Scaling

The scaling algorithm is based on fitting two distributions onto another with an exponential function. The distributions are based on a weighted, resolution-binned reflection averaging, akin to the well known Wilson plot in x-ray crystallography. One distribution serves as the reference, <Iref>, the other as the target , <I>.

A typical plot is shown in the figure above, and the exponential fitting function next to it. The scale S and exponential B-factor are sought. A small reorganization leads to a nice linear form.

The question is what to use as a reference. As it turns out, the first raw, unscaled merge is perfectly suited for this task, as long as the majority of reflections is not to much out of scale (approximately an order of magnitude). After a first round, this scaling can of course be applied iteratively, using the previous scaled dataset as a new reference; however, current experience has shown that the effect of the second and any subsequent round is neglectable. Alternatively, an existing dataset - e.g. from image processing - can be used to make a reference Wilson-type distribution. This weighted bin scaling approach works faster and better than common-line scaling. It also does not require incremental scaling, starting with small tilt angles, and then working up towards the higher angles. In principle, this allows data collection to focus on a few decent zero degree patterns, and then to collect the majority of data at 45 and beyond.

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