光学自由曲面面形检测技术

张磊; 刘东; 师途; 杨甬英; 李劲松; 俞本立; 张磊; 刘东; 师途; 杨甬英; 李劲松; 俞本立

doi:10.3788/CO.20171003.0283

[1]

TRICARD M. Practical examples of freeform optics[C]. Renewable Energy and the Environment Congress, OSA, 2013, FT3B.2:T2B-T3B.

[2]

MIÑANO J C, BENÍTEZ P, SANTAMARÍA A. Free-form optics for illumination[J]. Opt. Rev., 2009, 16(2):99-102. doi: 10.1007/s10043-009-0017-4

[3]

ASLANOV E, DOSKOLOVICH L L, MOISEEV M A. Thin LED collimator with free-form lens array for illumination applications[J]. Appl. Optics, 2012, 51(30):7200-7205. doi: 10.1364/AO.51.007200

[4]

HUA H. Past and future of wearable augmented reality displays and their applications[J]. SPIE, 2014, 9186:918600-918612. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1919482

[5]

CURATU C, HONG H, ROLLAND J. Dual-purpose lens for an eye-tracked projection head-mounted display[J]. SPIE, 2007, 6342:63420X-7.

[6]

HOWARD J M, WOLBACH S. Improving the performance of three-mirror imaging systems with Freeform Optics[C]. Freeform Optics, OSA, 2013, FT2B.6:T2B-T6B.

[7]

ROLT S, KIRBY A K, ROBERTSON D J. Metrology of complex astigmatic surfaces for astronomical optics[J]. SPIE, 2010, 7739:139-144. http://cat.inist.fr/?aModele=afficheN&cpsidt=23440340

[8]

张新, 许英朝.光学自由曲面的检测方法[J].中国光学, 2008, 1(1):92-99. http://www.cnki.com.cn/Article/CJFDTOTAL-ZGGA2008Z1015.htm

ZHANG X, XU Y. Study on free-form optical testing[J]. Chinese Optics, 2008, 1(1):92-99.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZGGA2008Z1015.htm

[9]

李圣怡, 陈善勇, 戴一帆.自由曲面光学器件检测技术[J].纳米技术与精密工程, 2005, 3(2):126-136. http://www.cnki.com.cn/Article/CJFDTOTAL-NMJM200502009.htm

LI SH Y, CHEN SH Y, DAI Y F. Inspection of free-form optics[J]. Nanotechnology and Precision Engineering, 2005, 3(2):126-136.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-NMJM200502009.htm

[10]

NEAL D R, ARMSTRONG D J, TURNER W T. Wavefront sensors for control and process monitoring in optics manufacture[J]. SPIE, 1997, 2993:211-220.

[11]

PULASKI P D, ROLLER J P, NEAL D R. Measurement of aberrations in microlenses using a Shack-Hartmann wavefront sensor[J]. SPIE, 2002, 4767:44-52. http://www.lumetrics.com/wp-content/uploads/2015/09/Measurement-1.pdf

[12]

JEONG T M, MENON M, YOON G. Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmann wave-front sensor[J]. Appl. Optics, 2005, 44(21):4523-4527. doi: 10.1364/AO.44.004523

[13]

GUO W, ZHAO L, TONG C S, et al.. Adaptive centroid-finding algorithm for freeform surface measurements[J]. Appl. Optics, 2013, 52(10):75-83. doi: 10.1364/AO.52.000D75

[14]

吴青青, 张效栋, 房丰洲, 等.基于波前传感法的立方相位板面形测量[J].光学技术, 2014(2):105-112. http://www.cnki.com.cn/Article/CJFDTOTAL-GXJS201402003.htm

WU Q, ZHANG X, FANG F, et al.. Shape measurement of the cubic phase plate with wavefront sensing technology[J]. Optical Technique, 2014(2):105-112.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXJS201402003.htm

[15]

赵必玉. 高精度面结构光三维测量方法研究[D]. 成都: 电子科技大学, 2015.

