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An extended matched filter approach for the detection of hidden periodicities smeared by roughness

From the known result that a periodic grating with a built-in roughness produces a Raman-Nath-type intensity profile, in which the peaks are smeared out by randomness, we show that an 'extended matched filtering method', developed by us, can reveal the hidden periodicities. The present method first anticipates the central peak, i.e. the n = 0 term, from a Raman-Nath intensity expression. From this residual of the intensity, the n = ′ 1 peaks are identified, both in terms of their location along v x as also in terms of their amplitude. We demonstrate the effectiveness of this method by examples in which the hidden periodicities are undetectable by conventional methods and show the region of its validity.