Scattering of Light by a Periodic Structure in the Presence of Randomness. III. Limit of the Extended Matched Filtering Method for the Detection of Weak Periodicities

Abstract

It is known that, for scattering of light by a rough grating, the periodically occurring intensity maxima that are characteristic of the periodic part of the scattering medium get smeared off and hence become undetectable if coherence length r0 of the randomness is much smaller than wavelength Λ of the periodic part of the grating. It is also known that by conventional intensity measurements the detectability region is r0/Λ ≥ 0.33, which can be extended to lower regions by intensity interferometry. It is established here that an extended matched filtering method enables one to detect the periodic part of the medium, even in the presence of higher roughness (i.e., lower r0), and the limit is placed at r0/Λ ≈ 0.11 by our numerical experiments.