Speckle in achromatic-Fourier-transform systems

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.

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