Evaluation of the summations in equation (13) is the most time
consuming component of the source search. It is therefore important to limit
the summations to a suitable range -- an overlarge range may result in
excessive processing time, whilst too small a range will cause some source
flux to be omitted from the cross-correlation, reducing the detection
significance. The latter effect may be quantified by considering the case
where a point source of strength A is located, so that
. Substituting this in (13), the
detection significance should be
where the x,y indices have been suppressed for simplicity.
Consider the common case of an unscaled (i.e. counts) image with Poissonian
errors. In the limit of a strong source, such that background is
insignificant, 
and (14) reduces to
Hence, setting the range of i,j such that 
of the psf is
excluded would lead to a loss of significance of 
(e.g. a box extending to 90% enclosed energy would include about 95% of
the significance).
In the weak source limit, 
is dominated by background counts.
Assuming these to be constant over the region, so that
, equation (14) becomes
In this limit, the loss in sensitivity due to truncation is much smaller than
for a strong source, since
is dominated by the central pixels where
is largest.
In practice, then, there is rarely any need to extend the psf box beyond the 90% enclosed energy radius, and a somewhat smaller radius will often give acceptable results.
