Collimation and Beam Flux

Although the X-ray source produces a decently parallel beam, it is still too divergent for even a medium $q$-range and still too large for a typical sample cross-section.

For a precisely defined beam size and divergence, we use a three-pinhole collimation scheme which we optimize on a case-by-case basis (details are published here).

The system consists of three motorized pinhole stages, each one of these housing five pinholes of different diameters. The pinhole stages are sitting on an X95 optical railing, and the distance between them can be varied by inserting ISO-KF spacers of various lengths.

Every time a different angular range is selected (based on the requirements of the scientific problem in question), an optimal experimental geometry is chosen, which provides the highest beam intensity on the sample with the required beam divergence. The highest $q$ is defined by the sample-to-detector distance (the kind and number of flight path tubes inserted after the sample chamber) and the size of the detector surface (the pixel farthest from the beam position). The lowest $q$ is limited by the beam stop.

Determining the best experimental geometry for any given q-range is done by a brute-force search among all possible collimation setups. This includes a selection of the pinhole sizes, the spacers between the pinholes, as well as the flight path tubes and the beam stop size to be used. The setups are first filtered to satisfy the criteria of

• the lowest attainable $q$ must be below a user-supplied threshold
• the beam size at the sample must be below a user-supplied threshold
• the third pinhole must be large enough not to cut the primary beam but small enough to cover most of the parasitic scattering from the first two pinholes
• the beam stop must be large enough not to let either the not scattered beam or the parasitic scattering through.

Those setups which satisfy the above criteria, are sorted according to the expected beam intensity (proportional to $d_1^2 d_2^2 / l_{1-2}^2$ where $d_1$ and $d_2$ are the diameters of the first two pinholes and $l_{1-2}$ is the distance between them). This empirical measure is found to be highly relevant, being approximately proportional to the true beam intensity at the sample:

Because low $q$-s need a highly parallel beam, divergent rays need to be cut out, which in turn reduces the beam intensity on the sample, worsening the signal-to-noise ratio of the measurement. The following figure shows the beam intensity with respect to the smallest $q$ in setups.

Going to very low angles results in a reduction of the beam intensity by a factor of ~ 30, causing a significant loss in signal-to-noise ratio.