The regularized phase tracking technique used in single closed interferogram phase retrieval
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摘要: 在利用干涉技术检测温度、压力、形貌等物理量时，往往需要通过各种调制手段将这些物理量的信息加载到干涉条纹图样中，并通过对其进行分析而得到被测信息。当实验条件不利于实验者实施移相、加载波等调制手段时，探测器得到的往往是单幅闭合条纹，此时常用的移相解调技术和频谱分析方法等不再适用。正则化相位跟随(Regularized Phase Tracking，RPT)技术可以对单幅闭合条纹进行相位恢复，是目前针对单幅闭合条纹相位恢复最有效的方法。近年来研究者们从复杂干涉图处理能力、算法稳定性、相位恢复精度等方面对RPT技术进行了改进和发展，使其逐渐走向实用化。本文介绍了RPT技术用于单幅干涉图相位恢复的基本原理，总结了近年来RPT技术的相关改进与发展，例举了采用RPT技术进行相位恢复的应用场合，并适当推测RPT技术的未来发展方向。Abstract: Different kinds of modulation methods are usually adopted when physical quantities, such as temperature, forces and deformation, are measured in interference. Fringe patterns carry measurement information of those quantities and are usually later analyzed for its retrieval. Single closed fringes are generally what is recorded by CCD. When the experimental conditions are not conducive to phase shifting, loading wave and other modulation means, the regularized phase tracking(RPT) technique can retrieve a continuous phase map directly from a single interferogram, making it the most effective method. In recent years, RPT technique has been improved to achieve higher processing power, algorithm robustness and retrieval accuracy for complex fringe patterns, ultimately making it more practical. In this paper, we introduce the basic algorithm principle and how the RPT technique is applied in the retrieval of single interferograms, review the technique's relevant modifications and developments in recent years, cite some examples used for phase retrieval and speculate the direction of its future development.
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Key words:
- interference /
- phase retrieval /
- single interferogram /
- regularization
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图 3 干涉图与利用恢复相位反求的干涉图
Figure 3. Interferograms before and after reversed phase recovery
图 4 对未归一化调制度干涉图的相位恢复(已包裹)
Figure 4. Phase recovery of unnormalized interferogram(rewrapped)
图 6 GRPT对干涉图的相位恢复(已包裹)
Figure 6. Phase retrieval of interferogram with GRPT(rewrapped)
图 7 RFS与RPT对同一幅干涉图解调结果
Figure 7. Demodulation results of RFS and RPT in the same interferogram
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[1] GÅSVIK K J. Optical Metrology[M]. 3rd ed. Hoboken:John Wiley & Sons, 2002. [2] 郑文军.介晶双丙烯酸酯在全息干涉光场中的指向性交联[J].液晶与显示, 2010, 25(5):611-616. doi: 10.3969/j.issn.1007-2780.2010.05.001ZHENG W J. Orientational crosslinking of mesogenic diacrylates in holographic interference field[J]. Chinese Journal of Liquid Crystals and Displays, 2010, 25(5):611-616.(in Chinese) doi: 10.3969/j.issn.1007-2780.2010.05.001 [3] 范应娟, 袁桃利, 张麦丽.偏光干涉法检测LCD间隔的均匀性[J].液晶与显示, 2015, 30(3):416-420. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yjyxs201503008FAN Y J, YUAN T L, ZHANG M L.Testing uniformity of spacers in LCD with the way of polarization interference[J]. Chinese Journal of Liquid Crystals and Displays, 2015, 30(3):416-420.(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yjyxs201503008 [4] MALACARA D, SERVÍN M, MALACARA Z. Interferogram Analysis for Optical Testing[M]. 