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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 9 — Sep. 1, 2012
  • pp: 2038–2047

Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry

Fengzhao Dai, Feng Tang, Xiangzhao Wang, and Osami Sasaki  »View Author Affiliations


JOSA A, Vol. 29, Issue 9, pp. 2038-2047 (2012)
http://dx.doi.org/10.1364/JOSAA.29.002038


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Abstract

A new zonal wavefront reconstruction method for lateral shearing interferometry was presented. The proposed algorithm allows shear amounts equal to arbitrary integral multiple of the sample intervals. High spatial resolution reconstruction is achieved with only two difference wavefronts measured in orthogonal shear directions. The presented algorithm was generalized to be applicable for general aperture shape by using zero padding and Gerchberg-type iterative methods. The capability of the presented algorithm was demonstrated by some numerical examples. Also, the reconstruction error was analyzed theoretically and numerically.

© 2012 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: May 4, 2012
Manuscript Accepted: July 19, 2012
Published: August 31, 2012

Citation
Fengzhao Dai, Feng Tang, Xiangzhao Wang, and Osami Sasaki, "Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry," J. Opt. Soc. Am. A 29, 2038-2047 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-9-2038


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References

  1. D. Malacara, Optical Shop Testing, 3rd ed. (CRC Press, 2007).
  2. J. B. Saunders, “Measurement of wave fronts without a reference standard. Part 1. The wave-front-shearing interferometer,” J. Res. Natl. Bur. Stand. Sect. B 65, 239–244 (1961).
  3. M. P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974). [CrossRef]
  4. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  5. 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]
  6. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]
  7. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979). [CrossRef]
  8. J. Herrmann, “Least-square wave-front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980). [CrossRef]
  9. D. C. Ghiglia and L. A. Romero, “Direct phase estimation from phase differences using fast elliptic partial differential equation solvers,” Opt. Lett. 14, 1107–1109 (1989). [CrossRef]
  10. X. Liu, Y. Gao, and M. Chang, “A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry,” J. Opt. A Pure Appl. Opt. 11, 045702 (2009). [CrossRef]
  11. H. Takajo and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988). [CrossRef]
  12. H. Takajo and T. Takahashi, “Noniterative method for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 1818–1827 (1988). [CrossRef]
  13. W. Zou and Z. Zhang, “Generalized wave-front reconstruction algorithm applied in a Shack–Hartmann test,” Appl. Opt. 39, 250–268 (2000). [CrossRef]
  14. W. Zou and J. P. Rolland, “Iterative zonal wave-front estimation algorithm for optical testing with generalshaped pupils,” J. Opt. Soc. Am. A 22, 938–951 (2005). [CrossRef]
  15. C. Elster and I. Weingärtner, “Solution to the shearing problem,” Appl. Opt. 38, 5024–5031 (1999). [CrossRef]
  16. C. Elster and I. Weingärtner, “Exact wave-front reconstruction from two lateral shearing interferograms,” J. Opt. Soc. Am. A 16, 2281–2285 (1999). [CrossRef]
  17. C. Elster, “Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears,” Appl. Opt. 39, 5353–5359 (2000). [CrossRef]
  18. Z. Yin, “Exact wavefront recovery with tilt from lateral shear interferograms,” Appl. Opt. 48, 2760–2766 (2009). [CrossRef]
  19. T. Nomura, S. Okuda, K. Kamiya, H. Tashiro, and K. Yoshikawa, “Improved Saunders method for the analysis of lateral shearing interferograms,” Appl. Opt. 41, 1954–1961 (2002). [CrossRef]
  20. R. J. Noll, “Phase estimates from slope-type wave-front sensors,” J. Opt. Soc. Am. 68, 139–140 (1978). [CrossRef]
  21. W. Zou and J. P. Rolland, “Quantifications of error propagation in slope-based wavefront estimations,” J. Opt. Soc. Am. A 23, 2629–2638 (2006). [CrossRef]
  22. G.-m. Dai, Wavefront Optics for Vision Correction (SPIE, 2008).
  23. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  24. C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673(1987). [CrossRef]
  25. F. Roddier and C. Roddier, “Wave-front reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327(1991). [CrossRef]
  26. J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology, Vol. XI, Applied Optics and Optical Engineering Series (Academic, 1992), p. 28.

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