Development of surface reconstruction algorithms for optical interferometric measurement
Dongxu WU, Fengzhou FANG
Development of surface reconstruction algorithms for optical interferometric measurement
Optical interferometry is a powerful tool for measuring and characterizing areal surface topography in precision manufacturing. A variety of instruments based on optical interferometry have been developed to meet the measurement needs in various applications, but the existing techniques are simply not enough to meet the ever-increasing requirements in terms of accuracy, speed, robustness, and dynamic range, especially in on-line or on-machine conditions. This paper provides an in-depth perspective of surface topography reconstruction for optical interferometric measurements. Principles, configurations, and applications of typical optical interferometers with different capabilities and limitations are presented. Theoretical background and recent advances of fringe analysis algorithms, including coherence peak sensing and phase-shifting algorithm, are summarized. The new developments in measurement accuracy and repeatability, noise resistance, self-calibration ability, and computational efficiency are discussed. This paper also presents the new challenges that optical interferometry techniques are facing in surface topography measurement. To address these challenges, advanced techniques in image stitching, on-machine measurement, intelligent sampling, parallel computing, and deep learning are explored to improve the functional performance of optical interferometry in future manufacturing metrology.
surface topography / measurement / optical interferometry / coherence envelope / phase-shifting algorithm
[1] |
Brinksmeier E, Gläbe R, Schönemann L. Review on diamond-machining processes for the generation of functional surface structures. CIRP Journal of Manufacturing Science and Technology, 2012, 5(1): 1–7
CrossRef
Google scholar
|
[2] |
Jain V, Ranjan P, Suri V,
CrossRef
Google scholar
|
[3] |
Yamamura K, Takiguchi T, Ueda M,
CrossRef
Google scholar
|
[4] |
Schmidt M, Merklein M, Bourell D,
CrossRef
Google scholar
|
[5] |
Hocken R, Chakraborty N, Brown C. Optical metrology of surfaces. CIRP Annals-Manufacturing Technology, 2005, 54(2): 169–183
CrossRef
Google scholar
|
[6] |
Savio E, De Chiffre L, Schmitt R. Metrology of freeform shaped parts. CIRP Annals-Manufacturing Technology, 2007, 56(2): 810–835
CrossRef
Google scholar
|
[7] |
Zhang X D, Zeng Z, Liu X L,
CrossRef
Google scholar
|
[8] |
Liu X L, Zhang X D, Fang F Z,
CrossRef
Google scholar
|
[9] |
Shore P, Cunningham C, DeBra D,
CrossRef
Google scholar
|
[10] |
Takaya Y. In-process and on-machine measurement of machining accuracy for process and product quality management: A review. International Journal of Automotive Technology, 2014, 8(1): 4–19
|
[11] |
Lee J C, Shimizu Y, Gao W,
CrossRef
Google scholar
|
[12] |
Novak E, Stout T. Interference microscopes for tribology and corrosion quantification. In: Proceedings of SPIE 6616, Optical Measurement Systems for Industrial Inspection V. Munich: SPIE, 2007, 66163B
CrossRef
Google scholar
|
[13] |
Coppola G, Ferraro P, Iodice M,
CrossRef
Google scholar
|
[14] |
Singh V R, Asundi A. In-line digital holography for dynamic metrology of MEMS. Chinese Optics Letters, 2009, 7(12): 1117–1122
CrossRef
Google scholar
|
[15] |
Potcoava M, Kim M. Optical tomography for biomedical applications by digital interference holography. Measurement Science and Technology, 2008, 19(7): 074010
CrossRef
Google scholar
|
[16] |
Merola F, Memmolo P, Miccio L,
CrossRef
Google scholar
|
[17] |
Fang F Z, Zhang X D, Weckenmann A,
CrossRef
Google scholar
|
[18] |
Taylor Hobson Ltd. Form Talysurf PGI Optics Surface Profilometers Brochure. Available from Taylor Hobson website, 2018
|
[19] |
Bruker Corporation. Dimension Icon Atomic Force Microscope Brochure. Available from Bruker website, 2013
|
[20] |
Zygo Corporation. NewViewTM 9000 3D Optical Surface Profiler Brochure. Available from Zygo website, 2018
|
[21] |
OLYMPUS Corporation. LEXT OLS5000 3D Measuring Laser Microscope Brochure. Available from OLYMPUS website, 2018
|
[22] |
Moore Nanotech. Workpiece measurement and Error Compensation System (WECS) Brochure. Available from Moore Nanotech website, 2020
|
[23] |
Vorburger T V, Rhee H G, Renegar T B,
CrossRef
Google scholar
|
[24] |
