Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform |
Optics Express, Vol. 20, Issue 21, pp. 23463-23479 (2012)
http://dx.doi.org/10.1364/OE.20.023463
Acrobat PDF (2148 KB)
Abstract
Presented method for fringe pattern enhancement has been designed for processing and analyzing low quality fringe patterns. It uses a modified fast and adaptive bidimensional empirical mode decomposition (FABEMD) for the extraction of bidimensional intrinsic mode functions (BIMFs) from an interferogram. Fringe pattern is then selectively reconstructed (SR) taking the regions of selected BIMFs with high modulation values only. Amplitude demodulation and normalization of the reconstructed image is conducted using the spiral phase Hilbert transform (HS). It has been tested using computer generated interferograms and real data. The performance of the presented SR-FABEMD-HS method is compared with other normalization techniques. Its superiority, potential and robustness to high fringe density variations and the presence of noise, modulation and background illumination defects in analyzed fringe patterns has been corroborated.
© 2012 OSA
1. Introduction
4. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997). [CrossRef] [PubMed]
5. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18(3), 689–695 (2001) (and references therein). [CrossRef]
6. H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009). [CrossRef] [PubMed]
7. C. Tian, Y. Yang, D. Liu, Y. Luo, and Y. Zhuo, “Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique,” Appl. Opt. 49(2), 170–179 (2010). [CrossRef] [PubMed]
4. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997). [CrossRef] [PubMed]
5. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18(3), 689–695 (2001) (and references therein). [CrossRef]
8. Q. Yu, K. Andresen, W. Osten, and W. Jueptner, “Noise-free normalized fringe patterns and local pixel transforms for strain extraction,” Appl. Opt. 35(20), 3783–3790 (1996). [CrossRef] [PubMed]
9. J. A. Quiroga, J. Antonio Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1–3), 43–51 (2001). [CrossRef]
10. J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224(4–6), 221–227 (2003). [CrossRef]
11. J. A. Guerrero, J. L. Marroquin, M. Rivera, and J. A. Quiroga, “Adaptive monogenic filtering and normalization of ESPI fringe patterns,” Opt. Lett. 30(22), 3018–3020 (2005). [CrossRef] [PubMed]
12. Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45(4), 045601 (2006). [CrossRef]
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
15. 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]
16. 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]
17. C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12(10), 701–704 (2005). [CrossRef]
18. 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]
19. J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003). [CrossRef]
20. 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. 01(02), 309–338 (2009). [CrossRef]
21. 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]
15. 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]
22. 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]
23. 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]
25. 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(164), 725356 (2008). [CrossRef]
26. 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]
27. 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]
28. K. G. Larkin, “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]
23. 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]
23. 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]
15. 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]
2. Proposed algorithm
2.1 The FABEMD method
25. 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(164), 725356 (2008). [CrossRef]
26. 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]
25. 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(164), 725356 (2008). [CrossRef]
2.2 Selective reconstruction approach
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
3. Numerical studies
9. J. A. Quiroga, J. Antonio Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1–3), 43–51 (2001). [CrossRef]
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
15. 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]
17. C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12(10), 701–704 (2005). [CrossRef]
3.1 Constant period circular fringe pattern analysis
29. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002). [CrossRef]
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
25. 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(164), 725356 (2008). [CrossRef]
3.2 Complex interferogram studies
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
9. J. A. Quiroga, J. Antonio Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1–3), 43–51 (2001). [CrossRef]
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
15. 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]
3.3 Phase demodulation accuracy evaluation
4. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997). [CrossRef] [PubMed]
6. H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009). [CrossRef] [PubMed]
30. M. Servin, J. L. Marroquin, and J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A 21(3), 411–419 (2004). [CrossRef] [PubMed]
31. L. Kai and Q. Kemao, “Fast frequency-guided sequential demodulation of a single fringe pattern,” Opt. Lett. 35(22), 3718–3720 (2010). [CrossRef] [PubMed]
32. K. Li and B. Pan, “Frequency-guided windowed Fourier ridges technique for automatic demodulation of a single closed fringe pattern,” Appl. Opt. 49(1), 56–60 (2010). [CrossRef] [PubMed]
33. J. Ma, Z. Wang, B. Pan, T. Hoang, M. Vo, and L. Luu, “Two-dimensional continuous wavelet transform for phase determination of complex interferograms,” Appl. Opt. 50(16), 2425–2430 (2011). [CrossRef] [PubMed]
4. Experimental data processing
34. K. Patorski and A. Olszak, “Digital in-plane electronic speckle pattern shearing interferometry,” Opt. Eng. 36(7), 2010–2015 (1997). [CrossRef]
14. N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef]
15. 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]
35. 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]
5. Conclusions
Acknowledgments
References and links
1. | J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics E. Wolf ed. (Elsevier, Amsterdam, 1990). |
2. | D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics Publishing, Bristol, 1993). |
3. | D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998). |
4. | M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36(19), 4540–4548 (1997). [CrossRef] [PubMed] |
5. | M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18(3), 689–695 (2001) (and references therein). [CrossRef] |
6. | H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009). [CrossRef] [PubMed] |
7. | C. Tian, Y. Yang, D. Liu, Y. Luo, and Y. Zhuo, “Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique,” Appl. Opt. 49(2), 170–179 (2010). [CrossRef] [PubMed] |
8. | Q. Yu, K. Andresen, W. Osten, and W. Jueptner, “Noise-free normalized fringe patterns and local pixel transforms for strain extraction,” Appl. Opt. 35(20), 3783–3790 (1996). [CrossRef] [PubMed] |
9. | J. A. Quiroga, J. Antonio Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1–3), 43–51 (2001). [CrossRef] |
10. | J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224(4–6), 221–227 (2003). [CrossRef] |
11. | J. A. Guerrero, J. L. Marroquin, M. Rivera, and J. A. Quiroga, “Adaptive monogenic filtering and normalization of ESPI fringe patterns,” Opt. Lett. 30(22), 3018–3020 (2005). [CrossRef] [PubMed] |
12. | Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng. 45(4), 045601 (2006). [CrossRef] |
13. | K. Patorski and K. Pokorski, “Examination of singular scalar light fields using wavelet processing of fork fringes,” Appl. Opt. 50(5), 773–781 (2011). |
14. | N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun. 270(2), 161–168 (2007). [CrossRef] |
15. | 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] |
16. | 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] |
17. | C. Damerval, S. Meignen, and V. Perrier, “A fast algorithm for bidimensional EMD,” IEEE Signal Process. Lett. 12(10), 701–704 (2005). [CrossRef] |
18. | 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] |
19. | J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003). [CrossRef] |
20. | 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. 01(02), 309–338 (2009). [CrossRef] |
21. | 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] |
22. | 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] |
23. | 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] |
24. | S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “A novel approach of fast and adaptive bidimensional empirical mode decomposition,” in Proceedings of IEEE International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, 2008), pp. 1313–1316. |
25. | 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(164), 725356 (2008). [CrossRef] |
26. | 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] |
27. | 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] |
28. | K. G. Larkin, “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] |
29. | Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9(3), 81–84 (2002). [CrossRef] |
30. | M. Servin, J. L. Marroquin, and J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A 21(3), 411–419 (2004). [CrossRef] [PubMed] |
31. | L. Kai and Q. Kemao, “Fast frequency-guided sequential demodulation of a single fringe pattern,” Opt. Lett. 35(22), 3718–3720 (2010). [CrossRef] [PubMed] |
32. | K. Li and B. Pan, “Frequency-guided windowed Fourier ridges technique for automatic demodulation of a single closed fringe pattern,” Appl. Opt. 49(1), 56–60 (2010). [CrossRef] [PubMed] |
33. | J. Ma, Z. Wang, B. Pan, T. Hoang, M. Vo, and L. Luu, “Two-dimensional continuous wavelet transform for phase determination of complex interferograms,” Appl. Opt. 50(16), 2425–2430 (2011). [CrossRef] [PubMed] |
34. | K. Patorski and A. Olszak, “Digital in-plane electronic speckle pattern shearing interferometry,” Opt. Eng. 36(7), 2010–2015 (1997). [CrossRef] |
35. | 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] |
36. | M. Gupta and S. K. Nayar, “Micro Phase Shifting,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Providence, Rhode Island, 2012), pp.1–8. |
OCIS Codes
(100.2000) Image processing : Digital image processing
(100.2980) Image processing : Image enhancement
(100.6890) Image processing : Three-dimensional image processing
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
ToC Category:
Image Processing
History
Original Manuscript: July 20, 2012
Revised Manuscript: August 30, 2012
Manuscript Accepted: September 8, 2012
Published: September 27, 2012
Citation
Maciej Trusiak, Krzysztof Patorski, and Maciej Wielgus, "Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform," Opt. Express 20, 23463-23479 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23463
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References
- J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics E. Wolf ed. (Elsevier, Amsterdam, 1990).
- D. W. Robinson and G. Reid, Interferogram Analysis: Digital Fringe Pattern Measurement (Institute of Physics Publishing, Bristol, 1993).
- D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).
- M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt.36(19), 4540–4548 (1997). [CrossRef] [PubMed]
- M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A18(3), 689–695 (2001) (and references therein). [CrossRef]
- H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express17(17), 15118–15127 (2009). [CrossRef] [PubMed]
- C. Tian, Y. Yang, D. Liu, Y. Luo, and Y. Zhuo, “Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique,” Appl. Opt.49(2), 170–179 (2010). [CrossRef] [PubMed]
- Q. Yu, K. Andresen, W. Osten, and W. Jueptner, “Noise-free normalized fringe patterns and local pixel transforms for strain extraction,” Appl. Opt.35(20), 3783–3790 (1996). [CrossRef] [PubMed]
- J. A. Quiroga, J. Antonio Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun.197(1–3), 43–51 (2001). [CrossRef]
- J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun.224(4–6), 221–227 (2003). [CrossRef]
- J. A. Guerrero, J. L. Marroquin, M. Rivera, and J. A. Quiroga, “Adaptive monogenic filtering and normalization of ESPI fringe patterns,” Opt. Lett.30(22), 3018–3020 (2005). [CrossRef] [PubMed]
- Z. Wang and H. Ma, “Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing,” Opt. Eng.45(4), 045601 (2006). [CrossRef]
- K. Patorski and K. Pokorski, “Examination of singular scalar light fields using wavelet processing of fork fringes,” Appl. Opt.50(5), 773–781 (2011).
- N. A. Ochoa and A. A. Silva-Moreno, “Normalization and noise reduction algorithm for fringe patterns,” Opt. Commun.270(2), 161–168 (2007). [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(36), 6862–6869 (2009). [CrossRef] [PubMed]
- N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for 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 Ph. 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.01(02), 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, “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]
- S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “A novel approach of fast and adaptive bidimensional empirical mode decomposition,” in Proceedings of IEEE International Conference on Acoustic, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, 2008), pp. 1313–1316.
- 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(164), 725356 (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]
- 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, “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]
- M. Servin, J. L. Marroquin, and J. A. Quiroga, “Regularized quadrature and phase tracking from a single closed-fringe interferogram,” J. Opt. Soc. Am. A21(3), 411–419 (2004). [CrossRef] [PubMed]
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