Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method

Optics Express

Volumn 19, Issue 21, 2011, Pages 20483-20492

  Xu, Jiancheng ^a   Jin, Weimin ^a   Chai, Liqun ^b   Xu, Qiao ^b  

^a ZHEJIANG NORMAL UNIVERSITY   (China)

^b CHENGDU FINE OPTICAL ENGINEERING RESEARCH CENTER   (China)

Author keywords

[No Author keywords available]

Indexed keywords

INTERFEROMETRY; LEAST SQUARES APPROXIMATIONS; NUMERICAL METHODS; PHASE SHIFT;

INTERFEROGRAMS; LEAST SQUARES METHODS; OPTICAL EXPERIMENTS; PHASE EXTRACTION; PHASE SHIFTED; RANDOM PHASE SHIFT; RESIDUAL PHASE;

PRINCIPAL COMPONENT ANALYSIS;

ALGORITHM; ARTICLE; COMPUTER PROGRAM; COMPUTER SIMULATION; INTERFEROMETRY; METHODOLOGY; PRINCIPAL COMPONENT ANALYSIS; REGRESSION ANALYSIS; REPRODUCIBILITY; STATISTICAL MODEL; THEORETICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; INTERFEROMETRY; LEAST-SQUARES ANALYSIS; MODELS, STATISTICAL; MODELS, THEORETICAL; PRINCIPAL COMPONENT ANALYSIS; REPRODUCIBILITY OF RESULTS; SOFTWARE;

EID: 80054014353     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.19.020483     Document Type: Article

References (34)

1. L. L. Deck, "Suppressing phase errors from vibration in phase-shifting interferometry", Appl. Opt. 48(20), 3948-3960 (2009).
2. Y.-Y. Cheng and J. C. Wyant, "Phase shifter calibration in phase-shifting interferometry", Appl. Opt. 24(18), 3049-3052 (1985).
3. P. Hariharan, B. F. Oreb, and T. Eiju, "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm", Appl. Opt. 26(13), 2504-2506 (1987).
4. P. L. Wizinowich, "Phase shifting interferometry in the presence of vibration: a new algorithm and system", Appl. Opt. 29(22), 3271-3279 (1990).
5. K. G. Larkin and B. F. Oreb, "Design and assessment of symmetrical phase-shifting algorithms", J. Opt. Soc. Am. A 9(10), 1740-1748 (1992).
6. Y. Surrel, "Phase stepping: a new self-calibrating algorithm", Appl. Opt. 32(19), 3598-3600 (1993).
7. Y. Ishii and R. Onodera, "Phase-extraction algorithm in laser-diode phase-shifting interferometry", Opt. Lett. 20(18), 1883-1885 (1995).
8. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase shifting for nonsinusoidal waveforms with phaseshift errors", J. Opt. Soc. Am. A 12(4), 761-768 (1995).
9. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, "Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts", J. Opt. Soc. Am. A 14(4), 918-930 (1997). (Pubitemid 127579214)
10. K. Okada, A. Sato, and J. Tsujiuchi, "Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry", Opt. Commun. 84(3-4), 118-124 (1991). (Pubitemid 21713923)
11. G.-S. Han and S.-W. Kim, "Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting", Appl. Opt. 33(31), 7321-7325 (1994).
12. B. Kong and S.-W. Kim, "General algorithm of phase-shifting interferometry by iterative least-squares fitting", Opt. Eng. 34(1), 183-188 (1995).
13. Z. Wang and B. Han, "Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms", Opt. Lett. 29(14), 1671-1673 (2004).
14. X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, "Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry", Opt. Lett. 31(13), 1966-1968 (2006). (Pubitemid 44542743)
15. R. Langoju, A. Patil, and P. Rastogi, "Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise", Opt. Lett. 31(8), 1058-1060 (2006). (Pubitemid 43837451)
16. H. Guo, Y. Yu, and M. Chen, "Blind phase shift estimation in phase-shifting interferometry", J. Opt. Soc. Am. A 24(1), 25-33 (2007). (Pubitemid 46172672)
17. A. Dobroiu, P. C. Logofatu, D. Apostol, and V. Damian, "Statistical self-calibrating algorithm for three-sample phase-shift interferometry", Meas. Sci. Technol. 8(7), 738-745 (1997). (Pubitemid 127555359)
18. A. Dobroiu, D. Apostol, V. Nascov, and V. Damian, "Self-calibrating algorithm for three-sample phase-shift interferometry by contrast leveling", Meas. Sci. Technol. 9(5), 744-750 (1998). (Pubitemid 128494317)
19. A. Dobroiu, D. Apostol, V. Nascov, and V. Damian, "Statistical self-calibrating algorithm for phase-shift interferometry based on a smoothness assessment of the intensity offset map", Meas. Sci. Technol. 9(9), 1451-1455 (1998).
20. L. Z. Cai, Q. Liu, and X. L. Yang, "Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects", Opt. Lett. 29(2), 183-185 (2004).
21. X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, "Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments", Opt. Lett. 33(8), 776-778 (2008). (Pubitemid 351656649)
22. X. Xian-Feng, C. Lu-Zhong, W. Yu-Rong, and L. Dai-Lin, "Accurate phase shift extraction for generalized phase-shifting interferometry", Chin. Phys. Lett. 27(2), 024215 (2010).
23. X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, J. P. Guo, and Y. R. Wang, "Wavefront reconstruction and threedimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities", Opt. Lett. 34(8), 1210-1212 (2009).
24. P. Gao, B. Yao, N. Lindlein, J. Schwider, K. Mantel, I. Harder, and E. Geist, "Phase-shift extraction for generalized phase-shifting interferometry", Opt. Lett. 34(22), 3553-3555 (2009).
25. K. A. Goldberg and J. Bokor, "Fourier-transform method of phase-shift determination", Appl. Opt. 40(17), 2886-2894 (2001).
26. X. Chen, M. Gramaglia, and J. A. Yeazell, "Phase-shifting interferometry with uncalibrated phase shifts", Appl. Opt. 39(4), 585-591 (2000).
27. X. Chen, M. Gramaglia, and J. A. Yeazell, "Phase-shift calibration algorithm for phase-shifting interferometry", J. Opt. Soc. Am. A 17(11), 2061-2066 (2000).
28. J. Xu, Y. Li, H. Wang, L. Chai, and Q. Xu, "Phase-shift extraction for phase-shifting interferometry by histogram of phase difference", Opt. Express 18(23), 24368-24378 (2010).
29. J. Vargas, J. A. Quiroga, and T. Belenguer, "Phase-shifting interferometry based on principal component analysis", Opt. Lett. 36(8), 1326-1328 (2011).
30. J. Vargas, J. A. Quiroga, and T. Belenguer, "Analysis of the principal component algorithm in phase-shifting interferometry", Opt. Lett. 36(12), 2215-2217 (2011).
31. J. Xu, L. Sun, Y. Li, and Y. Li, "Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts", Opt. Express 19(15), 14464-14472 (2011).
32. http://en. wikipedia.org/wiki/Principal-component-analysis.
33. http://en. wikipedia.org/wiki/Singular-value-decomposition.
34. http://en. wikipedia.org/wiki/Karhunen%E2%80%93Lo%C3%A8ve-theorem.