Abstract

The performance of image-plane sharpness criteria for purposes of image reconstruction is discussed in terms of a probabilistic model. This model provides a general framework for understanding sharpness criteria and predicts that the accuracy of the phase compensation process is proportional to the number of discrete phase correcting elements.

© 1978 Optical Society of America

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References

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  1. R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded images through sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [Crossref]
  2. F. J. Dyson, “Photon noise and atmospheric noise in active optical systems,” J. Opt. Soc. Am. 65, 551–558 (1975).
    [Crossref]
  3. J. P. Hamaker, J. D. O’Sullivan, and J. E. Noordam, “Image sharpness, Fourier optics and redundant-spacing interferometry,” J. Opt. Soc. Am. 67, 1122 (1977).
    [Crossref]
  4. T. M. Brown, “Reconstruction of turbulence-degraded images using nonredundant aperture arrays,” J. Opt. Soc. Am. 68, 883–889 (1978) (preceding paper).
    [Crossref]

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1974 (1)

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Figures (2)

FIG. 1
FIG. 1

Schematic two-dimensional projection of the level surfaces of the sharpness criterion P, as a function of two arbitrary ϕij. R0 is the point corresponding to the phases in the original, undistorted image, L is the level surface of P passing through R0, and S is the surface containing all possible distorted images.

FIG. 2
FIG. 2

Geometry for comparing the phases for the sharpest and undistorted images. The radius of curvature of L at R0 is denoted by r, and η is the angle between the normal to L and a vector lying within S.

Equations (1)

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ϕ i j = θ i j + ψ i - ψ j ,