Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://xmm.vilspa.esa.es/docs/documents/CAL-TN-0017-1-0.ps.gz Äàòà èçìåíåíèÿ: Thu Jun 21 18:04:18 2001 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:17:02 2012 Êîäèðîâêà:

Status of the RGS response
F. Paerels and J.W. den Herder on behalf of the RGS consortium
June 19, 2001
Abstract
This note decribes the present status of the RGS calibrations (June
2001). It should be read together with the instrument description
(RD \Gamma 1) and the release notes of the current calibration files. More
details are given in various internal calibration reports which are listed
at the end.
Contents
1 Introduction 3
2 Response representation 3
3 Mirror 4
3.1 Mirror response model . . . . . . . . . . . . . . . . . . . . . . 4
3.2 In­flight verification . . . . . . . . . . . . . . . . . . . . . . . 5
4 Reflection Grating Array 5
4.1 RGA Response Model . . . . . . . . . . . . . . . . . . . . . . 5
4.2 Inflight verification . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Reflection Grating Camera 10
5.1 RFC Response Model . . . . . . . . . . . . . . . . . . . . . . 10
5.2 In­flight verification . . . . . . . . . . . . . . . . . . . . . . . 12
6 Line Spread Function and wavelength scale 14
6.1 Line Spread Function . . . . . . . . . . . . . . . . . . . . . . . 14
6.2 Wavelength scale . . . . . . . . . . . . . . . . . . . . . . . . . 14
1

7 Effective Area 14
7.1 Individual Components . . . . . . . . . . . . . . . . . . . . . 15
7.2 Estimated Accuracy of the Pre­flight Effective Area Model . . 16
7.3 In­flight Verification . . . . . . . . . . . . . . . . . . . . . . . 17
8 Background in the RGS 18
A References 20
2

1 Introduction
As a general principle, the calibration of the RGS is based on a series of
explicit physical models for the various components of the instrument. The
parameters for these models were calibrated in the laboratory, and a gen­
eral pre­launch calibration was generated. This stage of the process is doc­
umented in a series of internal RGS Memo's, and a series of SPIE papers.
After launch, the model has been compared to astrophysical data, which
has prompted a number of refinements. Wherever possible, these adjust­
ments have taken the form of adjustments to the existing model parameters,
and the introduction of a few new ones, which means that the model still
has near­full generality, and can be inter­ and extrapolated as needed to
accommodate wavelengths and angles at which no explicit calibration data
exists.
2 Response representation
Monochromatic photons, incident on the spectrometer, will be (re­) dis­
tributed in angular­ and CCD pulse height space. Integrals over this 3­
dimensional 'Point Response Function' (PRF) yield the 'Point Spread Func­
tion' (PSF; the integral of the PRF over CCD pulse heights), and the 'Line
Spread Function' (LSF; the integral of the PRF over pulse heights and cross­
dispersion direction). Both the amplitude and, usually to a lesser extent,
the shape of the PSF and the LSF depend on the limits of integration on
the pulse height and cross­dispersion angle. Using a physical model for all
different components, allows for the generation of a correct response for any
reasonable selection in the pulse height and the cross­dispersion angle.
The response is the convolution of the angular response of the telescopes,
the 2D angular reponse of the Reflection Grating Arrays (RGA's), and the
CCD response. The observed monochromatic 2D response at the focal plane
also depends on the overall focusing of the instrument (i.e. whether the
detector bench is in the correct position), and on the detector quantum
efficiency.
3

3 Mirror
3.1 Mirror response model
The mirror module angular response and focusing are generated with a ray­
trace model written at Columbia University that incorporates the following
effects:
ffl The focusing of the telescope is modeled with the shape parameters for
the paraboloid and hyperboloid sections of the shells as provided in the
initial design document for the mirror modules (RD­2). Likewise, the
radii and thicknesses of the shells have been set at their design values.
The mirror modules have focal lengths that are slightly different from
their design values; this effect is dealt with in the RGS simulations by
simply adjusting the detector position to the new focus, rather than a
change to the shape parameters of the mirrors.
ffl Reflectivity of the Au mirror shells, as a function of wavelength and
graze angle (since we work at wavelengths – ? ¸ 4:5 š A, this effect is
only important at the extreme short wavelength end of the RGS). The
optical constants for this calculation are taken from the Henke Tables
for Au, available at the LBNL web site.
ffl Axial slope errors. These are modeled with a Lorentzian distribution
(in two angular coordinates) of adjustable width. The width has been
adjusted to reproduce the performance of the flight units.
ffl Distribution of mirror shell symmetry axes: to complement the angular
reponse as generated by the previous item, the symmetry axis of each
shell was assigned a small radial displacement from the mirror mod­
ule symmetry axis, drawn from a Gaussian distribution of adjustable
width, with a random angular phase.
ffl Scattering by microroughness on the mirror surfaces is not included
in the model. Given the level of roughness, no more than a very
small fraction of the light ( ! ¸ 0:2%) is ever scattered by the mirrors at
wavelengths in the RGS band.
The angular response generated with this model was compared to cali­
bration images obtained during the Ground Calibration campaigns (treating
the slight magnification of these images induced by the finite distance to the
source with the raytrace model).
4

3.2 In­flight verification
The results of the model were verified with images obtained in flight. The
flight data are drawn from observations of PKS0312\Gamma770 (orbit 0057). Using
the energy resolution of the MOS CCD detectors, the photon energies were
restricted to the RGS range. The total count rate in this source is low enough
that pileup effects do not appreciably affect the spatial distribution of the
photons. Images were integrated over the dispersion­ and cross­dispersion
directions, before comparison with the model (RGS data, for most purposes,
is integrated over a finite mask in the cross­dispersion direction, so that only
the integrated telescope resonse matters).
The comparison for both telescopes separately indicates satisfactory agree­
ment between the mirror model and the data (deviations in the core of the
integrated distributions ! ¸ 10% between model and data, cf. RD­3).
For reasons of computing efficiency, the modelled mirror response has
been fitted by a sum of a Gaussian and Lorentzian and this function is used
in the RGS response generator (see RD­4).
4 Reflection Grating Array
4.1 RGA Response Model
The RGA response model incorporates the following:
ffl The overall geometry of the integrating structures of the RGA's (the
grating centers lie on a toroidal surface, arranged in six rows, generated
by tilting a Rowland circle around an axis defined by the telescope
focus and the spectrometer blaze focus [– = 15 š A]).
ffl The location and orientation of each RGA with respect to its mirror
modules has been derived from precision metrology. These parameters
have been slightly refined using the line spectra of Capella and HR1099
(see the section on wavelength calibration).
ffl The focusing of the RGA's depends on the correct positioning of the
RGA wrt. to a mirror module, the correct positioning of the RGS
Focal Plane Camera (RFC) wrt. to the RGA, and knowing the focal
lengths of both RGA's and Mirror Modules. Each of these parameters
was calibrated in X­ray light in the laboratory, using a long­beam
facility to approximate plane parallel incident waves. The residual
5

