Optics and Precision Engineering, Volume. 33, Issue 5, 677(2025)
Deflectometric measurement technology for optical surfaces: principles, challenges, and prospects(invited)
[1] KNAUER M C, KAMINSKI J, HAUSLER G. Phase measuring deflectometry: a new approach to measure specular free-form surfaces[C], 5457, 366-376(2004).
[2] SAINES G, TOMILIN M G. Magic mirrors of the orient[J]. Journal of Optical Technology, 66, 758-765(1999).
[3] FOUCAULT L. Description des procedes employes pour reconnaitre la configuration des surfaces optiques[J]. Comptes Rendus de l'Académie des Sciences, 47, 47(1858).
[4] ALEJANDRO JUÁREZ-REYES S, SOSA-SÁNCHEZ C T, SILVA-ORTIGOZA G et al. The wire optical test: a thorough analytical study in and out of caustic surface, and advantages of a dynamical adaptation[J]. Journal of Optics, 20(2018).
[5] BAO X Z, HE F Y, ZHAO N et al. Design and experimental research of aspheric mirror system based on Ronchi grating testing[J]. Optical Technique, 49, 57-63(2023).
包兴臻, 何锋赟, 赵楠. Ronchi光栅检测非球面镜系统的设计及实验研究[J]. 光学技术, 49, 57-63(2023).
[6] HARTMANN J. Bemerkungen über den Bau und die Justirung von Spektrographen[J]. Zeitschrift für Instrumentenkunde, 20, 47(1900).
[7] PLATT B C, SHACK R. History and principles of Shack-Hartmann wavefront sensing[J]. Journal of Refractive Surgery, 17, S573-S577(001).
[8] HÄUSLER G, SCHNEIDER G. Testing optics by experimental ray tracing with a lateral effect photodiode[J]. Applied Optics, 27, 5160-5164(1988).
[9] CEYHAN U. Characterization of Aspherical Lenses by Experimental Ray Tracing[D](2013).
[10] ILLEMANN J, GECKELER R D, WEINGARTNER I et al. Topography measurement of nanometer synchrotron optics[C], 4782, 29-37(2002).
[11] HILBIG D, SCHULZE J, FLEISCHMANN F et al. Measurement of strongly curved surfaces by multi-beam experimental ray tracing[C], 10048, 500-507(2017).
[12] CHEN W X, CHEN L F, ZHANG X S et al. Geometrical aberration measurement by experimental ray-tracing based on fiber point diffraction interferometry[J]. Measurement Science and Technology, 33, 105004(2022).
[13] BEYERER J. Three-dimensional measurement of specular free-form surfaces with a structured-lighting reflection technique[C], 3204, 74-80(1997).
[14] GRAVES L R, QUACH H, KOSHEL R J et al. High contrast thermal deflectometry using long-wave infrared time modulated integrating cavity source[J]. Optics Express, 27, 28660-28678(2019).
[15] HUANG R. High Precision Optical Surface Metrology Using Deflectometry[D](2015).
[16] HUANG L, IDIR M, ZUO C et al. Review of phase measuring deflectometry[J]. Optics and Lasers in Engineering, 107, 247-257(2018).
[17] KAFRI O. Noncoherent method for mapping phase objects[J]. Optics Letters, 5, 555-557(1980).
[18] SETTLES G S, HARGATHER M J. A review of recent developments in schlieren and shadowgraph techniques[J]. Measurement Science and Technology, 28, -042025(2017).
[19] ZHANG Z Y. A flexible new technique for camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 1330-1334(2000).
[20] XIAO Y L, SU X Y, CHEN W J. Flexible geometrical calibration for fringe-reflection 3D measurement[J]. Optics Letters, 37, 620-622(2012).
[21] XU Y J, GAO F, ZHANG Z H et al. A holistic calibration method with iterative distortion compensation for stereo deflectometry[J]. Optics and Lasers in Engineering, 106, 111-118(2018).
