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Microroughness of the reflecting mirror surfaces leads to
non-specular reflection of X-rays, i.e., scattering.
The importance of scattering by the ROSAT XMA is small
compared to previously available X-ray mirrors,
offering the ability to perform high contrast imaging.
The form of the scattering is a complex function of energy,
grazing angle and the scale size of the mirror surface roughness.
Theoretically, assuming the grazing angle remains constant,
the scattering fraction should increase as 
.
Due to the laws of diffraction, the shape parameters should
be 
.
The detailed PSF parameters and their associated E dependences have been determined for the XMA as well as for the PSPC-A and PSPC-C using four monochromatic energies (0.28, 0.93, 1.49, and 1.70 keV) at the PANTER facility in Neuried. The resultant predicted PSF curves have been compared to a number of PVC and AO-1 datasets in OGIP calibration memo CAL/ROS/92-001 (see also Sect. 4.1).
The analytical form derived for the fraction of photons within the component of the PSF due to XMA scattering as a function of energy is given by:
Even at high energies 
is small compared to the other
components of the total PSF
[Hasinger
et al.1992].
The model and the PANTER data from which
Equation 2.1
was derived are also shown in [Hasinger
et al.1992].
The increase in 
with E is slower than the 
power law expected.
This is due to the fact that the effective grazing angle
averaged over all mirror shells is not constant.
The PANTER tests confirmed that this component was well approximated by a Lorentzian function, steepening to a power law at large r, i.e.,
where
and
The width of the lorentzian, 
, as a function of energy
was found to be:
The two parameters governing the shape of
(i.e., 
and 
)
were constrained to be proportional to 
(see Sect. 2.4.1) during the
analytical fitting to the PANTER data.
The normalization of the lorentzian, 
,is given by
where
is the renormalization factor such that
The mirror scattering has no significant dependance on off-axis angle of the observation. For further details see [Hasinger et al.1994].
Figure 2.6: The XMA point response as a function of off-axis angle,
, and the PSPC contribution of the PSF
at four different energies, 
, are compared.
The figure illustrates how the mirror effect dominates over
the PSPC effect outside of about 14'. The lines of
constant detector component represent (from top to bottom)
0.28, 0.50, 2.0 and 1.0 keV (the detector Gaussian has a
minimum between 1 and 2 keV, as detailed in
[Hasinger
et al.1992],
thus the inversion).
