Scattering of light by a periodic structure in the presence of randomness IV. Limit of detection by curve fitting

In the context of scattering of light, we determine the extent of randomness within which a hidden periodic part can still be detected. The detection is carried out using a technique called the extended matched filtering, first introduced by us in this context. The earlier prediction, before our technique was introduced, had placed the limit of detection, by intensity measurements alone, at (r ₀/Λ) ∼ 0.33, where r₀ is the coherence length of light for scattering by the rough part of the surface and Λ is the wavelength of the periodic part of the surface. In our earlier works we have shown that by intensity measurements alone, the limit of detection can be taken to a much lower value of (r ₀/Λ), when the extended matched filtering method is employed. In this paper we follow the extended matched filtering method, and try to reach the lowest possible value of detection in (r ₀/Λ) by fitting the data to a polynomial. It is concluded by our numerical work that the lowest possible limit for detection from intensity measurements alone is (r ₀/Λ) = 0.11.