Abstract

Polychromatic speckle in the output plane of an achromatic-Fourier-transform system is analyzed. The degree of speckle correlation is calculated and is found to factorize into spectral and spatial parts. Under conditions for sufficiently fine and rough phase modulation of the complex field amplitude in the object plane, the polychromatic intensity in a paraxial region of the transform plane is shown to be spatially wide-sense stationary and approximately ergodic. For normally distributed height statistics, the intensity is approximately spectrally stationary as well. Our calculations indicate that achromatic-transform-plane speckle should be useful for measuring surface roughness and that an achromatic-transform system may be useful in extending the usable stellar bandwidth in stellar speckle interferometry.

© 1983 Optical Society of America

Achromatic system for far-field diffraction with broadband illumination

R. Ferriere and J. P. Goedgebuer
Appl. Opt. 22(10) 1540-1545 (1983)

Diffraction theory for an achromatic Fourier transformation

G. M. Morris
Appl. Opt. 20(11) 2017-2025 (1981)

Achromatic Fourier transform holography

G. D. Collins
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Theory of speckle dependence on surface roughness*

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J. Opt. Soc. Am. 66(11) 1204-1210 (1976)

Phases of complex functions from the amplitudes of the functions and the amplitudes of the Fourier and Mellin transforms

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