Hilbert-Huang processing for single-exposure two-dimensional grating interferometry |
Optics Express, Vol. 21, Issue 23, pp. 28359-28379 (2013)
http://dx.doi.org/10.1364/OE.21.028359
Acrobat PDF (3522 KB)
Abstract
Single-shot crossed-type fringe pattern processing and analysis method called Hilbert-Huang grating interferometry (HHGI) is proposed. It consist of three main procedures: (1) crossed pattern is resolved into two fringe families using novel orthogonal empirical mode decomposition approach, (2) separated fringe sets are filtered using modified automatic selective reconstruction aided by enhanced fast empirical mode decomposition and mutual information detrending, and (3) Hilbert spiral transform is employed for fringe phase demodulation. Numerical and experimental studies corroborate the validity, versatility and robustness of the proposed HHGI technique. It can be successfully applied to multiplicative and additive type crossed patterns with sinusoidal and binary orthogonal component structures. Efficient adaptive filtering enables successful fast processing and analysis of complex and defected patterns.
© 2013 Optical Society of America
1. Introduction
- a) Interference of object and reference beams (reference beam interferometry, object phase maps are obtained [3]);
- b) Interference of object beam with its replica (shearing interferometry; first derivative of object phase is obtained under the assumptions of small displacement between the two beams and slow object phase variations [3]);
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
17. H. Canabal, J. A. Quiroga, and E. Bernabeu, “Improved phase-shifting method for automatic processing of moiré deflectograms,” Appl. Opt. 37(26), 6227–6233 (1998). [CrossRef] [PubMed]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
23. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010). [CrossRef] [PubMed]
24. I. Zanette, C. David, S. Rutishauser, T. Weitkamp, M. Denecke, and C. T. Walker, “2D grating simulation for X-ray phase-contrast and dark-field imaging with a Talbot interferometer,” AIP Conf. Proc. 1221, 73–79 (2010). [CrossRef]
27. S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011). [CrossRef]
28. S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, “X-ray submicrometer phase contrast imaging with a Fresnel zone plate and a two dimensional grating interferometer,” Opt. Lett. 37(10), 1622–1624 (2012). [CrossRef] [PubMed]
18. J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38(6), 974–982 (1999). [CrossRef]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
21. J. L. Flores, B. Bravo-Medina, and J. A. Ferrari, “One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns,” Appl. Opt. 52(26), 6537–6542 (2013). [CrossRef] [PubMed]
22. H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35(12), 1932–1934 (2010). [CrossRef] [PubMed]
25. H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval,” Opt. Express 19(4), 3339–3346 (2011). [CrossRef] [PubMed]
29. H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, “At-wavelength metrology using the moiré fringe analysis method based on a two-dimensional grating interferometer,” Nucl. Instrum. Methods Phys. Res. A 710, 78–81 (2013). [CrossRef]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
32. M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995). [CrossRef]
20. J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39(4), 502–508 (2000). [CrossRef] [PubMed]
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
26. K. S. Morgan, D. M. Paganin, and K. K. Siu, “Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid,” Opt. Express 19(20), 19781–19789 (2011). [CrossRef] [PubMed]
17. H. Canabal, J. A. Quiroga, and E. Bernabeu, “Improved phase-shifting method for automatic processing of moiré deflectograms,” Appl. Opt. 37(26), 6227–6233 (1998). [CrossRef] [PubMed]
20. J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39(4), 502–508 (2000). [CrossRef] [PubMed]
22. H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35(12), 1932–1934 (2010). [CrossRef] [PubMed]
29. H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, “At-wavelength metrology using the moiré fringe analysis method based on a two-dimensional grating interferometer,” Nucl. Instrum. Methods Phys. Res. A 710, 78–81 (2013). [CrossRef]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
21. J. L. Flores, B. Bravo-Medina, and J. A. Ferrari, “One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns,” Appl. Opt. 52(26), 6537–6542 (2013). [CrossRef] [PubMed]
