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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 67, Iss. 11 — Nov. 1, 1977
  • pp: 1583–1587

Transfer functions, correlation scales, and phase retrieval in speckle interferometry

Douglas P. Karo and Arthur M. Schneiderman  »View Author Affiliations

JOSA, Vol. 67, Issue 11, pp. 1583-1587 (1977)

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Properties of speckle imaging lens-atmosphere transfer functions that impact phase retrieval and subsequent image reconstruction have been measured under realistic conditions using bright stellar sources. These measurements generally support assumptions made by those who have proposed phase retrieval algorithms and tested them on simulated data.

© 1977 Optical Society of America

Douglas P. Karo and Arthur M. Schneiderman , "Transfer functions, correlation scales, and phase retrieval in speckle interferometry," J. Opt. Soc. Am. 67, 1583-1587 (1977)

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  1. J. Texereau, "Refiguring the 82-inch McDonald reflector's optics," Sky Telescope 28, 345–348 (1964).
  2. S. P. Worden, C. R. Lynds, and J. W. Harvey, "Reconstructed images of Alpha Orionis using stellar speckle interferometry," J. Opt. Soc. Am. 66, 1234–1246 (1976).
  3. A. Labeyrie, "Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images," Astron. Astrophys. 6, 85–87 (1970).
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  8. K. T. Knox, "Image retrieval from astronomical speckle patterns," J. Opt. Soc. Am. 66, 1236–39 (1976).
  9. M. Miller (private communication), see Ref. 17 for details.
  10. J. W. Sherman, "A posteriori restoration of atmospherically degraded images using multiframe imagery," in Image Processing, Proceedings of the S.P.I.E. 74, 249–258 (1976).
  11. D. Korff, "Analysis of a method for obtaining near-diffraction-limited information in the presence of atmospheric turbulence," J. Opt. Soc. Am. 63, 971–980 (1973).
  12. D. P. Karo and A. M. Schneiderman, "Speckle interferometry lens-atmosphere MTF measurements," J. Opt. Soc. Am. 66, 1252–1256 (1976).
  13. Using C(Δ) = exp[−l ½ D(Δ)], where D(Δ) is the wave structure function given by D(Δ) =6.88(Δ/r0)5/3. and this approach to defining a correlation scale produces the familiar incident wave correlation scale ro. Although in common use, this C(Δ) can not be correct since it fails to have the correct (parabolic) form for small Δ.
  14. The MTF corrected for the known low-frequency telescope MTF does follow the Fried theory out to nearly the seeinglimited spatial frequency. We weight the lowest-frequency points most strongly in determining the D/r0 value which best fits the short-exposure theory to the data.
  15. D. L. Fried, "Optical resolution through a randomly inhomogeneous medium for very long and very short exposures," J. Opt. Soc. Am. 56, 1372–79 (1966).
  16. D. Korff, G. Dryden, and M. G. Miller, "Information retrieval from atmospheric induced speckle patterns," Optics Commun. 5, 187–192 (1972).
  17. D. P. Karo and A. M. Schneiderman, "Image reconstruction in speckle interferometry," Imaging in Astronomy Technical Digest, ThC4-1, 3 OSA Topical Meeting, June 18–21, 1975, Cambridge, Massachusetts.

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