Since catcorr is used in the pipeline before any data quality assessment is performed, there is no information on whether the current fields are affected by problems such as very bright central sources, large extended sources, or various telescope artfacts. For this reason catcorr includes an initial rather basic attempt to detect an excess of spurious detections by finding whether any of them lie on what appear to be straight lines running through the centre of the field. Such lines are usually composed of mostly spurious detections, and so they are marked internally as of bad quality and not used in the cross-matching. Other detections ignored are those with RADEC_ERR exactly zero (a defect of source-finding) or those with RADEC_ERR over 3.0 arc-seconds, or with EP_EXTENT above 0.1 arc-seconds. Unless the number of good X-ray detections in the list exceeds the minimum specified by parameter mingood then the correction procedure is abandoned for this observation.
The matching procedure uses each of the reference catalogues separately: a statistic is computed which measures the overall goodness of fit between the set of XMM detections and the best matching reference source positions, allowing for the probability of positional coincidences. Only a proportion of the XMM sources will have counterparts and of course this proportion is unknown. Provided a reasonable number, perhaps five, appear to have counterparts, the following procedure appears to be reliable. Given the typical densities of X-ray and optical objects there may be a few false matches but not enough to affect the results significantly. The cross-matching is repeated while the position of the XMM frame is shifted by small increments in RA and DEC and rotated slightly about the centre of the field. A function minimisation routine due to Nelder and Mead (Computer Journal, January 1965, pp 308-313) is used is used to find the shift and rotation parameters which optimise the overall goodness of fit. This routine is similar in algorithm to routine AMOEBA which appears in Numerical Recipes, but the routine used here was originally from Rothamstead Research Establishment.
The reference catalogue which produces the highest maximum goodness of fit is adopted, provided it exceeds the minimum fit (parameter minfit) and the resulting absolute offset measured in arc-seconds does not exceed the parameter maxoffset. This positional shift and rotation are then applied to all detetections in the OBSMLI file, and two new columns called RA_CORR and DEC_CORR are put in the FITS table (or updated if they already exist). The postion shifts and standard errors in them, and the goodness of fit, are inserted in the file as FITS headers.
