Wavelength and angular dependence of light scattering from beryllium: comparison of theory and experiment

The purpose of this study was (1) to measure angle-resolved scattering (ARS) and the wavelength dependence of scattering from polished and sputtered beryllium, (2) to measure surface-roughness parameters by profilometry, (3) to calculate the power spectral density (PSD) of the surface roughness and use it with ARS theory to compare with ARS measurements, and (4) to investigate a dual-source scattering theory and compare calculations from the theory with measured ARS. The wavelengths considered here were 0.633, 1.06, and 10.6 µm, the angle of incidence was 60°, and s and p polarization of the incident and scattered radiation were taken into account both in the theory and in the experiments.Two types of theoretical comparison were attempted. First, two-dimensional PSD functions were calculated from one-dimensional, mechanical-stylus-profile data, and these data were used in first-order roughness ARS theory to compare with ARS measurements. The calculated ARS curves were much too low at some wavelengths and showe incorrect wavelength scaling. Second, a dual-source (surfaceroughness and dielectric inhomogeneity) ARS theory was used. In this model the surface-roughness PSD functions calculated from surface-profile data were used, and reasonable values for parameters characterizing the dielectric inhomogeneities were used in an analytic PSD function. This dual-source ARS theory can predict a significantly different angle and wavelength dependence of ARS than that predicted by roughness-only ARS theory. In contrast to ARS predicted by surface roughness alone, it was found that the dual-source theory was able to provide good agreement with measured ARS in angular and wavelength dependence. It is concluded that, for the two beryllium samples studied here, scattering caused by spatial variations in the near-surface dielectric response (variations in reflectance) is a significant and sometimes dominant source of scattering, especially at a 10.6-µim wavelength.