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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. 11, Iss. 5 — May. 1, 1994
  • pp: 1589–1598

Reconstruction of photon-limited stellar images by generalized projections with use of the self-cross spectrum

Xiaotian Shi and Rabab K. Ward  »View Author Affiliations


JOSA A, Vol. 11, Issue 5, pp. 1589-1598 (1994)
http://dx.doi.org/10.1364/JOSAA.11.001589


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Abstract

We define self-cross correlation as the cross correlation between an image and a truncated part of it. A new method for finding tight object-support bounds by use of the self-cross-correlation information is addressed. These bounds are used in the generalized-projection method to reconstruct photon-limited atmosphere-degraded images. The iterative Fourier-transform algorithm and the generalized-projection method, with use of the autocorrelation function only, have not been preferred to the Knox–Thompson and the triple-correlation methods for phase-retrieval problems, because the use of the autocorrelation function only usually does not give tight object-support bounds. The tight-object-support-bounds constraint is crucial for the uniqueness of phase retrieval by generalized projections. We find that the information contained in the average self cross correlation gives the required tight object-support bounds. The advantage of our method over the triple-correlation method lies in the speed of computation.

© 1994 Optical Society of America

Citation
Xiaotian Shi and Rabab K. Ward, "Reconstruction of photon-limited stellar images by generalized projections with use of the self-cross spectrum," J. Opt. Soc. Am. A 11, 1589-1598 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-5-1589


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References

  1. A. Labeyrrie, "Attainment of diffraction limited resolution in large telescopes by Fourier speckle patterns in stars' images," Astron. Astrophys. 6, 85–87 (1970).
  2. J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3, 27–29 (1978). [CrossRef] [PubMed]
  3. J. R. Fienup, "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979). [CrossRef]
  4. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  5. A. Levi and H. Stark, "Restoration from phase and magnitude by generalized projections," in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), pp. 277–319.
  6. M. Nieto-Versperinas, R. Navarro, and F. J. Fuentes, "Performance of a simulated annealing algorithm for phase retrieval," J. Opt. Soc. Am. A 5, 30–38 (1988). [CrossRef]
  7. M. J. Perez and M. Nieto-Vesperinas, "Phase retrieval of photon-limited stellar images from information of the power spectrum only," J. Opt. Soc. Am. A 8, 908–917 (1991). [CrossRef]
  8. J. H. Seldin and J. R. Fienup, "Numerical investigation of the uniqueness of phase retrieval," J. Opt. Soc. Am. A 7, 412–427 (1990). [CrossRef]
  9. J. C. Dainty and J. R. Fienup, "Phase retrieval and image reconstruction for astronomy," in Image Recovery: Theory and Application, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.
  10. K. T. Knox and B. J. Thompson, "Recovery of images from atmospherically degraded short-exposure photographs," Astron. J. 193, L45–L48 (1974). [CrossRef]
  11. G. Weigelt and B. Wirnitzer, "Image reconstruction by the speckle-masking method," Opt. Lett. 8, 389–391 (1983). [CrossRef] [PubMed]
  12. A. W. Lohmann, G. P. Weigelt, and B. Wirnitzer, "Speckle masking in astronomy: triple correlation theory and applications," Appl. Opt. 22, 4028–4037 (1983). [CrossRef] [PubMed]
  13. R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  14. H. Takajo and T. Takahashi, "Suppression of the influence of noise in least-squares phase estimation from the phase difference," J. Opt. Soc. Am. A 7, 1153–1162 (1990). [CrossRef]
  15. H. Takajo and T. Takahashi, "Least-squares phase recovery from the bispectrum phase: an algorithm for a two-dimensional object," J. Opt. Soc. Am. A 8, 1038–1047 (1991). [CrossRef]
  16. J. Meng, G. J. M. Aitken, E. K. Hege, and J. S. Morgan, "Triple-correlation subplane reconstruction of photon-address stellar images," J. Opt. Soc. Am. A 7, 1243–1250 (1990). [CrossRef]
  17. J. Sebag, J. Arnaud, G. Lelievre, J. L. Nieto, and E. L. Coarer, "High-resolution imaging using pupil segmentation," J. Opt. Soc. Am. A 7, 1237–1242 (1990). [CrossRef]
  18. X. Shi and R. K. Ward, "Restoration of images degraded by atmospheric turbulence and detection noise," J. Opt. Soc. Am. A 9, 364–370 (1992). [CrossRef]
  19. T. R. Crimmins, J. R. Fienup, and B. J. Thelen, "Improved bounds on object support from autocorrelation support and application to phase retrieval," J. Opt. Soc. Am. A 7, 3–13 (1990). [CrossRef]
  20. B. J. Brames, "Efficient method of support reduction," Opt. Commun. 64, 333–337 (1990). [CrossRef]
  21. J. R. Fienup, T. R. Crimmins, and W. Holsztynski, "Reconstruction of the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 72, 610–624 (1982). [CrossRef]
  22. E. K. Hege, "Notes on noise calibration of speckle imagery," in Diffraction-Limited Imaging with Very Large Telescopes, D. M. Alloin and J. M. Mariotti, eds. (Kluwer, Norwell, Mass., 1989), pp. 113–124. [CrossRef]
  23. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 9.
  24. B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., 1986), Chap. 8.
  25. A. V. Oppenheim and J. S. Lim, "The importance of phase in signals," Proc. IEEE 69, 529–541 (1981). [CrossRef]
  26. R. H. T. Bates and F. W. Cady, "Toward true imaging by wideband speckle interferometry," Opt. Commun. 32, 365 (1980). [CrossRef]
  27. M. J. Northcott, G. R. Ayers, and J. C. Dainty, "Algorithms for image reconstruction from photon-limited data using the triple correlation," J. Opt. Soc. Am. A 5, 986–992 (1988) [CrossRef]

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