Relationship between Surface Scattering and Microtopographic Features

Abstract

In the smooth-surface limit, the angular distribution of the light scattered from a surface maps the power spectral density of its residual surface roughness. This result is essentially independent of the scattering theory used and the statistical properties of the surface roughness. The power spectral densities of engineering surfaces are generally broad and increase with increasing spatial wavelength. As a result, practical surface finish parameters are not intrinsic properties of the surface, but depend, with varying degrees of sensitivity, on the bandwidth limits inherent in their measurement or dictated by their application. These issues are discussed with reference to two classes of finish parameters: those related to the central moments of the scattering spectrum, and those related to the coefficients in the expansion of the shape of the spectrum in inverse powers of the scattering angle. The significance of "1/02" scattering in this context is emphasized. A shot model of surface roughness is then introduced to gain further insight into the relationship between scattering and surface features. In this model inverse power terms are related to "edge" scattering effects from critical points in various types of elemental microdefects. The relationship between this view and electronic noise is pointed out; in particular, the correspondence between "1/62" scattering and "1 /f" or flicker -noise phenomena.

Cross-check of different techniques for two-dimensional power spectral density measurements of x-ray optics

“…One of the most insightful approaches to these calculations is based on the two-dimensional (2D) power spectral density (PSD) distribution of the surface height, allowing for the evaluation of three-dimensional distributions of X-rays scattered by the optics. 2,3 A comprehensive discussion of the importance of characterization of highly finished optical surfaces via the PSD distribution can be found in Refs. 4 …”

Float-polishing process and analysis of float-polished quartz

“…The above equation can be integrated to give +c (8) where C is a constant of integration and the approximation…”

“….. form of the surface; it contains information of the frequency, amplitude, and phase of each harmonic. 8 Optical scatter measurements of the two polished surfaces of a quartz sample are shown in Fig. 6.…”

Grazing-incidence ellipsoidal reflector for longitudinally pumping short-wavelength lasers

“…For this low-resolution, nonimaging application, the surface accuracy and finish requirements of the optic appear to be quite moderate. For example, for c = 50 cm and a focal spot diameter of 4 mm, the surface slope error can be as large as 2 mr and scattering will not be important unless surface roughness exceeds -2-nm rms amplitude at spatial frequencies above 0.05 grm-K. 10 These requirements can be met by standard diamond-turned surfaces with light polishing." Debris ejected from the target, however, can degrade the quality of the surface in time.…”