Villarrubia J S. Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation. Journal of Research of the National Institute of Standards and Technology, 1997, 102(4): 425
CrossRef
Google scholar
|
[25] |
Wang Y, Xie F, Ma S,
CrossRef
Google scholar
|
[26] |
Nomura T, Yoshikawa K, Tashiro H,
CrossRef
Google scholar
|
[27] |
Shore P, Morantz P, Lee D,
CrossRef
Google scholar
|
[28] |
Jiang X. In situ real-time measurement for micro-structured surfaces. CIRP Annals-Manufacturing Technology, 2011, 60(1): 563–566
CrossRef
Google scholar
|
[29] |
Wang D, Fu X, Xu P,
CrossRef
Google scholar
|
[30] |
Gao W, Haitjema H, Fang F Z,
CrossRef
Google scholar
|
[31] |
Li D, Wang B, Tong Z,
CrossRef
Google scholar
|
[32] |
de Groot P. Principles of interference microscopy for the measurement of surface topography. Advances in Optics and Photonics, 2015, 7(1): 1–65
CrossRef
Google scholar
|
[33] |
Zuo C, Feng S, Huang L,
CrossRef
Google scholar
|
[34] |
Malacara D. Optical Shop Testing. Hoboken: John Wiley & Sons, 2007, 547–666
|
[35] |
Creath K. V phase-measurement interferometry techniques. Progress in Optics, 1988, 26: 349–393
CrossRef
Google scholar
|
[36] |
Cheng Y Y, Wyant J C. Multiple-wavelength phase-shifting interferometry. Applied Optics, 1985, 24(6): 804–807
CrossRef
Google scholar
|
[37] |
Lannes A. Integer ambiguity resolution in phase closure imaging. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2001, 18(5): 1046–1055
CrossRef
Google scholar
|
[38] |
Fornaro G, Franceschetti G, Lanari R,
CrossRef
Google scholar
|
[39] |
Davé D P, Akkin T, Milner T E,
CrossRef
Google scholar
|
[40] |
Wyant J C. White light interferometry. Proceedings of SPIE 4737, Holography: A Tribute to Yuri Denisyuk and Emmett Leith, 2002, 98–108
CrossRef
Google scholar
|
[41] |
Cheng Y Y, Wyant J C. Two-wavelength phase shifting interferometry. Applied Optics, 1984, 23(24): 4539–4543
CrossRef
Google scholar
|
[42] |
Onodera R, Ishii Y. Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes. Applied Optics, 1994, 33(22): 5052–5061
CrossRef
Google scholar
|
[43] |
Abdelsalam D, Kim D. Two-wavelength in-line phase-shifting interferometry based on polarizing separation for accurate surface profiling. Applied Optics, 2011, 50(33): 6153–6161
CrossRef
Google scholar
|
[44] |
Decker J E, Miles J R, Madej A A,
CrossRef
Google scholar
|
[45] |
Warnasooriya N, Kim M. LED-based multi-wavelength phase imaging interference microscopy. Optics Express, 2007, 15(15): 9239–9247
CrossRef
Google scholar
|
[46] |
Schmit J, Hariharan P. Two-wavelength interferometric profilometry with a phase-step error-compensating algorithm. Optical Engineering, 2006, 45(11): 115602
CrossRef
Google scholar
|
[47] |
Pförtner A, Schwider J. Red-green-blue interferometer for the metrology of discontinuous structures. Applied Optics, 2003, 42(4): 667–673
CrossRef
Google scholar
|
[48] |
Upputuri P K, Mohan N K, Kothiyal M P. Measurement of discontinuous surfaces using multiple-wavelength interferometry. Optical Engineering, 2009, 48(7): 073603
CrossRef
Google scholar
|
[49] |
Caber P J. Interferometric profiler for rough surfaces. Applied Optics, 1993, 32(19): 3438–3441
CrossRef
Google scholar
|
[50] |
Sandoz P, Devillers R, Plata A. Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry. Journal of Modern Optics, 1997, 44(3): 519–534
CrossRef
Google scholar
|
[51] |
Debnath S K, Kothiyal M P. Experimental study of the phase-shift miscalibration error in phase-shifting interferometry: Use of a spectrally resolved white-light interferometer. Applied Optics, 2007, 46(22): 5103–5109
CrossRef
Google scholar
|
[52] |
Yang C, Wax A, Dasari R R,
CrossRef
Google scholar
|
[53] |
Deck L, de Groot P. High-speed noncontact profiler based on scanning white-light interferometry. Applied Optics, 1994, 33(31): 7334–7338
CrossRef
Google scholar
|
[54] |
Harasaki A, Schmit J, Wyant J C. Improved vertical-scanning interferometry. Applied Optics, 2000, 39(13): 2107–2115
CrossRef
Google scholar
|
[55] |
Balasubramanian N. US Patent, 4340306, 1982-07-20
|
[56] |
Kumar U P, Haifeng W, Mohan N K,
CrossRef
Google scholar
|
[57] |
Gianto G, Salzenstein F, Montgomery P. Comparison of envelope detection techniques in coherence scanning interferometry. Applied Optics, 2016, 55(24): 6763–6774
CrossRef
Google scholar
|
[58] |
Gianto G, Montgomery P, Salzenstein F,
CrossRef
Google scholar
|
[59] |
Zhou Y, Cai H, Zhong L,
CrossRef