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
2. Method and algorithm description
34. 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, 230–240 (2014). [CrossRef]
35. 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 non-linear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454(1971), 903–995 (1998). [CrossRef]
36. C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12(10), 701–704 (2005). [CrossRef]
37. C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, “The quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22(4), 469–483 (1996). [CrossRef]
38. J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003). [CrossRef]
39. S. M. A. Bhuiyan, N. O. Attoh-Okine, K. E. Barner, A. Y. Ayenu-Prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data Anal. 1(2), 309–338 (2009). [CrossRef]
40. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47(14), 2592–2598 (2008). [CrossRef] [PubMed]
41. 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(36), 6862–6869 (2009). [CrossRef] [PubMed]
42. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition,” Appl. Opt. 50(5), 641–647 (2011). [CrossRef] [PubMed]
43. M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt. 50(28), 5513–5523 (2011). [CrossRef] [PubMed]
44. Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express 19(19), 18207–18215 (2011). [CrossRef] [PubMed]
47. X. Zhou, A. G. Podoleanu, Z. Yang, T. Yang, and H. Zhao, “Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns,” Opt. Express 20(22), 24247–24262 (2012). [CrossRef] [PubMed]
48. S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “A novel approach of fast and adaptive bidimensional empirical mode decomposition,” in Proc. IEEE Int. Conf. Acoustic, Speech and Signal Process. (Institute of Electrical and Electronics Engineers, 2008), 1313–1316. [CrossRef]
49. S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(21), 728356 (2008). [CrossRef]
50. K. Patorski, K. Pokorski, and M. Trusiak, “Fourier domain interpretation of real and pseudo-moiré phenomena,” Opt. Express 19(27), 26065–26078 (2011). [CrossRef] [PubMed]
51. M. Trusiak and K. Patorski, “Space domain interpetation of incoherent moiré superimpositions using FABEMD,” Proc. SPIE 8697, 18th Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 869704 (December 18, 2012). [CrossRef]
52. 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]
54. Y. Zhou, S.-T. Zhou, Z.-Y. Zhong, and H.-G. Li, “A de-illumination scheme for face recognition based on fast decomposition and detail feature fusion,” Opt. Express 21(9), 11294–11308 (2013). [CrossRef] [PubMed]
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
- 1. Obtaining the orientation angle for both fringe sets (a priori knowledge is needed; the case of grating (moiré) interferometry is simple – the orientation of the fringe families likely corresponds to the specimen grating lines and with the grid we often have 0 and 90 degree orientation angles).
- 2. Detecting the fringe pattern extrema, estimating the filter window width w using Eq. (1) and setting proper a value. Designing the orthogonal 1D filter arrays.
- 3. Calculating the lower and upper envelopes using order-statistic and smoothing filters with previously designed masks (besides the mask dimension modification the decomposition is performed like in the FABEMD method [34, 48
34. 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, 230–240 (2014). [CrossRef]
–5448. S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “A novel approach of fast and adaptive bidimensional empirical mode decomposition,” in Proc. IEEE Int. Conf. Acoustic, Speech and Signal Process. (Institute of Electrical and Electronics Engineers, 2008), 1313–1316. [CrossRef]
]).54. Y. Zhou, S.-T. Zhou, Z.-Y. Zhong, and H.-G. Li, “A de-illumination scheme for face recognition based on fast decomposition and detail feature fusion,” Opt. Express 21(9), 11294–11308 (2013). [CrossRef] [PubMed]
- 4. Calculating the mean envelope as an arithmetic mean of upper and lower envelopes.
- 5. Subtracting the mean envelope from the initial cross interferogram to obtain single fringe family extraction. Only one iteration is required for single fringe family separation (in a single BIMF). The extracted fringe set orientation is perpendicular to the one dimensional filter array direction. In case of noisy interferograms additional Matlab's 'motion' filter is employed to directionally smooth the separated fringe set. The 'motion' filter has the same direction as the extracted fringe set and the same window width w as estimated before.
