S Chatterjee
Articles written in Pramana – Journal of Physics
Volume 65 Issue 3 September 2005 pp 413-424
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 (
Volume 70 Issue 5 May 2008 pp 875-886 Research Articles
Detection of periodic structures, hidden in random surfaces has been addressed by us for some time and the `extended matched filter' method, developed by us, has been shown to be effective in detecting the hidden periodic part from the light scattering data in circumstances where conventional data analysis methods cannot reveal the successive peaks due to scattering by the periodic part of the surface. It has been shown that if $r_{0}$ is the coherence length of light on scattering from the rough part and 𝛬 is the wavelength of the periodic part of the surface, the extended matched filter method can detect hidden periodic structures for $(r_{0}/\Lambda) \geq 0:11$, while conventional methods are limited to much higher values ($(r_{0}/\Lambda) \geq 0:33)$. In the method developed till now, the detection of periodic structures involves the detection of the central peak, first peak and second peak in the scattered intensity of light, located at scattering wave vectors $v_{x} = 0, Q, 2Q$, respectively, where $Q = 2\pi/\Lambda$, their distinct identities being obfuscated by the fact that the peaks have width $\Delta v_{x} = 2\pi/r_{0} \gg Q$. The relative magnitudes of these peaks and the consequent problems associated in identifying them is discussed. The Kolmogorov-Smirnov statistical goodness test is used to justify the identification of the peaks. This test is used to `reject' or `not reject' the null hypothesis which states that the successive peaks do exist. This test is repeated for various values of $r_{0}/\Lambda$, which leads to the conclusion that there is really a periodic structure hidden behind the random surface.
Volume 77 Issue 4 October 2011 pp 611-626 Research Articles
Detection of a periodic structure embedded in surface roughness, for various correlation functions
This paper deals with surface proﬁlometry, where we try to detect a periodic structure, hidden in randomness using the matched ﬁlter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we ﬁnd that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched ﬁlter method as the nature of the correlation function is varied.
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