The elliptical average of small-angle scattering data

Inhomogeneities that on the average have an atom density function with rotational symmetry around some unique axis give rise to elliptically symmetric small-angle scattering. The usual analysis involves cuts along the principal axes of the contours, which uses only part of the data. A better method is to perform an elliptical average of all the data using least-squares analysis to obtain a two-dimensional representation of intensity as a function of a reduced scattering vector. This technique makes no assumption regarding the dependence of the intensity on scattering vector, but assumes that the data may be represented by elliptical contours of some eccentricity and orientation. This procedure allows all the familiar forms for circularly averaged small-angle scattering data to be used, with the derived size parameter having an elliptical dependence.