ZHAO B Y. High acuracy surface structured light projection three dimensional measurement[D]. Chengdu:University of Electronic Science and Technology of China, 2015.(in Chinese)

[16]

NGUYEN H, NGUYEN D, WANG Z, et al.. Real-time, high-accuracy 3D imaging and shape measurement[J]. Appl. Optics, 2014, 54(1):A9-A17.

[17]

WANG Z, DU H, BI H. Out-of-plane shape determination in generalized fringe projectionprofilometry[J]. Opt. Express, 2006, 14(25):12122-12133. doi: 10.1364/OE.14.012122

[18]

DU H, WANG Z. Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system[J]. Opt. Lett., 2007, 32(16):2438-2440. doi: 10.1364/OL.32.002438

[19]

HOANG T, PAN B, NGUYEN D, et al.. Generic gamma correction for accuracy enhancement in fringe-projection profilometry[J]. Opt. Lett., 2010, 35(12):1992-1994. doi: 10.1364/OL.35.001992

[20]

VO M, WANG Z, HOANG T, et al.. Flexible calibration technique for fringe-projection-based three-dimensional imaging[J]. Opt. Lett., 2010, 35(19):3192-3194. doi: 10.1364/OL.35.003192

[21]

WANG Z, NGUYEN D A, BARNES J C. Some practical considerations in fringe projection profilometry[J]. Optics & Lasers in Engineering, 2010, 48(2):218-225.

[22]

WANG Z, DU H, PARK S, et al.. Three-dimensional shape measurement with a fast and accurate approach[J]. Appl. Optics, 2009, 48(6):1052-1061. doi: 10.1364/AO.48.001052

[23]

WANG Z, HANB. Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms[J]. Opt. Lett., 2004, 29(14):1671-1673. doi: 10.1364/OL.29.001671

[24]

ZHANG S, HUANG P S. Novel method for structured light system calibration[J]. Opt. Eng., 2006, 45(8):83601. doi: 10.1117/1.2336196

[25]

ZHANG S, HUANG P S. Phase error compensation for a 3-D shape measurement system based on the phase-shifting method[J]. SPIE, 2005, 6000:60000E-12.

[26]

HUANG P S, ZHANG C, CHIANG F P. High-speed 3-D shape measurement based on digital fringe projection[J]. Opt. Eng., 2003, 42(1):163-168. doi: 10.1117/1.1525272

[27]

徐红兵, 任乃飞.基于Atos的光学扫描测量[J].工具技术, 2006, 40(11):74-77. doi: 10.3969/j.issn.1000-7008.2006.11.025

XU H, REN N. Measuring based on Atos optical scanner[J]. Tool Engineering, 2006, 40(11):74-77.(in Chinese) doi: 10.3969/j.issn.1000-7008.2006.11.025

[28]

张潇予. 基于ATOS扫描的异形件形貌检测与逆向技术研究[D]. 长春: 长春理工大学, 2014.

ZHANG X Y. Based on the atos profiled morphorpholgy detection and reverse technology research[D]. Changchun:Changchun University of Science and Technology, 2014.(in Chinese)

[29]

ZUO C, CHEN Q, GU G, et al.. High-speed three-dimensional profilometry for multiple objects with complex shapes[J]. Opt. Express, 2012, 20(17):19493-19510. doi: 10.1364/OE.20.019493

[30]

ZHONG M, SU X, CHEN W, et al.. Modulation measuring profilometry with auto-synchronous phase shifting and vertical scanning[J]. Opt. Express, 2014, 22(26):31620-31634. doi: 10.1364/OE.22.031620

[31]

XIAO Y L, XUE J, SU X. Robust self-calibration three-dimensional shape measurement in fringe-projection photogrammetry[J]. Opt. Lett., 2013, 38(5):694-696. doi: 10.1364/OL.38.000694

[32]

OLESCH E, HÄUSLER G, WÖRNLEIN A, et al.. Deflectometric measurement of large mirrors[J]. Advanced Optical Technologies, 2014, 3(3):335-343.

[33]

SU T, MALDONADO A, SU P, et al.. Instrument transfer function of slope measuring deflectometry systems[J]. Appl. Optics, 2015, 54(10):2981-2990. doi: 10.1364/AO.54.002981

[34]

SPECK A, ZELZER B, KANNENGIEβER M, et al.. Inspection of freeform intraocular lens topography by phase measuring deflectometric methods[J]. Appl. Optics, 2013, 52(18):4279-4286. doi: 10.1364/AO.52.004279

[35]

HUANG L, NG C S, ASUNDI A K. Fast full-field out-of-plane deformation measurement using fringe reflectometry[J]. Optics & Lasers in Engineering, 2012, 50(4):529-533. https://www.researchgate.net/publication/241079493_Fast_full-field_out-of-plane_deformation_measurement_using_fringe_reflectometry

[36]

PAN B, XIE H, WANG Z. Equivalence of digital image correlation criteria for pattern matching[J]. Appl. Optics, 2010, 49(28):5501-5509. doi: 10.1364/AO.49.005501

[37]

PAN B, XIE H, WANG Z, et al.. Study on subset size selection in digital image correlation for speckle patterns[J]. Opt. Express, 2008, 16(10):7037-7048. doi: 10.1364/OE.16.007037

[38]

TANG Y, SU X, HU S. Measurement based on fringe reflection for testing aspheric optical axis precisely and flexibly[J]. Appl. Optics, 2011, 50(31):5944-5948. doi: 10.1364/AO.50.005944

[39]

HÄUSLER G, FABER C, ETTL S. Deflectometry vs. interferometry[J]. SPIE, 2013, 8788:87881C. https://www.deepdyve.com/lp/spie/deflectometry-vs-interferometry-yLvTE2nmIH

[40]

YAO J, ROLLAND J P. Freeform optics metrology using optical coherence tomography[C]. Optical Fabrication and Testing, 2014, DOI:10.1364/OFT2014.OW3B.4:W3B-W4B.

[41]

YAO J, XU D, ROLLAND J P. Freeform metrology using swept-source optical coherence tomography with custom pupil-relay precision scanning configuration[J]. SPIE, 2015, 9633:96331A. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2461986

[42]

DI X, YAO J, ZHAO N, et al.. Scanning customized Swept-source Optical Coherence Tomography (SS-OCT) for the metrology of freeform optical surfaces[C]. Frontiers in Optics, 2016, DOI:10.1364/FIO.2016.FW5H.6.

[43]

师途, 杨甬英, 张磊, 等.非球面光学元件的面形检测技术[J].中国光学, 2014, 7(1):26-46. http://www.chineseoptics.net.cn/CN/abstract/abstract9094.shtml

SHI T, YANG Y, ZHANG L, et al.. Surface testing methods of aspheric optical elements[J]. Chinese J. Optics, 2014, 7(1):26-46.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9094.shtml

[44]

OFFNER A. A null corrector for paraboloidal mirrors[J]. Appl. Optics, 1963, 2(2):153-155. doi: 10.1364/AO.2.000153

[45]

VEZIN W R. Wavefront errors in the small lens dall null-test-corrigendum[J]. J. British Astronomical Association, 1982:92. http://adsabs.harvard.edu/abs/1982JBAA...92..145V

[46]

MACGOVERN A J, WYANT J C. Computer generated holograms for testing optical elements[J]. Appl. Optics, 1971, 10(3):619-624. doi: 10.1364/AO.10.000619

[47]

LIU D, YANG Y, TIAN C, et al.. Practical methods for retrace error correction in nonnull aspheric testing[J]. Opt. Express, 2009, 17(9):7025-7035. doi: 10.1364/OE.17.007025

[48]

高峰, 朱建华, 黄奇忠, 等.电子束直写计算全息图[J].中国激光, 2001, 28(6):556-558. http://www.cnki.com.cn/Article/CJFDTOTAL-JJZZ200106021.htm

GAO F, ZHU J, HUANG Q, et al.. Computer-generated hologram fabricated by electron-beam direct-writing[J]. Chinese J. Lasers, 2001, 28(6):556-558.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JJZZ200106021.htm

[49]

李明. 基于CGH的非球面混合补偿检测及离轴光学系统装调的关键技术研究[D]. 长春: 中国科学院研究生院(长春光学精密机械与物理研究所), 2015.

