Publication: Noise robust linear dynamic system for phase unwrapping and smoothing
Loading...
Official URL
Full text at PDC
Publication Date
2011-03-14
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
The Optical Society Of America
Citations
Exportar
Abstract
Phase unwrapping techniques remove the modulus 2 π ambiguities of wrapped phase maps. The present work shows a first-order feedback system for phase unwrapping and smoothing. This system is a fast phase unwrapping system which also allows filtering some noise since in deed it is an Infinite Impulse Response (IIR) low-pass filter. In other words, our system is capable of low-pass filtering the wrapped phase as the unwrapping process proceeds. We demonstrate the temporal stability of this unwrapping feedback system, as well as its low-pass filtering capabilities. Our system even outperforms the most common and used unwrapping methods that we tested, such as the Flynn's method, the Goldstain's method, and the Ghiglia least-squares method (weighted or unweighted). The comparisons with these methods show that our system filters-out some noise while preserving the dynamic range of the phase-data. Its application areas may cover: optical metrology, synthetic aperture radar systems, magnetic resonance, and those imaging systems where information is obtained as a demodulated wrapped phase map.
Description
© 2011 Optical Society of America
UCM subjects
Unesco subjects
Keywords
Citation
1. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
2. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693 (1974).
3. Q. Kemao, “Two-dimensional windowed fourier transform for fringe pattern analysis: Principles, applications and implementations,” Optics And Lasers In Engineering 45, 304–317 (2007).
4. M. Servín, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express 17, 21867–21881 (2009).
5. L. N. Mertz, “Speckle imaging, photon by photon,” Appl. Opt. 18, 611–614 (1979).
6. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979).
7. K. A. Stetson, J. Wahid, and P. Gauthier “Noise-immune phase unwrapping by use of calculated wrap regions,” Appl. Opt. 36, 4830–4838 (1997).
8. K. Itoh, “Analysis of the phase unwrapping algorithm,” Appl. Opt. 21, 2470–2470 (1982).
9. T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Optics and Lasers in Engineering 21, 199 – 239 (1994).
10. D. C. Ghiglia and M. D. Pritt, Two-dimensional Phase Unwrapping; Theory, Algorithms, and Software (Wiley-Interscience, 1998).
11. D. C. Ghiglia, G. A. Mastin, and L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
12. J. M. Huntley, “Noise-immune phase unwrapping algorithm,” Appl. Opt. 28, 3268–3270 (1989).
13. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107–117 (1994).
14. J. L. Marroquín and M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995).
15. J. L. Marroquín, M. Tapia, R. Rodríguez-Vera, and M. Servín, “Parallel algorithms for phase unwrapping based on Markov random field models,” J. Opt. Soc. Am. A 12, 2578–2585 (1995).
16. K. M. Hung and T. Yamada, “Phase unwrapping by regions using least-squares approach,” Optical Engineering 37, 2965–2970 (1998).
17. V. V. Volkov and Y. Zhu, “Deterministic phase unwrapping in the presence of noise,” Opt. Lett. 28, 2156–2158 (2003).
18. M. Servín, F. J. Cuevas, D. Malacara, J. L. Marroquín, and R. Rodríguez-Vera, “Phase unwrapping through demodulation by use of the regularized phase-tracking technique,” Appl. Opt. 38, 1934–1941 (1999).
19. J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Principles, Algorithms, and Applications (Prentice-Hall, October 5, 1995), 3rd ed.