[22] NIU Z Q, ZHANG X C, YE J Q et al. Flexible one-shot geometric calibration for off-axis deflectometry[J]. Applied Optics, 59, 3819-3824(2020).
[23] STURM P, CHENG Z L, CHEN P C Y et al. Focal length calibration from two views: method and analysis of singular cases[J]. Computer Vision and Image Understanding, 99, 58-95(2005).
[24] DUDA A, FRESE U. Accurate detection and localization of checkerboard corners for calibration[C], 126(2018).
[25] BU L B, HUO H T, LIU X Y et al. Concentric circle grids for camera calibration with considering lens distortion[J]. Optics and Lasers in Engineering, 140, 106527-106535(2021).
[26] CAI B L, WANG Y W, WANG K Y et al. Camera calibration robust to defocus using phase-shifting patterns[J]. Sensors, 17, 2361-2374(2017).
[27] XU Y J, GAO F, REN H Y et al. An iterative distortion compensation algorithm for camera calibration based on phase target[J]. Sensors, 17, 1188(2017).
[28] RICHARDSON A, STROM J, OLSON E. AprilCal: Assisted and repeatable camera calibration[C], 1814-1821(7).
[29] ROJTBERG P, KUIJPER A. Efficient pose selection for interactive camera calibration[C], 16, 31-36(2018).
[30] CAO J B, ZHANG X, TU D W et al. A visual guidance calibration method for out-of-focus cameras based on iterative phase target[J]. Measurement, 218, 113104-113115(2023).
[31] HUANG P S. High-speed 3-D shape measurement based on digital fringe projection[J]. Optical Engineering, 42, 163-168(2003).
[32] HUANG P S. Phase error compensation for a 3-D shape measurement system based on the phase-shifting method[J]. Optical Engineering, 46, -063609(2007).
[33] ZHANG S, YAU S T. Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector[J]. Applied Optics, 46, 36-43(2007).
[34] HOANG T, PAN B, NGUYEN D et al. Generic gamma correction for accuracy enhancement in fringe-projection profilometry[J]. Optics Letters, 35, 1992-1994(2010).
[35] NÜSS J R, PRINZLER M, KALMS M et al. Effects of non-ideal display properties in phase measuring deflectometry: a model-based investigation[C], 10678, 192-201(2018).
[36] BARTSCH J, KALMS M, BERGMANN R B. Improving the calibration of phase measuring deflectometry by a polynomial representation of the display shape[J]. Journal of the European Optical Society-Rapid Publications, 15, 20-27(2019).
[37] YANG D K, WU S T[M]. Fundamentals of Liquid Crystal Devices(2006).
[38] PETZ M, TUTSCH R. Rasterreflexions-photogrammetrie zur messung spiegelnder oberflächen (reflection grating photogrammetry for the measurement of specular surfaces)[J]. Tm-Technisches Messen, 71, 389-397(2004).
[39] MAESTRO-WATSON D, IZAGUIRRE A, ARANA-AREXOLALEIBA N. LCD screen calibration for deflectometric systems considering a single layer refraction model[C], 24, 1-6(2017).
[40] SU P, WANG Y H, BURGE J H et al. Non-null full field X-ray mirror metrology using SCOTS: a reflection deflectometry approach[J]. Optics Express, 20, 12393-12406(2012).
[41] HUANG R, SU P, BURGE J H. Deflectometry measurement of Daniel K. inouye solar telescope primary mirror[C], 9517, 195-209(2015).
[42] XIAO Y L, SU X Y, CHEN W J. Flexible geometrical calibration for fringe-reflection 3D measurement[J]. Optics Letters, 37, 620-622(2012).
[43] XU X Y, ZHANG X C, NIU Z Q et al. Self-calibration of
[44] GRAVES L R, CHOI H, ZHAO W C et al. Model-free deflectometry for freeform optics measurement using an iterative reconstruction technique[J]. Optics Letters, 43, 2110-2113(2018).