LI M. Research on key technology of hybrid null testing of aspheric mirror and off-axis optical system alignment based on CGH[D]. Changchun:Changchun Institute of optics, fine mechanics and Physics, 2015.(in Chinese)

[50]

ZHOU P, BURGE J H. Fabrication error analysis and experimental demonstration for computer-generated holograms[J]. Appl. Optics, 2007, 46(5):657-663. doi: 10.1364/AO.46.000657

[51]

ZHAO C, ZEHNDER R, BURGE J H, et al.. Testing an off-axis parabola with a CGH and a spherical mirror as null lens[J]. Optical Manufacturing & Testing VI, 2005:5869. http://www.loft.optics.arizona.edu/

[52]

PETERHÄNSEL S, PRUSS C, OSTEN W. Phase errors in high line density CGH used for aspheric testing:beyond scalar approximation[J]. Opt. Express, 2013, 21(10):11638-11651. doi: 10.1364/OE.21.011638

[53]

REICHELT S, PRUSS C, TIZIANI H J. Absolute interferometric test of aspheres by use of twin computer-generated holograms[J]. Appl. Optics, 2003, 42(22):4468-4479. doi: 10.1364/AO.42.004468

[54]

FENG J, DENG C, XING T. Design of aspheric surfaces testing system based on computer-generated holograms[J]. SPIE, 2012, 8418:84180R-9. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1380787

[55]

FENG J, DENG C, XING T. Design and location deviation of the computer generated holograms used for aspheric surface testing[J]. SPIE, 2013, 8788:878820-7. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1687473

[56]

赵龙波, 张志宇, 朱德燕, 等.用于非球面检验的激光直写高精度计算全息图制作[J].激光与光电子学进展, 2014(11):122-128. http://www.cnki.com.cn/Article/CJFDTOTAL-JGDJ201411016.htm

ZHAO L B, ZHANG ZH Y, ZHU D Y, et al.. Fabrication of high precision computer generated hologram for aspheric surface testing by laser-direct writing[J]. Laser & Optoelectronics Progress, 2014(11):122-128.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JGDJ201411016.htm

[57]

卢振武, 李凤有, 刘华, 等.利用曲面计算全息图进行凸面非球面检测[J].光电子·激光, 2004, 15(9):1088-1090. http://www.cnki.com.cn/Article/CJFDTOTAL-GDZJ200409016.htm

LU ZH W, LI F Y, LIU H, et al.. Testing the convex aspheric surface by using CGH on curved surface[J]. J. Optoelectronics·Laser, 2004, 15(9):1088-1090.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GDZJ200409016.htm

[58]

席庆奎, 朱日宏, 陈磊, 等.计算全息用于非球面检测的方法[J].激光杂志, 2004, 25(6):67-69. http://cpfd.cnki.com.cn/Article/CPFDTOTAL-ZGGY200609001612.htm

XI Q K, ZHU R H, CHEN L, et al.. Methods on testing an aspheric with a computer generated hologram[J]. Laser Journal, 2004, 25(6):67-69.(in Chinese) http://cpfd.cnki.com.cn/Article/CPFDTOTAL-ZGGY200609001612.htm

[59]

王小鹏, 高志山, 马骏, 等.非球面测量中零位计算全息的测量不确定度分析研究[J].光学学报, 2011, 31(1):111-115. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201101021.htm

WANG X P, GAO ZH SH, MA J, et al.. Investigation of measurement uncertainty of aspheric surface based on null-computer-generated holography[J]. Acta Optica Sinica, 2011, 31(1):111-115.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201101021.htm

[60]

