S. Equis and P. Jacquot, “The empirical mode decomposition: a must have tool in speckle interferometry?” Opt. Express 17, 611–623 (2009).

[CrossRef]
[PubMed]

X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34, 2033–2035 (2009).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt. 48, 6862–6869 (2009).

[CrossRef]
[PubMed]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47, 1310–1316(2008).

[CrossRef]

A. Federico and G. H. Kaufmann, “Phase recovery in temporal speckle pattern interferometry using the generalized S-transform,” Opt. Lett. 33, 866–868 (2008).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).

[CrossRef]
[PubMed]

M. Venouziou and H. Zhang, “Characterizing the Hilbert transform by the Bedrosian theorem,” J. Math. Anal. Appl. 338, 1477–1481 (2008).

[CrossRef]

A. Styk and K. Patorski, “Fizeau interferometer for quasi parallel optical plate testing,” Proc. SPIE 7063, 70630P (2008).

[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Commun. 45, 723–729 (2007).

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).

[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).

[CrossRef]

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624(2007).

[CrossRef]
[PubMed]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).

[CrossRef]

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704(2005).

[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).

[CrossRef]

M. Ragulskis, R. Maskeliunas, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962(2005).

[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1871–18810 (2001).

[CrossRef]

T. Bülow and G. Sommer, “Hypercomplex signals—a novel extension of the analytic signal to the multidimensional case,” IEEE Trans. Signal Process. 49, 2844–2852 (2001).

[CrossRef]

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1862–1870 (2001).

[CrossRef]

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

[CrossRef]

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal,” Proc. IEEE 80, 520–568(1992).

[CrossRef]

B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).

[CrossRef]

M. Nishida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376(1964).

[CrossRef]

C. Barber, D. Dobkin, and H. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).

[CrossRef]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt. 48, 6862–6869 (2009).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).

[CrossRef]
[PubMed]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Commun. 45, 723–729 (2007).

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal,” Proc. IEEE 80, 520–568(1992).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1871–18810 (2001).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1862–1870 (2001).

[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).

[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).

[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

J. E. Greivenkamp and J. H. Brunning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara ed. (Wiley, 1992), pp. 501–598.

T. Bülow and G. Sommer, “Hypercomplex signals—a novel extension of the analytic signal to the multidimensional case,” IEEE Trans. Signal Process. 49, 2844–2852 (2001).

[CrossRef]

T. Bülow, D. Pallek, and G. Sommer, “Riesz transforms for the isotropic estimation of the local phase of moiré interferograms,” presented at the 22nd DAGM Symposium Mustererkennung, (Heidelberg, 2000).

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).

[CrossRef]

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704(2005).

[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

C. Barber, D. Dobkin, and H. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).

[CrossRef]

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).

[CrossRef]

M. Bernini, A. Federico, and G. Kaufmann, “Phase measurement in temporal speckle pattern interferometry signals presenting low modulated regions by means of the bidimensional empirical mode decomposition,” Appl. Opt. 50, 641–647(2011).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt. 48, 6862–6869 (2009).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).

[CrossRef]
[PubMed]

A. Federico and G. H. Kaufmann, “Phase recovery in temporal speckle pattern interferometry using the generalized S-transform,” Opt. Lett. 33, 866–868 (2008).

[CrossRef]
[PubMed]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47, 1310–1316(2008).

[CrossRef]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).

[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Commun. 45, 723–729 (2007).

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).

[CrossRef]

Q. He, R. Gao, and P. Freedson, “Midpoint-based empirical decomposition for nonlinear trend estimation,” in Proceedings of IEEE Engineering in Medicine and Biology Society Conference 2009 (IEEE, 2009), pp. 2228–2231.

X. Yang, Q. Yu, and S. Fu, “A combined method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).

[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Commun. 45, 723–729 (2007).

Q. He, R. Gao, and P. Freedson, “Midpoint-based empirical decomposition for nonlinear trend estimation,” in Proceedings of IEEE Engineering in Medicine and Biology Society Conference 2009 (IEEE, 2009), pp. 2228–2231.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

J. E. Greivenkamp and J. H. Brunning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara ed. (Wiley, 1992), pp. 501–598.