55. C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit. 32(1), 71–86 (1999). [CrossRef]
56. S. Osman and W. Wang, “An enhanced Hilbert-Huang transform technique for bearing condition monitoring,” Meas. Sci. Technol. 24(8), 085004 (2013). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
57. Z. Wu, N. E. Huang, S. R. Long, and C. K. Peng, “On the trend, detrending, and variability of nonlinear and nonstationary time series,” Proc. Natl. Acad. Sci. U.S.A. 104(38), 14889–14894 (2007). [CrossRef] [PubMed]
61. G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
35. 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 non-linear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454(1971), 903–995 (1998). [CrossRef]
44. Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express 19(19), 18207–18215 (2011). [CrossRef] [PubMed]
46. X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34(13), 2033–2035 (2009). [CrossRef] [PubMed]
52. 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]
57. Z. Wu, N. E. Huang, S. R. Long, and C. K. Peng, “On the trend, detrending, and variability of nonlinear and nonstationary time series,” Proc. Natl. Acad. Sci. U.S.A. 104(38), 14889–14894 (2007). [CrossRef] [PubMed]
62. 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. A 18(8), 1862–1870 (2001). [CrossRef] [PubMed]
63. 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. A 18(8), 1871–1881 (2001). [CrossRef] [PubMed]
43. M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt. 50(28), 5513–5523 (2011). [CrossRef] [PubMed]
34. 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, 230–240 (2014). [CrossRef]
43. M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt. 50(28), 5513–5523 (2011). [CrossRef] [PubMed]
52. 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]
3. Numerical studies
3.1 Additive type crossed interferogram processing
3.1.1 Noise free additive crossed patterns
64. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
40. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47(14), 2592–2598 (2008). [CrossRef] [PubMed]
41. 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(36), 6862–6869 (2009). [CrossRef] [PubMed]
47. X. Zhou, A. G. Podoleanu, Z. Yang, T. Yang, and H. Zhao, “Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns,” Opt. Express 20(22), 24247–24262 (2012). [CrossRef] [PubMed]
52. 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]
3.1.2 Noisy additive crossed patterns
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
35. 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 non-linear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454(1971), 903–995 (1998). [CrossRef]
57. Z. Wu, N. E. Huang, S. R. Long, and C. K. Peng, “On the trend, detrending, and variability of nonlinear and nonstationary time series,” Proc. Natl. Acad. Sci. U.S.A. 104(38), 14889–14894 (2007). [CrossRef] [PubMed]
58. Z. Yang, B. W.-K. Ling, and C. Bingham, “Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum,” Measurement 46(8), 2481–2491 (2013). [CrossRef]
18. J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38(6), 974–982 (1999). [CrossRef]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
32. M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995). [CrossRef]
18. J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38(6), 974–982 (1999). [CrossRef]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
32. M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995). [CrossRef]
19. H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef]
20. J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39(4), 502–508 (2000). [CrossRef] [PubMed]
32. M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995). [CrossRef]
3.2 Fringe pattern detrending using mutual information
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
34. 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, 230–240 (2014). [CrossRef]
49. S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(21), 728356 (2008). [CrossRef]
50. K. Patorski, K. Pokorski, and M. Trusiak, “Fourier domain interpretation of real and pseudo-moiré phenomena,” Opt. Express 19(27), 26065–26078 (2011). [CrossRef] [PubMed]
34. 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, 230–240 (2014). [CrossRef]
3.3 Multiplicative type crossed interferogram processing
17. H. Canabal, J. A. Quiroga, and E. Bernabeu, “Improved phase-shifting method for automatic processing of moiré deflectograms,” Appl. Opt. 37(26), 6227–6233 (1998). [CrossRef] [PubMed]
20. J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39(4), 502–508 (2000). [CrossRef] [PubMed]
22. H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35(12), 1932–1934 (2010). [CrossRef] [PubMed]