2nd ed. Florida, USA:CRC Press, 2005. [5] CHENG ZH T, LIU D. Fast and accurate wavefront reconstruction in two-frame phase-shifting interferometry with unknown phase step[J]. Optics Letters, 2018, 43(13):3033-3036. doi: 10.1364/OL.43.003033 [6] TIAN CH, LIU SH CH. Phase retrieval in two-shot phase-shifting interferometry based on phase shift estimation in a local mask[J]. Optics Express, 2017, 25(18):21673-21683. doi: 10.1364/OE.25.021673 [7] TIAN CH, YANG Y Y, WEI T, et al.. Demodulation of a single-image interferogram using a Zernike-polynomial-based phase-fitting technique with a differential evolution algorithm[J]. Optics Letters, 2011, 36(12):2318-2320. doi: 10.1364/OL.36.002318 [8] LIU F W, WANG J, WU Y Q, et al.. Simultaneous extraction of phase and phase shift from two interferograms using Lissajous figure and ellipse fitting technology with Hilbert-Huang prefiltering[J]. Journal of Optics, 2016, 18(10):105604. doi: 10.1088/2040-8978/18/10/105604 [9] QIAN K M. Windowed Fringe Pattern Analysis[M]. Bellingham, Washington, USA:SPIE Press, 2013. [10] SERVIN M, MARROQUIN J L, CUEVAS F J. Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique[J]. Applied Optics, 1997, 36(19):4540-4548. doi: 10.1364/AO.36.004540 [11] 刘东, 杨甬英, 田超, 等.高精度单幅闭合条纹干涉图相位重构技术[J].中国激光, 2010, 37(2):531-536. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgjg201002039LIU D, YANG Y Y, TIAN CH, et al..Study on phase retrieval from single close fringe pattern with high precision[J]. Chinese Journal of Lasers, 2010, 37(2):531-536.(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgjg201002039 [12] TIAN CH, YANG Y Y, LIU D, et al.. Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique[J]. Applied Optics, 2010, 49(2):170-179. doi: 10.1364/AO.49.000170 [13] LI K, QIAN K M. Improved generalized regularized phase tracker for demodulation of a single fringe pattern[J]. Optics Express, 2013, 21(20):24385-24397. doi: 10.1364/OE.21.024385 [14] LI K, QIAN K M. A generalized regularized phase tracker for demodulation of a single fringe pattern[J]. Optics Express, 2012, 20(11):12579-12592. doi: 10.1364/OE.20.012579 [15] HE A H, DEEPAN B, QUAN C. Simplified paraboloid phase model-based phase tracker for demodulation of a single complex fringe[J]. Applied Optics, 2017, 56(25):7217-7224. doi: 10.1364/AO.56.007217 [16] DEEPAN B, QUAN CH G, TAY C J. Determination of slope, curvature, and twist from a single shearography fringe pattern using derivative-based regularized phase tracker[J]. Optical Engineering, 2016, 55(12):121707. doi: 10.1117/1.OE.55.12.121707 [17] DEEPAN B, QUAN C, TAY C J. A derivative based simplified phase tracker for a single fringe pattern demodulation[J]. Optics and Lasers in Engineering, 2016, 83:83-89. doi: 10.1016/j.optlaseng.2016.03.012 [18] QUIROGA J A, SERVIN M. Isotropic n-dimensional fringe pattern normalization[J]. Optics Communications, 2003, 224(4-6):221-227. doi: 10.1016/j.optcom.2003.07.014 [19] QUIROGA J A, GÓMEZ-PEDRERO J A, GARCÍA-BOTELLA Á. Algorithm for fringe pattern normalization[J]. Optics Communications, 2001, 197(1-3):43-51. doi: 10.1016/S0030-4018(01)01440-7 [20] BERNINI M B, FEDERICO A, KAUFMANN G H. Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform[J]. Applied Optics, 2009, 48(36):6862-6869. doi: 10.1364/AO.48.006862 [21] TIEN C L, JYU S S, YANG H M. A method for fringe normalization by Zernike polynomial[J]. Optical Review, 2009, 16(2):173-175. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=c06bcbb19181532f4aae8fd8000e9f8a [22] OCHOA N A, SILVA-MORENO A. Normalization and noise-reduction algorithm for fringe patterns[J]. Optics Communications, 2007, 270(2):161-168. doi: 10.1016/j.optcom.2006.09.062 [23] STASZEK K, BOGUSZ M. Simple fringe pattern normalization algorithm[J]. IFAC Proceedings Volumes, 2012, 45(7):353-356. doi: 10.3182/20120523-3-CZ-3015.00067 [24] SERVIN M, MARROQUIN J L, CUEVAS F J. Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms[J]. Journal of the Optical Society of America A, 2001, 18(3):689-695. doi: 10.1364/JOSAA.18.000689 [25] LEGARDA-SAENZ R, RIVERA M. Fast half-quadratic regularized phase tracking for nonnormalized fringe patterns[J]. Journal of the Optical Society of America A, 2006, 23(11):2724-2731. doi: 10.1364/JOSAA.23.002724 [26] LEGARDA-SÁENZ R, OSTEN W, JUPTNER W. Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns[J]. Applied Optics, 2002, 41(26):5519-5526. doi: 10.1364/AO.41.005519 [27] TIAN CH, YANG Y Y, ZHANG SH N, et al.. Regularized frequency-stabilizing method for single closed-fringe interferogram demodulation[J]. Optics Letters, 2010, 35(11):1837-1839. doi: 10.1364/OL.35.001837 [28] QUIROGA J A, VILLA J, CRESPO D. Automatic techniques for evaluation of moire deflectograms[J]. Proceedings of SPIE, 1999, 3744:328-334. doi: 10.1117/12.357730 [29] VILLA J, SERVIN M. Robust profilometer for the measurement of 3-D object shapes based on a regularized phase tracker[J]. Optics and Lasers in Engineering, 1999, 31(4):279-288. doi: 10.1016/S0143-8166(99)00023-8 [30] SERVIN M, CUEVAS F J, MALACARA D, et al.. Direct ray aberration estimation in Hartmanngrams by use of a regularized phase-tracking system[J]. Applied Optics, 1999, 38(13):2862-2869. doi: 10.1364/AO.38.002862 [31] VILLA J, QUIROGA J A, SERVÍN M. Improved regularized phase-tracking technique for the processing of squared-grating deflectograms[J]. Applied Optics, 2000, 39(4):502-508. doi: 10.1364/AO.39.000502 [32] RAMESH K, KASIMAYAN T, NEETHI SIMON B. Digital photoelasticity A comprehensive review[J]. The Journal of Strain Analysis for Engineering Design, 2011, 46(4):245-266. doi: 10.1177/0309324711401501 [33] PATTERSON E A. Digital photoelasticity:principles, practice and potential:measurements lecture[J]. Strain, 2002, 38(1):27-39. doi: 10.1046/j.0039-2103.2002.00004.x [34] QUIROGA J A, GONZALEZ-CANO A. Application of regularization methods to the analysis of photoelastic fringe patterns[J]. Proceedings of SPIE, 1999, 3744:318-327. doi: 10.1117/12.357729 [35] SIEGMANN P, DÍAZ-GARRIDO F, PATTERSON E A. Robust approach to regularize an isochromatic fringe map[J]. Applied Optics, 2009, 48(22):E24-E34. doi: 10.1364/AO.48.000E24 [36] SERVIN M, QUIROGA J A. Isochromatics demodulation from a single image using the regularized phase tracking technique[J]. Journal of Modern Optics, 2001, 48(3):521-531. doi: 10.1080/09500340108230929 [37] QUIROGA J A, SERVIN M, MARROQUIN J L. Regularized phase tracking technique for demodulation of isochromatics from a single tricolour image[J]. Measurement Science and Technology, 2002, 13(1):132-140. doi: 10.1088/0957-0233/13/1/317 [38] QUIROGA J A, GONZÁLEZ-CANO A. Separation of isoclinics and isochromatics from photoelastic data with a regularized phase-tracking technique[J]. Applied Optics, 2000, 39(17):2931-2940. doi: 10.1364/AO.39.002931 -
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