Google scholar
|
[60] |
de Groot P. Coherence scanning interferometry. In: Leach R, ed. Optical Measurement of Surface Topography. Berlin: Springer, 2011, 187–208
CrossRef
Google scholar
|
[61] |
Fang F Z, Zeng Z, Zhang X D,
CrossRef
Google scholar
|
[62] |
de Groot P, Deck L. Surface profiling by analysis of white-light interferograms in the spatial frequency domain. Journal of Modern Optics, 1995, 42(2): 389–401
CrossRef
Google scholar
|
[63] |
Kino G S, Chim S S. Mirau correlation microscope. Applied Optics, 1990, 29(26): 3775–3783
CrossRef
Google scholar
|
[64] |
Bowe B W, Toal V. White light interferometric surface profiler. Optical Engineering, 1998, 37(6): 1796–1800
CrossRef
Google scholar
|
[65] |
Lehmann P, Tereschenko S, Xie W. Fundamental aspects of resolution and precision in vertical scanning white-light interferometry. Surface Topography: Metrology and Properties, 2016, 4(2): 024004
CrossRef
Google scholar
|
[66] |
Yamaguchi I, Yamamoto A, Yano M. Surface topography by wavelength scanning interferometry. Optical Engineering, 2000, 39(1): 40–47
CrossRef
Google scholar
|
[67] |
Yamamoto A, Yamaguchi I. Profilometry of sloped plane surfaces by wavelength scanning interferometry. Optical Review, 2002, 9(3): 112–121
CrossRef
Google scholar
|
[68] |
Kuwamura S, Yamaguchi I. Wavelength scanning profilometry for real-time surface shape measurement. Applied Optics, 1997, 36(19): 4473–4482
CrossRef
Google scholar
|
[69] |
Yamamoto A, Kuo C C, Sunouchi K,
CrossRef
Google scholar
|
[70] |
Yamamoto A, Yamaguchi I. Surface profilometry by wavelength scanning Fizeau interferometer. Optics & Laser Technology, 2000, 32(4): 261–266
CrossRef
Google scholar
|
[71] |
Ishii Y. Wavelength-tunable laser-diode interferometer. Optical Review, 1999, 6(4): 273–283
CrossRef
Google scholar
|
[72] |
Jiang X, Wang K, Gao F,
CrossRef
Google scholar
|
[73] |
Muhamedsalih H, Jiang X, Gao F. Comparison of fast Fourier transform and convolution in wavelength scanning interferometry. Proceedings of SPIE 8082, Optical Measurement Systems for Industrial Inspection VII, 2011, 8082: 80820Q
CrossRef
Google scholar
|
[74] |
Gao F, Muhamedsalih H, Jiang X. Surface and thickness measurement of a transparent film using wavelength scanning interferometry. Optics Express, 2012, 20(19): 21450–21456
CrossRef
Google scholar
|
[75] |
Muhamedsalih H, Jiang X, Gao F. Accelerated surface measurement using wavelength scanning interferometer with compensation of environmental noise. Procedia CIRP, 2013, 10: 70–76
CrossRef
Google scholar
|
[76] |
Moschetti G, Forbes A, Leach R K,
CrossRef
Google scholar
|
[77] |
Zhang T, Gao F, Jiang X. Surface topography acquisition method for double-sided near-right-angle structured surfaces based on dual-probe wavelength scanning interferometry. Optics Express, 2017, 25(20): 24148–24156
CrossRef
Google scholar
|
[78] |
Zhang T, Gao F, Muhamedsalih H,
CrossRef
Google scholar
|
[79] |
Swanson E A, Huang D, Hee M R,
CrossRef
Google scholar
|
[80] |
Huang Y C, Chou C, Chou L Y,
CrossRef
Google scholar
|
[81] |
Zhao H, Liang R, Li D,
CrossRef
Google scholar
|
[82] |
Demarest F C. High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics. Measurement Science & Technology, 1998, 9(7): 1024–1030
CrossRef
Google scholar
|
[83] |
Xie Y, Wu Y. Zeeman laser interferometer errors for high-precision measurements. Applied Optics, 1992, 31(7): 881–884
CrossRef
Google scholar
|
[84] |
Gelmini E, Minoni U, Docchio F. Tunable, double-wavelength heterodyne detection interferometer for absolute-distance measurements. Optics Letters, 1994, 19(3): 213–215
CrossRef
Google scholar
|
[85] |
Park Y, Cho K. Heterodyne interferometer scheme using a double pass in an acousto-optic modulator. Optics Letters, 2011, 36(3): 331–333
CrossRef
Google scholar
|
[86] |
Matsumoto H, Hirai A. A white-light interferometer using a lamp source and heterodyne detection with acousto-optic modulators. Optics Communications, 1999, 170(4–6): 217–220
CrossRef
Google scholar
|
[87] |
Hirai A, Matsumoto H. High-sensitivity surface-profile measurements by heterodyne white-light interferometer. Optical Engineering, 2001, 40(3): 387–392
CrossRef
Google scholar
|
[88] |
Dai X, Katuo S. High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry. Measurement Science & Technology, 1998, 9(7): 1031–1035
CrossRef
Google scholar
|
[89] |
Xu X, Wang Y, Ji Y,
CrossRef
Google scholar
|