29. H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, “At-wavelength metrology using the moiré fringe analysis method based on a two-dimensional grating interferometer,” Nucl. Instrum. Methods Phys. Res. A 710, 78–81 (2013). [CrossRef]
20. J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39(4), 502–508 (2000). [CrossRef] [PubMed]
32. M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995). [CrossRef]
3.4 Binary versus cosinusoidal profile
65. L. Xiong and S. Jia, “Phase-error analysis and elimination for nonsinusoidal waveforms in Hilbert transform digital-fringe projection profilometry,” Opt. Lett. 34(15), 2363–2365 (2009). [CrossRef] [PubMed]
66. N. Sun, Y. Song, J. Wang, Z.-H. Li, and A.-Z. He, “Volume moiré tomography based on double cross gratings for real three-dimensional flow field diagnosis,” Appl. Opt. 51(34), 8081–8089 (2012). [CrossRef] [PubMed]
4. Experimental data processing
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
4.1 Grating (moiré) interferometry data processing
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
67. J. Schmit, K. Patorski, and K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36(8), 2240–2248 (1997). [CrossRef]
33. K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed]
4.2 Talbot interferometry data processing
68. K. Patorski, “Grating shearing interferometer with variable shear and fringe orientation,” Appl. Opt. 25(22), 4192–4198 (1986). [CrossRef] [PubMed]
69. K. Patorski, “Conjugate lateral shear interferometry and its implementation,” J. Opt. Soc. Am. A 3(11), 1862–1870 (1986). [CrossRef]
51. M. Trusiak and K. Patorski, “Space domain interpetation of incoherent moiré superimpositions using FABEMD,” Proc. SPIE 8697, 18th Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 869704 (December 18, 2012). [CrossRef]
5. Conclusions
66. N. Sun, Y. Song, J. Wang, Z.-H. Li, and A.-Z. He, “Volume moiré tomography based on double cross gratings for real three-dimensional flow field diagnosis,” Appl. Opt. 51(34), 8081–8089 (2012). [CrossRef] [PubMed]
Acknowledgments
References and links
1. | D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics Publishing, 1993). |
2. | D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998). |
3. | D. Malacara, ed., Optical Shop Testing (John Wiley, 2007). |
4. | D. Post, B. Han, and P. Ifju, High Sensitivity Moirè (Springer, 1994). |
5. | K. Patorski, Handbook of the Moirè Fringe Technique (Elsevier, 1993). |
6. | S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt. 10(7), 1575–1580 (1971). [CrossRef] [PubMed] |
7. | S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter. Part 2,” Appl. Opt. 10(7), 1690–1693 (1971). [CrossRef] [PubMed] |
8. | A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971). [CrossRef] |
9. | A. W. Lohmann and D. E. Silva, “A Talbot interferometer with circular gratings,” Opt. Commun. 4(5), 326–328 (1972). [CrossRef] |
10. | D. E. Silva, “Talbot interferometer for radial and lateral derivatives,” Appl. Opt. 11(11), 2613–2624 (1972). [CrossRef] [PubMed] |
11. | O. Kafri, “Noncoherent method for mapping phase objects,” Opt. Lett. 5(12), 555–557 (1980). [CrossRef] [PubMed] |
12. | K. Patorski, “Diffraction effects in moiré deflectometry: comment,” J. Opt. Soc. Am. A 3(5), 667–668 (1986). [CrossRef] |
13. | E. Keren and O. Kafri, “Diffraction effects in moiré deflectometry: reply to comment,” J. Opt. Soc. Am. A 3(5), 669–670 (1986). [CrossRef] |
14. | E. Bar-Ziv, S. Sgulim, O. Kafri, and E. Keren, “Temperature mapping in flames by moire deflectometry,” Appl. Opt. 22(5), 698–705 (1983). [CrossRef] [PubMed] |
15. | G. Oster, M. Wasserman, and C. Zwerling, “Theoretical interpretation of moiré patterns,” J. Opt. Soc. Am. 54(2), 169–175 (1964). [CrossRef] |
16. | K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf ed., vol. 27, 1–108 (Elsevier, 1989). |
17. | H. Canabal, J. A. Quiroga, and E. Bernabeu, “Improved phase-shifting method for automatic processing of moiré deflectograms,” Appl. Opt. 37(26), 6227–6233 (1998). [CrossRef] [PubMed] |
18. | J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38(6), 974–982 (1999). [CrossRef] |
19. | H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE 3744, 231–240 (1999). [CrossRef] |
20. | J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt. 39(4), 502–508 (2000). [CrossRef] [PubMed] |
21. | J. L. Flores, B. Bravo-Medina, and J. A. Ferrari, “One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns,” Appl. Opt. 52(26), 6537–6542 (2013). [CrossRef] [PubMed] |
22. | H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35(12), 1932–1934 (2010). [CrossRef] [PubMed] |
23. | I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett. 105(24), 248102 (2010). [CrossRef] [PubMed] |
