• S Chatterjee

      Articles written in Pramana – Journal of Physics

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

      S Chatterjee V C Vani

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      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 (r0/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 (r0/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 (r0/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 (r0/Λ) = 0.11.

    • Scattering of light by a periodic structure in the presence of randomness VII: Application of statistical detection test

      V C Vani S Chatterjee

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      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.

    • Detection of a periodic structure embedded in surface roughness, for various correlation functions

      V C Vani S Chatterjee

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      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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