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As detailed in CAL/ROS/92-001 and 001a [Hasinger et al.1992, Hasinger et al.1993] and CAL/ROS/93-015 [Hasinger et al.1994], the point spread function (PSF) of the ROSAT X-ray mirror assembly (XMA) + PSPC is a convolution of five components:
There is also some residual ellipsoidal blur due to uncorrected attitude motion, but for the PSPC, this component is usually negligible compared to the other effects (see [Hasinger et al.1992] for more details). The XMA scattering profile, the intrinsic spatial resolution of the PSPC, and focus and detector penetration effects have already been described in [Hasinger et al.1992] and [Hasinger et al.1993]. The PSF was parameterized for on-axis observations from PANTER ground calibration measurements. In [Hasinger et al.1992] it was shown that the derived analytical functions satisfactorily described five moderate signal-to-noise datasets in all but the softest band where ghost imaging was already known to be a problem. The treatment was extended to include a parameterization of the change in shape of the PSF with off-axis angle. [Hasinger et al.1993]
Examination of a bright point source observed off-axis reveals asymmetry in the distribution of source counts which becomes easily noticeable once the source is observed outside of the central ring of the PSPC (i.e., >20' off-axis). The asymmetry is produced because for off-axis irradiation, half of the mirror sees a different grazing angle compared to the other. The two relatively sharp outer boundaries of the blur area, which have different radii of curvature, are produced by the front and rear aperture planes of the mirrors, respectively. The hole in the PSF is due to the central hole in the mirror aperture (the mirror consists of four shells). The imaged is defocussed at large angles as the detector is flat (actually bowed out slightly by counter gas pressure) but the focal plane is curved (in the sense opposite to the bowing of the detector). The radial struts also interfere with the photon distribution as they shadow part of the detector. This combination produces the diffraction-like radial pattern seen on bright sources observed at large offset angles.
While early attempts to parameterize the change in shape of the PSF concentrated on the ground calibration data taken at the PANTER facility, a comparison of those data with in-flight data showed significant differences. These differences are due to the finite source distance in the PANTER facility, which results in a beam divergence of about 10'. The consequence of this divergence is that the PANTER data have the hole on the inner side of the peak of counts for off-axis sources, while the in-flight data show the hole on the opposite side. In addition, the PANTER image shows greater interference between the PSF and the PSPC wire grid (effects which are reduced by the wobble of in-flight observations). As a consequence of these differences, in-flight data, collected from a variety of bright serendipitous sources detected in pointed observations, were finally used to parameterize the off-axis dependence of the PSF, while the components which are independent of off-axis angle were carried over from the higher-quality on-axis data.
The off-axis blur of the telescope, although highly structured and asymmetric, has been modeled by a simple Gaussian for comparison to a radially integrated profile. This Gaussian term for the off-axis blur is added in quadrature to the Gaussian term describing the intrinsic PSPC resolution. Since the model approximates the behaviour of the detector by the addition of Gaussian, exponential, and Lorentzian terms, instead of a mathematically correct convolution of terms, the contribution of the other terms must be adjusted relative to the on-axis case, to allow for the off-axis behaviour of the Gaussian term. The new term for the exponential fraction describes the relative diminishing of this term with increasing offset angle, due to the increase of the Gaussian term.
The mirror scattering term remains as noted in Sect. 2.4