Scattering of light by a periodic structure in the presence of randomness. V. Detection of successive peaks in a periodic structure

We address the problem of detecting periodic structures hidden behind roughness. We have shown that if r(0) is the coherence length of the scattered radiation, due to the random part of the surface, and A is the wavelength of the periodic part of the surface, then with a matched filtering method that we introduce, and by using simple computations with the intensity data, it is possible to detect the hidden first-order peak even when (r(0)/Lambda) similar to 0.11. Here we advance the method to bring out very weak second-order peaks, which we demonstrate for what we believe is the first time. The unmistakable presence of both the first-and second-order peaks, which have identical shapes as the zeroth-order peak, is strong evidence of the hidden periodicity and serves as a novel method for the detection of weak periodicities hidden behind strong randomness. (c) 2006 Optical Society of America.