[90] |
Deck L L. Fourier-transform phase-shifting interferometry. Applied Optics, 2003, 42(13): 2354–2365
CrossRef
Google scholar
|
[91] |
Kafri O. Fundamental limit on accuracy in interferometry. Optics Letters, 1989, 14(13): 657–658
CrossRef
Google scholar
|
[92] |
Zhai Z, Li Z, Zhang Y,
CrossRef
Google scholar
|
[93] |
Vo Q, Fang F Z, Zhang X D,
CrossRef
Google scholar
|
[94] |
Chou C, Shyu J, Huang Y,
CrossRef
Google scholar
|
[95] |
Chang W Y, Chen K H, Chen D C,
CrossRef
Google scholar
|
[96] |
Ajithaprasad S, Gannavarpu R. Non-invasive precision metrology using diffraction phase microscopy and space-frequency method. Optics and Lasers in Engineering, 2018, 109: 17–22
CrossRef
Google scholar
|
[97] |
Venkata Satya Vithin A, Ajithaprasad S, Rajshekhar G. Step phase reconstruction using an anisotropic total variation regularization method in a diffraction phase microscopy. Applied Optics, 2019, 58(26): 7189–7194
CrossRef
Google scholar
|
[98] |
Rajshekhar G, Bhaduri B, Edwards C,
CrossRef
Google scholar
|
[99] |
Larkin K G. Efficient nonlinear algorithm for envelope detection in white light interferometry. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 1996, 13(4): 832–843
CrossRef
Google scholar
|
[100] |
Kim J H, Yoon S W, Lee J H,
CrossRef
Google scholar
|
[101] |
Tien C L, Yu K C, Tsai T Y,
CrossRef
Google scholar
|
[102] |
Lei Z, Liu X, Chen L,
CrossRef
Google scholar
|
[103] |
Muhamedsalih H, Gao F, Jiang X. Comparison study of algorithms and accuracy in the wavelength scanning interferometry. Applied Optics, 2012, 51(36): 8854–8862
CrossRef
Google scholar
|
[104] |
Sandoz P. Wavelet transform as a processing tool in white-light interferometry. Optics Letters, 1997, 22(14): 1065–1067
CrossRef
Google scholar
|
[105] |
Recknagel R J, Notni G. Analysis of white light interferograms using wavelet methods. Optics Communications, 1998, 148(1–3): 122–128
CrossRef
Google scholar
|
[106] |
Hart M, Vass D G, Begbie M L. Fast surface profiling by spectral analysis of white-light interferograms with Fourier transform spectroscopy. Applied Optics, 1998, 37(10): 1764–1769
CrossRef
Google scholar
|
[107] |
Freischlad K, Koliopoulos C L. Fourier description of digital phase-measuring interferometry. Journal of the Optical Society of America. A, Optics and Image Science, 1990, 7(4): 542–551
CrossRef
Google scholar
|
[108] |
Larkin K, Oreb B. Design and assessment of symmetrical phase-shifting algorithms. Journal of the Optical Society of America. A, Optics and Image Science, 1992, 9(10): 1740–1748
CrossRef
Google scholar
|
[109] |
de Groot P. Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window. Applied Optics, 1995, 34(22): 4723–4730
CrossRef
Google scholar
|
[110] |
Schmit J, Creath K. Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry. Applied Optics, 1995, 34(19): 3610–3619
CrossRef
Google scholar
|
[111] |
Kumar U P, Bhaduri B, Kothiyal M,
CrossRef
Google scholar
|
[112] |
Bankhead A D, McDonnell I. US Patent, 7385707, 2008-06-10
|
[113] |
Ai C, Novak E L. US Patent, 5633715, 1997-05-27
|
[114] |
Chen S, Palmer A, Grattan K,
CrossRef
Google scholar
|
[115] |
Alexander B F, Ng K C. Elimination of systematic error in subpixel accuracy centroid estimation. Optical Engineering, 1991, 30(9): 1320–1332
CrossRef
Google scholar
|
[116] |
Harasaki A, Wyant J C. Fringe modulation skewing effect in white-light vertical scanning interferometry. Applied Optics, 2000, 39(13): 2101–2106
CrossRef
Google scholar
|
[117] |
Suematsu M, Takeda M. Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis. Applied Optics, 1991, 30(28): 4046–4055
CrossRef
Google scholar
|
[118] |
Takeda M, Ina H, Kobayashi S. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. Journal of the Optical Society of America, 1982, 72(1): 156–160
CrossRef
Google scholar
|
[119] |
Takeda M, Mutoh K. Fourier transform profilometry for the automatic measurement of 3-D object shapes. Applied Optics, 1983, 22(24): 3977
CrossRef
Google scholar
|
[120] |
Su X, Chen W. Fourier transform profilometry: A review. Optics and Lasers in Engineering, 2001, 35(5): 263–284
CrossRef
Google scholar
|
[121] |
Chim S S, Kino G S. Correlation microscope. Optics Letters, 1990, 15(10): 579–581
CrossRef
Google scholar
|
[122] |
Chim S S, Kino G S. Phase measurements using the Mirau correlation microscope. Applied Optics, 1991, 30(16): 2197–2201
CrossRef
Google scholar
|
[123] |
