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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

  • Vol. 2, Iss. 5 — May. 1, 1985
  • pp: 635–643

Image construction through diffraction-limited high-contrast imaging systems: an iterative approach

Karen M. Nashold and Bahaa E. A. Saleh  »View Author Affiliations


JOSA A, Vol. 2, Issue 5, pp. 635-643 (1985)
http://dx.doi.org/10.1364/JOSAA.2.000635


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Abstract

It is desired to preprocess an input image so that, when it is distorted by an imaging system, a prescribed output image is produced. The system of interest is a linear, shift-invariant, band-limited system followed by a hard limiter. Such a system is found, for example, in microphotography, when a camera that is band limited by diffraction effects is used to print on very-high-contrast film. In this paper, an iterative solution that employs alternating projections is presented. Two variations of the procedure, which is similar to the Gerchberg–Papoulis algorithm, are applied to several examples having different space–bandwidth products. Also, a method of overrelaxing the projections to improve convergence is studied.

© 1985 Optical Society of America

History
Original Manuscript: July 24, 1984
Manuscript Accepted: January 7, 1985
Published: May 1, 1985

Citation
Karen M. Nashold and Bahaa E. A. Saleh, "Image construction through diffraction-limited high-contrast imaging systems: an iterative approach," J. Opt. Soc. Am. A 2, 635-643 (1985)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-5-635


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References

  1. Eastman Kodak Company, Techniques of Microphotography, Pub. P-52 (Eastman Kodak Company, Rochester, N.Y., 1967).
  2. B. E. A. Saleh, S. I. Sayegh, “Reduction of errors of microphotographic reproductions by optimal corrections of original masks,” Opt. Eng. 20, 781–784 (1981). [CrossRef]
  3. S. I. Sayegh, B. E. A. Saleh, “Image design: generation of a prescribed image at the output of a band-limited system,”IEEE Trans. Pattern Recognition Mach. Intell. PAMI-5, 441–445 (1983). [CrossRef]
  4. S. I. Sayegh, B. E. A. Saleh, K. M. Nashold, “Image design: generation of a prescribed image through a diffraction-limited system with high-contrast recording,” IEEE Trans. Acoust. Speech Signal Process. (to be published).
  5. A. Papoulis, “A new algorithm in spectral analysis and bandlimited extrapolation,”IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975). [CrossRef]
  6. R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]
  7. D. C. Youla, “Generalized image restoration by the method of alternating orthogonal projections,”IEEE Trans. Circuits Syst. CAS-25, 695–702 (1978).
  8. D. C. Youla, H. Webb, “Image restoration by the method of convex projections: Part 1—Theory,”IEEE Trans. Med. Imaging MI-1, 81–94 (1982). [CrossRef]
  9. Z. Opial, “Weak convergence of the sequence of successive approximations for nonexpansive mappings,” Bull. Am. Math. Soc. 73, 591–597 (1967). [CrossRef]
  10. S. I. Sayegh, Department of Electrical Engineering and Systems Science, Michigan State University, East Lansing, Michigan 48824 (personal communication).

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