B. Chen and C. Basaran, “Automatic full strain field Moire interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).

[CrossRef]

C. Han and B. Han, “Phase-shifting in achromatic moiré interferometry system,” Opt. Express 15, 9970–9976 (2007).

[CrossRef]
[PubMed]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).

[CrossRef]

Z. Wang and B. Han, “Advanced iterative algorithm for randomly phase-shifted interferograms with intra- and inter-frame intensity variations,” Opt. Lasers Eng. 45, 274–280(2007).

[CrossRef]

H. Guo, Z. Zhao, and M. Chen, “Efficient iterative algorithm for phase-shifting interferometry,” Opt. Lasers Eng. 45, 281–292 (2007).

[CrossRef]

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).

[CrossRef]
[PubMed]

M. Rivera, R. Bizuet, A. Martinez, and J. A. Rayas, “Half-quadratic cost function for computing arbitrary phase shifts and phase: adaptive out of step phase shifting,” Opt. Express 14, 3204–3213 (2006).

[CrossRef]
[PubMed]

C. A. Sciammarella and T. Kim, “Frequency modulation interpretation of fringes and computation of strains,” Exp. Mech. 45, 393–403 (2005).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).

[CrossRef]

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).

[CrossRef]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

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).

[CrossRef]

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).

[CrossRef]

C. T. Farrell and M. A. Player, “Phase-step insensitive algorithms for phase-shifting interferometry,” Meas. Sci. Technol. 5, 648–654 (1994).

[CrossRef]

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).

[CrossRef]

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

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).

[CrossRef]

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).

[CrossRef]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

E. Batschelet, Circular Statistics in Biology, Mathematics in Biology (Academic, 1981).

L. R. Shenton and K. O. Bowman, Maximum Likelihood Estimation in Small Samples, Griffin’s Statistical Monographs & Courses (Macmillan, 1977).

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]

B. Chen and C. Basaran, “Automatic full strain field Moire interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).

[CrossRef]

H. Guo, Z. Zhao, and M. Chen, “Efficient iterative algorithm for phase-shifting interferometry,” Opt. Lasers Eng. 45, 281–292 (2007).

[CrossRef]

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).

[CrossRef]

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).

[CrossRef]

A. W. F. Edwards, Likelihood: An Account of the Statistical Concept of Likelihood and Its Application to Scientific Inference (Cambridge University, 1972).

[PubMed]

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).

[CrossRef]

C. T. Farrell and M. A. Player, “Phase-step insensitive algorithms for phase-shifting interferometry,” Meas. Sci. Technol. 5, 648–654 (1994).

[CrossRef]

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).

[CrossRef]

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

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).

[CrossRef]

H. Guo, Z. Zhao, and M. Chen, “Efficient iterative algorithm for phase-shifting interferometry,” Opt. Lasers Eng. 45, 281–292 (2007).

[CrossRef]

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).

[CrossRef]

S. R. S. A. Jammalamadaka, Topics in Circular Statistics, Series on Multivariate Analysis (World Scientific, 2001).

[CrossRef]

S. M. Kay, Fundamentals of Statistical Signal Processing, Prentice Hall Signal Processing Series (Prentice-Hall, 1993).

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).

[CrossRef]

C. A. Sciammarella and T. Kim, “Frequency modulation interpretation of fringes and computation of strains,” Exp. Mech. 45, 393–403 (2005).

[CrossRef]

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).

[CrossRef]

M. Vetterli and J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, 1995).

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

D. Malacara, S. Manuel, and M. Zacarias, Interferogram Analysis for Optical Testing, 2nd ed., Optical Engineering and Science (Taylor & Francis, 2005).

[CrossRef]

D. Malacara, S. Manuel, and M. Zacarias, Interferogram Analysis for Optical Testing, 2nd ed., Optical Engineering and Science (Taylor & Francis, 2005).

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]

C. T. Farrell and M. A. Player, “Phase-step insensitive algorithms for phase-shifting interferometry,” Meas. Sci. Technol. 5, 648–654 (1994).

[CrossRef]

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).

[CrossRef]

C. A. Sciammarella and T. Kim, “Frequency modulation interpretation of fringes and computation of strains,” Exp. Mech. 45, 393–403 (2005).

[CrossRef]

L. R. Shenton and K. O. Bowman, Maximum Likelihood Estimation in Small Samples, Griffin’s Statistical Monographs & Courses (Macmillan, 1977).

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).

[CrossRef]

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).

