Light scattering from periodic rough cylindrical surfaces

Light scattering from rough cylindrical surfaces at near-zero grazing angle is investigated by applying Beckmann's scalar scattering model to the surface's tangential planes and superimposing the individual intensities to form the scattering pattern. A solution for sinusoidal surface-roughness profiles is derived and numerical results are obtained to study the influences of surface wavelength and amplitude on the far-field scattering pattern. The spatial and intensity distributions of the fringe (across and along thefringe) are found to be related to the surface wavelength and amplitude, respectively. Scattering intensity-distribution measurements are carried out on turned surfaces, and the results obtained are in agreement with the model's prediction. As a direct application, a technique to estimate the surface broughness of turned surfaces is proposed. This technique offers an absolute measurement in which the roughness amplitude and wavelength of the surface are defined relative to the illumination wavel gth.