Statistical phase-shifting step estimation algorithm based on the continuous wavelet transform for high-resolution interferometry metrology

Applied Optics

Volumn 50, Issue 4, 2011, Pages 586-593

  Chen, Bicheng ^a   Basaran, Cemal ^a  

^a UNIVERSITY AT BUFFALO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMIC LOADS; INTERFEROMETRY; STATISTICS; WAVELET TRANSFORMS;

CONTINUOUS WAVELET TRANSFORM; CONTINUOUS WAVELET TRANSFORMS; DIRECTIONAL STATISTICS; DYNAMIC LOADING CONDITIONS; ESTIMATION ALGORITHM; HIGH RESOLUTION INTERFEROMETRY; SPATIAL INFORMATIONS; STATISTICAL MODELING;

PHASE SHIFT;

EID: 79551558478     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.50.000586     Document Type: Article

References (36)

1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, "Digital wavefront measuring interferometer for testing optical surfaces and lenses," Appl. Opt. 13, 2693-2703 (1974).
2. C. J. Morgan, "Least-squares estimation in phasemeasurement interferometry," Opt. Lett. 7, 368-370 (1982).
3. J. E. Greivenkamp, "Generalized data reduction for heterodyne interferometry," Opt. Eng. 23, 350-352 (1984).
4. G. Lai and T. Yatagai, "Generalized phase-shifting interferometry," J. Opt. Soc. Am. A 8, 822-827 (1991).
5. K. Larkin, "A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns," Opt. Express 9, 236-253 (2001).
6. C. T. Farrell and M. A. Player, "Phase-step insensitive algorithms for phase-shifting interferometry," Meas. Sci. Technol. 5, 648-654 (1994).
7. C. Wei, M. Chen, and Z. Wang, "General phase-stepping algorithm with automatic calibration of phase steps," Opt. Eng. 38, 1357-1360 (1999).
8. I.-B. Kong and S.-W. Kim, "General algorithm of phaseshifting interferometry by iterative least-squares fitting," Opt. Eng. 34, 183-188 (1995).
9. M. Rivera, R. Bizuet, A. Martinez, and J. A. Rayas, "Halfquadratic cost function for computing arbitrary phase shifts and phase: adaptive out of step phase shifting," Opt. Express 14, 3204-3213 (2006).
10. Z. Wang and B. Han, "Advanced iterative algorithm for randomly phase-shifted interferograms with intra- and interframe intensity variations," Opt. Lasers Eng. 45, 274-280 (2007).
11. L. Z. Cai, Q. Liu, and X. L. Yang, "Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps," Opt. Lett. 28, 1808-1810 (2003).
12. L. Z. Cai, Q. Liu, and X. L. Yang, "Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects," Opt. Lett. 29, 183-185 (2004).
13. 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, 1966-1968 (2006).
14. H. Guo, Z. Zhao, and M. Chen, "Efficient iterative algorithm for phase-shifting interferometry," Opt. Lasers Eng. 45, 281-292 (2007).
15. Y.-Y.ChengandJ.C.Wyant, "Phaseshifter calibrationin phaseshifting interferometry," Appl. Opt. 24, 3049-3052 (1985).
16. C. Ai and J. C. Wyant, "Effect of piezoelectric transducer nonlinearity on phase shift interferometry," Appl. Opt. 26, 1112-1116 (1987).
17. B. Gutmann and H. Weber, "Phase-shifter calibration and error detection in phase-shifting applications: a new method," Appl. Opt. 37, 7624-7631 (1998).
18. D. Malacara, S. Manuel, and M. Zacarias, Interferogram Analysis for Optical Testing, 2nd ed., Optical Engineering and Science (Taylor & Francis, 2005).
19. B. Chen and C. Basaran, "Automatic full strain field Moire interferometry measurement with nano-scale resolution," Exp. Mech. 48, 665-673 (2008).
20. H. Liu, "Phase reconstruction of phase shifted moire interferograms using continuous wavelet transforms," Ph.D. dissertation (State University of New York at Buffalo, 2003).
21. C. Han and B. Han, "Phase-shifting in achromatic moiré interferometry system," Opt. Express 15, 9970-9976 (2007).
22. L. R. Watkins, S. M. Tan, and T. H. Barnes, "Interferometer profile extraction using continuous wavelet transform," Electron. Lett. 33, 2116-2117 (1997).
23. L. R. Watkins, S. M. Tan, and T. H. Barnes, "Determination of interferometer phase distributions by use of wavelets," Opt. Lett. 24, 905-907 (1999).
24. H. Liu, A. N. Cartwright, and C. Basaran, "Moire interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms," Appl. Opt. 43, 850-857 (2004).
25. L. R. Watkins, "Phase recovery from fringe patterns using the continuous wavelet transform," Opt. Lasers Eng. 45, 298-303 (2007).
26. C. A. Sciammarella and T. Kim, "Frequency modulation interpretation of fringes and computation of strains," Exp. Mech. 45, 393-403 (2005).
27. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, 1995).
28. M. Afifi, A. Fassi-Fihri, M. Marjane, K. Nassim, M. Sidki, and S. Rachafi, "Paul wavelet-based algorithm for optical phase distribution evaluation," Opt. Commun. 211, 47-51 (2002).
29. N. Delprat, B. Escudie, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, and B. Torresani, "Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies," IEEE Trans. Inf. Theory 38, 644-664 (1992).
30. R. A. Carmona, W. L. Hwang, and B. Torresani, "Characterization of signals by the ridges of their wavelet transforms," IEEE Trans. Signal Process. 45, 2586-2590 (1997).
31. A. van den Bos, Parameter Estimation for Scientists and Engineers (Wiley-Interscience, 2007).
32. A. W. F. Edwards, Likelihood: An Account of the Statistical Concept of Likelihood and Its Application to Scientific Inference (Cambridge University, 1972).
33. L. R. Shenton and K. O. Bowman, Maximum Likelihood Estimation in Small Samples, Griffin's Statistical Monographs & Courses (Macmillan, 1977).
34. S. M. Kay, Fundamentals of Statistical Signal Processing, Prentice Hall Signal Processing Series (Prentice-Hall, 1993).
35. E. Batschelet, Circular Statistics in Biology, Mathematics in Biology (Academic, 1981).
36. S. R. S. A. Jammalamadaka, Topics in Circular Statistics, Series on Multivariate Analysis (World Scientific, 2001).