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arXiv:astro­ph/0403647
v1
29
Mar
2004
In-orbit Vignetting Calibrations of XMM-NewtonTelescopes
D. H. Lumb (dlumb@rssd.esa.int)
Adv. Concepts & Science Payloads Oôce, European Space Agency,
ESTEC,2200AG Noordwijk, Netherlands
A. Finoguenov
Max-Planck Institut fur extraterrestrische Physik, Giessenbachstrae 1, D-85748
Garching, Germany
R. Saxton
XMM Survey Science Centre, Dept. of Physics & Astronomy, Leicester University,
Leicester LE1 7RH, U.K.
B. Aschenbach
Max-Planck Institut fur extraterrestrische Physik, Giessenbachstrae 1, D-85748
Garching, Germany
P. Gondoin
Adv. Concepts & Science Payloads Oôce, European Space Agency, ESTEC,
2200AG Noordwijk, Netherlands
M. Kirsch
XMM Science Ops. Centre, European Space Agency, Apartado - P.O. Box 50727,
28080 Madrid, Spain
I. M. Stewart
XMM Survey Science Centre, Dept. of Physics & Astronomy, Leicester University,
Leicester LE1 7RH, U.K.
Abstract. We describe measurements of the mirror vignetting in the XMM-Newton
Observatory made in-orbit, using observations of SNR G21.5-09 and SNR 3C58
with the EPIC imaging cameras. The instrument features that complicate these
measurements are brie y described. We show the spatial and energy dependences of
measured vignetting, outlining assumptions made in deriving the eventual agreement
between simulation and measurement. Alternate methods to conrm these are de-
scribed, including an assessment of source elongation with o-axis angle, the surface
brightness distribution of the diuse X-ray background, and the consistency of Coma
cluster emission at dierent position angles. A synthesis of these measurements leads
to a change in the XMM calibration data base, for the optical axis of two of the
three telescopes, by in excess of 1 arcminute. This has a small but measureable eect
on the assumed spectral responses of the cameras for on-axis targets.
Keywords: XMM-Newton, X-ray mirrors, X-ray detectors, X-ray astronomy, CCDs
1. INTRODUCTION
XMM-Newton (Jansen et al., 2001) comprises 3 co-aligned telescopes,
each with eective area at 1.5keV of 1500cm 2 , and Full Width Half
c
2004 Kluwer Academic Publishers. Printed in the Netherlands.
vign_09.tex; 29/03/2004; 7:28; p.1

2
Maximum (FWHM) angular resolution of 5 arcseconds. The 3 tele-
scopes each have a focal plane CCD imaging spectrometer camera
provided by the EPIC consortium. Two also have a re ection grating
array, which splits o half the light, to provide simultaneous high resolu-
tion dispersive spectra. These two telescopes are equipped with EPIC
MOS cameras (Turner et al., 2001), which are conventional CMOS
CCD-based images enhanced for X-ray sensitivity. The third employs
the EPIC PN camera (Struder et al., 2001) which is based on a pn-
junction multi-linear readout CCD. The EPIC cameras oer a eld of
view (FOV) of 30 arcminute diameter, and an energy resolution of
typically 100 eV (FWHM) in the range 0.2{10 keV. The two MOS
telescopes are equipped with a Re ection Grating instrument (den
Herder et al., 2001) that has its own dedicated readout camera.
The in-orbit calibration of the XMM-Newton mirrors has been re-
ported elsewhere (Aschenbach et al., 2000), with special reference to the
on-axis angular resolution (Point Spread Function, PSF). A second im-
portant calibration data set that is critical for analyzing spectroscopic
information is the energy-dependent eective area (Aschenbach, 2002).
Both these features are under constant review as a result of improving
knowledge of the instrumentation, and the requirements imposed by
new science investigations. In this work we concentrate on dierent
aspects of mirror performance that must be calibrated in the context
of other scientic drivers which include, for example, cluster radial
brightness distribution for determining gas mass, exposure maps and
counts-to- ux conversions in population studies and diuse background
normalization measurements etc.. The reduction in eective area with
radial distance from the eld of view centre, or vignetting, must be
accurately determined to support these investigations.
To highlight the eect visually, Figures 1 and 2 show the excess
ux per source detected in the 1XMM catalogue of EPIC serendipitous
source detections (plotted in units of sigma). The images are displayed
in the EPIC camera detector coordinates, and ux determinations as-
sume the nominal vignetting correction centred on the reference pixel
of the detector co-ordinate system (DETX, DETY in the nomenclature
of the XMM data analysis system). These gures show that some low
level discrepancy in the spatial variation in eective area calibration
must be present.
For XMM-Newton, direct measurement on the ground of the X-
ray vignetting function was prevented because nearly all X-ray beam
measurements were performed in a non-parallel beam. The installation
of an X-ray stray-light bae in front of the mirrors, and the Re ection
Grating Array (RGA) stack at the mirror exit plane (den Herder et al.,
2001), introduced potential complications that were only measured in
vign_09.tex; 29/03/2004; 7:28; p.2

