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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1536–1544

Local phase from local orientation by solution of a sequence of linear systems

J. L. Marroquin, R. Rodriguez-Vera, and M. Servin  »View Author Affiliations

JOSA A, Vol. 15, Issue 6, pp. 1536-1544 (1998)

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A technique for recovering the phase from single fringe-pattern images is presented. It is based on the estimation of the local frequency of the pattern by successive decoupled estimation of the local orientation, direction, and magnitude of the frequency field. Once this field is known, the local phase is recovered from the complex output of an adaptive quadrature filter. It is shown that by the use of Gauss–Markov measure field models all these estimation steps may be implemented by solving linear systems of equations (i.e., minimizing quadratic functions), which makes the procedure robust and computationally efficient. Examples are presented of the application of this technique to the recovery of phase from single electronic speckle-pattern interferograms.

© 1998 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(200.1130) Optics in computing : Algebraic optical processing

Original Manuscript: June 20, 1997
Revised Manuscript: February 4, 1998
Manuscript Accepted: January 20, 1998
Published: June 1, 1998

J. L. Marroquin, R. Rodriguez-Vera, and M. Servin, "Local phase from local orientation by solution of a sequence of linear systems," J. Opt. Soc. Am. A 15, 1536-1544 (1998)

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  1. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform methods of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  2. Th. Kreis, “Digital holographic interference phase measurement using the Fourier transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986). [CrossRef]
  3. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1989).
  4. J. H. Bruning, D. R. Herriott, J. E. Gallager, D. P. Rosefeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  5. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–393.
  6. A. Davila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996). [CrossRef]
  7. D. I. Farrant, G. H. Kaufmann, J. N. Petzing, J. R. Tyrer, B. F. Oreb, D. Kerr, “Transient deformation measurement using dual-pulse addition ESPI,” in Ultrahigh- and High-Speed Photography and Image-Based Motion Measurement, D. R. Snyder, A. Davidhazy, T. Etoh, C. Johnson, J. S. Walton, eds., Proc. SPIE3173, 132–140 (1997). [CrossRef]
  8. K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984). [CrossRef]
  9. J. L. Marroquin, M. Servin, R. Rodriguez-Vera, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A 14, 1742–1753 (1997). [CrossRef]
  10. J. L. Marroquin, “Gauss–Markov measure fields for image processing,” (Centro de Investigacion en Matemáticas, Guanajuato, Mexico, 1997).
  11. J. Marroquin, S. Mitter, T. Poggio, “Probabilistic solution of ill-posed problems in computational vision,” J. Am. Stat. Assoc. 82, 76–89 (1987). [CrossRef]
  12. J. L. Marroquin, “Random measure fields and the integration of visual information,” IEEE Trans. Syst. Man Cybern. 22, 705–716 (1992). [CrossRef]
  13. N. I. Fisher, Statistical Analysis of Circular Data (Cambridge U. Press, Cambridge, UK, 1993).
  14. J. L. Marroquin, M. Servin, J. E. Figueroa, “Robust quadrature filters,” J. Opt. Soc. Am. A 14, 779–791 (1997). [CrossRef]
  15. G. H. Gollub, C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1990).
  16. D. C. Ghiglia, 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). [CrossRef]
  17. J. L. Marroquin, M. Rivera, “Quadratic regularization functionals for phase unwrapping,” J. Opt. Soc. Am. A 12, 2393–2400 (1995). [CrossRef]
  18. M. Rivera, R. Rodriguez-Vera, J. L. Marroquin, “Robust procedure for fringe analysis,” Appl. Opt. 36, 8391–8396 (1997). [CrossRef]

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