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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 22 — Aug. 1, 2007
  • pp: 5038–5043

Efficient reconstruction of spatially limited phase distributions from their sheared representation

Claas Falldorf, Yvonne Heimbach, Christoph von Kopylow, and Werner Jüptner  »View Author Affiliations

Applied Optics, Vol. 46, Issue 22, pp. 5038-5043 (2007)

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We present a method that allows the reconstruction of smooth phase distributions from their laterally sheared representation. The proposed approach is efficient in the sense that only one sheared distribution is needed to completely restore the signal. A mandatory requirement is that the phase distribution is spatially limited. The method is exemplified by means of a synthetic signal, and in addition a practical algorithm is given. Finally, experimental results are presented. The deformation of a metallic surface is investigated by both speckle shearography and electronic speckle pattern interferometry (ESPI) respectively. To give proof of the proposed technique, the phase distribution reconstructed from the shearographic measurement is shown to match the results obtained by the ESPI.

© 2007 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4630) Instrumentation, measurement, and metrology : Optical inspection

ToC Category:
Image Processing

Original Manuscript: January 24, 2007
Revised Manuscript: April 25, 2007
Manuscript Accepted: April 25, 2007
Published: July 6, 2007

Claas Falldorf, Yvonne Heimbach, Christoph von Kopylow, and Werner Jüptner, "Efficient reconstruction of spatially limited phase distributions from their sheared representation," Appl. Opt. 46, 5038-5043 (2007)

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  1. W. J. Bates, "A wavefront shearing interferometer," Proc. Phys. Soc. London 59, 940-952 (1947). [CrossRef]
  2. V. Ronchi, "Forty years of history of a grating interferometer," Appl. Opt. 3, 437-450 (1964).
  3. M. Servin, D. Malacara, and J. L. Marroquin, "Wave-front recovery from two orthogonal sheared interferograms," Appl. Opt. 35, 4343-4348 (1996).
  4. D. L. Fried, "Least-square fitting a wave-front distortion estimate to an array of phase difference measurements," J. Opt. Soc. Am. A 67, 370-375 (1977).
  5. R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. A 67, 375-378 (1977).
  6. P. Liang, J. Ding, Z. Jin, C. Guo, and H. Wang, "Two-dimensional wave-front reconstruction from lateral shearing interferograms," Opt. Express 14(2), 625-634 (2006). [CrossRef]
  7. K. R. Freischlad and C. L. Koliopoulos, "Modal estimation of a wave front from difference measurements using the discrete Fourier transform," J. Opt. Soc. Am. A 3, 1852-1861 (1986).
  8. G. Harbers, P. J. Kunst, and G. W. R. Leibbrandt, "Analysis of lateral shearing interferograms by use of Zernike polynomials," Appl. Opt. 35, 6162-6172 (1996).
  9. H. Brug, "Zernike polynomials as a basis for wave-front fitting in lateral shearing interferometry," Appl. Opt. 36, 2788-2790 (1997).
  10. S. Loheide, "Innovative evaluation method for shearing interferograms," Opt. Commun. 141, 254-258 (1997). [CrossRef]
  11. C. Elster and I. Weingärtner, "Solution to the shearing problem," Appl. Opt. 38, 5024-5031 (1999).
  12. C. Elster, "Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears," Appl. Opt. 38, 5024-5031 (1999).
  13. E. T. Whittaker, "On the functions which are represented by the expansion of the interpolation theory," Proc. Royal Soc. Edinburgh , Sec. A 35, 181-194 (1915).
  14. C. E. Shannon, "Communication in the presence of noise," Proc. Inst. Radio Eng. 37(1), 10-21 (1949).
  15. K. Kondo, Y. Ichioka, and T. Suzuki, "Image restoration by Wiener filtering in the presence of signal-dependent noise," Appl. Opt. 16(9), 2554-2558 (1977).
  16. R. S. Caprari, A. S. Goth, and E. K. Moffatt, "Noise and speckle reduction in synthetic aperture radar imagery by nonparametric Wiener filtering," Appl. Opt. 39, 6633-6640 (2000).

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