Correction algorithm

From Figures 2 and 3 it is evident that the residual misalignment of LECS and MECS coordinates can be described in terms of sinusoidal functions of the satellite roll angle.

We have fitted the RA and Dec deviations as a function of roll angle obtaining the following best fits:
 
 

  $~~~~~~~~~~~~~~~~~~~~~~~~ \Delta {\mathrm RA_{LECS}} = 15 ~ {\mathrm cos}(\phi - 140) + 2~~~~~~~~ {\mathrm [arcsec]}~~~~~~~~~~~~~~~~~~~~~~~~~$                       (1a)
$~~~~~~~~~~~~~~~~~~~~~~~~~ \Delta {\mathrm Dec_{LECS}} = 19 ~ {\mathrm cos}(\phi - 236) - 4~~~~~~~~ {\mathrm [arcsec]}~~~~~~~~~~~~~~~~~~~~~~~~~~$                       (1b)
 
 

$~~~~~~~~~~~~~~~~~~~~~~~~~~ \Delta {\mathrm RA_{MECS}} = 27 ~ {\mathrm cos}(\phi - 12.5) + 3.5~~~~~~~~ {\mathrm [arcsec]}~~~~~~~~~~~~~~~~~~~~~~~~$               (2a)
$~~~~~~~~~~~~~~~~~~~~~~~~~~ \Delta {\mathrm Dec_{MECS}} = 26 ~ {\mathrm cos}(\phi - 99.5) - 4.0~~~~~~~~ {\mathrm [arcsec]}~~~~~~~~~~~~~~~~~~~~~~~~$              (2b)

where $\phi$ is the value of the roll angle expressed in degrees.

These best fits have been plotted as solid lines in Figures 2 and 3 respectively.

A separate fit of MECS1, MECS2 and MECS3 data has been performed. Since very small differences (of the order of 2-3 arcsec) between the three units have been found, we have adopted a single correction formula for MECS data, obtained averaging the best fit parameters of the three units.

Equations (1) and (2) can been used to correct LECS and MECS event files coordinates. The correction is obtained adding$\Delta {\mathrm RA}$ and $\Delta {\mathrm Dec}$ to the LECS and MECS coordinates:
 
 

$~~~~~~~~~~~~~~~~~~~~~~~~ {\mathrm RA_{corrected} = RA}+ \Delta {\mathrm RA/cos(Dec)}$
$~~~~~~~~~~~~~~~~~~~~~~~~ {\mathrm Dec_{corrected} = Dec}+ \Delta {\mathrm Dec}$
 

A specific task (saxposcor) that corrects LECS and MECS event files has been developed and is available at  /bepposax/saxposcor/saxposcor.html