Modelling the vignetting function of eROSITA

This is a holding page to gather together notes on produsing an analytic vignetting model for eSASS tasks

Problem: The current method to represent the eROSITA vignetting function in the eSASS required interpolation from a tabulated grid of calibration measurements, this is computationally awkward, and can lead to discontinuities in the derived system response. Desired improvement: Compute an analytic description of the vignetting function of each eROSITA telescope module, and save the parameters of this model into the CALDB

First step

• Start from the vignetting description file supplied with the current version of SIXTE (share/sixte/instruments/srg/erosita_vignetting_v2.1.fits)
  • this contains a list of vignetting values evaluated at 3 energy bands and 31 offaxis angles
    • it is not clear what mean energy should be assumed for each energy band, we assume 1.25keV, 4.5keV and 7.5keV.
• For each energy value we fit a simple model as a function of off-axis angle
  • A pseudo-Moffat distribution is found to give a reasonable match to the tabulated values, i.e. vign(oa) = [1 + (oa/theta0)**alpha]**beta
• The values of theta0,beta,alpha are then interpolated using a quadratic expression to allow evaluation of the expression at any energy
  • This quadratic form is probably bad at energies above the upper tabulated energy band
• The parameters describing this fit are as follows: