On the scattering of light by a periodic structure in the presence of randomness II. On the detection of weak periodicities

Abstract

Light scattering by a rough grating is examined in the context of detecting a hidden periodic part. We make use of the fact that differentiated signals enhance the structures contained in the signal so that these derivatives help to obtain a priori ideas about the structure of the surface from which details about the surface profile can be worked out. The suggested numerical methods to extract the statistical properties of the surface and of the periodic grating involve simple algebraic operations and are similar to 'matched filtering' in signal detection problems. Numerical illustrations are provided to elucidate the method and to explain its usefulness. The suggested method, although simple, is seen to be an improvement vis--vis existing notions about detectability of periodic structures hidden behind a disorder