[45] WANG D D, ZHANG S, WU R M et al. Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test[J]. Optics Express, 24, 19671-19681(2016).
[46] ZHANG X D, JIANG L L, ZHANG G X. Novel method of positioning optical freeform surfaces based on fringe deflectometry[J]. CIRP Annals, 66, 507-510(2017).
[47] HUANG L, NG C S, ASUNDI A K. Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry[J]. Optics Express, 19, 12809-12814(2011).
[48] LIU Y K, OLESCH E, YANG Z et al. Fast and accurate deflectometry with crossed fringes[J]. Advanced Optical Technologies, 3, 441-445(2014).
[49] LIU T, ZHOU C, LIU Y et al. Deflectometry for phase retrieval using a composite fringe[J]. Optica Applicata, 44, 451-461(2014).
[50] BUDIANTO B, LUN P K D, HSUNG T C. Marker encoded fringe projection profilometry for efficient 3D model acquisition[J]. Applied Optics, 53, 7442-7453(2014).
[51] LIANG H, SAUER T, FABER C. Using wavelet transform to evaluate single-hot phase measuring deflectometry data[C], 11510, 404-410(2020).
[52] VILLA J, QUIROGA J A, SERVÍN M. Improved regularized phase-tracking technique for the processing of squared-grating deflectograms[J]. Applied Optics, 39, 502-508(2000).
[53] QIN Y, WAN S J, WAN Y H et al. Direct and accurate phase unwrapping with deep neural network[J]. Applied Optics, 59, 7258-7267(2020).
[54] FAN L Y, WU Z X, WANG J et al. Deep learning-based Phase Measuring Deflectometry for single-shot 3D shape measurement and defect detection of specular objects[J]. Optics Express, 30, 26504-26518(2022).
[55] HUANG P S. Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring[J]. Optical Engineering, 38, 1065-1071(1999).
[56] ZHANG Z H, TOWERS C E, TOWERS D P. Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency Selection[J]. Optics Express, 14, 6444-6455(2006).
[57] TRUMPER I, CHOI H, KIM D W. Instantaneous phase shifting deflectometry[J]. Optics Express, 24, 27993-28007(2016).
[58] WU Y X, YUE H M, YI J Y et al. Dynamic specular surface measurement based on color-encoded fringe reflection technique[J]. Optical Engineering, 55(2016).
[59] SHAO J F, NI Y B, MENG Z Z et al. Three-dimensional shape measurement of composite surface based on defocused binary display and fringe projection[J]. Opto-Electronic Engineering, 51, 90-102(2024).
邵金凤, 倪育博, 孟召宗. 基于离焦二值显示和条纹投影的复合表面三维测量方法[J]. 光电工程, 51, 90-102(2024).
[60] ZHANG Z H, WANG Y M, HUANG S J et al. Three-dimensional shape measurements of specular objects using phase-measuring deflectometry[J]. Sensors, 17, 2835(2017).
[61] GHIGLIA D C, PRITT M D[M]. Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software(1998).
[62] SU X Y, CHEN W J. Reliability-guided phase unwrapping algorithm: a review[J]. Optics and Lasers in Engineering, 42, 245-261(2004).
[63] ZHAO M, HUANG L, ZHANG Q C et al. Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies[J]. Applied Optics, 50, 6214-6224(2011).
[64] TIAN J D, PENG X, ZHAO X B. A generalized temporal phase unwrapping algorithm for three-dimensional profilometry[J]. Optics and Lasers in Engineering, 46, 336-342(2008).
[65] ZUO C, HUANG L, ZHANG M L et al. Temporal phase unwrapping algorithms for fringe projection profilometry: a comparative review[J]. Optics and Lasers in Engineering, 85, 84-103(2016).
