An investigation of light scattering from flat periodic rough surfaces for surface roughness estimation

Abstract

An investigation was made into the scattering of light from flat periodic rough surfaces where the roughness amplitude is much greater than the illumination wavelength. A special scattering geometry is adopted in which the plane of incidence was parallel to the lay and grazing angles were small. The Beckmann's scattering model was applied to calculate the scattering intensity, and numerical solutions were obtained for sinusoidal rough surface profiles. The results were used to determine the influence of the surface roughness amplitude and surface spatial wavelength on the scattering pattern. It was observed that for any given scattering order, the scattered intensity oscillated as the angle of incidence increased. The degree of oscillation was found to be directly related to the surface roughness amplitude because higher roughness amplitude results in a higher oscillation frequency. This characteristic was subsequently confirmed by the experimental results. Scattering intensity distributions were also measured and they were shown to have similar trends as predicted for the low scattering orders. By adopting the results from this investigation, a new method of surface roughness estimation can be developed that would cover the roughness range of normal machined surfaces. Because it is based on the intensity variation frequency rather than on absolute scattering intensity values, the method is independent of the surface spatial wavelength and material's optical properties.