XMMNewton Science Analysis System
epicbscalgen (ccftools1.36) [xmmsas_20211130_094120.0.0]
The basic idea is to minimize the difference between the true source
coordinates and the ones computed by the eboxdetect
as
a function of the three angles. More explicitly, the following
steps are carried out:

 Set
, i.e. assume perfect
alignment between the star tracker/spacecraft and instrument boresight frame
in Fig. 1.
 run the task attcalc
on the event list
producing a new event list with sky coordinates
corresponding to the tuple
.
 accumulate a sky image from event list
with task evselect
 run eboxdetect
on which gives a list of source positions
in absolute sky coordinates
,
 identify the reference sources in the new source list and compute
(1)
 if is small enough the sought set of angles is found:
(2)
else
 compute new angles for the next iteration
 set boresight angles to
via the CAL
 goto 3
endif
Thus, the procedure is a minimization of the sum of squares of the
absolute deviations of the reference source positions from the true
values in the 3dimensional parameter space of the boresight misalignment
angles. The actual minimization scheme employed is the NelderMead Simplex
method[3] which uses only function evaluations. It has been
found that the Simplex scheme is much better suited than conventional
conjugate gradient methods which often fail to efficiently find
the direction to the global minimum. The dependency of
on the third angle , i.e., the calibration around the optical axis,
has been found to be fairly weak. For the sake of efficiency, the
search for the global minimum has therefore been split into two stages:
 Minimization of
with a fairly relaxed stopping criterion.
 Starting from the local minimum found in step 1, full minimization
of
with a more stringent
stopping criterion.
XMMNewton SOC  20211130