[66] PRITT M D, SHIPMAN J S. Least-squares two-dimensional phase unwrapping using FFT’s[J]. IEEE Transactions on Geoscience and Remote Sensing, 32, 706-708(1994).
[67] YIN A H, ZHANG Q M, JIANG H M. Study of improved phase unwrapping method based on weighted least squares[J]. Computer Engineering and Applications, 49, 159-162(2013).
殷爱菡, 张清淼, 姜辉明. 一种改进的加权最小二乘相位展开方法研究[J]. 计算机工程与应用, 49, 159-162(2013).
[68] XU L H, SU X Y. Analysis on the processing on three classes of residuals for phase unwrapping[J]. Journal of Optoelectronics Laser, 12, 1267-1270(2001).
徐利华, 苏显渝. 相位展开中的3类极点分析和处理[J]. 光电子·激光, 12, 1267-1270(2001).
[69] NIU Z Q, XU X Y, ZHANG X C et al. Efficient phase retrieval of two-directional phase-shifting fringe patterns using geometric constraints of deflectometry[J]. Optics Express, 27, 8195-8207(2019).
[70] TSAI R Y. A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses[J]. IEEE Journal on Robotics and Automation, 221-244(1992).
[71] HEALEY G, JAIN R[M]. Depth Recovery from Surface Normals(1984).
[72] WEI T G, KLETTE R. Depth recovery from noisy gradient vector fields using regularization[C], 116-123(2003).
[73] FRIED D L. Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements[J]. Journal of the Optical Society of America, 67, 370-375(1977).
[74] HUDGIN R H. Wave-front reconstruction for compensated imaging[J]. Journal of the Optical Society of America, 67, 375-378(1977).
[75] SOUTHWELL W H. Wave-front estimation from wave-front slope measurements[J]. Journal of the Optical Society of America, 70, 998-1006(1980).
[76] ARES M, ROYO S. Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction[J]. Applied Optics, 45, 6954-6964(2006).
[77] DAI F Z, TANG F, WANG X Z et al. Modal wavefront reconstruction based on Zernike polynomials for lateral shearing interferometry: comparisons of existing algorithms[J]. Applied Optics, 51, 5028-5037(2012).
[78] MOCHI I, GOLDBERG K A. Modal wavefront reconstruction from its gradient[J]. Applied Optics, 54, 3780-3785(2015).
[79] KEWEI E, ZHANG C, LI M Y et al. Wavefront reconstruction algorithm based on Legendre polynomials for radial shearing interferometry over a square area and error analysis[J]. Optics Express, 23, 20267-20279(2015).
[80] ETTL S, KAMINSKI J, OLESCH E et al. Fast and robust 3D shape reconstruction from gradient data[J]. Applied Optics, 108, 26(2007).
[81] LANG W, ZHANG X C, CHEN Y N et al. A general reconstruction framework for deflectometric measurement based on nonuniform B-splines[J]. IEEE Transactions on Instrumentation Measurement, 72, 3279466(2023).
[82] LEGARDA-SA´ENZ R. Accurate procedure for the calibration of a structured light system[J]. Optical Engineering, 43, 464(2004).
[83] KANNALA J, BRANDT S S. A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1335-1340(2006).
[84] BOTHE T, LI W S, SCHULTE M et al. Vision ray calibration for the quantitative geometric description of general imaging and projection optics in metrology[J]. Applied Optics, 49, 5851-5860(2010).
[85] BRÄUER-BURCHARDT C. Correcting lens distortion in 3D measuring systems using fringe projection[C], 5962, 155-165(2005).
[86] BAKER S, NAYAR S K. A theory of catadioptric image formation[C], 35-42(1998).
[87] STURM P, RAMALINGAM S.
[88] GROSSBERG M D, NAYAR S K. A general imaging model and a method for finding its parameters[C], 108-115(2001).
[89] CAI Z W, LIU X L, PENG X et al. Structured light field 3D imaging[J]. Optics Express, 24, 20324-20334(2016).
