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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 29 — Oct. 10, 2000
  • pp: 5353–5359

Exact Two-Dimensional Wave-Front Reconstruction From Lateral Shearing Interferograms With Large Shears

Clemens Elster  »View Author Affiliations


Applied Optics, Vol. 39, Issue 29, pp. 5353-5359 (2000)
http://dx.doi.org/10.1364/AO.39.005353


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Abstract

A method is proposed for exact discrete reconstruction of a two-dimensional wave front from four suitably designed lateral shearing experiments. The method reconstructs any wave front at evaluation points of a circular aperture exactly up to an arbitrary constant for noiseless data, and it shows excellent stability properties in the case of noisy data. Application of large shears is allowed, and high resolution of the reconstructed wave front can be achieved. Results of numerical experiments are presented that demonstrate the capability of the method.

© 2000 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Citation
Clemens Elster, "Exact Two-Dimensional Wave-Front Reconstruction From Lateral Shearing Interferograms With Large Shears," Appl. Opt. 39, 5353-5359 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-29-5353


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References

  1. V. Ronchi, “Le frangi die combazione nello studio delle superficie e dei sistemi ottici,” Riv. Ottica Mecc. Precis. 2, 9–35 (1923).
  2. W. J. Bates, “A wavefront shearing interferometer,” Proc. Phys. Soc. 59, 940–952 (1947).
  3. V. Ronchi, “Forty years of history of a grating interferometer,” Appl. Opt. 3, 437–450 (1964).
  4. H. Schreiber and J. Schwider, “Lateral shearing interferometer based on two Ronchi gratings in series,” Appl. Opt. 36, 5321–5324 (1997).
  5. M. P. Rimmer and J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975).
  6. 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).
  7. G. Harbers, P. J. Kunst, G. W. R. Leibbrandt, “Analysis of lateral shearing interferograms by use of Zernike polynomials,” Appl. Opt. 35, 6162–6172 (1996).
  8. M. Servin, D. Malacara, and J. L. Marroquin, “Wave-front recovery from two orthogonal sheared interferograms,” Appl. Opt. 35, 4343–4348 (1996).
  9. M. P. Rimmer, “Method for evaluating lateral shearing interferometer,” Appl. Opt. 13, 623–629 (1974).
  10. D. L. Fried, “Least-squares fitting a wavefront distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977).
  11. R. H. Hudgin, “Wavefront reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
  12. R. J. Noll, “Phase estimates from slope-type wavefront sensors,” J. Opt. Soc. Am. 68, 139–140 (1978).
  13. R. L. Frost, C. K. Rushforth, and B. S. Baxter, “Fast FFT-based algorithm for phase estimation in speckle imaging,” Appl. Opt. 18, 2056–2061 (1979).
  14. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979).
  15. W. H. Southwell, “Wavefront estimation from wavefront slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
  16. K. Freischlad, “Sensitivity of heterodyne shearing interferometers,” Appl. Opt. 26, 4053–4054 (1987).
  17. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988).
  18. D. C. Ghiglia and L. A. Romero, “Direct phase estimation from phase differences using elliptic partial differential equation solvers,” Opt. Lett. 14, 1107–1109 (1989).
  19. F. Roddier and C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991).
  20. X. Tian, M. Itoh, and T. Yatagai, “Simple algorithm for large-grid phase reconstruction of lateral-shearing interferometry,” Appl. Opt. 34, 7213–7220 (1995).
  21. G. W. R. Leibbrandt, G. Harbers, and P. J. Kunst, “Wavefront analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 35, 6151–6161 (1996).
  22. H. von Brug, “Zernike polynomials as a basis for wavefront fitting in lateral shearing interferometry,” Appl. Opt. 36, 2788–2790 (1997).
  23. S. Loheide and I. Weingärtner, “New procedure for wavefront reconstruction,” Optik 108, 53–62 (1998).
  24. C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. 16, 2281–2285 (1999).
  25. C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38, 5024–5031 (1999).
  26. C. Elster, “Recovering wavefronts from difference measurements in lateral shearing interferometry,” J. Comp. Appl. Math. 110, 177–180 (1999).
  27. C. Elster, “Evaluation of lateral shearing interferograms,” in Advanced Mathematical Tools in Metrology IV, P. Ciarlini, ed. (World Scientific, Singapore, 2000), pp. 76–87.
  28. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic, London, 1981).
  29. IMSL Math/library (Visual Numerics Inc., Houston, Tex., 1994).

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