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XMA Scattering Profile


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 tex2html_wrap_inline16607 . Due to the laws of diffraction, the shape parameters should be tex2html_wrap_inline16609 .

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 tex2html_wrap_inline16613 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 tex2html_wrap_inline16615 with E is slower than the tex2html_wrap_inline16619 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.,






The width of the lorentzian, tex2html_wrap_inline16623 , as a function of energy was found to be:


The two parameters governing the shape of tex2html_wrap_inline16625 (i.e., tex2html_wrap_inline16627 and tex2html_wrap_inline16629 ) were constrained to be proportional to tex2html_wrap_inline16631 (see Sect. 2.4.1) during the analytical fitting to the PANTER data. The normalization of the lorentzian, tex2html_wrap_inline16633 ,is given by




is the renormalization factor such thatgif  


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, tex2html_wrap_inline16635 , and the PSPC contribution of the PSF at four different energies, tex2html_wrap_inline16637 , 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).

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