Calibration Access and Data Handbook

Procedure

Returns a modified PSF map based on the effect of core suppression due to pile-up. The suppression is mildly energy and pattern dependent, but for the usage of supplying a PSF brightness distribution (for checking if a source is truly point-like, or as an aid to determining if the pileup is sufficent to give concern for spectral analysis), then the approximations employed herein may be sufficient.

Supplying a total input events/point source/second is the preferred activation input. This is converted to input events/point source/CCD frame according to the frame time in ModeParams. The input PSFimage is normalised to unity, and from this the localised pixel-by-pixel count rate per frame is established.

The calculation depends on the pattern types selected, with progressively more complex arithmetic for the larger patterns (see J Ballet Ast Ap Suppl Ser v 135 pp371-381).

The output intensity ($\mu$) in each case is modelled as follows, where $\lambda$ is the input intensity per pixel :
Mono-Pixels

$\mu_{1} =(1 -\exp(-\alpha_{1}\lambda)) exp(-\gamma_{1}\lambda)$
where
$\gamma_{1} =9 + 3\alpha_{2} + 6\alpha_{3} + 7\alpha_{4}$
and the $\alpha_{i}$ are the fractional pattern occurrences taken from the pattern library CCF, but $\alpha_{2}$ corresponds to patterns 1,2,3 and 4 , $\alpha_{3}$ corresponds to patterns 5,6,7 and 8 and $\alpha_{4}$ corresponds to patterns 9,10,11 and 12.

Bi-Pixels
$\mu_{2} =2(p_{2}+(1-p_{2})p^{2}_{1}) exp(-(\gamma_{2}-2\alpha_{1}-0.5\alpha_{2})\lambda)$
where
$\gamma_{2}=12 + 3.5\alpha_{2} + 7\alpha_{3} +8\alpha_{4}$
$p_{1} = 1 - exp(-\alpha_{1}\lambda)$
$p_{2} = 1 - exp(-\alpha_{2}\lambda / 2)$

Tri-Pixels
$\mu_{3} = 4(1 - (1-T_{3}) exp(-\alpha_{3}\lambda /4)) exp(-\gamma_{3}\lambda)$
where
$T_{3}=p^{3}_{1}/3 exp(-\alpha_{2}\lambda) + 0.5p_{1}p_{2}exp(-\alpha_{2}\lambda/2) + 0.75p^{2}_{2}$
$\gamma_{3} = 15 + 4\alpha_{2} +7.75\alpha_{3} + 9\alpha_{4} -3\alpha_{1} -\alpha_{2} -0.25\alpha_{3}$

Quad-Pixels
$\mu_{4}=[1 - exp(-\alpha_{4}\lambda)(1-Q_{3})]exp(-\lambda(\gamma_{4}-1-3\alpha_{1}-\alpha_{2}))$
where
$Q_{3}=1-(1-Q_{2})exp(-\alpha_{3}\lambda) - 4(1-exp(-\alpha_{3}\lambda/4))exp(-\lambda(\alpha_{1}+\alpha_{2}+0.75\alpha_{3}))$
$Q_{2}=p^{4}_{1}exp(-2\alpha_{2}\lambda) + 4p^{2}_{1}p_{2}exp(-3\alpha_{2}\lambda/2) + 4p_{1}p^{2}_{2} exp(-\alpha_{2}\lambda) +p^{2}_{2}(2-p^{2}_{2})$
$\gamma_{4}=16 + 4\alpha_{2} + 8\alpha_{3} + 9\alpha_{4}$