Analysis of chord-length distributions

A closed-form analytical solution for the inversion of the integral equation relating small-angle scattering intensity distributions of two-phase systems to chord-length distributions is presented. The result is generalized to arbitrary derivatives of higher order of the autocorrelation function and to arbitrary projections of the scattering intensity (including slit collimation). This inverse transformation offers an elegant way to investigate the impact of certain features, e.g. singularities, in the chord-length distribution or its higher-order derivatives on the scattering curve, e.g. oscillatory components in the asymptotic behavior at a large scattering vector. Several examples are discussed.