Abstract

The spectral density functions g(k) of the surface roughness for polished optical surfaces of CaF2, MgF2, and LiF are computed from autocovariance functions, which in turn have been determined from surface profiles obtained by using a microdensitometer analysis of electron micrographs of shadowed surface replicas. The fast-Fourier-transform algorithm and a smoothing procedure have been used to determine the g(k) estimates. It is shown that g(k) is not a Gaussian function throughout, as is usually assumed. Spectral density functions gS(k) of the surface slopes are also computed, and it is shown that results obtained are consistent with those deduced from g(k). Limitations of our method at low spatial frequency are discussed. An analytical model for g(k) is investigated that should be useful in performing theoretical calculations on scattering problems.

© 1983 Optical Society of America

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