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Applied Optics

Applied Optics


  • Vol. 43, Iss. 5 — Feb. 10, 2004
  • pp: 1108–1113

Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform

Alfredo Dubra, Carl Paterson, and Christopher Dainty  »View Author Affiliations

Applied Optics, Vol. 43, Issue 5, pp. 1108-1113 (2004)

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Fast wave-front reconstruction methods are becoming increasingly important, for example, in large astronomical adaptive optics systems and high spatial resolution shear interferometry, where pseudoinverse matrix methods scale poorly with problem size. Wave-front reconstruction from difference measurements can be achieved by use of fast implementations of the discrete Fourier transform (DFT), obtaining performance comparable with that of the pseudoinverse in terms of the noise propagation coefficient. Existing methods that are based on the use of the DFT give exact results (in the absence of noise) only for the particular case in which the shear is a divisor of the number of samples to be reconstructed. We present two alternate solutions for the more general case when the shear is any integer. In the first solution the dimensions of the problem are enlarged, and in the second the problem is subdivided into a set of smaller problems with shear amplitude equal to one. We also show that the retrieved solutions have minimum norm and calculate the noise propagation coefficient for both methods. The proposed algorithms are implemented and timed against pseudoinverse multiplication. The results show a speed increase by a factor of 50 over the pseudoinverse multiplication for a grid with N = 3 × 103 samples.

© 2004 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.4840) Optical design and fabrication : Testing

Original Manuscript: June 27, 2003
Revised Manuscript: November 4, 2003
Published: February 10, 2004

Alfredo Dubra, Carl Paterson, and Christopher Dainty, "Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform," Appl. Opt. 43, 1108-1113 (2004)

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  1. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  2. D. L. Fried, “Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  3. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]
  4. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, LAPACK Users’ Guide, 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999). [CrossRef]
  5. K. R. Freischlad, 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). [CrossRef]
  6. F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991). [CrossRef] [PubMed]
  7. C. Elster, I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16, 2281–2285 (1999). [CrossRef]
  8. C. Elster, I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38, 5024–5031 (1999). [CrossRef]
  9. C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39, 5353–5359 (2000). [CrossRef]
  10. L. A. Poyneer, D. T. Gavel, J. M. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002). [CrossRef]
  11. A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  12. D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, New York, 1998).

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