aberration due the finite source distance was modeled with raytrace
codes. Final positioning of the optical elements on the spacecraft
included corrections for the expected change in length of the telescope
tube due to outgassing, slight thermal corrections, etc., as calculated
by the spacecraft contractor.
ffl The locations of the gratings in this structure are known to high pre­
cision from metrology, and uncertainties in these positions do not con­
tribute measurably to the shape and width of the PSF. The angular
orientation of the gratings was actively controlled during integration
using an interferometer. Counting fringes in the interferogram of the
gratings, compared to a reference plane, in principle allowed for a pre­
cision of a few arcseconds. These orientations were recorded for each
grating as it was fixed in the integrating structure.
Testing at the Panter Long Beam facility of the Max Planck Institut
fur Extraterrestrische Physik subsequently revealed a slight aberration
in the first grating assembly (RGA1, on RGS2), which could largely
be corrected for by a slight adjustment of the focal length of the unit
(6 mm longer). The origin of the aberration was found in a system­
atic error in the angular interferometer equipment used to control the
orientation of the structure at integration. The focal length adjust­
ment was calculated using an explicit model for this systematic effect
(which yielded the correct actual angular orientations of the gratings),
which was subsequently experimentally verified at the long beam facil­
ity. Model calculations and measurements are in excellent agreement,
so that there is no doubt about the actual focal length of RGA1. Mea­
surements of the shape of the LSF revealed that RGA2 also exhibited
some additional variance in the grating orientations, leading to a pro­
file width slightly larger than expected. A preliminary calibration of
this effect was performed on the ground using the monochromatic light
sources available, but final calibration was postponed to flight, since
the lab sources were found to be not sufficiently monochromatic.
RGA2 (on RGS1) was subsequently constructed with corrections to
the equipment, and performed entirely to specification in tests at the
long beam facility, both with respect to the focal length, as well as
with respect to the shape of the PSF.
ffl The figure of each grating was measured using an IR interferometer.
The distribution of surface slopes was calculated, and these distri­
6

butions, modeled as Gaussians with individual widths, were used to
model the effect of grating non­flatness (use of the explicit surface fig­
ures does not increase the accuracy of the model, and using a simple
parameterized analytical distribution is much faster). This term is
almost negligible in the total budget of perturbations.
ffl The reflectivity of each grating was measured for selection and cali­
bration purposes. The theoretical reflectivity model will be discussed
below, under Effective Area. The reflectivity in principle enters into
the PRF, because different gratings contribute different perturbations
to the PRF, so that the final PRF is made up of the weighted per­
turbations introduced by each of the gratings. The weights are the
products of reflectivity times a vignetting factor times an illumination
factor (fraction of the grating illuminated by the optics). In practice,
this coupling between PRF and efficiency is only a weak effect.
ffl Surface roughness on the gratings scatters light out of the diffracted
beams, and the angular response of the RGA's should strictly speaking
again be a weighted sum that includes the angular redistribution due
to the scattering by each grating. In practice, we employ a single
scattering redistribution function (or kernel), with which the beam
pattern of the RGS is then convolved.
We calculated a simple model 2D scattering redistribution kernel,
based on scalar diffraction theory, in the first order perturbation ex­
pansion (small surface roughness) and small angle approximation. Once
a characteristic power spectral density function for the surface rough­
ness has been chosen, this model has two free parameters, a surface
roughness rms amplitude, and a correlation length. The fraction of
light scattered is not a free parameter, but follows directly in terms
of the surface roughness, the correlation length, the radiation wave­
length, the incidence angle on the grating, and the dispersion angle.
Examination of the preflight angular response and effective area data
indicated that scattering occurs on two different angular scales, corre­
sponding to two different correlation lengths. 'Small Angle Scattering'
scatters light out of the core of the profile, over a (wavelength and dis­
persion angle dependent) width of order a few RGS spectral resolution
elements. The 'Large Angle Scattering' is responsible for a faint con­
tribution of 'inter­order' scattered light, far outside the core of the
spectrometer profile. This faint light is still important: it contains
7

