On-axis PSF

Each of the three Wolter-type X-ray telescopes onboard XMM has its own point-spread function (PSF). As an example, Fig. 4 shows the on-axis PSF of one of the X-ray telescopes, as measured on-ground at the Panter test beam facility, at an energy of 1.49 keV. The PSFs of the two other telescopes are similar and therefore not displayed here.

**Figure 4:** *The on-axis PSF of one* **XMM** mirror module at an energy of 1.49 keV as measured at the Panter facility. The radial pattern created by the mirror support spiders is clearly visible. To enhance the visibility of the wings, intensities are scaled logarithmically.
$\begin{figure} \begin{center} \leavevmode \epsfig{width=0.57\hsize, file=figs/fm2_1.49kev_psf.eps} \end{center} \end{figure}$

Note that the on-ground PSF measurements will probably differ slightly, but measurably from the in-flight performance, because they are not fully illuminated by the source due to its finite distance. Fig. 4 is primarily provided to show the shape of the PSF, with for example the radial substructures caused by the spiders holding the mirror shells. Values for the PSF's FWHM and HEW, which come from SciSim modeling and fits of the modeled profiles to data, are listed in Tab. 2.

Fig. 5 displays the radially averaged profile of the PSF of one mirror module, from a SciSim model run.

**Table 2:** *The on-axis 1.5 keV X-ray PSFs of the different mirror modules*
Mirror module	1	2	3
Instr. chain¹	pn	MOS-1+RGS-1	MOS-2+RGS-2
FWHM [ '']	6.6	6.0	4.5
HEW [ '']	15.1	13.6	12.8
W90² [ '']	53.3	50.7	58.4

**Figure 5:** *Radial average of one* **XMM** *mirror module's on-axis PSF, from a SciSim model simulation.*
$\begin{figure} \begin{center} \leavevmode \epsfig{width=0.6\hsize, angle=270, file=figs/psf_radprof.eps} \end{center} \end{figure}$

Figs. 6 and 7 show the fractional encircled energy as a function of radius from the centre of the PSF for several different energies. One can see that the PSF wings become more prominent with increasing photon energy. At 14-15 keV the effective area, A_e, is very small, which makes simulations and the calibration of the PSF at such high energies unreliable.

**Figure 6:** *Curves of fractional encircled energy as a function of angular radius (on-axis), at several different energies (linear scale).*
$\begin{figure} \begin{center} \leavevmode \epsfig{width=0.6\hsize, angle=270, file=figs/encE_onaxis.eps} \end{center} \end{figure}$

**Figure 7:** *Curves of fractional encircled energy as a function of angular radius (on-axis), at several different energies (logarithmic scale).*
$\begin{figure} \begin{center} \leavevmode \epsfig{width=0.6\hsize, angle=270, file=figs/encE_onaxis_log.eps} \end{center} \end{figure}$

XMM Users' Handbook

On-axis PSF