Optimized pinhole geometry for small-angle scattering

In order to make the most of the low photon flux in laboratory small-angle X-ray scattering instruments, the experimental geometry has to be chosen carefully, with special stress on the beam-shaping system. The optimum collimation scheme should enable accurate measurements over the desired range of the scattering variable, while yielding the highest flux and the lowest possible instrumental background. In order to identify the best setting, a phase-space optimization of the collimating scheme is carried out in the present work, including constraints on the beam size at the sample position and on the detector surface. The resulting formulae are implemented in a Python script with a graphical user interface, to aid the planning, construction and daily operation of pinhole small-angle scattering cameras.