a wavelength­ and dispersion angle dependent fraction of the total
dispersed light, and to first order therefore appears as an important
correction to the effective area associated with a given spatial/pulse
height mask.
The small angle scattering was calibrated in the laboratory on a se­
lection of individual gratings. An adequate description of the average
scattering kernel was found in terms of a Gaussian power spectral den­
sity. Subsequent comparison of the small angle scattering model with
monochromatic line images obtained during the end­to­end ground
calibration at the Panter facility indicates that the model works very
well over its expected range of validity. The scalar diffraction approx­
imation may become questionable at the shortest wavelengths, where
the interaction of the radiation with the grating material becomes rel­
atively more important. The small surface roughness approximation
implies that the scattering model becomes questionable whenever the
total amount of scattered light becomes a major fraction of the to­
tal diffracted light. When that happens, the angular distribution of
scattered light start to deviate from the simple model we employ. To
model the fraction of scattered light in this regime, we extrapolate the
integrated scattering probability based on the simple assumption of a
Gaussian distribution of surface perturbations, to obtain a probability
that coincides with the explicit scattering model at small probabili­
ties, and has the correct saturation behavior at large probability. The
fraction of small­angle scattered light only exceeds 20 % shortward of
¸ 12 š A in first order, and shortward of ¸ 15 š A in second order.
The large angle scattered light produces observable scattered light
along the dispersion direction ('inter­order light'), as well as in the
cross dispersion direction. In both directions, the angular distribu­
tion integrated over the other direction appears to be satisfactorily
described by a Lorentzian, which implies that the roughness can be
described by a single isotropic exponential autocorrelation function.
The two free parameters, the large angle scattering correlation length,
and the large angle scattering surface roughness parameter, were cal­
ibrated on laboratory data, and subsequently refined using in­flight
data.
The angular intensity distribution is reasonably well modeled (discrep­
ancies between model and data ! ¸ 10% close to the main diffraction
peaks, and ! ¸ 30% far from the peaks, out to beyond second order),
8

somewhat surprising given the fact that the small angle approximation
is not supposed to really work here. But the most important effect of
the large angle scattering is actually in the 'aperture correction' to
the effective area for a chosen spatial/pulse height mask, and the in­
tegral scattering distribution is less sensitive to the approximations.
Nevertheless, at the shortest wavelengths, where scattering is most
important, it was found necessary to incorporate an empirical modifi­
cation to the aperture correction, which was modeled ad­hoc as a slight
wavelength dependence to the surface roughness parameter that sets
the amplitude of the scattered light. The rms amplitude of the small­
coherence length surface roughness is comparable to the amplitude of
the large­coherence length roughness (i.e. small angle scattering), so
that the aperture correction is ! ¸ 20% for a typical integration mask,
for – ? ¸ 12 š A in first order. With the value of the correction itself
accurate to ! ¸ 20%, we estimate that the typical uncertainty in the
aperture correction is ! ¸ 5% at the shortest wavelengths, and negligi­
ble at longer wavelengths.
4.2 Inflight verification
The in­flight calibration of the overall RGS LSF is particularly important
in view of the following. RGA1 (RGS2) was mated to a mirror module that
was not identical to the one used during the focusing tests at the long beam
facility, and for the overall performance of this RGS we therefore have to
rely on modeling of the imaging performance. In addition, the focal lengths
of both mirror modules were determined to be slightly but significantly
different from the design values. This deviation was explicitly taken into
account during integration of the instrument onto the spacecraft, but for
RGS it was never tested on the ground.
The flight calibration of the PSF was carried out using the emission line
spectra of the bright coronal stars Capella, HR1099, Procyon, – And, and
AT Mic. Measured line shapes were compared with predicted shapes for
bright, isolated emission lines; in practice, the list contained most or all of
the following transitions: O VIII Lyff –18:97 š A, O VII n = 2 \Gamma 1 resonance
–21:6 š A, N VI Lyff –24:78 š A, C VI Lyff –33:73 š A, Fe XVII –15:01 š A (first
and second order), Fe XVII –16:78 š A (first and second order), Ne X Lyff; fi
–12:13; 10:24 š A. A very good agreement between the predicted and measured
line shapes was found. Details of this comparison are given in RD­6.
Finally the resolutions deduced for the above mentioned emission lines
9