3
Figure 1. Image in the MOS-2 detector plane, of the mean dierence in the to-
tal-band (0.2-12 keV) ux seen by MOS-2 and MOS-1 expressed in Sigma. Bright
pixels indicate an excess of ux in MOS-2 and dark pixels an excess in MOS-1.
long wavelength, visible light at an EUV parallel beam facility (Tock
et al., 1997).
Although the measured geometric vignetting factor at longer wave-
lengths was comparable with predictions, it was necessary to use in-
orbit data to conrm the X-ray energy dependence, and check that
vign_09.tex; 29/03/2004; 7:28; p.3

4
Figure 2. The equivalent image for the Epic-pn detector plane, of the mean dier-
ence in the total-band (0.2-12 keV) ux seen by Epic-pn and MOS-1 expressed in
Sigma. Bright pixels indicate an excess of ux in pn and dark pixels an excess in
MOS-1.
the geometric factor was maintained through the spacecraft assembly,
integration, verication and launch campaigns.
2. Telescope
The design of the XMM-Newton optics was originally driven by the re-
quirement to obtain the highest possible eective collecting area over a
wide band of energies up to 10 keV. The three, nominally identical, mir-
ror systems utilize a shallow grazing angle of 0.5 ô in order to provide
suôcient re ectivity at high energies. The eective area is increased by
nesting 58 mirror shells in each telescope to ll the front apertures as
vign_09.tex; 29/03/2004; 7:28; p.4

5
eôciently as possible. Both the paraboloid and the hyperboloid sections
of each shell were replicated as a single piece from a single mandrel (de
Chambure et al., 1996). Each telescope is complemented by an X-ray
bae, which minimizes X-ray straylight from sources outside the eld
of view, when rays reach the focal plane detectors by single re ection
from the hyperbola.
The energy dependence of vignetting, which is superposed on any ge-
ometrical component, becomes apparent at the critical angle for grazing
incidence at the o-axis angle of the target. There may be an increase
in eective area again at higher energies as a consequence of the fact
that only the innermost mirror shells provide substantial re ectivity.
For a small diameter shell, at high energies, the area increases initially
with o-axis angle: on one side of the mirror the parabola grazing
angle is shallower than for the on-axis geometry. The corresponding
hyperbola graze angle is then larger but because of the asymmetry of
the re ectance vs. angle curve the higher re ectivity on the parabola
dominates the product of the re ectances.
Each shell was individually aligned during assembly of the telescope
to a design accuracy of 10's arcseconds and glued into a mounting
\spider". The whole mechanical assembly was provided with alignment
ducials and optical alignment cubes and mirrors to ensure correct
placement during the various activities for on-ground calibration and
assembly into the spacecraft. The nominal error budget allowed for
possible misalignment of the telescope axis of 30 arcseconds.
Two of the three telescopes were equipped with Re ection Grat-
ing Arrays that also required alignment with the telescope axes. The
three telesope assemblies were mounted on a spacecraft mirror platform
that contained star trackers providing an absolute reference for the
co-ordinate system of the spacecraft.
The focal plane detectors were aligned so that a reference pixel was
located on the nominal telescope optical axis. In the case of the EPIC
MOS cameras the reference was the central pixel of its middle CCD,
while for the PN camera a dead gap at the physical centre of the
camera, between CCDs, meant that the reference pixel was chosen to
be slightly oset to ensure that on-axis targets were not lost onto the
gap. The location of the RGA readout cameras were dened to ensure
that no expected bright emission lines in dispersed spectra would fall
on gaps between its CCD detectors. These reference pixels were the
origin of the DETX,DETY co-ordinate system of the XMM-Newton
Science Analysis System (SAS, Watson et al., 2001), in units of 0.05
arcseconds per pixel.
The physical alignment of the cameras was subject to possible error
in addition to uncertainty in locating the telescope axis, and the design
vign_09.tex; 29/03/2004; 7:28; p.5

6
had to allow also for the possibility of 10's arcsecond relative shifts
due to the eects of launch loads, and eventual dierential shrinkage
of the carbon-bre optical bench tube due to water vapour out-gassing
in orbit. One of the rst in-orbit calibration tasks was to determine
the extent of any such shifts and also determine the co-alignment to
the spacecraft (star-tracker) reference axis. For any observation a user
could potentially request any one of six (including the Optical Monitor)
instruments to be the prime, and for which a preferred detector location
was dened to avoid inter-CCD gaps. The mis-alignment for each of
these \boresight axes" had to be determined. Fortunately the initial
mechanical alignment was suôciently good, and preserved into orbit so
that a single optimised boresight could be dened for all X-ray imaging
congurations, and one for RGA spectroscopic observations. It should
be highlighted that this complicated set of axis denitions is a peculiar
consequence of the multiple telescope conguration of XMM-Newton
compounded by the use of dierent instruments in the same telescopes
and between dierent telescopes.
3. SuperNova Remnant Data
3.1. Observation Configuration for SNR Targets
The measurement of vignetting requires a compact, simple-spectrum,
non-variable source at locations o-axis, with which to compare the
inferred spectrum with that of the same object measured on-axis. True
point sources with reasonable brightness are precluded because the
eects of pile-up (Ballet, 1999) are severe, and furthermore vary with
the changes in o-axis Point Spread Function (PSF), as well as with
the count rate reduction due to the vignetting itself.
Extended objects require a complex ray-tracing and PSF-folding
to account properly for the vignetting component. While a number
of viable targets were selected for the in-orbit calibration, we have
concentrated on G21.5-09 (Warwick et al., 2001) and 3C58 (Bocchino
et al., 2001) for this work. The initial choice of pointing locations was
complicated by the need to ensure that no signicant portion of the
remnants fell near CCD gaps. Given the orthogonal orientation of the
two MOS cameras, together with the totally dierent gap patterns in
the pn (Figure 3), this severely constrained the orientation available,
and an angle 7 degrees rotated from the nominal detector axes, and
a eld angle of 10 arcminutes were chosen for the initial measurements
of G21.5-09.
As a consequence of the grating array angles and blocking fraction,
the vignetting in the MOS cameras is expected to be a strong function
vign_09.tex; 29/03/2004; 7:28; p.6

7
Figure 3. Schematic drawing of the CCD orientations in the 3 co-aligned EPIC
cameras.
of azimuthal angle, so four locations were scheduled for G21.5-09 to
sample the extreme ranges of RGA blocking (see Figure 4).
SNR G21.5-09 is a hard, bright source ideal for determining the en-
ergy dependent vignetting. A set of observations of the softer, somewhat
fainter, SNR 3C58 were subsequently made to supplement the earlier
observations and better sample the azimuthal dependency of the MOS
camera vignetting. Measurements of 3C58 were scheduled to fall within
the central CCD of the MOS cameras, to minimize the possible eect
of varying quantum eôciency over the detector. Again the limitations
of chip gaps cause a compromise in the actual rotations employed, such
that the ensemble of pointings is as shown in Figure 5.
vign_09.tex; 29/03/2004; 7:28; p.7

8
Figure 4. Merged pn image of the 5 major pointings made on G21.5-09 SNR. White
gaps are physical gaps between CCDs or noisy columns
Figure 5. Merged image of the major pointings made on SNR 3C58
vign_09.tex; 29/03/2004; 7:28; p.8

9
Table I summarises the requested pointings and observation details
for these data sets
3.2. Analysis of SNR Pointings
Spatial regions of interest were dened around the centroid of each
SNR, and xed in sky co-ordinates for all observations, ensuring that
the region was large enough compared with the PSF, but small enough
to avoid a CCD gap in any single observation. Background regions
of similar size were selected. Concerns about enhanced particle back-
ground in some of the observations led us to choose regions at simi-
lar eld angle and azimuth to ensure representative conditions, while
strict selection of low background count rate intervals minimised any
systematic eects of any possible incomplete background subtraction.
The analysis proceeded by determining the number of background-
subtracted photon counts per energy bin at various pseudo on- and o-
axis locations of G21.5-09 or 3C58. The relative vignetting between the
corresponding locations were determined according to the count rate
variations. The energy bins' widths were varied semi-logarithmically to
maintain reasonable signal:noise per bin.
vign_09.tex; 29/03/2004; 7:28; p.9

10
Table
I.
Summary
data
for
the
SNR
observations
used
in
the
analysis
Target
Revolution
Observation
ID
Date
RA
2000
DEC
2000
G21.5-09
60
0122700101
2000-04-07T12:35:28
18:33:33
-10:34:01
G21.5-09
S
61
0122700201
2000-04-09T12:22:17
18:33:40
-10:44:18
G21.5-09
W
62
0122700301
2000-04-11T12:25:38
18:32:52
-10:35:47
G21.5-09
N
64
0122700401
2000-04-15T12:25:52
18:33:26
-10:24:02
G21.5-09
E
65
0122700501
2000-04-17T12:13:09
18:34:14
-10:32:32
G21.5-09
NE
244
0122701001
2001-04-09T17:06:14
18:34:23
-10:30:40
3C58
506
0153752101
2002-09-13T04:22:11
02:05:38
+64:49:40
3C58
W
505
0153752201
2002-09-11T04:29:35
02:04:43
+64:51:13
3C58
SW
505
0153751801
2002-09-11T13:09:58
02:05:03
+64:47:38
3C58
S
505
0153752501
2002-09-11T20:03:41
02:05:23
+64:43:52
3C58
E
505
0153752401
2002-09-12T03:20:44
02:06:32
+64:48:06
3C58
NW
506
0153751701
2002-09-13T10:57:39
02:05:18
+64:53:23
3C58
NE
506
0153751901
2002-09-13T17:51:22
02:06:13
+64:51:41
3C58
N
506
0153752001
2002-09-13T23:45:05
02:05:52
+64:55:27
vign_09.tex; 29/03/2004; 7:28; p.10

11
Unless there were gross misalignments of shells within a telescope,
the vignetting in the EPIC PN telescope would be radially symmetric
about its optical axis. True azimuthal variations are expected in the
MOS telescopes as a consequence of dierential shadowing according
to the angles of the RGA grating plates. Verication of the predictions
for these MOS azimuthal variations in vignetting were undermined by
unexpected and signicant variations (10%) in relative vignetting
measured in the pn camera, from azimuth to azimuth. This was at-
tributed initially to a combination of incomplete background correction
and to discrepancies in the exposure dead-time calculations in uenced
by the higher than nominal background. Eventually it was realised that
these relative variations were correlated with camera orientations.
It was recalled that unresolved discrepancies between mirror optical
alignment cube axes and inferred telescope axes measured at the EUV
test facility (Stockman et al., 1997) had occurred. At the time these
orientation discrepancies were claimed to be irreproducible to 20 arc-
second level, but were also seen in similar magnitude and direction
in the Panter X-ray test facility calibration of maximum throughput
orientation (Egger et al., 1997). The variation was in addition to any
xed and systematic oset between the mechanical and optical telescope
module axes (designed to be less than 30 arcseconds). For the PN
camera, we therefore simply vary the location of assumed telescope
optical axis and recompute the expected vignetting function at each
observed location. The axis origin is dened where the dierence in
low energy vignetting for all measured points is minimised.
Once reasonable agreement for the PN data was obtained, we pro-
ceeded to treat the MOS cameras in a similar manner, except in this
case the azimuthal eect of RGA shadowing partially mimics a poten-
tial axis shift. We therefore assumed the nominal RGA performance in
the calculation. In principal the two eects can not be distinguished,
except:
A gross error in RGA shadowing angles would have been detected
in the dispersion relation and/or eective area of that instrument
(not the case)
For most science analysis we just need to have an empirical veri-
cation of the MOS vignetting function, whatever the cause of the
azimuthal changes
vign_09.tex; 29/03/2004; 7:28; p.11

12
Figure 6. (a - upper) Relative (i.e. compared with nominal on-axis location) vi-
gnetting of the pn telescope for an o-axis angle of 11.3 arcminutes from the nominal
boresight location. (b - lower) Relative vignetting of the MOS1 telescope for an
o-axis angle of 10.4 arcminutes, compared with the nominal boresight location.
The theoretical prediction for energy dependent vignetting is shown as a solid line
in each case. This is the leftmost observation depicted in Fig 4
vign_09.tex; 29/03/2004; 7:28; p.12

13
Figure 7. Relative vignetting of the pn telescope after averaging all azimuths around
10.3 arcminutes o-axis. The energy dependence is in good agreement (solid line)
3.2.1. Vignetting Results
A single azimuth vignetting measurement for the pn camera, in the
lowest background exposure, is shown in Fig. 6a. A subsequent cali-
bration observation in circa April 2001 at larger o-axis angle allowed
some measure of sensitivity to the change in  (o-axis angle), and
conrms the validity of the model.
A comparable vignetting measurement for the MOS cameras is shown
in Figure 6b. Due to the lower eective area of the MOS cameras, the
S:N is lower than for the pn camera, and the energy scale is binned
more coarsely. It was found, as with the pn camera, that there was a
potential telescope axis misalignment. However records of the tests in
ground facility were less clear than for those of the pn, because the
installation of the RGA had blocked the access to the mirror alignment
lens for most tests. Relying purely on inferred alignment of the axis
based on the vignetting itself undermines the goal of directly measuring
the eect of RGA azimuthal blocking factor.
3.2.2. Energy Dependence
The pn data sets were relatively close in o-axis angle and should
have no intrinsic azimuthal dependence. We should be able to aver-
age the 4 separate locations of G21.5-09 to check the predicted energy
dependence is correctly reproduced. This is shown in Fig. 7.
vign_09.tex; 29/03/2004; 7:28; p.13

14
Figure 8. Relative vignetting of the MOS1 telescope after averaging all azimuths
around 10.3 arcminutes o-axis. The energy dependence is in good agreement
For the MOS data, repeating the exercise is not really valid, given
the large variation in RGA blocking with azimuth. However to discern
if the placement of RGA gratings and ribs upsets the energy-dependent
lter properties via. dierential shadowing of some sub-sets of shells,
we nevertheless form the same average response in the 2 MOS cases.
There seem to be no signicant energy-dependent discrepancies (see
Figures 8 and 9).
3.2.3. Location of optical-axes
It can be seen that the energy dependence of vignetting is almost
negligible in these data sets up to 4keV. Initially therefore, spectral
parameters were independently found for each SNR by a joint t of
an absorbed power-law to all observations with energy range limited
to E< 4keV and varying normalizations per observation, in order to
reduce statistical eects of spectral determination. The best-t spectral
model was then applied individually to each observation to nd the
relative normalizations, and the energy dependence for E>4keV. After
renormalization the combined data of G21.5-09 and 3C58 were used to
locate the optical axis of each camera using a minimization technique.
A good t to the predicted low energy vignetting, as a function of o-
axis and azimuthal angle, was achieved by applying a small shift in the
optical axis position for MOS-1 (Fig. 10). A larger oset, of the order
vign_09.tex; 29/03/2004; 7:28; p.14

15
Figure 9. Relative vignetting of the MOS2 telescope after averaging all azimuths
around 10.3 arcminutes o-axis. The energy dependence is in good agreement
Figure 10. Comparison of G21.5-09 (stars) and 3C58 (squares) MOS-1 data with
the expected mirror vignetting, centered at DETX=200, DETY=-50. The data have
been corrected for RGA blocking.
vign_09.tex; 29/03/2004; 7:28; p.15

16
Figure 11. Comparison of G21.5-09 (stars) and 3C58 (squares) MOS-2 data with
the expected mirror vignetting, centered at DETX=340, DETY=-1300. The data
have been corrected for RGA blocking.
Figure 12. Comparison of G21.5-09 (stars) and 3C58 (squares) pn data with the
expected mirror vignetting, centered at DETX=1300, DETY=450.
vign_09.tex; 29/03/2004; 7:28; p.16

17
of 1 arcminute, was found to be necessary to obtain a good t for the
MOS-2 and pn telescopes (Figs. 11,12).
4. Alternative Measurements
In order to provide corroborating evidence for these axis shifts, dierent
measures were proposed.
4.1. Source elongation
The PSF broadens with o-axis angle, especially in a direction perpen-
dicular to a vector connecting the source and optical axis positions.
A plot of source PSF elongation versus o-axis angle should therefore
be symmetrical about the optical axis. We selected a large sample of
serendipitously detected sources, after removal of non-point-like ob-
jects, from the 1XMM catalogue, for each camera. Figure 13 shows the
variation of this elongation with o-axis angle for the pn sample. The
centroid of the distribution was found by minimizing the function:
E = A +B 2 + C 4
where E is the measured elongation,  the o-axis angle measured from
the telescope axis and A,B and C are coeôcients.
The elongation E was dened as follows:
the source image out to a cuto radius of 20 arcsec was resampled
in source-centric polar coordinates r and ;
the resulting image was multiplied by r to preserve scaling, then
Fourier-transformed in the  coordinate;
the ratio between the magnitudes of the 0 th and 2 nd Fourier coef-
cients was taken as the elongation.
The best t centroids reveal a qualitatively similar axis shift to
that measured with G21.5-09 and 3C58. The measured values are: PN
(DETX,DETY = 1140,340), MOS1 (DETX,DETY = -320,+540) and
MOS2 (DETX,DETY = -340,-1700).
A small discrepancy was noted for the MOS cameras, again sus-
pected to be due to the eects of the RGA assembly. A raytrace for
a nominal XMM telescope was made, in which multiple sources were
traced through to the focal plane, and then their elongations in fo-
cal spot determined as a function of position in the focus, by simple
Gaussian tting. For an unobscured telescope, the minimum elongation
vign_09.tex; 29/03/2004; 7:28; p.17

18
Figure 13. Relative elongation of point sources in the pn camera as a function of
o-axis angle
occurred at the centre of the focal plane. However for a telescope tted
with a nominal RGA structure, the minimum elongation occurred o-
axis, in a direction parallel with the dispersion axis. It is believed this
can be attributed to shadowing of rays that are intercepted by the
grating plates, restricting the scattering (and hence elongation) in a
direction parallel with the dispersion direction. As the RGA plates
are angled to the telescope axis, the location of elongation minimum is
hence oset. The ray trace estimate of this oset is about 22 1 arcsec.
4.2. Diffuse Background
In (Lumb et al., 2002), the compilation of a set of data from high
galactic elds was described. After exclusion of individual point sources,
this eld represents the average properties of the diuse Cosmic X-Ray
Background (CXB). Although this background represents the superpo-
sition of many unresolved faint sources, the averaging over several elds
with XMM-Newton ensures any \cosmic variance" is minimized, and
the articial eld should be very uniform. In such a case the centroid
of surface brightness distribution should map to the optical axis of
maximum throughput.
This is diôcult to interpret in the case of the MOS cameras in
particular because the apparent vignetting varies in a direction parallel
to the grating array dispersion direction. The dierential blocking of
vign_09.tex; 29/03/2004; 7:28; p.18

19
the grating must therefore be unfolded from any potential telescope
axis tilt eects.
The data set from high galactic latitudes was binned into images
in the energy band 0.5-4keV for each camera. The surface brightness
distribution was projected in detector X, and Y co-ordinates and was
corrected for exposure eects (bad pixels, CCD gaps, CCD dead times
etc.). Next the predicted amount of RGA blocking as a function of
;  was calculated by raytrace, and divided into the surface brightness
proles. The centroid of brightness was then calculated by a polynomial
t. See as an example Fig. 14.
Figure 14. Surface brightness (0.5{4 keV) in spatial bins of the merged image of
several high latitude background elds. The solid curve is the best polynomial t.
The lack of symmetry is attributed to the oset of the circular aperture of the
camera from the centre of the telescope
The main weakness of this approach is that the RGA blocking
is assumed to be correctly modeled, and not left as a free parame-
ter. The justication is supported by the nominal performance of the
RGA dispersion properties as measured in-orbit by the spectrometer
instrument.
4.3. Coma Cluster
The Coma cluster of galaxies is one of the brightest diuse X-ray ob-
jects on the sky, lling the eld of view of XMM-Newton detectors. An
additional possibility to calibrate the vignetting of the mirror system of
vign_09.tex; 29/03/2004; 7:28; p.19

20
Figure 15. Ratio of surface brightness (0.5{2 keV) in spatial bins of the Coma
Cluster, for two dierent camera orientations. Dotted line - vignetting corrected with
initial calibration. Solid line - vignetting corrected according to improved estimate
of telescope axis
Epic pn is provided by performance of a special calibration observation
of the Coma centre in addition to the existing set, described in Briel
et al. (2001). The idea is to use the same region on the sky but with
a position angle of  120 degrees between observations. In this case
a vignetting miscalibration producing an under-corrected part of the
emission in the rst observation will be compared to over-corrected part
in the second. In case of the shift of telescope axis, such deviations occur
symmetrically. so that a ratio map of the two images has one side of
the image being larger and the other smaller than unity.
Additional uctuations on the ratio map are introduced unless OOTE
(Out-Of-Time Events) subtraction is performed. This is a specic fea-
ture of the pn camera (compared to MOS where OOTE are small in
fraction), where events are accumulated in the CCD while the previ-
ous image frame is still being read out. The OOTE may be removed
statistically, using o-line products generated by XMMSAS epchain
program for every observation. In this particular instance the impor-
tance of OOTE is caused by a change in the read-out mode for pn in
vign_09.tex; 29/03/2004; 7:28; p.20

21
the second observation to full frame from extended full frame mode,
that was employed for the other XMM Coma observations, such that
this fraction of smeared events changed from 0.023 to 0.063.
We choose the 0:5 2 keV band for the primary analysis, while
energy-dependent eects where checked using the 0:25 0:5 keV and
5 7:9 keV bands, considering previous data from mirror test results
from the PANTER facility as well as the presence of strong background
lines > 7:9 keV.
In order to achieve good statistics a binning of 3232 of original pn
pixels was employed (128128 for MOS). Border pixels in this binning
can have much lower fraction of valid pixels and were excluded from the
analysis. The best telescope position was chosen to achieve the lowest
scatter among about a hundred independent points of the image ratio
map, for both pn and each MOS camera. The eect of the change in the
position of the telescope axis was emulated in the calibration version
of the exposure map, where by changing the vignetting we still retain
proper position of the detector chips.
In deatil the procedure comprised two main parts: preparation of the
dataset and a loop of calculations repeated with varied input position
of the telescope axis to minimize the spread in the dataset points.
The data preparation part comprised:
screening both observations for background ares, as described in
Briel et al. (2001).
for both observations extracting source and OOTE images in the
0:5 2 keV band
Correcting both images for OOTE
subtracting the instrumental background, using Filter Wheel Closed
background accumulation (for description of this background dataset
see e.g. (Lumb et al., 2002))
Translate the image for one observation to the reference frame of
the other
Calculate the mask le where both observations have suôcient
data. Only FLAG = 0 events are considered (large detector gaps).
Also only the pn event types with PATTERN < 5 are considered.
Discard image pixels absent in at least one observation, using the
cross-correlation of the mask les for both observations. The re-
sulting mask le is retained to be later applied to experimental
exposure maps.
vign_09.tex; 29/03/2004; 7:28; p.21

22
bin the image to achieve good statistics.
The calibration loop comprised:
For input parameters of the test telescope axis position create
exposure maps for both observations
Normalize the exposure map to correct for loss of the ux due to
subtraction of OOTE, by multiplying the maps by (1 f OOTE ),
0.937 and 0.977 for full and extended full frames, respectively
Translate the exposure map for one observation to the reference
frame of the other
Discard exposure pixels absent in at least one observation, using
the pre-calculated mask le
Bin the exposure maps in accordance to binning of the image
De-vignette the images and produce their ratio
estimate the dispersion around the mean. The position of the
telescope axis is searched to minimize this dispersion.
Uncertainty in the parameter estimate is calculated using 90% con-
dence level estimate for the  2 method. However the systematic un-
certainty seems to drive the error, and is related to an astrometric
uncertainty for the position of each image.
Epic pn data comparison shows a very small dispersion at a telescope
axis position DETX = 1243  30 pixels DETY = 402  30) pixels in
detector coordinates. The one-dimensional scatter of pixels around the
mean is plotted in Figure 15. Note that the mean value of 1.000 is
not enforced and is an additional argument in favor of the method.
The original calibration introduced a 14% r.m.s. scatter in the surface
brightness data, while the proposed revised calibration decreases the
r.m.s. to 3%, comparable with the statistical noise. This result is con-
sistent with the large r.m.s. scatter found in pn-MOS1 comparison of
serendipitous sources (see Figures 1 and 2 and Saxton, 2002).
Table II illustrates the quality of the calibration.
A change in the position twice the quoted error bar, presented in Ta-
ble II above produces noticeable changes on the image being dimming
and brightening of the opposite sides. Variation in the background level
can introduce additional 1% errors for furthermost from on-axis pixels.
The adopted error on the position of the telescope axis includes
various systematics e.g. caused by the small misalignment between
the two Coma pointings and changes in the instrumental background
vign_09.tex; 29/03/2004; 7:28; p.22

23
Table II. Residual dispersion in the pn vi-
gnetting calibration.
Radius Dispersion, %
arcmin best t at 2 sigma deviation
8{11 3.712 3.826
4{8 2.376 2.422
0{4 2.186 2.199
level, while the formal statistical error is smaller, 10 pixels. However,
the precision at which the position of the telescope axis is achieved
exceeds by far the typical resolution at which e.g. the exposure maps
are calculated (200 DETX/DETY pixels or 10 arcseconds).
Figure 16. Ratio of the new and old exposure maps for MOS 1 and 2, showing the
amplitude and direction of the change. Fine structure on these images (a line and
annuli) is an artifact produced by nite precision at which the exposure maps are
generated. Vignetting is azimuthally symmetric, while the line-like feature of CCD
gaps are parallel to the direction of equal RGA transmission, and not this vignetting
shift.
4.4. Calibrating MOS vignetting using the Coma
observations
Calibration of the MOS vignetting using the Coma cluster has been
rst done by cross-calibration with pn and later repeated using a self-
calibration method, as has been described above for pn. Table III lists
three independent measurements of the positions of the telescope axis
obtained using both Coma MOS observations, 2001 and 2000 denoting
the MOS-pn comparison, using the year of MOS observation to describe
vign_09.tex; 29/03/2004; 7:28; p.23

24
the observational dataset, the 'average' of the two and 2000 vs 2001
'self ' calibration of MOS.
Table III. Positions of the MOS telescope axis from
the analysis of Coma cluster. Units are internal camera
values of 0.05 arcsecond.
Dataset DETX DETY Dispersion, %
MOS2
2001 653  60 1260  30 4.50
2000 440  60 1250  30 4.65
average 550  60 1255  30
self 492  60 1256  30 4.73
MOS1
2001 136  40 134  70 4.56
2000 87  40 281  70 4.76
average 110  40 200  70
self 159  40 303  70 4.68
The dierence in the normalization between 2000 and 2001 MOS1
observations amounts to 6%, and is due to dierences in the best-t
positions. The self-calibration nds the mean ux ratio between two
observations of 1.005, which is acceptable. The similarity of the results
of cross and self calibration of MOS is reassuring and demonstrates
negligible eect of possible chip-to-chip sensitivity variations for MOS.
However, the dispersion achieved in the best-t position is worse, com-
pared to pn results and could partly be caused by lack of delity in the
description of the RGA shadowing in the current version of SAS.
Fig.16 shows the magnitude of the proposed changes in the vi-
gnetting for MOS 1 and 2 cameras. Only a small change is proposed for
MOS 1, while vignetting for MOS 2 is substantially revised. The eect
of RGA-vignetting degeneracy reduces the sensitivity of the method
to the absolute value of the telescope shift, yet the direction of the
shift is rather well determined. Since the problem originates in the low
contrast in the exposure map, caused by these changes, it implies little
importance of the precision in the MOS calibration to absolute ux
measurements, however, a possible caveat could be larger uncertainty in
the energy-dependent vignetting eects, that are important at energies
> 5 keV. Achievement of the agreement in the MOS position with other
calibration methods presented in this paper is therefore of importance.
vign_09.tex; 29/03/2004; 7:28; p.24

25
Table IV. Summary of the dierent axis displacement values for the EPIC cameras
inferred with the various measurement techniques. Units are internal camera values
of 0.05 arcsecond in \Detector" coordinates.
Instrument M e t h o d
coordinate G21.5-09/3C58 Source Diuse Coma
Elongation Background
pn DET X 1300  300 1140  200 1100  300 1243  30
pn DET Y 450  300 340  200 400  300 402  30
MOS-1 DET X 200  300 320  200 0  200 110  40
MOS-1 DET Y 50  300 540  200 0  200 200  70
MOS-2 DET X 340  300 340  200 300  200 550  60
MOS-2 DET Y 1300  300 1700  200 1300  200 1255  30
4.5. Comparison of Methods
The main method is important in that it denes rather well the energy
dependent eect of the vignetting but gave some concerns about the
rather large oset in telescope axis. The later methods give condence
that this oset is real, and give similar magnitudes for the eect.
Table IV summarises the inferred axis shifts from these dierent
existing measurements.
The discrepancy in axis value obtained by source elongation method
for the MOS cameras is partly explained by the dierential shadowing
of RGA stack that modulates the PSF shape. this was modelled by
ray trace as described in section 4.1. The RGA dispersion direction
is parallel with the MOS1 detector -Y axis, and the MOS2 detector
+X axis. The calculated shift due to dierential shadowing amounts
to 44020 units, which reduces the discrepancy in that axis to 1.
The discrepancy in the orthogonal direction is not explicable by the
ray trace, but is only 2. Additional systematic uncertainty may be
brought about by the non-circular shape of the PSF (roughly pentangle
and triangle shapes for MOS1 and MOS2 respectively) that is invariant
with eld angle and due to some distortion encountered on mounting
the mirrors to the spacecraft interface plate.
5. CONCLUSIONS
The energy dependent vignetting calibration can be well matched to
pre-launch predictions, but only on an assumption that the telescope
vign_09.tex; 29/03/2004; 7:28; p.25

26
optical axis is not perfectly aligned with the telescope boresight. This is
not unexpected following diôculties on-ground of maintaining and/or
measuring the telescope axis to better than 10's arcseconds. We note
that the assumed telescope axis misalignment implies that \on-axis"
targets at the common boresight location are actually at a slightly
dierent vignetting value per telescope. We speculate that this partly
accounts for some of the observed ux discrepancies between the MOS
and pn cameras (Figure 17). After reviewing these data sets, it was
decided that the XMM-Newton calibration database would be up-
dated in 2004 to account for new reference axes to be centred at PN
(DETX,DETY = 1240,400 ), MOS1 (DETX,DETY = 100,-200 ) and
MOS2 (DETX,DETY = 500,-1250 ).
Figure 17. Ratio of uncorrected and vignetted eective areas for an on-axis target.
The ux dierences for typical 0.5-2keV band will be  a few % for typical objects,
and a small dierence in recovered spectral slope will be caused by the change with
energy
6. Acknowledgments
All the EPIC instrument calibration team who have contributed to
understanding the instrument are warmly thanked for their eorts.
We thank the XMM-Newton Science Operations Centre team for their
help in scheduling the calibration observations that needed special
arrangements. AF acknowledges receiving the Max-Plank-Gesellschaft
Fellowship. XMM-Newton is an ESA science mission with instruments
vign_09.tex; 29/03/2004; 7:28; p.26

27
and contributions directly funded by ESA Member States and the USA
(NASA).
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