[CrossRef]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]

A. van den Bos, Parameter Estimation for Scientists and Engineers (Wiley-Interscience, 2007).

[CrossRef]

M. Vetterli and J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, 1995).

Z. Wang and B. Han, “Advanced iterative algorithm for randomly phase-shifted interferograms with intra- and inter-frame intensity variations,” Opt. Lasers Eng. 45, 274–280(2007).

[CrossRef]

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).

[CrossRef]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).

[CrossRef]

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).

[CrossRef]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

D. Malacara, S. Manuel, and M. Zacarias, Interferogram Analysis for Optical Testing, 2nd ed., Optical Engineering and Science (Taylor & Francis, 2005).

[CrossRef]

H. Guo, Z. Zhao, and M. Chen, “Efficient iterative algorithm for phase-shifting interferometry,” Opt. Lasers Eng. 45, 281–292 (2007).

[CrossRef]

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).

[CrossRef]
[PubMed]

Y.-Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24, 3049–3052 (1985).

[CrossRef]
[PubMed]

C. Ai and J. C. Wyant, “Effect of piezoelectric transducer nonlinearity on phase shift interferometry,” Appl. Opt. 26, 1112–1116 (1987).

[CrossRef]
[PubMed]

B. Gutmann and H. Weber, “Phase-shifter calibration and error detection in phase-shifting applications: a new method,” Appl. Opt. 37, 7624–7631 (1998).

[CrossRef]

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).

[CrossRef]
[PubMed]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

B. Chen and C. Basaran, “Automatic full strain field Moire interferometry measurement with nano-scale resolution,” Exp. Mech. 48, 665–673 (2008).

[CrossRef]

C. A. Sciammarella and T. Kim, “Frequency modulation interpretation of fringes and computation of strains,” Exp. Mech. 45, 393–403 (2005).

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]

C. T. Farrell and M. A. Player, “Phase-step insensitive algorithms for phase-shifting interferometry,” Meas. Sci. Technol. 5, 648–654 (1994).

[CrossRef]

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).

[CrossRef]

C. Wei, M. Chen, and Z. Wang, “General phase-stepping algorithm with automatic calibration of phase steps,” Opt. Eng. 38, 1357–1360 (1999).

[CrossRef]

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995).

[CrossRef]

J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984).

M. Rivera, R. Bizuet, A. Martinez, and J. A. Rayas, “Half-quadratic cost function for computing arbitrary phase shifts and phase: adaptive out of step phase shifting,” Opt. Express 14, 3204–3213 (2006).

[CrossRef]
[PubMed]

K. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001).

[CrossRef]
[PubMed]

C. Han and B. Han, “Phase-shifting in achromatic moiré interferometry system,” Opt. Express 15, 9970–9976 (2007).

[CrossRef]
[PubMed]

Z. Wang and B. Han, “Advanced iterative algorithm for randomly phase-shifted interferograms with intra- and inter-frame intensity variations,” Opt. Lasers Eng. 45, 274–280(2007).

[CrossRef]

H. Guo, Z. Zhao, and M. Chen, “Efficient iterative algorithm for phase-shifting interferometry,” Opt. Lasers Eng. 45, 281–292 (2007).

[CrossRef]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303 (2007).

[CrossRef]

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).

[CrossRef]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

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).

[CrossRef]
[PubMed]

C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7, 368–370 (1982).

[CrossRef]
[PubMed]

D. Malacara, S. Manuel, and M. Zacarias, Interferogram Analysis for Optical Testing, 2nd ed., Optical Engineering and Science (Taylor & Francis, 2005).

[CrossRef]

H. Liu, “Phase reconstruction of phase shifted moire interferograms using continuous wavelet transforms,” Ph.D. dissertation (State University of New York at Buffalo, 2003).

A. van den Bos, Parameter Estimation for Scientists and Engineers (Wiley-Interscience, 2007).

[CrossRef]

A. W. F. Edwards, Likelihood: An Account of the Statistical Concept of Likelihood and Its Application to Scientific Inference (Cambridge University, 1972).

[PubMed]

L. R. Shenton and K. O. Bowman, Maximum Likelihood Estimation in Small Samples, Griffin’s Statistical Monographs & Courses (Macmillan, 1977).

S. M. Kay, Fundamentals of Statistical Signal Processing, Prentice Hall Signal Processing Series (Prentice-Hall, 1993).

E. Batschelet, Circular Statistics in Biology, Mathematics in Biology (Academic, 1981).

S. R. S. A. Jammalamadaka, Topics in Circular Statistics, Series on Multivariate Analysis (World Scientific, 2001).

[CrossRef]

M. Vetterli and J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, 1995).