24. | I. Zanette, C. David, S. Rutishauser, T. Weitkamp, M. Denecke, and C. T. Walker, “2D grating simulation for X-ray phase-contrast and dark-field imaging with a Talbot interferometer,” AIP Conf. Proc. 1221, 73–79 (2010). [CrossRef] |
25. | H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval,” Opt. Express 19(4), 3339–3346 (2011). [CrossRef] [PubMed] |
26. | K. S. Morgan, D. M. Paganin, and K. K. Siu, “Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid,” Opt. Express 19(20), 19781–19789 (2011). [CrossRef] [PubMed] |
27. | S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett. 99(22), 221104 (2011). [CrossRef] |
28. | S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, “X-ray submicrometer phase contrast imaging with a Fresnel zone plate and a two dimensional grating interferometer,” Opt. Lett. 37(10), 1622–1624 (2012). [CrossRef] [PubMed] |
29. | H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, “At-wavelength metrology using the moiré fringe analysis method based on a two-dimensional grating interferometer,” Nucl. Instrum. Methods Phys. Res. A 710, 78–81 (2013). [CrossRef] |
30. | L. Salbut, “Multichannel system for automatic analysis of u,v,w displacements in grating interferometry,” in Physical Research, W. Juptner and W. Osten, eds. 19, 282–287 (Akademie, 1993). |
31. | M. Kujawinska and M. Pirga, “Fringe pattern analysis for the investigation of dynamic processes in experimental mechanics,” in Physical Research, W. Juptner and W. Osten, eds. 19, 391–394 (Akademie, 1993). |
32. | M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34(8), 2459–2466 (1995). [CrossRef] |
33. | K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt. 51(35), 8433–8439 (2012). [CrossRef] [PubMed] |
34. | 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, 230–240 (2014). [CrossRef] |
35. | 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 non-linear and non-stationary time series analysis,” Proc. R. Soc. Lond. A 454(1971), 903–995 (1998). [CrossRef] |
36. | C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12(10), 701–704 (2005). [CrossRef] |
37. | C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, “The quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22(4), 469–483 (1996). [CrossRef] |
38. | J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003). [CrossRef] |
39. | S. M. A. Bhuiyan, N. O. Attoh-Okine, K. E. Barner, A. Y. Ayenu-Prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data Anal. 1(2), 309–338 (2009). [CrossRef] |
40. | M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47(14), 2592–2598 (2008). [CrossRef] [PubMed] |
41. | 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(36), 6862–6869 (2009). [CrossRef] [PubMed] |
42. | M. B. Bernini, A. Federico, and G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition,” Appl. Opt. 50(5), 641–647 (2011). [CrossRef] [PubMed] |
43. | M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt. 50(28), 5513–5523 (2011). [CrossRef] [PubMed] |
44. | Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express 19(19), 18207–18215 (2011). [CrossRef] [PubMed] |
45. | X. Zhou, T. Yang, H. Zou, and H. Zhao, “Multivariate empirical mode decomposition approach for adaptive denoising of fringe patterns,” Opt. Lett. 37(11), 1904–1906 (2012). [CrossRef] [PubMed] |
46. | X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34(13), 2033–2035 (2009). [CrossRef] [PubMed] |
47. | X. Zhou, A. G. Podoleanu, Z. Yang, T. Yang, and H. Zhao, “Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns,” Opt. Express 20(22), 24247–24262 (2012). [CrossRef] [PubMed] |
48. | S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “A novel approach of fast and adaptive bidimensional empirical mode decomposition,” in Proc. IEEE Int. Conf. Acoustic, Speech and Signal Process. (Institute of Electrical and Electronics Engineers, 2008), 1313–1316. [CrossRef] |
49. | S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(21), 728356 (2008). [CrossRef] |
50. | K. Patorski, K. Pokorski, and M. Trusiak, “Fourier domain interpretation of real and pseudo-moiré phenomena,” Opt. Express 19(27), 26065–26078 (2011). [CrossRef] [PubMed] |
51. | M. Trusiak and K. Patorski, “Space domain interpetation of incoherent moiré superimpositions using FABEMD,” Proc. SPIE 8697, 18th Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 869704 (December 18, 2012). [CrossRef] |
52. | 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] |
53. | M. Wielgus, M. Bartys, A. Antoniewicz, and B. Putz, “Fast and adaptive bidimensional empirical mode decomposition for the real-time video fusion, ” in Proc. 15th Int. Conf. Inform. Fusion (FUSION,2012), 649–654. |