Trusiak M, Wielgus M, Patorski K. Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition. Optics and Lasers in Engineering, 2014, 52: 230–240
CrossRef
Google scholar
|
[124] |
Huang L, Kemao Q, Pan B,
CrossRef
Google scholar
|
[125] |
Kemao Q. Applications of windowed Fourier fringe analysis in optical measurement: A review. Optics and Lasers in Engineering, 2015, 66: 67–73
CrossRef
Google scholar
|
[126] |
Kemao Q. Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations. Optics and Lasers in Engineering, 2007, 45(2): 304–317
CrossRef
Google scholar
|
[127] |
Kemao Q, Wang H, Gao W. Windowed Fourier transform for fringe pattern analysis: Theoretical analyses. Applied Optics, 2008, 47(29): 5408–5419
CrossRef
Google scholar
|
[128] |
Kemao Q. Windowed Fourier transform for fringe pattern analysis. Applied Optics, 2004, 43(13): 2695–2702
CrossRef
Google scholar
|
[129] |
Zweig D A, Hufnagel R E. Hilbert transform algorithm for fringe-pattern analysis. Proceedings of SPIE 1333, Advanced Optical Manufacturing and Testing, 1990, 1333: 295–303
CrossRef
Google scholar
|
[130] |
Chim S S, Kino G S. Three-dimensional image realization in interference microscopy. Applied Optics, 1992, 31(14): 2550–2553
CrossRef
Google scholar
|
[131] |
Zhao Y, Chen Z, Ding Z,
CrossRef
Google scholar
|
[132] |
Onodera R, Watanabe H, Ishii Y. Interferometric phase-measurement using a one-dimensional discrete Hilbert transform. Optical Review, 2005, 12(1): 29–36
CrossRef
Google scholar
|
[133] |
Li M, Quan C, Tay C. Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry. Optics & Laser Technology, 2008, 40(7): 920–929
CrossRef
Google scholar
|
[134] |
Li S, Su X, Chen W. Wavelet ridge techniques in optical fringe pattern analysis. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2010, 27(6): 1245–1254
CrossRef
Google scholar
|
[135] |
Watkins L, Tan S, Barnes T. Determination of interferometer phase distributions by use of wavelets. Optics Letters, 1999, 24(13): 905–907
CrossRef
Google scholar
|
[136] |
Zhong J, Weng J. Phase retrieval of optical fringe patterns from the ridge of a wavelet transform. Optics Letters, 2005, 30(19): 2560–2562
CrossRef
Google scholar
|
[137] |
de Groot P J, Deck L L. Surface profiling by frequency-domain analysis of white light interferograms. Proceedings of SPIE 2248, Optical Measurements and Sensors for the Process Industries, 1994, 2248: 101–105
CrossRef
Google scholar
|
[138] |
de Groot P, Colonna de Lega X, Kramer J,
CrossRef
Google scholar
|
[139] |
de Groot P, Colonna de Lega X. Signal modeling for low-coherence height-scanning interference microscopy. Applied Optics, 2004, 43(25): 4821–4830
CrossRef
Google scholar
|
[140] |
Zhang S. Recent progresses on real-time 3D shape measurement using digital fringe projection techniques. Optics and Lasers in Engineering, 2010, 48(2): 149–158
CrossRef
Google scholar
|
[141] |
Hariharan P, Oreb B, Eiju T. Digital phase-shifting interferometry: A simple error-compensating phase calculation algorithm. Applied Optics, 1987, 26(13): 2504–2506
CrossRef
Google scholar
|
[142] |
Sandoz P. An algorithm for profilometry by white-light phase-shifting interferometry. Journal of Modern Optics, 1996, 43(8): 1545–1554
CrossRef
Google scholar
|
[143] |
de Groot P J. Long-wavelength laser diode interferometer for surface flatness measurement. Proceedings of SPIE 2248, Optical Measurements and Sensors for the Process Industries, 1994, 2248: 136–141
CrossRef
Google scholar
|
[144] |
Dong Z, Chen Z. Advanced Fourier transform analysis method for phase retrieval from a single-shot spatial carrier fringe pattern. Optics and Lasers in Engineering, 2018, 107: 149–160
CrossRef
Google scholar
|
[145] |
Ma S, Quan C, Zhu R,
CrossRef
Google scholar
|
[146] |
Ma S, Quan C, Zhu R,
CrossRef
Google scholar
|
[147] |
Zhang Z, Jing Z, Wang Z,
CrossRef
Google scholar
|
[148] |
Huang J, Chen W, Su X. Application of two-dimensional wavelet transform in the modulation measurement profilometry. Optical Engineering, 2017, 56(3): 034105
CrossRef
Google scholar
|
[149] |
Serizawa T, Suzuki T, Choi S,
CrossRef
Google scholar
|
[150] |
de Groot P J. 101-frame algorithm for phase-shifting interferometry. Proceedings of SPIE 3098, Optical Inspection and Micromeasurements II, 1997, 3098: 283–293
CrossRef
Google scholar
|
[151] |
