2.6. Uncertainties in the coordinates

The coordinates of a pixel may not always be known exactly. Instead, they are often subject to both random, statistical errors and various systematic errors. The former are not particularly correlated between pixels, whereas the latter may have a high degree of correlation across the whole data set. For example, single-dish radio images may be accurate on a pixel-to-pixel basis to a fraction of an arcsec, but have a 5-10 arcsec uncertainty in the reference point value. Two optional keywords are hereby reserved to specify these uncertainties in coordinates. They are

where both are given in units of CUNITia and have default value zero. They are understood to give a representative average value of the error over the range of the coordinate in the data file. The total error in the coordinate would be given by summing the two errors in quadrature.

The errors in actual coordinates may be very much more complex than this simple representation. In the most general case, one might require, at each pixel, a covariance matrix to describe the dependence of the uncertainty in one coordinate on the uncertainties in the others. Furthermore, the errors in one coordinate description may, or may not, be completely predictable from those of an alternate description. Such usages, while perhaps important under some circumstances, are well beyond the needs of most users and the scope of this manuscript.