The maximum-likelihood source detection algorithms do take into account the general vignetting (mirror vignetting) but they do not take into account the obscuration by the PSPC window support structure (ribs). Therefore the source count rates obtained with the EXSAS source detection are too low for sources which are partially obscured by the PSPC ribs.
In principle there are two methods to get a more or less reasonable estimate of the true, unobscured source count rates:
It should be noted that none of these methods is exact. The reason is that the point spread function is extended. The obscuration by the rib structure usually varies over the extent of the extraction circles used by the source detection - this leads to a mismatch between source profile and the point spread function model which is fitted to the source in the source detection. The counts resulting from the source detection are therefore less reliable than for unobscured sources.
Both methods as described above furthermore can be affected much by small uncertainties in the attitude information. For the second method see also the discussion at the end of section 5.2.35.
Corrected source count rates for partially obscured sources obtained as described above should therefore be seen only as estimates. Their formal errors do not represent the true errors.