[90] YANG Y, MIAO Y P, LIU X L et al. Intrinsic parameter-free calibration of FPP using a ray phase mapping model[J]. Optics Letters, 47, 3564-3567(2022).
[91] LANG W, ZHANG X C, CHEN Y N et al. Holistic calibration method of deflectometry by holonomic framework priors[J]. Optics Letters, 49, 702-705(2024).
[92] PETZ M, RITTER R. Reflection grating method for 3D measurement of reflecting surfaces[C], 4399, 35-41(2001).
[93] BAER G, GARBUSI E, LYDA W et al. Automated alignment of aspheric and freeform surfaces in a non-null test interferometer[C], 8082, 490-498(2011).
[94] SU P, PARKS R E, WANG L R et al. Software configurable optical test system: a computerized reverse Hartmann test[J]. Applied Optics, 49, 4404-4412(2010).
[95] ZHANG Z H, LIU Y, HUANG S J et al. Full-field 3D shape measurement of specular surfaces by direct phase to depth relationship[C], 10023, 164-174(2016).
[96] ZHANG X C, REN Y R, CHEN Y N et al. Large-area measurement with stereo deflectometry[C](2021).
[97] HÄUSLER G, FABER C, OLESCH E et al. Deflectometry
[98] BALZER J, WERLING S. Principles of shape from specular reflection[J]. Measurement, 43, 1305-1317(2010).
[99] SU T Q, MALDONADO A, SU P et al. Instrument transfer function of slope measuring deflectometry systems[J]. Applied Optics, 54, 2981-2990(2015).
[100] SUN H Y, WANG L, SONG Z et al. Three-dimensional mirror surface measurement based on local blur analysis of phase measuring deflectometry system[J]. Traitement Du Signal, 37, 763-771(2020).
[101] NIU Z Q, GAO N, ZHANG Z H et al. 3D shape measurement of discontinuous specular objects based on advanced PMD with bi-telecentric lens[J]. Optics Express, 26, 1615-1632(2018).
[102] ZHANG X C, NIU Z Q, YE J Q et al. Correction of aberration-induced phase errors in phase measuring deflectometry[J]. Optics Letters, 46, 2047-2050(2021).
[103] CHEN Y N, ZHANG X C, CHEN T et al. Transition imaging phase measuring deflectometry for high-precision measurement of optical surfaces[J]. Measurement, 199, 111589(2022).
[104] VOGIATZIS G, HERNÁNDEZ C. Self-calibrated, multi-spectral photometric stereo for 3D face capture[J]. International Journal of Computer Vision, 97, 91-103(2012).
[105] WOODHAM R J. Photometric method for determining surface orientation from multiple images[J]. Optical Engineering, 513-531(1989).
[106] ROBEIN E[M]. Seismic Imaging: A Review of the Techniques, Their Principles, Merits and Limitations(2010).
[107] HARKER M, O'LEARY P. Regularized reconstruction of a surface from its measured gradient field[J]. Journal of Mathematical Imaging and Vision, 51, 46-70(2015).
[108] HARKER M, O’LEARY P. Least squares surface reconstruction from measured gradient fields[C], 23, 1-7(2008).
[109] BARTELS R H, STEWART G W. Algorithm 432 [C2]: solution of the matrix equation AX + XB = C [F4[J]. Communications of the ACM, 15, 820-826(1972).
[110] GOLUB G H, HANSEN P C, O’LEARY D P. Tikhonov regularization and total least squares[J]. SIAM Journal on Matrix Analysis and Applications, 21, 185-194(1999).
[111] QUÉAU Y, DUROU J D, AUJOL J F. Normal integration: a survey[J]. Journal of Mathematical Imaging and Vision, 60, 576-593(2018).
[112] HUANG L, XUE J P, GAO B et al. Model mismatch analysis and compensation for modal phase measuring deflectometry[J]. Optics Express, 25, 881-887(2017).
