A direct indirect method of small-angle scattering data treatment

A new method of treatment of small-angle scattering data is proposed. The real-space distribution function is developed into a series of linearly independent functions in such a way that the scattering intensity is represented as a series of orthonormal Hermite polynomials. The coefficients of this series are found by the least-squares method. The scale transformation factor ensures fast convergence of the series in real and reciprocal space and the number of terms is chosen using the orthogonal properties of the Hermite polynomials and perceptual criteria. The method allows evaluation of the distribution functions for monodisperse and polydisperse systems directly from the raw experimental data without a priori information on the particle sizes.