Shen M H, Hwang C H, Wang W C. Center wavelength measurement based on higher steps phase-shifting algorithms in white-light scanning interferometry. Procedia Engineering, 2014, 79: 447–455
CrossRef
Google scholar
|
[152] |
Shen M H, Hwang C H, Wang W C. Using higher steps phase-shifting algorithms and linear least-squares fitting in white-light scanning interferometry. Optics and Lasers in Engineering, 2015, 66: 165–173
CrossRef
Google scholar
|
[153] |
Sifuzzaman M, Islam M, Ali M. Application of wavelet transform and its advantages compared to Fourier transform. Journal of Physiological Sciences, 2009, 13: 121–134
|
[154] |
Wei D, Xiao M, Yang P. Do we need all the frequency components of a fringe signal to obtain position information in a vertical scanning wideband interferometer? Optics Communications, 2019, 430: 234–237
CrossRef
Google scholar
|
[155] |
Wei D, Aketagawa M. Automatic selection of frequency domain filter for interference fringe analysis in pulse-train interferometer. Optics Communications, 2018, 425: 113–117
CrossRef
Google scholar
|
[156] |
Pavliček P, Michalek V. White-light interferometry—Envelope detection by Hilbert transform and influence of noise. Optics and Lasers in Engineering, 2012, 50(8): 1063–1068
CrossRef
Google scholar
|
[157] |
Huang N E, Shen Z, Long S R,
|
[158] |
Trusiak M, Patorski K, Pokorski K. Hilbert-Huang processing for single-exposure two-dimensional grating interferometry. Optics Express, 2013, 21(23): 28359–28379
CrossRef
Google scholar
|
[159] |
Trusiak M, Służewski Ł, Patorski K. Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis. Optics Express, 2016, 24(4): 4221–4238
CrossRef
Google scholar
|
[160] |
Trusiak M, Mico V, Garcia J,
CrossRef
Google scholar
|
[161] |
Deepan B, Quan C, Tay C. Determination of phase derivatives from a single fringe pattern using Teager Hilbert Huang transform. Optics Communications, 2016, 359: 162–170
CrossRef
Google scholar
|
[162] |
Trusiak M, Styk A, Patorski K. Hilbert–Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects. Optics and Lasers in Engineering, 2018, 110: 100–112
CrossRef
Google scholar
|
[163] |
Deng J, Wu D, Wang K,
CrossRef
Google scholar
|
[164] |
Rajshekhar G, Rastogi P. Multiple signal classification technique for phase estimation from a fringe pattern. Applied Optics, 2012, 51(24): 5869–5875
CrossRef
Google scholar
|
[165] |
Rajshekhar G, Rastogi P. Fringe demodulation using the two-dimensional phase differencing operator. Optics Letters, 2012, 37(20): 4278–4280
CrossRef
Google scholar
|
[166] |
Vishnoi A, Ramaiah J, Rajshekhar G. Phase recovery method in digital holographic interferometry using high-resolution signal parameter estimation. Applied Optics, 2019, 58(6): 1485–1490
CrossRef
Google scholar
|
[167] |
Feng S, Chen Q, Gu G,
CrossRef
Google scholar
|
[168] |
Gomez C, Su R, de Groot P,
CrossRef
Google scholar
|
[169] |
Gdeisat M, Burton D, Lilley F,
CrossRef
Google scholar
|
[170] |
Zhong M, Chen F, Xiao C,
CrossRef
Google scholar
|
[171] |
Bernal O D, Seat H C, Zabit U,
CrossRef
Google scholar
|
[172] |
Rajshekhar G, Rastogi P. Phase estimation using a state-space approach based method. Optics and Lasers in Engineering, 2013, 51(8): 1004–1007
CrossRef
Google scholar
|
[173] |
Gurov I, Volynsky M. Interference fringe analysis based on recurrence computational algorithms. Optics and Lasers in Engineering, 2012, 50(4): 514–521
CrossRef
Google scholar
|
[174] |
Gao W, Huyen N T T, Loi H S,
CrossRef
Google scholar
|
[175] |
Vishnoi A, Rajshekhar G. Rapid deformation analysis in digital holographic interferometry using graphics processing unit accelerated Wigner-Ville distribution. Applied Optics, 2019, 58(16): 4420–4424
CrossRef
Google scholar
|
[176] |
Ramaiah J, Ajithaprasad S, Rajshekhar G. Graphics processing unit assisted diffraction phase microscopy for fast non-destructive metrology. Measurement Science & Technology, 2019, 30(12): 125202
CrossRef
Google scholar
|
[177] |
Hariharan P. Phase-shifting interferometry: Minimization of systematic errors. Optical Engineering, 2000, 39(4): 967–970
CrossRef
Google scholar
|
[178] |
de Groot P J. Correlated errors in phase-shifting laser Fizeau interferometry. Applied Optics, 2014, 53(19): 4334–4342
CrossRef
Google scholar
|
[179] |
Kim Y, Hibino K, Sugita N,
CrossRef
Google scholar
|
[180] |
Wang Z, Han B. Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms. Optics Letters, 2004, 29(14): 1671–1673
CrossRef
Google scholar
|
[181] |
