M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52(1), 230–240 (2014).

[CrossRef]

Y. Lei, J. Lin, Z. He, and M. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 35(1–2), 108–126 (2013).

[CrossRef]

M. Zhong, W. Chen, T. Wang, and X. Su, “Application of two-dimensional S-Transform in fringe pattern analysis,” Opt. Lasers Eng. 51(10), 1138–1142 (2013).

[CrossRef]

K. Pokorski and K. Patorski, “Processing and phase analysis of fringe patterns with contrast reversals,” Opt. Express 21(19), 22596–22614 (2013).

[CrossRef]
[PubMed]

L. Kai and Q. Kemao, “Improved generalized regularized phase tracker for demodulation of a single fringe pattern,” Opt. Express 21(20), 24385–24397 (2013).

[CrossRef]
[PubMed]

L. Kai and Q. Kemao, “A generalized regularized phase tracker for demodulation of a single fringe pattern,” Opt. Express 20(11), 12579–12592 (2012).

[CrossRef]
[PubMed]

P. Etchepareborda, A. L. Vadnjal, A. Federico, and G. H. Kaufmann, “Phase-recovery improvement using analytic wavelet transform analysis of a noisy interferogram cepstrum,” Opt. Lett. 37(18), 3843–3845 (2012).

[CrossRef]
[PubMed]

M. Trusiak, K. Patorski, and M. Wielgus, “Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform,” Opt. Express 20(21), 23463–23479 (2012).

[CrossRef]
[PubMed]

L. R. Watkins, “Review of fringe pattern phase recovery using 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).

[CrossRef]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).

[CrossRef]

J. Ma, Z. Wang, B. Pan, T. Hoang, M. Vo, and L. Luu, “Two-dimensional continuous wavelet transform for phase determination of complex interferograms,” Appl. Opt. 50(16), 2425–2430 (2011).

[CrossRef]
[PubMed]

G. Wang, Y. J. Li, and H. Ch. Zhou, “Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe,” Appl. Opt. 50(19), 3110–3117 (2011).

[CrossRef]
[PubMed]

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

N. E. Huang and Z. H. Wu, “A review on Hilbert-Huang transform method and its applications to geophysical studies,” Rev. Geophys. 46(2), 1–23 (2008).

[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principle, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).

[CrossRef]

K. Patorski and L. Salbut, “Simple polarization phase-stepping scatterplate interferometry,” Opt. Eng. 43(2), 393–397 (2004).

[CrossRef]

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42(7), 2010–2014 (2003).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

K. Creath and J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).

[CrossRef]

O. Y. Kwon and D. M. Sough, “Multichannel grating phase-shift interferometers,” Proc. SPIE 599, 273–279 (1985).

[CrossRef]

P. Craven and G. Wahba, “Smoothing noisy data with spline functions estimating the correct degree of smoothing by the method of generalized cross validation,” Numer. Math. 31, 377–403 (1979).

[CrossRef]

C. Reinsch, “Smoothing by spline functions,” Numer. Math. 10, 177–183 (1967).

[CrossRef]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).

[CrossRef]

M. Zhong, W. Chen, T. Wang, and X. Su, “Application of two-dimensional S-Transform in fringe pattern analysis,” Opt. Lasers Eng. 51(10), 1138–1142 (2013).

[CrossRef]

P. Craven and G. Wahba, “Smoothing noisy data with spline functions estimating the correct degree of smoothing by the method of generalized cross validation,” Numer. Math. 31, 377–403 (1979).

[CrossRef]

K. Creath and J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).

[CrossRef]

C. de Boor, A Practical Guide to Splines (Springer, 1994).

C. de Boor, “Calculation of the smoothing spline with weighted roughness measure,” this paper can be downloaded at http://www.cs.wisc.edu .

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 2 (Cambridge University, 1992).

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).

[CrossRef]

M. A. Gdeisat, D. R. Burton, and D. R. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45(34), 8722–8732 (2006).

[CrossRef]
[PubMed]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

Y. Lei, J. Lin, Z. He, and M. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 35(1–2), 108–126 (2013).

[CrossRef]

N. E. Huang and Z. H. Wu, “A review on Hilbert-Huang transform method and its applications to geophysical studies,” Rev. Geophys. 46(2), 1–23 (2008).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

P. Etchepareborda, A. L. Vadnjal, A. Federico, and G. H. Kaufmann, “Phase-recovery improvement using analytic wavelet transform analysis of a noisy interferogram cepstrum,” Opt. Lett. 37(18), 3843–3845 (2012).

[CrossRef]
[PubMed]

A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44(14), 2728–2735 (2005).

[CrossRef]
[PubMed]

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42(7), 2010–2014 (2003).

[CrossRef]

L. Kai and Q. Kemao, “Improved generalized regularized phase tracker for demodulation of a single fringe pattern,” Opt. Express 21(20), 24385–24397 (2013).

[CrossRef]
[PubMed]

L. Kai and Q. Kemao, “A generalized regularized phase tracker for demodulation of a single fringe pattern,” Opt. Express 20(11), 12579–12592 (2012).

