Shapelet fits to PANTER PSF Measurements
FM2:
Based on Panter FM2 measurements done between 5-14 Feb 2016 using the 256x256 pixel TRoPIC. The CCD and the mirror were rotated together with respect to the fixed X-ray source, but, in order to cover the outer PSFs, the CCD was shifted along its plane four times. This resulted in a grid of 11 x 11 PSFs, spaced by 6'. In addition, in order to get a denser sampling of smaller off-axis angles, there was another central grid of 6 x 6 PSFs, also spaced by 6', but displaced with respect to the other grid by 3'. For more details see attachement (TRoPIC_eROSITA_PSF_scan_layout_VB_final.pdf) produced by Vadim.
Shapelets (Refregier A. 2003, MNRAS 338 35, Massey R. & Refregier A. 2005, MNRAS 363, 197) are used to represent the FM2 PSF. The limitation of shapelets is that they are assigned a scale parameter (beta). Features larger than the scale parameter cannot be reproduced. The eROSITA PSF shows complexities over a range of scales, both small (i.e. PSF core) and large (i.e. PSF wings). To represent this complexity two sets of shapelet coefficients were used. The first is to represent the core of the PSF and has a shapelet beta scale of 2.5 pixels and a total number of 91 coefficients (shapelet order N = 12). The second is for the extended wings of the PSF and has a scale beta=7.0 pixels and a total of 66 coefficients (shapelet order N = 10).
The Panter images are first smoothed by boxcar filter with size 2 pixels and then processed with sextractor to determine the centroid position (x0, y0), the overall ellipticity and positional angle of the measured PSF. The PSF position (x0, y0) is kept fixed during the fit. In the future one may want to also optimise for that but in the current implementation this is not possible. Fitting shapelet coefficients to images is a simple linear least squares problem, under the assumption that errors are Gaussian, i.e. standard chi2 statistic applies. This assumptions may not be correct in the case of nearly zero background images.
The attached files below show the (i) input Panter PSF after smoothing (originalXXX.fits), (ii) the shapelet reconstructed PSFs (reconXXX.fits) and (iii) the residuals (residXXX.fits). The attached PDF files show the fractional difference in aperture flux between the Panter and Shapelet reconstructed PSF as a function of aperture size in pixels. This is essential the difference between the curve of growth of the Panter and shapelet reconstructed PSFs. It shows how well the reconstruction follows the PSF flux distribution in the Panter measurements.
Finally, the relevant eROSITA caldb file is also attached fm2_slet_psf_010416v01.fits.
0.3 keV line
original_0.3keV-C-K.fits: 0.3keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon0.3keV-C-K.fits: 0.3keV Shapelet Reconstructed PSF
resid0.3keV-C-K.fits: 0.3keV residuals, i.e. Panter - Shapelet Reconstructed PSF
0.3keV-C-K.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF
0.9 keV line
original_0.9keV-Cu-L.fits: 0.9keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon0.9keV-Cu-L.fits: 0.9keV Shapelet Reconstructed PSF
resid0.9keV-Cu-L.fits: 0.9keV residuals, i.e. Panter - Shapelet Reconstructed PSF
0.9keV-Cu-L.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF
1.5 keV line
original_1.5keV-Al-K.fits: 1.5keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon1.5keV-Al-K.fits: 1.5keV Shapelet Reconstructed PSF
resid1.5keV-Al-K.fits: 1.5keV residuals, i.e. Panter - Shapelet Reconstructed PSF
1.5keV-Al-K.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF
3.0 keV line
original_3.0keV-Ag-L.fits: 3.0keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon3.0keV-Ag-L.fits: 3.0keV Shapelet Reconstructed PSF
resid3.0keV-Ag-L.fits: 3.0keV residuals, i.e. Panter - Shapelet Reconstructed PSF
3.0keV-Ag-L.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF
4.5 keV line
original_4.5keV-Ti-K.fits: 4.5keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon4.5keV-Ti-K.fits: 4.5keV Shapelet Reconstructed PSF
resid4.5keV-Ti-K.fits: 4.5keV residuals, i.e. Panter - Shapelet Reconstructed PSF
4.5keV-Ti-K.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF
6.4 keV line
original_6.4keV-Fe-K.fits: 6.4keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon6.4keV-Fe-K.fits: 6.4keV Shapelet Reconstructed PSF
resid6.4keV-Fe-K.fits: 6.4keV residuals, i.e. Panter - Shapelet Reconstructed PSF
6.4keV-Fe-K.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF
8.0 keV line
original_8.0keV-Cu-K.fits: 8.0keV Panter PSF smoothed by boxcar filter of 2 pixels size
recon8.0keV-Cu-K.fits: 8.0keV Shapelet Reconstructed PSF
resid8.0keV-Cu-K.fits: 8.0keV residuals, i.e. Panter - Shapelet Reconstructed PSF
8.0keV-Cu-K.pdf: PDF curve of growth fraction difference between Panter and Shapelet Reconstructed PSF