[113] QUÉAU Y, DUROU J D, AUJOL J F. Variational methods for normal integration[J]. Journal of Mathematical Imaging and Vision, 60, 609-632(2018).
[114] SU P, KHREISHI M A H, SU T Q et al. Aspheric and freeform surfaces metrology with software configurable optical test system: a computerized reverse Hartmann test[J]. Optical Engineering, 53(2014).
[115] 王华荣, 李彬, 王志峰. 基于条纹反射术的槽式抛物面单元镜面形测量[J]. 光学学报, 33, 130-133(2013).
WANG H R, LI B, WANG ZH F et al. Surface measurement of parabolic trough unit mirror based on fringe reflection[J]. Acta Optica Sinica, 33, 130-133(2013).
[116] WANG L R, SU P, PARKS R E et al. A low-cost, flexible, high dynamic range test for free-form illumination optics[C](2010).
[117] BUTEL G P, SMITH G A, BURGE J H. Deflectometry using portable devices[J]. Optical Engineering, 54(2015).
[118] JIANG X Q, WANG K W, GAO F et al. Fast surface measurement using wavelength scanning interferometry with compensation of environmental noise[J]. Applied Optics, 49, 2903-2909(2010).
[119] XIAO Y L, SU X Y, CHEN W J et al. Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry[J]. Applied Optics, 51, 457-464(2012).
[120] LIU Y, HUANG S J, ZHANG Z H et al. Full-field 3D shape measurement of discontinuous specular objects by direct phase measuring deflectometry[J]. Scientific Reports, 7, 10293(2017).
[121] CHANG C X, ZHANG Z H, GAO N et al. Measurement of the three-dimensional shape of discontinuous specular objects using infrared phase-measuring deflectometry[J]. Sensors, 19, 4621(2019).
[122] KNAUER M C, KAMINSKI J, HÄUSLER G. Absolute Phase Nmessende Deflektometrie[M]. Lehrstuhl für Mikrocharakterisierung(2006).
[123] SKYDAN O A, LALOR M J, BURTON D R. Three-dimensional shape measurement of non-full-field reflective surfaces[J]. Applied Optics, 44, 4745-4752(2005).
[124] XU J, ZHANG C et al. A geometry and optical property inspection system for automotive glass based on fringe patterns[J]. Optica Applicata, 40, 827-841(2010).
[125] DÍAZ-URIBE R, HUERTA-CARRANZA O, RODRÍGUEZ-RODRÍGUEZ M I et al. Testing free forms with optical deflectometry[C](2018).
[126] PAN J D, YAN N, ZHU L L et al. Comprehensive defect-detection method for a small-sized curved optical lens[J]. Applied Optics, 59, 234-243(2020).
[127] SUN C, ZHENG Y M, ZENG F et al. Simultaneous measurement of displacement, pitch, and yaw angles of a cavity output mirror based on phase measuring deflectometry[J]. Applied Optics, 59, 3270-3284(2020).
[128] MUÑOZ-POTOSI A F, GRANADOS-AGUSTÍN F, CAMPOS-GARCÍA M et al. Deflectometry using a Hartmann screen to measure tilt, decentering and focus errors in a spherical surface[J]. Optics Communications, 402, 375-381(2017).
[129] YU L Z, LI D H, RUAN Y L et al. Wavefront aberration measurement deflectometry for imaging lens tests[J]. Applied Sciences, 12, 7857(2022).
Get Citation
Copy Citation Text
Xiangchao ZHANG, Xingman NIU, Siyuan HAO, Wei LANG, Pingfeng LI, Ruiyang LIU, Zonghua ZHANG. Deflectometric measurement technology for optical surfaces: principles, challenges, and prospects(invited)[J]. Optics and Precision Engineering, 2025, 33(5): 677
Category:
Received: Dec. 12, 2024
Accepted: --
Published Online: May. 20, 2025
The Author Email: