Four-Step Spatial Quasi-Phase-Shifting Technique for Phase Demodulation from a Single Carrier Fringe Pattern

Lin Jinxin; Ma Xiao; Li Shiping; Zhong Jingang

doi:10.3788/lop54.011203

[1] Rastogi P, Hack E. Phase estimation in optical interferometry［M］. Boca Raton: CRC Press, 2014.

[2] Su Xianyu, Zhang Qican, Chen Wenjing. Three-dimensional imaging based on structured illumination［J］. Chinese J Lasers, 2014, 41(2): 0209001.

[3] Zhang S. Recent progresses on real-time 3D shape measurement using digital fringe projection techniques［J］. Optics & Lasers in Engineering, 2010, 48(2): 149-158.

[4] Zhu X J, Tang C, Li B Y, et al. Phase retrieval from single frame projection fringe pattern with variational image decomposition［J］. Optics & Lasers in Engineering, 2014, 59: 25-33.

[5] Martino J M D, Fernández A, Ayubi G A, et al. Differential 3D shape retrieval［J］. Optics & Lasers in Engineering, 2014, 58: 114-118.

[6] Takeda M, Ina H, Kobayashi S. Fourier-transform algorithm of fringe-pattern analysis for computer-based topography and interferometry［J］. Journal of the Optical Society of America, 1982, 72(1): 156-160.

[7] Qian K M. Windowed Fourier transform for fringe pattern analysis［J］. Applied Optics, 2004, 43(13): 2695-2702.

[8] Zhong J G, Weng J W. Dilating Gabor transform for the fringe analysis of 3-D shape measurement［J］. Optical Engineering, 2004, 43(4): 895-899.

[9] Zhong J, Zeng H. Multiscale windowed Fourier transform for phase extraction of fringe patterns［J］. Applied Optics, 2007, 46(14): 2670-2675.

[10] Wang Chenxing, Da Feipeng. Anovel adaptive windowed Fourier transform for phase retrieval in 3D shape measurement［J］. Acta Optica Sinica, 2012, 32(6): 0612005.

[11] Dong Fuqiang, Da Feipeng, Huang Hao. Windowed Fouriertransform profilometry based on advanced S-transform［J］. Acta Optica Sinica, 2012, 32(5): 0512008.

[12] Zhong J, Weng J. Spatial carrier-fringe pattern analysis by means of wavelet transform: Wavelet transform profilometry［J］. Applied Optics, 2004, 43(26): 4993-4998.

[13] Zhong J, Weng J. Phase retrieval of optical fringe patterns from the ridge of a wavelet transform［J］. Optics Letters, 2005, 30(19): 2560-2562.

[14] Yu Cheng, Li Sikun, Wang Xiangzhao. Fastthree-dimensional shape measurement technique by means of wavelet transform based on parallel computing［J］. Acta Optica Sinica, 2014, 34(5): 0512005.

[15] Zheng Yi, Chen Wenjing, Zhong Min, et al. Study of profilometry measurement precision improvement based on Morlet wavelet transform［J］. Laser & Optoelectronics Progress, 2014, 51(11): 111203.

[16] Wang Z, Ma H. Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing［J］. Optical Engineering, 2006, 45(4): 045601.

[17] Gdeisat M A, Burton D R, Lalor M J. Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform［J］. Applied Optics, 2006, 45(34): 8722-8732.

[18] Zhang Z, Zhong J. Applicability analysis of wavelet-transform profilometry［J］. Optics Express, 2013, 21(16): 18777-18796.

[19] Kujawinska M. Spatial phase measurement methods in interferogram analysis［J］. London: Institute of Physics Publishing, 1993: 141-193.

[20] Ferrari J A, Frins E M. Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier［J］. Optics Communications, 2007, 271(1): 59-64.

[21] Zhang R, Guo H. Phase gradients from intensity gradients: A method of spatial carrier fringe pattern analysis［J］. Optics Express, 2014, 22(19): 22432-22445.

[22] Wyant J C. Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems［J］. Applied Optics, 1975, 14(11): 2622-2626.

[23] Ei-Morsy M, Harada K, Itoh M, et al. A subfringe integration algorithm for multiple-beam Fizeau fringe analysis［J］. Optics & Laser Technology, 2003, 35(3): 223-232.

[24] Wang M, Zhong J, Li D. Subfringe integration profilometry of three-dimensional diffuse objects［J］. Optical Engineering, 1997, 36(9): 2567-2572.

[25] Zhang Z, Zhong J. Spatial quasi-phase-shifting technique for single-frame dynamic fringe analysis［J］. Optics Express, 2014, 22(3): 2695-2705.

[26] Hu Kui, Ma Xiao, Zhong Jingang. Improved sub-fringe integration technique for phase analysis［J］. Journal of Applied Optics, 2016, 37(2): 215-220.

[27] Carré P. Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures［J］. Metrologia, 1996, 2(1): 13-23.

[28] Servin M, Gonzalez A. Linear analysis of the four-step Carré phase shifting algorithm: Spectrum, signal-to-noise ratio, and harmonics response［R/OL］. (2012-03-08)［2016-07-03］ https://arxiv.org/abs/1203.1947.

[29] Ransom P, Kokal J V. Interferogram analysis by a modified sinusoid fitting technique［J］. Applied Optics, 1986, 25(22): 4199-4204.

[30] Larkin K. Efficient nonlinear algorithm for envelope detection in white light interferometry［J］. Journal of the Optical Society of America A, 1996, 13(4): 832-843.

[31] Stoilov G, Dragostinov T. Phase-stepping interferometry: Five-frame algorithm with an arbitrary step［J］. Optics & Lasers in Engineering, 1997, 28(1): 61-69.

[32] Asundi A, Wensen Z. Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill［J］. Applied Optics, 1998, 37(23): 5416-5420.