Proceedings of
International Conference on Advances in Electronics Devices and Circuits EDC 2012
"FOURIER TRANSFORM AND DISTANCE DISTRIBUTION FUNCTION: NEW INSIGHTS INTO DATA ANALYSIS"
Abstract: “We revisit the standard procedure for analyzing the static light intensity curves I(q) measured in scattering from chemical/biological samples as done in the literature. By utilizing some algebraic properties of Fourier integrals we show that; i) the theoretical forward intensity I(0) extracted via the Glatter/Moore algorithm must be consistently higher than all peaks occurring in the input I(q) curve ; ii) the attenuated oscillations of input I(q) data at intermediate q may be a direct consequence of the presence of a bump in the output distance distribution profile P(r) ; iii) if the input intensity is modified by the Gaussian damping factor exp (-Kq2) then extrapolation of the output results down to K = 0 is liable to become numerically unstable ; and iv) due to the exp (-Kq2) artifact the output distance distribution function profile may exhibit a bump having the correct location but wrong width if K is nonzero.”
Keywords: Bump, morphology, Fourier integrals, truncation etc