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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 13 — May. 1, 2002
  • pp: 2408–2413

Analysis of Seidel aberration by use of the discrete wavelet transform

Rong-Seng Chang, Jin-Yi Sheu, and Ching-Huang Lin  »View Author Affiliations


Applied Optics, Vol. 41, Issue 13, pp. 2408-2413 (2002)
http://dx.doi.org/10.1364/AO.41.002408


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Abstract

Seidel aberration coefficients can be expressed by Zernike coefficients. The least-squares matrix-inversion method of determining Zernike coefficients from a sampled wave front with measurement noise has been found to be numerically unstable. We present a method of estimating the Seidel aberration coefficients by using a two-dimensional discrete wavelet transform. This method is applied to analyze the wave front of an optical system, and we obtain not only more-accurate Seidel aberration coefficients, but we also speed the computation. Three simulated wave fronts are fitted, and simulation results are shown for spherical aberration, coma, astigmatism, and defocus.

© 2002 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets

History
Original Manuscript: November 14, 2001
Published: May 1, 2002

Citation
Rong-Seng Chang, Jin-Yi Sheu, and Ching-Huang Lin, "Analysis of Seidel aberration by use of the discrete wavelet transform," Appl. Opt. 41, 2408-2413 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-13-2408


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References

  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Section 9.2.
  2. F. Zernike, “Beugungstheorie des Schnridenver-Eahrens und Seiner Verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689 (1934). [CrossRef]
  3. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980). [CrossRef] [PubMed]
  4. D. Malacara, J. M. Carpio-Valadéz, J. J. Sánchez-Mondragón, “Wave-front fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29, 672–675 (1990). [CrossRef]
  5. M. Antonin, M. Barlaud, P. Mathieu, I. Daubechies, “Image coding using vector quantization in the wavelet transform domain,” in Proceedings of the International Conference on Acoustical Speech and Signal Processing (IEEE, New York, 1990), pp. 2297–2300. [CrossRef]
  6. D. Philippe, M. Benoit, T. M. Dirk, “Signal adapted multiresolution transform for image coding,” IEEE Trans. Inf. Theory 38, 897–904 (1992). [CrossRef]
  7. R. A. Devore, B. Jawerth, P. J. Lucier, “Image compression through wavelet transform coding,” IEEE Trans. Inf. Theory 38, 719–746 (1992). [CrossRef]
  8. G. Strang, “Wavelets and dilation equations: a brief introduction,” SIAM (Soc. Ind. Appl. Math.) Rev. 31, 614–627 (1989).
  9. S. G. Mallat, “Multifrequency channel decomposition of images and wavelet models,” IEEE Trans. Acoust. Speech Signal Process. 37, 2091–2110 (1989). [CrossRef]
  10. M. Unser, “An improved least squares Laplacian pyramid for image compression,” Signal Process. 27, 187–203 (1992). [CrossRef]
  11. D. Malacara, Optical Shop Testing (Wiley, New York, 1992), Chap. 13, p. 465.
  12. S. Mallat, A Wavelet Tour of Signal Processing (Academic, New York, 1998), Chap. 7, pp. 236–240.
  13. S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989). [CrossRef]
  14. M. Vetterli, J. Kovacevic, Wavelets and Subband Coding (Prentice-Hall, Englewood Cliffs, N.J., 1995).
  15. M. Vetterli, “Multi-dimensional subband coding: some theory and algorithms,” Signal Process. 6, 97–112 (1984). [CrossRef]
  16. D. Esteban, C. Galand, “Applications of quadrature mirror filters to split band voice coding schemes,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (IEEE, New York, 1977), pp. 585–589.
  17. Wavelet Toolbox For Use with MATLAB (The Math Works, Natick, Mass., 1997).

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