Ronald Driggers, Editor-in-Chief
Qian Kemao, Le Tran Hoai Nam, Lin Feng, and Seah Hock Soon
Qian Kemao,1,* Le Tran Hoai Nam,1 Lin Feng,1 and Seah Hock Soon1
1School of Computer Engineering, Nanyang Technological University, Singapore 639798
*Corresponding author: firstname.lastname@example.org
Some effective filtering methods for wrapped phase maps, a regularized phase-tracking method (RPT) without the regularization term, a multiple-parameter least-square method (MPLS), a windowed Fourier ridges method (WFR), an autocorrelation function method (ACF), and a sine∕cosine average filter (SCAF), are analyzed in order to establish their transversal relationship. The analysis shows that principles of the RPT,
MPLS, WFR, and ACF are equivalent and the SCAF also leads to the WFR by some extension, which elegantly unifies all these methods for filtering unwrapped phase maps.
© 2007 Optical Society of America
S. Fu, H. Lin, J. Chen, and Q. Yu, "Influence of window size on the fringe orientation estimation," Opt. Commun. 272, 73-80 (2007).
Q. Kemao, "Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations," Opt. Lasers Eng. 45, 304-317 (2007).
Q. Kemao, "A simple phase unwrapping approach based on filtering by windowed Fourier transform: the phase near edges," Opt. Laser Technol. 39, 1364-1369 (2007).
C. Tang, W. Wang, H. Yan, and X. Gu, "Tangent least-square fitting filtering method for electrical speckle pattern interferometry phase fringe patterns," Appl. Opt. 46, 2907-2913 (2007).
Q. Kemao and S. H. Soon, "A simple phase unwrapping approach based on filtering by windowed Fourier transform (II)," Key Eng. Mater. 326-328, 67-70 (2006).
V. Rosso, F. Michel, V. Moreau, Y. Renotte, B. Tilkens, and Y. Lion, "Highlighting properties for filters for their application in temporal phase shifting interferometry," in Photonic Applications in Biosensing and Imaging, C. W. Chan, K. Yu, U. J. Krull, R. I. Hornsey, B. C. Wilson, and R. A. Weersink, eds., Proc. SPIE 5969, 59692M (2005).
K. Qian, S. H. Soon, and A. Asundi, "A simple phase unwrapping approach based on filtering by windowed Fourier transform," Opt. Laser Technol. 37, 458-462 (2005).
M. J. Huang and W. Sheu, "Histogram-data-orientated filter for inconsistency removal of interferometric phase maps," Opt. Eng. 44, 045602 (2005).
F. Palacios, E. Goncalves, J. Ricardo, and J. L. Valin, "Adaptive filter to improve the performance of phase-unwrapping in digital holography," Opt. Commun. 238, 245-251 (2004).
G. Chunsheng, Z. Zhaoda, and Z. Daiyin, "InSAR interferogram filtering based on PD operator," J. Nanjing University of Aeronautics and Astronautics 35, 72-76 (2003).
H. Y. Yun, C. K. Hong, and S. W. Chang, "Least-square phase estimation with multiple parameters in phase-shifting electronic speckle pattern interferometry," J. Opt. Soc. Am. A 20, 240-247 (2003).
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, 689-695 (2001).
F. Qian, X. Wang, X. Wang, and Y. Bu, "Adaptive filter for unwrapping noisy phase image in phase-stepping interferometry," Opt. Laser Technol. 33, 479-486 (2001).
G. Bo, S. Dellepiane, and G. Beneventano, "A locally adaptive noise filtering approach for phase-unwrapping improvement," in SPIE Conference on SAR Image Analysis, Modeling, and Techniques, Florence, Italy, September 1999, Proc. SPIE 3869, 116-125 (1999).
H. A. Aebischer and S. Waldner, "A simple and effective method for filtering speckle-interferometric phase fringe patterns," Opt. Commun. 162, 205-210 (1999).
S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. (Academic, 1999).
M. Servin, F. J. Cuevas, D. Malacara, J. L. Marroguin, and R. Rodriguez-Vera, "Phase unwrapping through demodulation by use of the regularized phase-tracking technique," Appl. Opt. 38, 1934-1941 (1999).
R. M. Goldstein and C. L. Werner, "Radar interferogram filtering for geophysical applications," Geophys. Res. Lett. 25, 4035-4038 (1998).
E. Trouve, J. Nicolas, and H. Maitre, "Improving phase unwrapping techniques by the use of local frequency estimates," IEEE Trans. Geosci. Remote Sens. 36, 1963-1972 (1998).
J. M. Huntley, "Random phase measurement errors in digital speckle pattern interferometry," Opt. Lasers Eng. 26, 131-150 (1997).
A. Capanni, L. Pezzati, D. Bertani, M. Cetica, and F. Francini, "Phase-shifting speckle interferometry: a noise reduction filter for phase unwrapping," Opt. Eng. 36, 2466-2472 (1997).
M. Servin, J. L. Marroguin, and F. J. Cucvas, "Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique," Appl. Opt. 36, 4540-4548 (1997).
E. Trouve, M. Caramma, and H. Maitre, "Fringe detection in noisy complex interferograms," Appl. Opt. 35, 3799-3806 (1996).
J. Lee, "Speckle suppression and analysis for synthetic aperture radar images," Opt. Eng. 25, 636-643 (1986).
D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithm, and Software (Wiley, 1998).
R. Kramer and O. Loffeld, "Presentation of an improved phase unwrapping algorithm based on Kalman filters combined with local slope estimation," in Proceedings of Fringe'96 ESA Workshop Applications of ERS SAR Interferometry (ESA, 1996).
M. Servin and M. Kujawinska, "Modern fringe pattern analysis in interferometry," Handbook of Optical Engineering, D. Malacara and B. J. Thompson, eds. (Dekker, 2001), Chap. 12, pp. 373-426.
C. M. Loeffler and R. E. Leonard, Jr., "Phase unwrapping via media filtering," in IEEE International Conference Acoustics, Speech, and Signal Process. (ICASSP) (IEEE, 1984), pp. 48.6.1-48.6.3.
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Filtering by the SCAF,
(a) simulated noisy wrapped phase map,
(b) phase filtered by the SCAF with
and 10 repetitions,
(c) phase compensated by a horizontal local frequency of
and then filtered,
(d) phase filtered by the WFR.
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Table 1 Parameter Settings for Numerical Comparison of Different Filters
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