OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 31 — Nov. 1, 1996
  • pp: 6162–6172

Analysis of lateral shearing interferograms by use of Zernike polynomials

G. Harbers, P. J. Kunst, and G. W. R. Leibbrandt  »View Author Affiliations


Applied Optics, Vol. 35, Issue 31, pp. 6162-6172 (1996)
http://dx.doi.org/10.1364/AO.35.006162


View Full Text Article

Enhanced HTML    Acrobat PDF (816 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A modal phase-reconstruction method for wave-front analysis in lateral shearing interferometry is presented. Pseudo-Zernike polynomial functions describe the differential wave fronts and are related to a Zernike polynomial description of the original wave front. We show that this reconstruction is robust for shear ratios in the range 0.15–0.50. The error propagation properties of this differential Zernike polynomial matrix-inversion method are discussed on the basis of both analysis and simulation. It is concluded that the method allows wave-front analysis with an absolute inaccuracy of 2 mλ rms for diffraction-limited wave fronts and with 1% relative inaccuracy for more strongly aberrated wave fronts.

© 1996 Optical Society of America

History
Original Manuscript: October 23, 1995
Revised Manuscript: April 15, 1996
Published: November 1, 1996

Citation
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)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-31-6162


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. V. R. K. Murty, “The use of a single plane parallel plate as a lateral shearing interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964). [CrossRef]
  2. P. Hariharan, W. H. Steel, J. C. Wyant, “Double grating interferometer with variable lateral shear,” Opt. Commun. 11, 317–320 (1974). [CrossRef]
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  4. G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by the use of a double-grating lateral shearing interferometer,” Appl. Opt. 35, 6151–6161 (1996). [CrossRef] [PubMed]
  5. H. Sumita, “Orthonormal expansion of the aberration difference function and its application to image evaluation,” Jpn. J. Appl. Phys. 8, 1027–1036 (1969). [CrossRef]
  6. M. P. Rimmer, J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975). [PubMed]
  7. 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]
  8. R. H. Hudgin, “Wave-front reconstruction for compensating imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  9. R. J. Noll, “Phase estimates from slope-type wave-front sensors,” J. Opt. Soc. Am. 68, 139–140 (1978). [CrossRef]
  10. R. Cubalchini, “Modal wave-front estimation from phase derivative measurements,” J. Opt. Soc. Am. 69, 972–977 (1979). [CrossRef]
  11. B. R. Hunt, “Matrix formulation of the reconstruction of phase values from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979). [CrossRef]
  12. R. L. Frost, C. K. Rushforth, B. S. Baxter, “Fast FFT-based algorithm for phase estimation in speckle imaging,” Appl. Opt. 18, 2056–2061 (1979). [CrossRef] [PubMed]
  13. J. Herrmann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980). [CrossRef]
  14. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]
  15. J. Herrmann, “Cross coupling and aliasing in modal wavefront estimation,” J. Opt. Soc. Am. 71, 989–992 (1981). [CrossRef]
  16. D. Korwan, “Lateral shearing interferogram analysis,” in Precision Surface Metrology, J. C. Wyant, ed., Proc. SPIE429, 194–198 (1983).
  17. 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]
  18. F. Zernike, “Beugungstheorie des Schneidenverfahrans und Seiner Verbesserten Form, der Phasekontrastmethode,” Physica 1, 689–704 (1934). [CrossRef]
  19. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  20. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), pp. 470–472.
  21. M. P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13, 623–629 (1974). [CrossRef] [PubMed]
  22. W. H. Press, B. P. Flannery, S. A. Teukolsky, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1986).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited