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Confirmation of the RGA Self­vignetting Function by
a Simulation by SciSim
XMM­SOC­CAL­TN­0021, v1.0
C. Erd
October 26, 2001
1 Introduction
Due to the close stacking of the grating plates in the RGA module, light that is diffracted
at large angles is vignetted by the back of the neighboring grating plate. This effectively
reduces the available active reflection surface of the grating plates as a function of
dispersion angle.
In principle this function is of purely geometric nature and was implemented in
the SAS/CAL (up to version 5.2) in the form of an analytical function (see [1, section
3.4.27]), which was obtained straightforwardly from the distance of the grating plates,
based on measurements during integration. The reduction of the effective area is effective
for fi ? fi vig
, and has the following parameterization:
F (fi) =
(
1 ; for fi ! fi vig
fi vig
tan fi
; for fi ? fi vig
; (1)
with fi vig = 2:97873882195 deg.
2 Application of this Vignetting Function
In order to understand the necessary constraints on the simulations, it is important to
understand the way in which this function is being used by the response generation task
of the SAS rgsrmfgen.
The following effects of the LSF are parameterized:
ffl all geometrical distortions of the surface of the XRT shells
ffl scattering due to reflection of the XRT
ffl all geometrical distortions of the surface of the RGA gratings
ffl scattering due to reflection of the gratings
1

First, these items are convolved and are parameterized as a function of dispersion
angle, resulting in an initial function of an LSF. Then the corrections for the effective
area are bing applied, among which this self­vignetting function. The LSF, which is a
function of dispersion angle fi is corrected by multiplication of this function.
Hence, to confirm the shape of this function, only geometrical effects, without dis­
tortions need to be included in the simulations.
3 Simulations
A set of simulations was performed with SciSim 2.3.7, which contains the following
major enhancements, which are of relevance to this investigation:
ffl Focal length: the shape parameters of the XRT shells was modified such that the
measured reduced focal length of 7496 mm is reproduced.
ffl Location of units: the physical locations of the units (XRT, RGA, RFC, EPIC)
is obtained from the CCF LinCoord, and thus the geometry is matching the one
that was determined from in­flight calibrations.
To obtain the geometrical vignetting only, the following effects of SciSim were dis­
abled off:
ffl Reflection efficiency: The reflectivity of the XRT surface and of the grating effi­
ciency was set = 1
ffl no distortions of the any kind were applied neither to the XRT, nor to the RGA
(ideal mirror and ideal RGA.
ffl only events which had only one reflection in the RGA were selected, and which
were diffracted into first order 1 .
ffl no scatter was applied to the direction of the reflected rays (neither on XRT, nor
on the RGA)
The results of these simulations are shown in Figure 1. The geometrical effective
area is plotted as a function of dispersion angle fi. The circles are the results from
simulations, with a statistical error of about 1%. The black line indicates the results of
a fit with a function that is given by Eq. (1), with the normalization and fi vig being free
parameters. The values obtained for fi vig are
fi vig = 3:0418 \Sigma 0:0127 deg (red. ü 2 = 0:67, 97 dof) for RGS1
fi vig = 3:0349 \Sigma 0:0119 deg (red. ü 2 = 0:90, 97 dof) for RGS2
which are consisted with each other, but which are slightly larger than the value of
fi vig obtained from geometrical considerations.
The red line indicates the current implementation, which was also fit to results, by
only leaving the normalization as a free parameter.It can be seen that the difference
between the two parameterizations is small, it about \Sigma1%.
1 The fi­dependence was obtained by variation of the incidence energy.
2

4 Conclusion
It is concluded that the current implementation of the analytical function of the self­
vignetting is adequate. The parameter fi vig is available in the CCF QuantumEf and
should be modified to the values found by the fit.
RGS1
b in deg
Geometrical
area
in
mm
2 64.70 / 98
P1 0.6860E+05 222.8
P2 3.043 0.1214E­01
40000
45000
50000
55000
60000
65000
70000
75000
2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5
RGS2
b in deg
Geometrical
area
in
mm
2 87.51 / 98
P1 0.6882E+05 222.8
P2 3.035 0.1194E­01
40000
45000
50000
55000
60000
65000
70000
75000
2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5
Figure 1: Result of the simulation for RGS1 (upper) and RGS2 (lower).
References
[1] Christian Erd, Phillipe Gondoin, David Lumb, Rudi Much, Uwe Lam­
3

mers, and Giuseppe Vacanti. Calibration Access and Data Handbook.
Technical Report XMM­PS­GM­20, issue 2.1, ESA/SSD, July 2001.
http://xmm.vilspa.esa.es/calibration/docs/general/calhb.ps.gz.
4