A Consistent Theory Of Scatter From Optical Surfaces

Alan W Greynolds

doi:10.1117/12.948085

5 April 1989 A Consistent Theory Of Scatter From Optical Surfaces

Alan W Greynolds

Proceedings Volume 0967, Stray Light and Contamination in Optical Systems; (1989) https://doi.org/10.1117/12.948085
Event: 32nd Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1988, San Diego, CA, United States

Abstract

A mathematically rigorous theory of surface scatter that can explain the descrepancies between sur-face statistics determined directly from profiler measurements and those predicted indirectly from scatter measurements is presented. The theory is based on the assumption that the Spectral Density Function (SDF) of the random height variations is the fundamental invariant of the surface and not its Fourier transform, the autocorrelation function. The autocorrelation function and RMS roughness are then calculated from a finite Fourier integral operation whose limits of integration are determined by the measurement bandwidth, and thus, they depend not only on the intrinsic surface statistics but also on the measurement method. A simple form for the SDF that seems to match optical surfaces quite well is assumed. It encompasses surfaces with a definite autocorrelation length and those that have none at all, i.e. fractal surfaces. For the latter, the theory closely resembles that of 1/f noise in electrical systems where the RMS noise (equivalent to the RMS surface roughness) increases with signal bandwidth (equivalent to the surface or incident beam size). An extensive numerical calculation is performed to show that for smooth optical-like surfaces with RMS roughnesses much less than the wavelength, the scatter becomes directly proportional to the SDF if the effective autocorrelation length is set approximately to the surface or incident beam size. This formulation allows one to easily extra-polate the scatter component right down to the specular beam from measurements taken at relatively large angles.

Citation Download Citation

Alan W Greynolds "A Consistent Theory Of Scatter From Optical Surfaces", Proc. SPIE 0967, Stray Light and Contamination in Optical Systems, (5 April 1989); https://doi.org/10.1117/12.948085

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