[CrossRef]
[PubMed]

H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009).

[CrossRef]
[PubMed]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principle, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).

[CrossRef]

O. Y. Kwon and D. M. Sough, “Multichannel grating phase-shift interferometers,” Proc. SPIE 599, 273–279 (1985).

[CrossRef]

Y. Lei, J. Lin, Z. He, and M. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 35(1–2), 108–126 (2013).

[CrossRef]

Y. Lei, J. Lin, Z. He, and M. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 35(1–2), 108–126 (2013).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45(4), 045601 (2006).

[CrossRef]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (CRC, 2005).

[CrossRef]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (CRC, 2005).

[CrossRef]

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52(1), 230–240 (2014).

[CrossRef]

K. Pokorski and K. Patorski, “Processing and phase analysis of fringe patterns with contrast reversals,” Opt. Express 21(19), 22596–22614 (2013).

[CrossRef]
[PubMed]

M. Trusiak, K. Patorski, and M. Wielgus, “Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform,” Opt. Express 20(21), 23463–23479 (2012).

[CrossRef]
[PubMed]

K. Patorski and L. Salbut, “Simple polarization phase-stepping scatterplate interferometry,” Opt. Eng. 43(2), 393–397 (2004).

[CrossRef]

M. J. D. Powell, “A hybrid method for nonlinear equations,” in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed. (Gordon and Breach, 1970), pp. 87–114.

M. J. D. Powell, “A Fortran subroutine for solving systems of nonlinear algebraic equations,” in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed. (Gordon and Breach, 1970), pp. 115–161.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 2 (Cambridge University, 1992).

C. Reinsch, “Smoothing by spline functions,” Numer. Math. 10, 177–183 (1967).

[CrossRef]

K. Patorski and L. Salbut, “Simple polarization phase-stepping scatterplate interferometry,” Opt. Eng. 43(2), 393–397 (2004).

[CrossRef]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).

[CrossRef]

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

K. Creath and J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

O. Y. Kwon and D. M. Sough, “Multichannel grating phase-shift interferometers,” Proc. SPIE 599, 273–279 (1985).

[CrossRef]

M. Zhong, W. Chen, T. Wang, and X. Su, “Application of two-dimensional S-Transform in fringe pattern analysis,” Opt. Lasers Eng. 51(10), 1138–1142 (2013).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 2 (Cambridge University, 1992).

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52(1), 230–240 (2014).

[CrossRef]

M. Trusiak, K. Patorski, and M. Wielgus, “Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform,” Opt. Express 20(21), 23463–23479 (2012).

[CrossRef]
[PubMed]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 2 (Cambridge University, 1992).

P. Craven and G. Wahba, “Smoothing noisy data with spline functions estimating the correct degree of smoothing by the method of generalized cross validation,” Numer. Math. 31, 377–403 (1979).

[CrossRef]

M. Zhong, W. Chen, T. Wang, and X. Su, “Application of two-dimensional S-Transform in fringe pattern analysis,” Opt. Lasers Eng. 51(10), 1138–1142 (2013).

[CrossRef]

J. Ma, Z. Wang, B. Pan, T. Hoang, M. Vo, and L. Luu, “Two-dimensional continuous wavelet transform for phase determination of complex interferograms,” Appl. Opt. 50(16), 2425–2430 (2011).

[CrossRef]
[PubMed]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45(4), 045601 (2006).

[CrossRef]

L. R. Watkins, “Review of fringe pattern phase recovery using 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).

[CrossRef]

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52(1), 230–240 (2014).

[CrossRef]

M. Trusiak, K. Patorski, and M. Wielgus, “Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform,” Opt. Express 20(21), 23463–23479 (2012).

[CrossRef]
[PubMed]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

N. E. Huang and Z. H. Wu, “A review on Hilbert-Huang transform method and its applications to geophysical studies,” Rev. Geophys. 46(2), 1–23 (2008).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

M. Zhong, W. Chen, T. Wang, and X. Su, “Application of two-dimensional S-Transform in fringe pattern analysis,” Opt. Lasers Eng. 51(10), 1138–1142 (2013).

[CrossRef]

Y. Lei, J. Lin, Z. He, and M. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 35(1–2), 108–126 (2013).

[CrossRef]

Y. Ichioka and N. Inuiya, “Direct phase detecting system,” Appl. Opt. 11(7), 1507–1514 (1972).

[CrossRef]
[PubMed]

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[CrossRef]
[PubMed]

C. Rodier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26(9), 1668–1673 (1987).

[CrossRef]

A. Federico and G. H. Kaufmann, “Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines,” Appl. Opt. 44(14), 2728–2735 (2005).

[CrossRef]
[PubMed]

M. A. Gdeisat, D. R. Burton, and D. R. Lalor, “Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45(34), 8722–8732 (2006).

[CrossRef]
[PubMed]

C. Tian, Y. Y. Yang, D. Liu, Y. J. Luo, and Y. M. Zhuo, “Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique,” Appl. Opt. 49(2), 170–179 (2010).