54. | Y. Zhou, S.-T. Zhou, Z.-Y. Zhong, and H.-G. Li, “A de-illumination scheme for face recognition based on fast decomposition and detail feature fusion,” Opt. Express 21(9), 11294–11308 (2013). [CrossRef] [PubMed] |
55. | C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit. 32(1), 71–86 (1999). [CrossRef] |
56. | S. Osman and W. Wang, “An enhanced Hilbert-Huang transform technique for bearing condition monitoring,” Meas. Sci. Technol. 24(8), 085004 (2013). [CrossRef] |
57. | Z. Wu, N. E. Huang, S. R. Long, and C. K. Peng, “On the trend, detrending, and variability of nonlinear and nonstationary time series,” Proc. Natl. Acad. Sci. U.S.A. 104(38), 14889–14894 (2007). [CrossRef] [PubMed] |
58. | Z. Yang, B. W.-K. Ling, and C. Bingham, “Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum,” Measurement 46(8), 2481–2491 (2013). [CrossRef] |
59. | P. Flandrin, P. Goncalves, and G. Rilling, “Detrending and denoising with empirical mode decomposition,” In EUSIPCO 2004. September 6–10, Vienna, Austria (2004) |
60. | G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, Grado (I), 2003. |
61. | G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008). [CrossRef] |
62. | 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. A 18(8), 1862–1870 (2001). [CrossRef] [PubMed] |
63. | 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. A 18(8), 1871–1881 (2001). [CrossRef] [PubMed] |
64. | Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002). [CrossRef] |
65. | L. Xiong and S. Jia, “Phase-error analysis and elimination for nonsinusoidal waveforms in Hilbert transform digital-fringe projection profilometry,” Opt. Lett. 34(15), 2363–2365 (2009). [CrossRef] [PubMed] |
66. | N. Sun, Y. Song, J. Wang, Z.-H. Li, and A.-Z. He, “Volume moiré tomography based on double cross gratings for real three-dimensional flow field diagnosis,” Appl. Opt. 51(34), 8081–8089 (2012). [CrossRef] [PubMed] |
67. | J. Schmit, K. Patorski, and K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng. 36(8), 2240–2248 (1997). [CrossRef] |
68. | K. Patorski, “Grating shearing interferometer with variable shear and fringe orientation,” Appl. Opt. 25(22), 4192–4198 (1986). [CrossRef] [PubMed] |
69. | K. Patorski, “Conjugate lateral shear interferometry and its implementation,” J. Opt. Soc. Am. A 3(11), 1862–1870 (1986). [CrossRef] |
OCIS Codes
(100.2650) Image processing : Fringe analysis
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4120) Instrumentation, measurement, and metrology : Moire' techniques
ToC Category:
Instrumentation, Measurement, and Metrology
History
Original Manuscript: September 18, 2013
Revised Manuscript: October 25, 2013
Manuscript Accepted: October 27, 2013
Published: November 11, 2013
Citation
Maciej Trusiak, Krzysztof Patorski, and Krzysztof Pokorski, "Hilbert-Huang processing for single-exposure two-dimensional grating interferometry," Opt. Express 21, 28359-28379 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28359
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References
- D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics Publishing, 1993).
- D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
- D. Malacara, ed., Optical Shop Testing (John Wiley, 2007).
- D. Post, B. Han, and P. Ifju, High Sensitivity Moirè (Springer, 1994).
- K. Patorski, Handbook of the Moirè Fringe Technique (Elsevier, 1993).
- S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter,” Appl. Opt.10(7), 1575–1580 (1971). [CrossRef] [PubMed]
- S. Yokozeki and T. Suzuki, “Shearing interferometer using the grating as the beam splitter. Part 2,” Appl. Opt.10(7), 1690–1693 (1971). [CrossRef] [PubMed]
- A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun.2(9), 413–415 (1971). [CrossRef]
- A. W. Lohmann and D. E. Silva, “A Talbot interferometer with circular gratings,” Opt. Commun.4(5), 326–328 (1972). [CrossRef]
- D. E. Silva, “Talbot interferometer for radial and lateral derivatives,” Appl. Opt.11(11), 2613–2624 (1972). [CrossRef] [PubMed]
- O. Kafri, “Noncoherent method for mapping phase objects,” Opt. Lett.5(12), 555–557 (1980). [CrossRef] [PubMed]
- K. Patorski, “Diffraction effects in moiré deflectometry: comment,” J. Opt. Soc. Am. A3(5), 667–668 (1986). [CrossRef]
- E. Keren and O. Kafri, “Diffraction effects in moiré deflectometry: reply to comment,” J. Opt. Soc. Am. A3(5), 669–670 (1986). [CrossRef]
- E. Bar-Ziv, S. Sgulim, O. Kafri, and E. Keren, “Temperature mapping in flames by moire deflectometry,” Appl. Opt.22(5), 698–705 (1983). [CrossRef] [PubMed]
- G. Oster, M. Wasserman, and C. Zwerling, “Theoretical interpretation of moiré patterns,” J. Opt. Soc. Am.54(2), 169–175 (1964). [CrossRef]
- K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf ed., vol. 27, 1–108 (Elsevier, 1989).
