A discrete phase-unwrapping technique for interferograms
Falih H. Ahmad
Department of Engineering Technology, University of North Carolina, Charlotte, Charlotte, North Carolina 28223
Search for more papers by this authorGary L. Helms
Department of Engineering Technology, University of North Carolina, Charlotte, Charlotte, North Carolina 28223
Search for more papers by this authorRay M. Castellane
Waterways Experiment Station, Engineer Research and Development Center, Department of the Army, Vicksburg, Mississippi 39180-6199
Search for more papers by this authorBartley P. Durst
Waterways Experiment Station, Engineer Research and Development Center, Department of the Army, Vicksburg, Mississippi 39180-6199
Search for more papers by this authorFalih H. Ahmad
Department of Engineering Technology, University of North Carolina, Charlotte, Charlotte, North Carolina 28223
Search for more papers by this authorGary L. Helms
Department of Engineering Technology, University of North Carolina, Charlotte, Charlotte, North Carolina 28223
Search for more papers by this authorRay M. Castellane
Waterways Experiment Station, Engineer Research and Development Center, Department of the Army, Vicksburg, Mississippi 39180-6199
Search for more papers by this authorBartley P. Durst
Waterways Experiment Station, Engineer Research and Development Center, Department of the Army, Vicksburg, Mississippi 39180-6199
Search for more papers by this authorAbstract
A discrete technique for phase unwrapping is presented. The technique is based on constructing the mth-degree interpolating polynomials to approximate the involved functions using Legendre–Gauss–Lobatto collocation nodes. The relationship between the known wrapped phase and the unknown unwrapped phase and that between their derivatives are converted into a set of linear algebraic equations. This set of equations is solved for the unknown coefficients to produce the unwrapped phase. A numerical example is included to demonstrate the performance of the technique, where a comparison is made with exact results. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 101–104, 2002.
References
- 1 G. Fornaro and E. Sansosti, A two-dimensional region growing least squares phase unwrapping algorithm for interferometric SAR processing, IEEE Trans Geosci Remote Sensing 37 ( 1999), 2215–2226.
- 2 L. Xue and X. Su, Phase-unwrapping algorithm based on frequency analysis for measurement of a complex object by the phase-measuring-profilometry method, Appl Opt 40 ( 2001), 1207–1215.
- 3 J. Strand, T. Taxt, and A. Jain, Two-dimensional phase unwrapping using a block least-squares method, IEEE Trans Image Processing 8 ( 1999), 375–386.
- 4 I. Lyuboshenko and H. Maître, Phase unwrapping for interferometric synthetic aperture radar by use of Helmholtz equation eigenfunctions and the first Green's identity, J Opt Soc Amer A 16 ( 1999), 378–395.
- 5 L. Guerriero, G. Nico, G. Pasquariello, and S. Stramaglia, New regularization scheme for phase unwrapping, Appl Opt 37 ( 1998), 3053–3058.
- 6 G. Davidson and R. Bamler, Multiresolution phase unwrapping for SAR interferometry, IEEE Trans Geosci Remote Sensing 37 ( 1999), 163–174.
- 7 G. Carballo and P. Fieguth, Probabilistic cost functions for network phase unwrapping, IEEE Trans Geosci Remote Sensing 38 ( 2000), 2192–2201.
- 8 J. Strand and T. Taxt, Performance evaluation of two-dimensional phase unwrapping algorithms, Appl Opt 38 ( 1999), 4333–4344.
- 9 M. Servin, F. Cuevas, D. Malacara, J. Marroquin, and R. Rodriquez-Vera, Phase unwrapping through demodulation by use of the regularized phase-tracking technique, Appl Opt 38 ( 1999), 1934–1941.
- 10 B. Gutmann and H. Weber, Phase unwrapping with the branch-cut method: Role of phase-field direction, Appl Opt 39 ( 2000), 4802–4816.
- 11 R. Hardie, Md. Younus, and J. Blackshire, Robust phase-unwrapping algorithm with a spatial binary-tree image decomposition, Appl Opt 37 ( 1998), 4468–4476.
- 12 J. Yañez-Mendola, M. Servín, and D. Malacara-Hernández, Iterative method to obtain the wrapped phase in an interferogram with a linear carrier, Opt Commun 178 ( 2000), 291–296.
- 13 A. Baldi, Two-dimensional phase unwrapping by quad-tree decomposition, Appl Opt 40 ( 2001), 1187–1194.
- 14 H. Saldner and J. Huntley, Temporal phase unwrapping: Application to surface profiling of discontinuous objects, Appl Opt 36 ( 1997), 2770–2775.
- 15 P. Ettl and K. Creath, Comparison of phase-unwrapping algorithms by using gradient of first failure, Appl Opt 35 ( 1996), 5108–5114.
- 16 M. Servin, J. Marroquin, D. Malacara, and F. Cuevas, Phase unwrapping with a regularized phase-tracking system, Appl Opt 37 ( 1998), 1917–1923.
- 17 K. Stetson, J. Wahid, and P. Gauthier, Noise-immune phase unwrapping by use of calculated wrap regions, Appl Opt 36 ( 1997), 4830–4838.
- 18 C. Canuto, M. Hussaini, A. Quarteroni, and T. Zang, Spectral methods in fluid dynamic, Springer-Verlag, Berlin, Germany, 1987.
- 19 F. Ahmad and M. Razzaghi, On the Green-function technique and phase velocity approximation of axially symmetric fields in stratified media, J Math Phys 37 ( 1996), 3824–3832.
- 20 F. Ahmad and M. Razzaghi, On the approximation of the permittivity profiles of an inhomogeneous dielectric slab, J Electromag Waves Appl 12 ( 1998), 713–722.
- 21 F. Ahmad and M. Razzaghi, A pseudospectral technique for the discrete reconstruction of the three-dimensional equivalent current density, IEEE Trans Microwave Theory Tech 89 ( 1999), 802–805.
- 22 F. Ahmad and M. Razzaghi, A collocation method for the solution of an inverse scattering problem from gradient-type interfaces, Phys Scr 61 ( 2000), 468–471.
- 23 D. Gottlieb, M. Hussaini, and S. Orszg, Theory and applications of spectral methods in spectral methods for partial differential equations, SIAM, Philadelphia, PA, 1984.
- 24 H. Van Brugg, Temporal phase unwrapping and its application in shearography systems, Appl Opt 37 ( 1998), 6701–6706.
- 25 H.-J. Su, J.-L. Li, and X.-Y. Su, Phase algorithm without the influence of carrier frequency, Opt Eng 36 ( 1997), 1799–1805.
