New insights into optical Fourier transforms, radial distribution function, and Glatter’smethod

Abstract

We address several subtle issues concerning the static scattering of light or x-rays fromphysical/chemical/biological systems. In the context of Fourier integrals we point out thatthe Glatter–Moore algorithms can efficiently perform sine inversion between two functionsJ(q) andL(r) of calculus, andthe structure factor S(q) can be correct only if the asymptotic value of the pair correlation function differs from unity. Next, concerning the radial distributionfunction g(r), we derive a new integral equation for and use it to find the effective potential when the input pair potential is parabolic. Finally, turning to data analysis,we demonstrate that a bump in the underlying distance distribution functionP(r) plays a major role in producing attenuated oscillations in the experimental structure factor,and also in the study of a subtle convolution integral.