- H. Canabal, J. A. Quiroga, and E. Bernabeu, “Improved phase-shifting method for automatic processing of moiré deflectograms,” Appl. Opt.37(26), 6227–6233 (1998). [CrossRef] [PubMed]
- J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng.38(6), 974–982 (1999). [CrossRef]
- H. Canabal and E. Bernabeu, “Phase extraction methods for analysis of crossed fringe patterns,” Proc. SPIE3744, 231–240 (1999). [CrossRef]
- J. Villa, J. A. Quiroga, and M. Servín, “Improved regularized phase-tracking technique for the processing of squared-grating deflectograms,” Appl. Opt.39(4), 502–508 (2000). [CrossRef] [PubMed]
- J. L. Flores, B. Bravo-Medina, and J. A. Ferrari, “One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns,” Appl. Opt.52(26), 6537–6542 (2013). [CrossRef] [PubMed]
- H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett.35(12), 1932–1934 (2010). [CrossRef] [PubMed]
- I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-dimensional x-ray grating interferometer,” Phys. Rev. Lett.105(24), 248102 (2010). [CrossRef] [PubMed]
- I. Zanette, C. David, S. Rutishauser, T. Weitkamp, M. Denecke, and C. T. Walker, “2D grating simulation for X-ray phase-contrast and dark-field imaging with a Talbot interferometer,” AIP Conf. Proc.1221, 73–79 (2010). [CrossRef]
- H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval,” Opt. Express19(4), 3339–3346 (2011). [CrossRef] [PubMed]
- K. S. Morgan, D. M. Paganin, and K. K. Siu, “Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid,” Opt. Express19(20), 19781–19789 (2011). [CrossRef] [PubMed]
- S. Rutishauser, I. Zanette, T. Weitkamp, T. Donath, and C. David, “At-wavelength characterization of refractive x-ray lenses using a two-dimensional grating interferometer,” Appl. Phys. Lett.99(22), 221104 (2011). [CrossRef]
- S. Berujon, H. Wang, I. Pape, K. Sawhney, S. Rutishauser, and C. David, “X-ray submicrometer phase contrast imaging with a Fresnel zone plate and a two dimensional grating interferometer,” Opt. Lett.37(10), 1622–1624 (2012). [CrossRef] [PubMed]
- H. Wang, S. Berujon, I. Pape, S. Rutishauser, C. David, and K. Sawhney, “At-wavelength metrology using the moiré fringe analysis method based on a two-dimensional grating interferometer,” Nucl. Instrum. Methods Phys. Res. A710, 78–81 (2013). [CrossRef]
- L. Salbut, “Multichannel system for automatic analysis of u,v,w displacements in grating interferometry,” in Physical Research, W. Juptner and W. Osten, eds. 19, 282–287 (Akademie, 1993).
- M. Kujawinska and M. Pirga, “Fringe pattern analysis for the investigation of dynamic processes in experimental mechanics,” in Physical Research, W. Juptner and W. Osten, eds. 19, 391–394 (Akademie, 1993).
- M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng.34(8), 2459–2466 (1995). [CrossRef]
- K. Pokorski and K. Patorski, “Separation of complex fringe patterns using two-dimensional continuous wavelet transform,” Appl. Opt.51(35), 8433–8439 (2012). [CrossRef] [PubMed]
- 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, 230–240 (2014). [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 non-linear and non-stationary time series analysis,” Proc. R. Soc. Lond. A454(1971), 903–995 (1998). [CrossRef]
- C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett.12(10), 701–704 (2005). [CrossRef]
- C. B. Barber, D. P. Dobkin, and H. Huhdanpaa, “The quickhull algorithm for convex hulls,” ACM Trans. Math. Softw.22(4), 469–483 (1996). [CrossRef]
- J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput.21(12), 1019–1026 (2003). [CrossRef]
- S. M. A. Bhuiyan, N. O. Attoh-Okine, K. E. Barner, A. Y. Ayenu-Prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data Anal.1(2), 309–338 (2009). [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(14), 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(36), 6862–6869 (2009). [CrossRef] [PubMed]
- M. B. Bernini, A. Federico, and G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition,” Appl. Opt.50(5), 641–647 (2011). [CrossRef] [PubMed]
- M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt.50(28), 5513–5523 (2011). [CrossRef] [PubMed]
- Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express19(19), 18207–18215 (2011). [CrossRef] [PubMed]
