the real centroids are redistributed evenly within their 1/16th bins, at 1/1024th pixel resolution. The cumulative sum of this new distribution is its cumulative probability distribution, and this can be divided by the constant-slope line of the theoretical probability distribution to get the correction factor for each 1/1024th bin. In other words, each 1/1024th bin of the interpolated centroid data is multiplied by the correction factor, which is the ratio of the real cumulative probability distribution over the theoretical one. If the real data were composed of centroids from a “flat” illumination of photons, then the systematic centroiding bias effects will have been corrected for. This flat-field correction curve can then be applied to data which has sources and other topological variations - i.e. valuable scientific information, and the correction will only apply to the existing systematic bias within the data, but leave the source-topological variations undisturbed.

Paper 1 gives more detailed description of the corrections, and shows how the signal is redistributed within a pixel. Essentially, the distribution is remapped by performing a division by the correction factor. All photons are conserved, so no photometric error is introduced.

The fraction of out-of-pixel centroids depends to some extent on the 