Resolution of small-angle scattering with Soller collimation

The effect of Soller collimation on the resolution characteristics of small-angle scattering spectrometers for which there is a limitation to the total length, as in the case of a pulsed source instrument, is examined. Any finite distance between the exit of the collimation and the sample position causes the resolution of the instrument to deteriorate. This results from a correlation in angle and position for points at the sample producing an extra (cross-correlation) term in the resolution function. Expressions for this general case are derived. They are similar to those when the incident beam is defined at the sample position, except that both the source and the sample contributions have an extra term which is proportional to the finite distance between the end of the incident collimation and the sample.