- X. Zhou, T. Yang, H. Zou, and H. Zhao, “Multivariate empirical mode decomposition approach for adaptive denoising of fringe patterns,” Opt. Lett.37(11), 1904–1906 (2012). [CrossRef] [PubMed]
- X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett.34(13), 2033–2035 (2009). [CrossRef] [PubMed]
- X. Zhou, A. G. Podoleanu, Z. Yang, T. Yang, and H. Zhao, “Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns,” Opt. Express20(22), 24247–24262 (2012). [CrossRef] [PubMed]
- S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “A novel approach of fast and adaptive bidimensional empirical mode decomposition,” in Proc. IEEE Int. Conf. Acoustic, Speech and Signal Process. (Institute of Electrical and Electronics Engineers, 2008), 1313–1316. [CrossRef]
- S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process.2008(21), 728356 (2008). [CrossRef]
- K. Patorski, K. Pokorski, and M. Trusiak, “Fourier domain interpretation of real and pseudo-moiré phenomena,” Opt. Express19(27), 26065–26078 (2011). [CrossRef] [PubMed]
- M. Trusiak and K. Patorski, “Space domain interpetation of incoherent moiré superimpositions using FABEMD,” Proc. SPIE 8697, 18th Czech-Polish-Slovak Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 869704 (December 18, 2012). [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. Express20(21), 23463–23479 (2012). [CrossRef] [PubMed]
- M. Wielgus, M. Bartys, A. Antoniewicz, and B. Putz, “Fast and adaptive bidimensional empirical mode decomposition for the real-time video fusion, ” in Proc. 15th Int. Conf. Inform. Fusion (FUSION,2012), 649–654.
- Y. Zhou, S.-T. Zhou, Z.-Y. Zhong, and H.-G. Li, “A de-illumination scheme for face recognition based on fast decomposition and detail feature fusion,” Opt. Express21(9), 11294–11308 (2013). [CrossRef] [PubMed]
- C. Studholme, D. L. G. Hill, and D. J. Hawkes, “An overlap invariant entropy measure of 3D medical image alignment,” Pattern Recognit.32(1), 71–86 (1999). [CrossRef]
- S. Osman and W. Wang, “An enhanced Hilbert-Huang transform technique for bearing condition monitoring,” Meas. Sci. Technol.24(8), 085004 (2013). [CrossRef]
- Z. Wu, N. E. Huang, S. R. Long, and C. K. Peng, “On the trend, detrending, and variability of nonlinear and nonstationary time series,” Proc. Natl. Acad. Sci. U.S.A.104(38), 14889–14894 (2007). [CrossRef] [PubMed]
- Z. Yang, B. W.-K. Ling, and C. Bingham, “Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum,” Measurement46(8), 2481–2491 (2013). [CrossRef]
- P. Flandrin, P. Goncalves, and G. Rilling, “Detrending and denoising with empirical mode decomposition,” In EUSIPCO 2004. September 6–10, Vienna, Austria (2004)
- G. Rilling, P. Flandrin, and P. Goncalves, “On empirical mode decomposition and its algorithms,” IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, Grado (I), 2003.
- G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process.56(1), 85–95 (2008). [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. A18(8), 1862–1870 (2001). [CrossRef] [PubMed]
- 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. A18(8), 1871–1881 (2001). [CrossRef] [PubMed]
- Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett.9(3), 81–84 (2002). [CrossRef]
- L. Xiong and S. Jia, “Phase-error analysis and elimination for nonsinusoidal waveforms in Hilbert transform digital-fringe projection profilometry,” Opt. Lett.34(15), 2363–2365 (2009). [CrossRef] [PubMed]
- N. Sun, Y. Song, J. Wang, Z.-H. Li, and A.-Z. He, “Volume moiré tomography based on double cross gratings for real three-dimensional flow field diagnosis,” Appl. Opt.51(34), 8081–8089 (2012). [CrossRef] [PubMed]
- J. Schmit, K. Patorski, and K. Creath, “Simultaneous registration of in- and out-of-plane displacements in modified grating interferometry,” Opt. Eng.36(8), 2240–2248 (1997). [CrossRef]
- K. Patorski, “Grating shearing interferometer with variable shear and fringe orientation,” Appl. Opt.25(22), 4192–4198 (1986). [CrossRef] [PubMed]
- K. Patorski, “Conjugate lateral shear interferometry and its implementation,” J. Opt. Soc. Am. A3(11), 1862–1870 (1986). [CrossRef]
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