Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations

Applied Optics

Volumn 50, Issue 28, 2011, Pages 5513-5523

  Wielgus, M ^a   Patorski, K ^a  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

DATA HANDLING; INTERFEROMETRY; PHASE SHIFT; WAVELET TRANSFORMS;

AMPLITUDE MODULATED; BI-DIMENSIONAL EMPIRICAL MODE DECOMPOSITIONS; CONTINUOUS WAVELET TRANSFORMS; EXPERIMENTAL PROCEDURE; FILTRATION METHODS; FRINGE PATTERN; HILBERT TRANSFORM; VIBRATION MODES;

MATHEMATICAL TRANSFORMATIONS;

EID: 80053432595     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.50.005513     Document Type: Article

References (50)

1. J. Schwider, "Advanced evaluation techniques in interferometry, " in Progress in Optics, E. Wolf ed. (Elsevier, 1990), Vol. 28, pp. 271-359.
2. J. E. Greivenkamp and J. H. Brunning, "Phase shifting interferometry," in Optical Shop Testing, D. Malacara ed. (Wiley, 1992), pp. 501-598.
3. D. Robinson and G. Read, eds., Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics, 1993).
4. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
5. H. Osterberg, "An interferometer method of studying the vibrations of an oscillating quartz plate," J. Opt. Soc. Am. 22, 19-35 (1932).
6. G. Rosvold, "Video-based vibration analysis using projected fringes," Appl. Opt. 33, 775-786 (1994).
7. A. Bosseboeuf and S. Petitgrand, "Application of microscopic interferometry in the MEMS field," Proc. SPIE 5145, 1-16 (2003).
8. 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).
9. 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). (Pubitemid 40785713)
10. J. D. Hovanesian and Y. Hung, "Moiré contour-sum, contour difference and vibration analysis of arbitrary objects," Appl. Opt. 10, 2734-2738 (1971).
11. O. Bryngdahl, "Characteristics of superposed patterns in optics," J. Opt. Soc. Am. 66, 87-94 (1976).
12. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).
13. M. Nishida and H. Saito, "A new interferometric method of two-dimensional stress analysis," Exp. Mech. 4, 366-376 (1964).
14. R. J. Sanford and A. J. Durelli, "Interpretation of fringes in stress-holo-interferometry," Exp. Mech. 11, 161-166 (1971).
15. 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).
16. A. Styk and K. Patorski, "Fizeau interferometer for quasi parallel optical plate testing," Proc. SPIE 7063, 70630P (2008).
17. K. Patorski and K. Pokorski, "Examination of singular scalar fields using wavelet processing of fork fringes," Appl. Opt. 50, 773-781 (2011).
18. K. Patorski, Z. Sienicki, and A. Styk, "Phase-shifting method contrast calculations in time-averaged interferometry: error analysis," Opt. Eng. 44, 065601 (2005).
19. K. Patorski and A. Styk, "Interferogram intensity modulation calculations using temporal phase shifting: error analysis," Opt. Eng. 45, 085602 (2006).
20. 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).
21. 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). (Pubitemid 47388769)
22. K. Pokorski and K. Patorski, "Visualization of additivetype moiré and time-average fringe patterns using the continuous wavelet transform," Appl. Opt. 49, 3640-3651 (2010).
23. 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). (Pubitemid 128733183)
24. 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). (Pubitemid 46400864)
25. 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). (Pubitemid 46709962)
26. 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).
27. A. Federico and G. H. Kaufmann, "Phase recovery in temporal speckle pattern interferometry using the generalized S-transform," Opt. Lett. 33, 866-868 (2008). (Pubitemid 351656678)
28. S. Equis and P. Jacquot, "Phase extraction in dynamic speckle interferometry with empirical mode decomposition and Hilbert transform," Strain 46, 550-558 (2010).
29. S. Equis and P. Jacquot, "The empirical mode decomposition: a must have tool in speckle interferometry?" Opt. Express 17, 611-623 (2009).
30. 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).
31. 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).
32. 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).
33. 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).
34. 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).
35. 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.
36. C. Damerval, S. Meignen, and V. Perrier, "A fast algorithm for bidimensional EMD," IEEE Signal Process. Lett. 12, 701-704 (2005). (Pubitemid 41448579)
37. C. Barber, D. Dobkin, and H. Huhdanpaa, "The Quickhull algorithm for convex hulls," ACM Trans. Math. Softw. 22, 469-483 (1996). (Pubitemid 126417394)
38. 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).
39. X. Yang, Q. Yu, and S. Fu, "A combined method for obtaining fringe orientations of ESPI," Opt. Commun. 273, 60-66 (2007). (Pubitemid 46367090)
40. 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). (Pubitemid 33048453)
41. M. Felsberg and G. Sommer, "The monogenic signal," IEEE Trans. Signal Process. 49, 3136-3144 (2001). (Pubitemid 34035668)
42. 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).
43. 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.
44. 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).
45. B. Boashash, "Estimating and interpreting the instantaneous frequency of a signal," Proc. IEEE 80, 520-568 (1992).
46. M. Venouziou and H. Zhang, "Characterizing the Hilbert transform by the Bedrosian theorem," J. Math. Anal. Appl. 338, 1477-1481 (2008).
47. 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).
48. 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.
49. K. Patorski, D. Post, R. Czarnek, and Y. Guo, "Real-time optical differentiation for moire interferometry," Appl. Opt. 26, 1977-1982 (1987).
50. K. G. Larkin, "Efficient nonlinear algorithm for envelope detection in white light interferometry," J. Opt. Soc. Am. A 13, 832-843 (1996). (Pubitemid 126576938)