Q. He, R. Gao, and P. Freedson, “Midpoint-based empirical decomposition for nonlinear trend estimation,” in Proceedings of IEEE Engineering in Medicine and Biology Society Conference 2009 (IEEE, 2009), pp. 2228–2231.

Z. Wu and N. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Tech. Rep. No. 193, Centre for Ocean-Land-Atmosphere Studies(2005).

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

[CrossRef]

C. Barber, D. Dobkin, and H. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).

[CrossRef]

R. Onodera, Y. Yamamoto, and Y. Ishii, “Signal processing of interferogram using a two-dimensional discrete Hilbert transform,” in Fringe 2005, the 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten ed. (Springer, 2006), pp. 82–89.

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt. 48, 6862–6869 (2009).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).

[CrossRef]
[PubMed]

A. Federico and G. H. Kaufmann, “Phase recovery in temporal speckle pattern interferometry using the generalized S-transform,” Opt. Lett. 33, 866–868 (2008).

[CrossRef]
[PubMed]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47, 1310–1316(2008).

[CrossRef]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).

[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Commun. 45, 723–729 (2007).

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1862–1870 (2001).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1871–18810 (2001).

[CrossRef]

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).

[CrossRef]

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

[CrossRef]

Z. Liu, H. Wang, and S. Peng, “Texture classification through empirical mode decomposition,” in Proceedings of the 17th International Conference on Pattern Recognition (ICPR 2004) (IEEE, 2004), pp. 803–806.

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

[CrossRef]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47, 1310–1316(2008).

[CrossRef]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).

[CrossRef]

M. Ragulskis, R. Maskeliunas, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962(2005).

[CrossRef]

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704(2005).

[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

M. Nishida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376(1964).

[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1862–1870 (2001).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1871–18810 (2001).

[CrossRef]

R. Onodera, Y. Yamamoto, and Y. Ishii, “Signal processing of interferogram using a two-dimensional discrete Hilbert transform,” in Fringe 2005, the 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten ed. (Springer, 2006), pp. 82–89.

T. Bülow, D. Pallek, and G. Sommer, “Riesz transforms for the isotropic estimation of the local phase of moiré interferograms,” presented at the 22nd DAGM Symposium Mustererkennung, (Heidelberg, 2000).

K. Patorski and K. Pokorski, “Examination of singular scalar fields using wavelet processing of fork fringes,” Appl. Opt. 50, 773–781 (2011).

[CrossRef]
[PubMed]

K. Pokorski and K. Patorski, “Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform,” Appl. Opt. 49, 3640–3651(2010).

[CrossRef]
[PubMed]

A. Styk and K. Patorski, “Fizeau interferometer for quasi parallel optical plate testing,” Proc. SPIE 7063, 70630P (2008).

[CrossRef]

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624(2007).

[CrossRef]
[PubMed]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).

[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

K. Patorski, D. Post, R. Czarnek, and Y. Guo, “Real-time optical differentiation for moire interferometry,” Appl. Opt. 26, 1977–1982 (1987).

[CrossRef]
[PubMed]

K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993).

Z. Liu, H. Wang, and S. Peng, “Texture classification through empirical mode decomposition,” in Proceedings of the 17th International Conference on Pattern Recognition (ICPR 2004) (IEEE, 2004), pp. 803–806.

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704(2005).

[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).

[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).

[CrossRef]

M. Ragulskis, R. Maskeliunas, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962(2005).

[CrossRef]

M. Nishida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376(1964).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).

[CrossRef]

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf ed. (Elsevier, 1990), Vol. 28, pp. 271–359.

[CrossRef]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

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

[CrossRef]

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

[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).

[CrossRef]

T. Bülow and G. Sommer, “Hypercomplex signals—a novel extension of the analytic signal to the multidimensional case,” IEEE Trans. Signal Process. 49, 2844–2852 (2001).

[CrossRef]

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).

[CrossRef]

T. Bülow, D. Pallek, and G. Sommer, “Riesz transforms for the isotropic estimation of the local phase of moiré interferograms,” presented at the 22nd DAGM Symposium Mustererkennung, (Heidelberg, 2000).

A. Styk and K. Patorski, “Fizeau interferometer for quasi parallel optical plate testing,” Proc. SPIE 7063, 70630P (2008).

[CrossRef]

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624(2007).

[CrossRef]
[PubMed]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).

[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).

[CrossRef]

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

[CrossRef]

M. Ragulskis, R. Maskeliunas, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962(2005).

[CrossRef]

M. Venouziou and H. Zhang, “Characterizing the Hilbert transform by the Bedrosian theorem,” J. Math. Anal. Appl. 338, 1477–1481 (2008).

[CrossRef]

Z. Liu, H. Wang, and S. Peng, “Texture classification through empirical mode decomposition,” in Proceedings of the 17th International Conference on Pattern Recognition (ICPR 2004) (IEEE, 2004), pp. 803–806.

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

[CrossRef]

Z. Wu and N. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Tech. Rep. No. 193, Centre for Ocean-Land-Atmosphere Studies(2005).

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).

[CrossRef]

R. Onodera, Y. Yamamoto, and Y. Ishii, “Signal processing of interferogram using a two-dimensional discrete Hilbert transform,” in Fringe 2005, the 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten ed. (Springer, 2006), pp. 82–89.

X. Yang, Q. Yu, and S. Fu, “A combined method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).

[CrossRef]

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

[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).

[CrossRef]

M. Venouziou and H. Zhang, “Characterizing the Hilbert transform by the Bedrosian theorem,” J. Math. Anal. Appl. 338, 1477–1481 (2008).

[CrossRef]

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

[CrossRef]

C. Barber, D. Dobkin, and H. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).

[CrossRef]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).

[CrossRef]
[PubMed]

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt. 48, 6862–6869 (2009).

[CrossRef]
[PubMed]

M. Bernini, A. Federico, and G. Kaufmann, “Phase measurement in temporal speckle pattern interferometry signals presenting low modulated regions by means of the bidimensional empirical mode decomposition,” Appl. Opt. 50, 641–647(2011).

[CrossRef]
[PubMed]

J. D. Hovanesian and Y. Hung, “Moiré contour-sum, contour difference and vibration analysis of arbitrary objects,” Appl. Opt. 10, 2734–2738 (1971).

[CrossRef]
[PubMed]

A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity modulation determination,” Appl. Opt. 46, 4613–4624(2007).

[CrossRef]
[PubMed]

K. Pokorski and K. Patorski, “Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform,” Appl. Opt. 49, 3640–3651(2010).

[CrossRef]
[PubMed]

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier,” Appl. Opt. 47, 1310–1316(2008).

[CrossRef]

G. Rosvold, “Video-based vibration analysis using projected fringes,” Appl. Opt. 33, 775–786 (1994).

[CrossRef]
[PubMed]

K. Patorski and K. Pokorski, “Examination of singular scalar fields using wavelet processing of fork fringes,” Appl. Opt. 50, 773–781 (2011).

[CrossRef]
[PubMed]

K. Patorski, D. Post, R. Czarnek, and Y. Guo, “Real-time optical differentiation for moire interferometry,” Appl. Opt. 26, 1977–1982 (1987).

[CrossRef]
[PubMed]

M. Nishida and H. Saito, “A new interferometric method of two-dimensional stress analysis,” Exp. Mech. 4, 366–376(1964).

[CrossRef]

R. J. Sanford and A. J. Durelli, “Interpretation of fringes in stress-holo-interferometry,” Exp. Mech. 11, 161–166 (1971).

[CrossRef]

C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704(2005).

[CrossRef]

T. Bülow and G. Sommer, “Hypercomplex signals—a novel extension of the analytic signal to the multidimensional case,” IEEE Trans. Signal Process. 49, 2844–2852 (2001).

[CrossRef]

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).

[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and .Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vision Comput. 21, 1019–1026 (2003).

[CrossRef]

M. Venouziou and H. Zhang, “Characterizing the Hilbert transform by the Bedrosian theorem,” J. Math. Anal. Appl. 338, 1477–1481 (2008).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1871–18810 (2001).

