A relation from vector scattering theory has been used to predict the angular distribution of scattered light from optical surfaces as a function of the wavelength, optical constants of the material, and spectral density function. For calculations of one-dimensional (two-dimensional) scattering, the spectral density function of the surface roughness is obtained from the Fourier transform (Hankel transform) of the autocovariance function, which in turn is determined from surface-profile data. Measured statistics presented for various types of optical surfaces indicate that there are three basic components of surface structure: long-range waviness, short-range random roughness, and periodicity; one or more of which may be present on a given surface. Averaged and unaveraged surface-profile data for the same surface are shown to be consistent. Experimental data are presented that yield an exponential autocovariance function, and give a reasonably good fit to a Poisson distribution of zero crossings. Finally, angular scattering values calculated using measured surface statistics with vector scattering theory are compared to scattering values measured on the same surface. The shapes of the measured and calculated curves are similar, but the magnitudes are not. However, the rms surface roughnesses calculated from total integrated scattering measurements are in excellent agreement with values measured directly on these same surfaces.
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