New developments in direct shape determination from small-angle scattering. 1. Theory and model calculations

Improvements in the shape determination method based on multipole expansion [Stuhrmann (1970), Z. Phys. Chem. (Frankfurt am Main), 72, 177-198] are described. Fast algorithms for evaluating shape scattering from the multiple coefficients are developed. The relationship between the resolution in real and reciprocal space is established. The improved technique is verified by means of model calculations. It is shown that the low-resolution shape estimation can be performed as a straightforward procedure. Shape refinement at higher resolution is ambiguous; a variety of shapes can be generated which fit the given intensity curve neatly. A criterion is given to select the most plausible solution in higher-resolution studies.