Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness

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Abstract
The angular dependence and the polarization of light scattered by a small particle a distance d inside and outside a reflecting surface is calculated in the Rayleigh limit. This calculation yields expressions for the polarized bidirectional reflectance distribution function matrices for in-plane and out-of-plane scattering. The results are compared with those obtained from microroughness-induced scattering. For the p-in/p-out configuration with oblique incidence, there exist out-of-plane angles for which scattering that is due to one of the mechanisms vanishes, whereas that from the others does not. By exploiting this knowledge, we can make improvements in the detection of small particles or subsurface defects. It is also shown that one must take care when differentiating subsurface-defect-induced scattering from microroughness-induced scattering using in-plane scattering and wavelength scaling laws.