The non perfect calibration of the misalignment matrices may also concern the rotation around the Z axis, the one co-aligned with the NFI instruments. Since this corresponds to a rotation of the X-ray images, the analysis of LECS and MECS on-axis sources is not useful to investigate this issue.
The residual misalignment around the Z axis is expected to have a similar amplitude to those around the X and Y axes (~20-30 arcsec). As the following simple argument shows, the effect of the Z misalignment on the image coordinates is negligible. If we consider a 30 arcsec rotation of the image around its center the effect on the coordinates of a source located at an off-axis angle of 30 arcmin is a very small shift (~0.3 arcsec).
We have verified this conclusion comparing the BeppoSAX X-ray
and optical positions of a small sample of off-axis sources. In all cases
we found that there is no need of a rotation of the image and that the
RA and Dec coordinate correction described by Equations (1) and (2) corrects
very well also the positions of off-axis sources. An example of a MECS3
image before and after the correction is shown in Figure 6.