Wang Z, Han B. Advanced iterative algorithm for randomly phase-shifted interferograms with intra- and inter-frame intensity variations. Optics and Lasers in Engineering, 2007, 45(2): 274–280
CrossRef
Google scholar
|
[182] |
Cai L, Liu Q, Yang X. Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps. Optics Letters, 2003, 28(19): 1808–1810
CrossRef
Google scholar
|
[183] |
Cai L Z, Liu Q, Yang X L. Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors. Optics Communications, 2004, 233(1–3): 21–26
CrossRef
Google scholar
|
[184] |
Gao P, Yao B L, Lindlein N,
CrossRef
Google scholar
|
[185] |
Zhang X, Wang J, Zhang X,
CrossRef
Google scholar
|
[186] |
Larkin K G. A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns. Optics Express, 2001, 9(5): 236–253
CrossRef
Google scholar
|
[187] |
Guo H, Yu Y, Chen M. Blind phase shift estimation in phase-shifting interferometry. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 2007, 24(1): 25–33
CrossRef
Google scholar
|
[188] |
Guo H. Blind self-calibrating algorithm for phase-shifting interferometry by use of cross-bispectrum. Optics Express, 2011, 19(8): 7807–7815
CrossRef
Google scholar
|
[189] |
Wang Y, Lu X, Liu Y,
CrossRef
Google scholar
|
[190] |
Cao S, Wang Y, Lu X,
CrossRef
Google scholar
|
[191] |
Ghim Y S, Rhee H G, Davies A,
CrossRef
Google scholar
|
[192] |
Fuerschbach K, Thompson K P, Rolland J P. Interferometric measurement of a concave, ϕ-polynomial, Zernike mirror. Optics Letters, 2014, 39(1): 18–21
CrossRef
Google scholar
|
[193] |
Leong-Hoï A, Claveau R, Flury M,
CrossRef
Google scholar
|
[194] |
Zhou R, Edwards C, Arbabi A,
CrossRef
Google scholar
|
[195] |
Guo T, Gu Y, Chen J,
CrossRef
Google scholar
|
[196] |
Servin M, Quiroga J A, Padilla M. Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications. Weinheim: John Wiley & Sons, 2014, 57–145
|
[197] |
Petrov N V, Skobnikov V A, Shevkunov I A,
CrossRef
Google scholar
|
[198] |
Schmit J, Olszak A G. Challenges in white-light phase-shifting interferometry. Proceedings of SPIE 4777, Interferometry XI: Techniques and Analysis, 2002, 4777: 118–127
CrossRef
Google scholar
|
[199] |
Petzing J N, Coupland J M, Leach R K. The Measurement of Rough Surface Topography Using Coherence Scanning Interferometry. NPL Measurement Good Practice Guide 116. Middlesex: Queen’s Printer and Controller of HMSO, 2010, 91–110
|
[200] |
Fay M F, Colonna de Lega X, de Groot P. Measuring high-slope and super-smooth optics with high-dynamic-range coherence scanning interferometry. In: Proceedings of Optical Fabrication and Testing. Hawaii: Optical Society of America, 2014, OW1B.3
CrossRef
Google scholar
|
[201] |
Marinello F, Bariani P, Pasquini A,
CrossRef
Google scholar
|
[202] |
de Groot P J. Vibration in phase-shifting interferometry. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 1995, 12(2): 354–365
CrossRef
Google scholar
|
[203] |
Wiersma J T, Wyant J C. Vibration insensitive extended range interference microscopy. Applied Optics, 2013, 52(24): 5957–5961
CrossRef
Google scholar
|
[204] |
Liu Q, Li L, Zhang H,
CrossRef
Google scholar
|
[205] |
Li Y, Kästner M, Reithmeier E. Vibration-insensitive low coherence interferometer (LCI) for the measurement of technical surfaces. Measurement, 2017, 104: 36–42
CrossRef
Google scholar
|
[206] |
Liu Q, Huang W, Li L,
CrossRef
Google scholar
|
[207] |
Colonna de Lega X, de Groot P. Lateral resolution and instrument transfer function as criteria for selecting surface metrology instruments. In: Proceedings of Optical Fabrication and Testing. Monterey: Optical Society of America, 2012, OTu1D.4
|
[208] |
de Groot P, Colonna de Lega X, Sykora D,
|
[209] |
Indebetouw G, Tada Y, Rosen J, Brooker G. Scanning holographic microscopy with resolution exceeding the Rayleigh limit of the objective by superposition of off-axis holograms. Applied Optics, 2007, 46(6): 993–1000
CrossRef
Google scholar
|
[210] |
Dong J, Jia S, Jiang C. Surface shape measurement by multi-illumination lensless Fourier transform digital holographic interferometry. Optics Communications, 2017, 402: 91–96
CrossRef
Google scholar
|
[211] |
Merola F, Paturzo M, Coppola S,
CrossRef
Google scholar
|
[212] |
Bray M. Stitching interferometer for large Plano optics using a standard interferometer. Proceedings of SPIE 3134, Optical Manufacturing and Testing II, 1997, 3134: 39–51
CrossRef
Google scholar
|
[213] |