KINO M, KURITA M. Interferometric testing for off-axis aspherical mirrors with computer-generated holograms[J]. Appl. Optics, 2012, 51(19):4291-4297. doi: 10.1364/AO.51.004291

[61]

苏萍, 谭峭峰, 康果果, 等.自由曲面零补偿计算全息图离散相位的B样条拟合[J].光学学报, 2010(6):1767-1771. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201006047.htm

SU P, TAN Q F, KANG G G, et al.. B-spline interpolation of scattered phase data of computer generated hologram for null test of freeform surface[J]. Acta Optica Sinica, 2010(6):1767-1771.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201006047.htm

[62]

LIU H, LU Z, LI F, et al.. Using curved hologram to test large-aperture convex surface[J]. Opt. Express, 2004, 12(14):3251-3256. doi: 10.1364/OPEX.12.003251

[63]

LIU H, LU Z, LI F, et al.. Design of a novel hologram for full measurement of large and deep convex aspheric surfaces[J]. Opt. Express, 2007, 15(6):3120-3126. doi: 10.1364/OE.15.003120

[64]

黎发志, 郑立功, 闫锋, 等.自由曲面的CGH光学检测方法与实验[J].红外与激光工程, 2012, 41(4):1052-1056. http://www.cnki.com.cn/Article/CJFDTOTAL-HWYJ201204039.htm

LI F ZH, ZHENG L G, YAN F, et al.. Optical testing method and its experiment on freeform surface with computer-generated hologram[J]. Infrared and Laser Engineering, 2012, 41(4):1052-1056.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-HWYJ201204039.htm

[65]

朱德燕, 张学军.高精度相位型计算全息图的设计[J].光学学报, 2015, 35(7):174-180. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201507025.htm

ZHU D, ZHANG X. Design of high-precision phase computer-generated-hologram[J]. Acta Optica Sinica, 2015, 35(7):174-180.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201507025.htm

[66]

黄亚, 马骏, 朱日宏, 等.基于计算全息的光学自由曲面测量不确定度分析[J].光学学报, 2015(11):156-164. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201511020.htm

HUANG Y, MA J, ZHU R H, et al.. Investigation of measurement uncertainty of optical freeform surface based on computer-generated hologram[J]. Acta Optica Sinica, 2015(11):156-164.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201511020.htm

[67]

LIU H, ZHU Q, HAO Q. Design of novel part-compensating lens used in aspheric testing[J]. SPIE, 2003, 5253:480-484. http://cat.inist.fr/?aModele=afficheN&cpsidt=15759788

[68]

SULLIVAN J J, GREIVENKAMP J E. Design of partial nulls for testing of fast aspheric surfaces[J].SPIE, 2007, 6671:66710W. http://cat.inist.fr/?aModele=afficheN&cpsidt=20673277

[69]

LIU D, YANG Y, LUO Y, et al.. Non-null interferometric aspheric testing with partial null lens and reverse optimization[J]. SPIE, 2009, 7426:74260M-8. https://www.researchgate.net/publication/252766898_Non-null_interferometric_aspheric_testing_with_partial_null_lens_and_reverse_optimization

[70]

LIU D, SHI T, ZHANG L, et al.. Reverse optimization reconstruction of aspheric figure error in a non-null interferometer[J]. Appl. Optics, 2014, 53(24):5538-5546. doi: 10.1364/AO.53.005538

[71]

师途, 刘东, 张磊, 等.非球面非零位检测的逆向优化面形重构[J].光学学报, 2014(6):143-150. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201406024.htm

SHI T, LIU D, ZHANG L, et al.. Reverse optimization reconstruction method for aspheric testing in a nonnull interferometer[J]. Acta Optica Sinica, 2014(6):143-150.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201406024.htm

[72]

GARBUSI E, PRUSS C, LIESENER J, et al.. New technique for flexible and rapid measurement of precision aspheres[J]. SPIE, 2007, 6616:661629-11. http://cat.inist.fr/?aModele=afficheN&cpsidt=20507783

[73]

GARBUSI E, PRUSS C, OSTEN W. Interferometer for precise and flexible asphere testing[J]. Opt. Lett., 2008, 33(24):2973-2975. doi: 10.1364/OL.33.002973

[74]

BAER G, SCHINDLER J, PRUSS C, et al.. Correction of misalignment introduced aberration in non-null test measurements of free-form surfaces[J]. J. European Optical Society Rapid Publications, 2013, 8(23):6480-6484.

[75]

BAER G, SCHINDLER J, PRUSS C, et al.. Fast and flexible non-null testing of aspheres and free-form furfaces with the tilted-wave-interferometer[J]. Int. J. Optomechatroni., 2014, 8(4):242-250. doi: 10.1080/15599612.2014.942925

[76]

荣四海. 点光源阵列多重波面自由曲面检测系统设计与研究[D]. 南京: 南京理工大学, 2013.

RONG S H. Design and research of the point source multi-wavefront interferometer system[D]. Nanjing:Nanjing University of Science & Technology, 2013.(in Chinese)

[77]

沈华. 基于多重倾斜波面的光学自由曲面非零位干涉测量关键技术研究[D]. 南京: 南京理工大学, 2014.

SHEN H.Research on key techniques of tilted wave Interferometer used in the measurement of freeform surfaces[D]. Nanjing:Nanjing University of Science & Technology, 2014.(in Chinese)

[78]

KIN C J, WYANT J C. Subaperture test of a large flat or a fast aspheric surface[J]. J. Optical Society of America, 1981, 71:1587. http://adsabs.harvard.edu/abs/1981JOSA...71.1587K

[79]

MURPHY P, FLEIG J, FORBES G, et al.. Subaperture stitching interferometry for testing mild aspheres[J]. Optics & Photonics, 2006:62930J. http://cat.inist.fr/?aModele=afficheN&cpsidt=18559944

[80]

CHOW WW, LAWRENCE G N. Method for subaperture testing interferogram reduction[J]. Opt. Lett., 1983, 8(9):68-470. http://adsabs.harvard.edu/abs/1983OptL....8..468C

[81]

MURPHY P, FORBES G, FLEIG J, et al.. Stitching interferometry:a flexible solution for surface metrology[J]. Optics & Photonics News, 2003, 14(5):38-43. http://cat.inist.fr/?aModele=afficheN&cpsidt=14809897

[82]

程灏波.精密光学元件先进测量与评价[M].北京:科学出版社, 2014.

CHENG H B. Advanced Measurement and Evaluate of Precision Optical Elements[M]. Beijing:Science Press, 2014.(in Chinese)

[83]

TRICARD M, KULAWIEC A, BAUER M, et al.. Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null[J]. CIRP Annals-Manufacturing Technology, 2010, 59(1):547-550. doi: 10.1016/j.cirp.2010.03.125

[84]

MURPHY P, DEVRIES G, FLEIG J, et al.. Measurement of high-departure aspheric surfaces using subaperture stitching with variable null optics[J]. SPIE, 2009, 7426:74260P-10. https://www.deepdyve.com/lp/spie/measurement-of-high-departure-aspheric-surfaces-using-subaperture-YAowkhbszI

[85]

闫力松. 子孔径拼接干涉检测光学镜面算法的研究[D]. 北京: 中国科学院大学, 2015.

YAN L S. Research on the algorithm testing optical mirror by subaperture stitching interferometry[D]. Beijing:University of Chinese Academy of Sciences, 2015.(in Chinese)

[86]

陈善勇. 非球面子孔径拼接干涉测量的几何方法研究[D]. 长沙: 国防科学技术大学, 2006.

CHEN SH Y. Geometrical approach to subaperture stitching interferometry for aspheric surfaces[D]. Changsha:National University of Defense Technology, 2006.(in Chinese)

[87]

LIU Y M, LAWRENCE G N, KOLIOPOULOS C L. Subaperture testing of aspheres with annular zones[J]. Appl. Optics, 1988, 27(21):4504-4513. doi: 10.1364/AO.27.004504

[88]

MELOZZI A M, PEZZATI L, MAZZONI A. Testing aspheric surfaces using multiple annular interferograms[J]. Opt. Eng., 1993, 32(32):1073-1079.

[89]

GRANADOS-AGUST IAN F I, ESCOBAR-ROMERO J F, CORNEJO-RODR IAGUEZ A. Testing Parabolic Surfaces with Annular Subaperture Interferograms[J]. Opt. Rev., 2004, 11(2):82-86. doi: 10.1007/s10043-004-0082-7

[90]

HOU X, WU F, YANG L, et al.. Full-aperture wavefront reconstruction from annular subaperture interferometric data by use of Zernike annular polynomials and a matrix method for testing large aspheric surfaces[J]. Appl. Optics, 2006, 45(15):3442-3455. doi: 10.1364/AO.45.003442

[91]

HOU X, WU F, YANG L, et al.. Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method[J]. Opt. Express, 2007, 15(20):12890-12899. doi: 10.1364/OE.15.012890

[92]

CHEN S, LI S, DAI Y, et al.. Experimental study on subaperture testing with iterative stitching algorithm[J]. Opt. Express, 2008, 16(7):4760-4765. doi: 10.1364/OE.16.004760

[93]

王孝坤, 王丽辉, 张学军.子孔径拼接干涉法检测非球面[J].光学精密工程, 2007, 15(2):192-198. http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201007034.htm

WANG X K, WANG L H, ZHANG X J. Testing asphere by subaperture stitching interferometric method[J]. Opt. Precision Eng., 2007, 15(2):192-198.(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GXXB201007034.htm

[94]

KVCHEL M F. Interferometric measurement of rotationally symmetric aspheric surfaces[J]. SPIE, 2009, 7389:738916-11.

[95]

张磊, 田超, 刘东, 等.非球面非零位环形子孔径拼接干涉检测技术[J].光学学报, 2014, 34(8):156-164. http://cdmd.cnki.com.cn/Article/CDMD-10335-1013185937.htm

ZHANG L, TIAN CH, LIU D, et al.. Non-null annular subaperture stitching interferometry for aspheric test[J]. Acta Optica Sinica, 2014, 34(8):156-164.(in Chinese) http://cdmd.cnki.com.cn/Article/CDMD-10335-1013185937.htm

[96]

田超. 非球面非零位环形子孔径拼接干涉检测技术与系统研究[D]. 杭州: 浙江大学, 2013.

TIAN CH. Measurement of Aspheric Surfaces by Non-null Annular Subaperture Stitching Interferometry[D]. Hangzhou:Zhejiang University, 2013.(in Chinese)

[97]

ZHANG L, TIAN C, LIU D, et al.. Non-null annular subaperture stitching interferometry for steep aspheric measurement[J]. Appl. Optics, 2014, 53(25):5755-5762. doi: 10.1364/AO.53.005755

[98]

ZHANG L, LIU D, SHI T, et al.. Aspheric subaperture stitching based on system modeling[J]. Opt. Express, 2015, 23(15):19176-19188. doi: 10.1364/OE.23.019176

[99]

WANG X, ZHENG L, ZHANG B, et al.. Test of an off-axis asphere by subaperture stitching interferometry[J]. SPIE, 2009, 7283:72832J-6.

[100]

CHEN S, ZHAO C, DAI Y, et al.. Reconfigurable optical null based on counter-rotating Zernike plates for test of aspheres[J]. Opt. Express, 2014, 22(2):1381-1386. doi: 10.1364/OE.22.001381

[101]

张磊. 光学自由曲面子孔径拼接干涉检测技术[D]. 杭州: 浙江大学, 2016.

ZHANG L.Optical free-form surface subaperture stitching interferometry[D]. Hangzhou:Zhejiang University, 2016.(in Chinese)

[102]

LIU D, ZHOU Y, BAI J, et al.. Aspheric and free-form surfaces test with non-null subaperture stitching interferometry[C]. SPIE/COS Photonics Asia2016, 2016:10021N.