[CrossRef]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. 18, 1862–1870 (2001).

[CrossRef]

O. Bryngdahl, “Characteristics of superposed patterns in optics,” J. Opt. Soc. Am. 66, 87–94 (1976).

[CrossRef]

H. Osterberg, “An interferometer method of studying the vibrations of an oscillating quartz plate,” J. Opt. Soc. Am. 22, 19–35 (1932).

[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Commun. 45, 723–729 (2007).

F. A. Marengo-Rodriguez, A. Federico, and G. H. Kaufmann, “Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition,” Opt. Commun. 275, 38–41 (2007).

[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).

[CrossRef]

K. Patorski, Z. Sienicki, and A. Styk, “Phase-shifting method contrast calculations in time-averaged interferometry: error analysis,” Opt. Eng. 44, 065601 (2005).

[CrossRef]

K. Patorski and A. Styk, “Interferogram intensity modulation calculations using temporal phase shifting: error analysis,” Opt. Eng. 45, 085602 (2006).

[CrossRef]

B. Chatelain, “Holographic photo-elasticity: independent observation of the isochromatic and isopachic fringes for a single model subjected to only one process,” Opt. Laser Technol. 5, 201–204 (1973).

[CrossRef]

M. Ragulskis, R. Maskeliunas, and V. Turla, “Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moiré,” Opt. Lasers Eng. 43, 951–962(2005).

[CrossRef]

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal,” Proc. IEEE 80, 520–568(1992).

[CrossRef]

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

[CrossRef]

A. Bosseboeuf and S. Petitgrand, “Application of microscopic interferometry in the MEMS field,” Proc. SPIE 5145, 1–16(2003).

[CrossRef]

L. Salbut, K. Patorski, M. Jozwik, J. Kacperski, C. Gorecki, A. Jacobelli, and T. Dean, “Active micro-elements testing by interferometry using time-average and quasi-stroboscopic techniques,” Proc. SPIE 5145, 23–32 (2003).

[CrossRef]

A. Styk and K. Patorski, “Fizeau interferometer for quasi parallel optical plate testing,” Proc. SPIE 7063, 70630P (2008).

[CrossRef]

S. Petitgrand, R. Yahiaoui, A. Bosseboeuf, and K. Danaie, “Quantitative time-averaged microscopic interferometry for micromechanical device vibration mode characterization,” Proc. SPIE 4400, 51–60 (2001).

[CrossRef]

S. Equis and P. Jacquot, “Phase extraction in dynamic speckle interferometry with empirical mode decomposition and Hilbert transform,” Strain 46, 550–558 (2010).

[CrossRef]

K. Patorski, Handbook of the Moiré Fringe Technique(Elsevier, 1993).

Z. Wu and N. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Tech. Rep. No. 193, Centre for Ocean-Land-Atmosphere Studies(2005).

Z. Liu, H. Wang, and S. Peng, “Texture classification through empirical mode decomposition,” in Proceedings of the 17th International Conference on Pattern Recognition (ICPR 2004) (IEEE, 2004), pp. 803–806.

J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf ed. (Elsevier, 1990), Vol. 28, pp. 271–359.

[CrossRef]

J. E. Greivenkamp and J. H. Brunning, “Phase shifting interferometry,” in Optical Shop Testing, D.Malacara ed. (Wiley, 1992), pp. 501–598.

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

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).

Q. He, R. Gao, and P. Freedson, “Midpoint-based empirical decomposition for nonlinear trend estimation,” in Proceedings of IEEE Engineering in Medicine and Biology Society Conference 2009 (IEEE, 2009), pp. 2228–2231.

R. Onodera, Y. Yamamoto, and Y. Ishii, “Signal processing of interferogram using a two-dimensional discrete Hilbert transform,” in Fringe 2005, the 5th International Workshop on Automatic Processing of Fringe Patterns, W.Osten ed. (Springer, 2006), pp. 82–89.

T. Bülow, D. Pallek, and G. Sommer, “Riesz transforms for the isotropic estimation of the local phase of moiré interferograms,” presented at the 22nd DAGM Symposium Mustererkennung, (Heidelberg, 2000).