Otsubo M, Okada K, Tsujiuchi J. Measurement of large plane surface shapes by connecting small-aperture interferograms. Optical Engineering, 1994, 33(2): 608–613
CrossRef
Google scholar
|
[214] |
Murphy P, Forbes G, Fleig J,
CrossRef
Google scholar
|
[215] |
Fleig J, Dumas P, Murphy P E,
CrossRef
Google scholar
|
[216] |
Dumas P R, Fleig J, Forbes G W,
|
[217] |
Lei Z, Liu X, Zhao L,
CrossRef
Google scholar
|
[218] |
Niehaus F, Huttenhuis S, Danger T. New opportunities in freeform manufacturing using a long stroke fast tool system and integrated metrology. Proceedings of SPIE 9633, Optifab 2015, 2015, 9633: 96331E
|
[219] |
Lei W, Hsu Y. Accuracy enhancement of five-axis CNC machines through real-time error compensation. International Journal of Machine Tools and Manufacture, 2003, 43(9): 871–877
CrossRef
Google scholar
|
[220] |
Yang J, Altintas Y. A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools. International Journal of Machine Tools and Manufacture, 2015, 88: 9–23
CrossRef
Google scholar
|
[221] |
Suh S H, Lee E S, Sohn J W. Enhancement of geometric accuracy via an intermediate geometrical feedback scheme. Journal of Manufacturing Systems, 1999, 18(1): 12–21
CrossRef
Google scholar
|
[222] |
Ke Z, Yuen A, Altintas Y. Pre-compensation of contour errors in five-axis CNC machine tools. International Journal of Machine Tools and Manufacture, 2013, 74(8): 1–11
CrossRef
Google scholar
|
[223] |
Gao W, Tano M, Sato S,
CrossRef
Google scholar
|
[224] |
Gao W, Aoki J, Ju B F,
CrossRef
Google scholar
|
[225] |
Gao W, Chen Y L, Lee K W,
CrossRef
Google scholar
|
[226] |
Zou X, Zhao X, Li G, et al. Non-contact on-machine measurement using a chromatic confocal probe for an ultra-precision turning machine. International Journal of Advanced Manufacturing Technology, 2017, 90(5–8): 2163–2172
CrossRef
Google scholar
|
[227] |
Jiang X, Wang K, Martin H. Near common-path optical fiber interferometer for potentially fast on-line microscale-nanoscale surface measurement. Optics Letters, 2006, 31(24): 3603–3605
CrossRef
Google scholar
|
[228] |
Li D, Tong Z, Jiang X,
CrossRef
Google scholar
|
[229] |
Li D, Jiang X, Tong Z,
CrossRef
Google scholar
|
[230] |
ElKott D F, Veldhuis S C. Isoparametric line sampling for the inspection planning of sculptured surfaces. Computer Aided Design, 2005, 37(2): 189–200
CrossRef
Google scholar
|
[231] |
He G, Sang Y, Pang K,
CrossRef
Google scholar
|
[232] |
He G, Sang Y, Wang H,
CrossRef
Google scholar
|
[233] |
Babu M, Franciosa P, Ceglarek D. Adaptive measurement and modelling methodology for in-line 3D surface metrology scanners. Procedia CIRP, 2017, 60: 26–31
CrossRef
Google scholar
|
[234] |
Babu M, Franciosa P, Ceglarek D. Spatio-temporal adaptive sampling for effective coverage measurement planning during quality inspection of free form surfaces using robotic 3D optical scanner. Journal of Manufacturing Systems, 2019, 53: 93–108
CrossRef
Google scholar
|
[235] |
Chen Y, Peng C. Intelligent adaptive sampling guided by Gaussian process inference. Measurement Science & Technology, 2017, 28(10): 105005
CrossRef
Google scholar
|
[236] |
Yin Y, Ren M J, Sun L,
CrossRef
Google scholar
|
[237] |
Yin Y, Ren M J, Sun L. Dependant Gaussian processes regression for intelligent sampling of freeform and structured surfaces. CIRP Annals-Manufacturing Technology, 2017, 66(1): 511–514
CrossRef
Google scholar
|
[238] |
Gao W, Kemao Q. Parallel computing in experimental mechanics and optical measurement: A review. Optics and Lasers in Engineering, 2012, 50(4): 608–617
CrossRef
Google scholar
|
[239] |
Wang T, Kemao Q. Parallel computing in experimental mechanics and optical measurement: A review (II). Optics and Lasers in Engineering, 2018, 104: 181–191
CrossRef
Google scholar
|
[240] |
Karpinsky N, Zhang S. High-resolution, real-time 3D imaging with fringe analysis. Journal of Real-Time Image Processing, 2012, 7(1): 55–66
CrossRef
Google scholar
|
[241] |
Van der Jeught S, Soons J A, Dirckx J J. Real-time microscopic phase-shifting profilometry. Applied Optics, 2015, 54(15): 4953–4959
CrossRef
Google scholar
|
[242] |
Sinha A, Lee J, Li S,
CrossRef
Google scholar
|
[243] |
Rivenson Y, Göröcs Z, Günaydin H,
CrossRef
Google scholar
|
[244] |
Rivenson Y, Zhang Y, Günaydın H,
CrossRef
Google scholar
|
[245] |
Yin W, Chen Q, Feng S,
CrossRef
Google scholar
|
[246] |
Feng S, Zuo C, Yin W,
CrossRef
Google scholar
|
/
〈 | 〉 |