbus, OH

[237] Wolfs F, DeFisher S, Ross J and Wood K 2021 Challenges and best practices for manufacturing freeform optics Proc. SPIE 11889 118890Q

[238] Garrard K, Bruegge T, Hoffman J, Dow T and Sohn A 2005 Design tools for freeform optics Proc. SPIE 5874 58740A

[239] Aderneuer T, Fernandez O, Chaves J, Mohedano R and Ferrini R 2021 Design for manufacturing tools for free-form micro-optical arrays Proc. SPIE 11873 1187304

[240] Liu R X, Li Z X, Duan Y T and Fang F Z 2020 A design for a manufacturing-constrained off-axis four-mirror reflective system Appl. Sci. 10 5387

[241] Barbero S 2009 The Alvarez and Lohmann refractive lenses revisited Opt. Express 17 9376-90

[242] Smilie P J, Suleski T J, Dutterer B, Lineberger J L and Davies M A 2012 Design and characterization of an infrared Alvarez lens Opt. Eng. 51 013006

[243] Wilson A and Hua H 2019 Design and demonstration of a vari-focal optical see-through head-mounted display using freeform Alvarez lenses Opt. Express 27 15627-37

[244] Sieber I, Stiller P and Gengenbach U 2018 Design studies of varifocal rotation optics Opt. Eng. 57 125102