[CrossRef]
[PubMed]

J. Ma, Z. Wang, B. Pan, T. Hoang, M. Vo, and L. Luu, “Two-dimensional continuous wavelet transform for phase determination of complex interferograms,” Appl. Opt. 50(16), 2425–2430 (2011).

[CrossRef]
[PubMed]

G. Wang, Y. J. Li, and H. Ch. Zhou, “Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe,” Appl. Opt. 50(19), 3110–3117 (2011).

[CrossRef]
[PubMed]

M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997).

[CrossRef]
[PubMed]

A. Dursun, Z. Sarac, H. S. Topkara, S. Ozder, and F. N. Ecevit, “Phase recovery from interference fringes by using S-transform,” Measurement 41(4), 403–411 (2008).

[CrossRef]

Y. Lei, J. Lin, Z. He, and M. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mech. Syst. Signal Process. 35(1–2), 108–126 (2013).

[CrossRef]

C. Reinsch, “Smoothing by spline functions,” Numer. Math. 10, 177–183 (1967).

[CrossRef]

P. Craven and G. Wahba, “Smoothing noisy data with spline functions estimating the correct degree of smoothing by the method of generalized cross validation,” Numer. Math. 31, 377–403 (1979).

[CrossRef]

S. Fernandez, M. A. Gdeisat, J. Salvi, and D. Burton, “Automatic window size selection in Windowed Fourier Transform for 3D reconstruction using adapted mother wavelets,” Opt. Commun. 284(12), 2797–2807 (2011).

[CrossRef]

Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45(4), 045601 (2006).

[CrossRef]

G. H. Kaufmann, “Nondestructive testing with thermal waves using phase shifted temporal speckle pattern interferometry,” Opt. Eng. 42(7), 2010–2014 (2003).

[CrossRef]

K. Patorski and L. Salbut, “Simple polarization phase-stepping scatterplate interferometry,” Opt. Eng. 43(2), 393–397 (2004).

[CrossRef]

H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009).

[CrossRef]
[PubMed]

M. Trusiak, K. Patorski, and M. Wielgus, “Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform,” Opt. Express 20(21), 23463–23479 (2012).

[CrossRef]
[PubMed]

K. Pokorski and K. Patorski, “Processing and phase analysis of fringe patterns with contrast reversals,” Opt. Express 21(19), 22596–22614 (2013).

[CrossRef]
[PubMed]

L. Kai and Q. Kemao, “Improved generalized regularized phase tracker for demodulation of a single fringe pattern,” Opt. Express 21(20), 24385–24397 (2013).

[CrossRef]
[PubMed]

L. Kai and Q. Kemao, “A generalized regularized phase tracker for demodulation of a single fringe pattern,” Opt. Express 20(11), 12579–12592 (2012).

[CrossRef]
[PubMed]

L. R. Watkins, “Review of fringe pattern phase recovery using 1-D and 2-D continuous wavelet transforms,” Opt. Lasers Eng. 50(8), 1015–1022 (2012).

[CrossRef]

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52(1), 230–240 (2014).

[CrossRef]

M. Zhong, W. Chen, T. Wang, and X. Su, “Application of two-dimensional S-Transform in fringe pattern analysis,” Opt. Lasers Eng. 51(10), 1138–1142 (2013).

[CrossRef]

K. Creath and J. Schmit, “N-point spatial phase-measurement techniques for non-destructive testing,” Opt. Lasers Eng. 24, 365–379 (1996).

[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principle, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).

[CrossRef]

P. Etchepareborda, A. L. Vadnjal, A. Federico, and G. H. Kaufmann, “Phase-recovery improvement using analytic wavelet transform analysis of a noisy interferogram cepstrum,” Opt. Lett. 37(18), 3843–3845 (2012).

[CrossRef]
[PubMed]

L. Watkins, S. Tan, and T. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24(13), 905–907 (1999).

[CrossRef]

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. R. Soc. London A 454, 903–995 (1998).

[CrossRef]

O. Y. Kwon and D. M. Sough, “Multichannel grating phase-shift interferometers,” Proc. SPIE 599, 273–279 (1985).

[CrossRef]

N. E. Huang and Z. H. Wu, “A review on Hilbert-Huang transform method and its applications to geophysical studies,” Rev. Geophys. 46(2), 1–23 (2008).

[CrossRef]

D. Robinson and G. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurements (Institute of Physics, 1993).

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (CRC, 2005).

[CrossRef]

C. de Boor, A Practical Guide to Splines (Springer, 1994).

M. J. D. Powell, “A hybrid method for nonlinear equations,” in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed. (Gordon and Breach, 1970), pp. 87–114.

M. J. D. Powell, “A Fortran subroutine for solving systems of nonlinear algebraic equations,” in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed. (Gordon and Breach, 1970), pp. 115–161.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 2 (Cambridge University, 1992).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

C. de Boor, “Calculation of the smoothing spline with weighted roughness measure,” this paper can be downloaded at http://www.cs.wisc.edu .