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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 62, Iss. 10 — Oct. 1, 1972
  • pp: 1202–1210

Restoring with Maximum Entropy, II: Superresolution of Photographs of Diffraction-Blurred Impulses

B. ROY FRIEDEN and J. J. BURKE  »View Author Affiliations


JOSA, Vol. 62, Issue 10, pp. 1202-1210 (1972)
http://dx.doi.org/10.1364/JOSA.62.001202


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Abstract

Can photographic images, e.g., corresponding to star clusters, be superresolved? Or alternatively, can already good (diffraction-limited) images be improved by restoring methods? To test this hypothesis, objects have been prepared that can be resolved only if the bandwidth in the restoration exceeds that of the image data. The objects are double and triple slits with separations equal to fractions (0.33, 0.50, or 0.65) of Rayleigh’s resolution distance. These are incoherently imaged in quasimonochromatic light by a slit-aperture optical system, and developed as photographs. The amount of diffraction blur is made comparable with the grain-limited resolution distance, since this is the usual situation for an efficient optics-film design. The photos are scanned across the slit directions, digitized, and computer restored by the method of maximum entropy. Results indicate that two object slits can be well resolved when separated by one-half of Rayleigh’s resolution distance, and that three object slits are resolvable subject to a definite hierarchy of confidence: Most accurately restored is the number of object impulses, next are their positions, and least accurate is information on their amplitudes.

Citation
B. ROY FRIEDEN and J. J. BURKE, "Restoring with Maximum Entropy, II: Superresolution of Photographs of Diffraction-Blurred Impulses," J. Opt. Soc. Am. 62, 1202-1210 (1972)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-62-10-1202


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References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 62, 96, 115.
  2. J. L. Harris, J. Opt. Soc. Am. 54, 931 (1964).
  3. C. W. Barnes, J. Opt. Soc. Am. 56, 575 (1966).
  4. B. R. Frieden, J. Opt. Soc. Am. 57, 1013 (1967).
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  6. Y. Biraud, Astron. Astrophys. 1, 124 (1969).
  7. P. A. Jansson, R. H. Hunt, and E. K. Plyler, J. Opt. Soc. Am. 60, 596 (1970).
  8. B. R. Frieden, J. Opt. Soc. Am. 62, 511 (1972). Eqs. (17a)-(17d) comprise the restoring algorithm to be used.
  9. J. P. Burg (private communication).
  10. D. P. MacAdam, J. Opt. Soc. Am. 60, 1617 (1970).
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  12. R. Nathan, J. Opt. Soc. Am. 57, 578A (1967).
  13. C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967).

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