Introduction

The 2D powder diffraction integration algorithms in DAWN take a histogramming approach, where the intensity of the original image is "remapped" into a set of bins that become the 1D powder pattern. There are two algorithms available for this process, both take a different approach and are suitable for different purposes.

Non Pixel Splitting Integration

The q value for the center of each pixel is determined.  All the intensity of that pixel is put into a single bin whose q range contains the q value for the center of the pixel.

For the 2D algorithm, the azimuthal angle for the center of each pixel is also determined and all the intensity is put in the (q,azimuthal angle) bin that contains these values.

Pixel Splitting Integration

The q values of the corners of each pixel are calculated.  The minimum and maximum of these values specifies the q range that the pixel covers.  The intensity is split equally into the bins that this q range covers, each full bin getting the same intensity, the bins at the edge of the range are filled with a fraction of the intensity related to how much of the range is included in the bin.

For the 2D algorithm, the azimuth angle is also calculated for the edge of each pixel, and the intensity is split over the two dimensions (q, azimuthal angle)