Resolution of elliptically averaged small-angle scattering data

The elliptical average of small-angle scattering data requires the two-dimensional detector to be divided into concentric elliptical rings of some width with an eccentricity and orientation determined from the data. A modified scattering vector which contains the elliptical dependence is defined, and an expression is derived for the resolution of the elliptically binned data which has a form similar to that for the circularly averaged data. The optimization conditions are such that the appropriate binning width depends on the spectrometer apertures and on the eccentricity of the data.