was compared to the pre­flight predictions (see RD­4). Apart from the
various unit componets (mirror and grating angular distributions), the line
shapes depend also on the proper alignement of the units (e.g. defocussing).
Not all details of this alignment could not be determined preflight as the
line shapes were tested using a finite source distance (and hence a different
position of te RGAs with respect to the mirrors). In addition the RGA1
(RGS2) was mounted to a mirror module with which it had not actually
been tested on the ground. Therefore the LSF was compared to a model
that had the focusing of the spectrometer (i.e. the distance between the focal
plane camera and the RGA) as a free parameter. No significant defocussing
ot either RGS was detected (see RD­4) and some angular broadening was
introduced. The resulting model for the shape of the core of the LSF matches
the observed profiles to ! ¸ 5 \Gamma 10% within ¸ 2 FWHM's from the center, in
either direction (RD­6).
5 Reflection Grating Camera
The Reflection Grating Camera contains an array of 9 back­illuminated
CCDs on the Rowland circle. Using the energy resolution of the CCDs,
it is possible to separate te orders and the energy of the photons is deduced
from the position of the X­ray event, using the dispersion equation.
5.1 RFC Response Model
The response of the focal plane camera consists of a detailed response model
of each CCD and a model of the camera itself and includes the following
components
ffl The dimensions of the CCD itself. As these are set by the CCD pro­
duction process, these could be simply taken from the manufacturer.
In practice on chip binning of 3 \Theta 3 pixels is applied to reduce the
dark current. The resulting bin sizes are 81 ¯m squared.
ffl In addition to the unit alignement, the position of each CCD was
measured with a typical accuracy of 10 ¯m in the dispersion and cross
dispersion direction and somewhat less in the direction perpendicular
to the CCD plane.
ffl The quantum efficiency of each CCD was measured with a typical
accuracy of a few percent at a number of discrete energies (from C­K
10

at 0.277 keV up to Cl­K at 2.622 keV). These results were in excellent
agreement (better than a few percent) with the modelled QE using
the nominal thicknesses of the various CCD components (Si thickness,
a MgF 2
isolation layer and a Al layer with selected thicknesses to
reduce the sensitivity of the devices for optical light). Only at the
lower energies (below the O­K edge) the uncertainty increases from a
few percent to typically about 10 % (at low energy it becomes also
dependent on the used onboard event selection parameters).
ffl The uniformity of the Si thickness was determined by measuring the
number of fringes between the gate structure and the Al layer on top
of the backside. Typical accuracy of this interferometric measurement
is 140 nm, resulting in a very small uncertainty in the QE for X­rays
around the Si­edge. The typical thickness of the RGS devices is 25 --
31 ¯m and the effect is limited to the range between 1.3 and 1.8 keV
(see RD­8 for details).
ffl The thickness of the MgF 2 layer and Al layer on top of the CCDs has
been specified by the manufacturer with a typical accuracy of 10%.
In view of the thicknesses of these layers (¸ 25 nm for MgF 2 and
¸ 45, 68 and 75 nm for the Al) the effect on the QE is very small.
The uniformity of the Al layer has been verified using a very long X­
ray exposure of selected devices. Within the statistical accuracy, no
deviations from a homogeneous Al layer was observed (see RD­21).
The effect of the uncertainty on the QE due to these variations is
negligable except for the lower energies (below 0.5 keV) where it could
increase to a few percent (see RD­8 for details).
ffl Apart of the QE the pulse shape distribution needs to be modeled
as selections in this data space are applied to reduce the telemetry
rate and to separate the different orders at a given position of the
detector. A simplified phenemenologic model (see RD­7) has been
implemented for this redistribution, based on data collected during the
long beam test at the Panter facility (where the CCDs were illuminated
by almost mono­energetic energies). This model includes the energy of
the incomming photon, the charge collection efficiency, the absorption
depth and an event threshold (below which the pixels will be rejected
on­board). Provided the data selections are reasonable (e.g. more
than 90 % of the incident photons fall within the selected pulse height
region, the accuracy of this model is better than a few percent.
11

ffl To convert the recorded charge to the correct X­ray energy one has
to subtract the so­called dark frame and to apply the proper energy
conversion. The dark frames include the dark current, the optical load
of the CCDs due to straylight and any electronic effect during readout.
These were determined prior to flight but have been updated since
then using a number of bright astrophysical sources and the energies
corresponding to the 4 on­board calibration sources in each camera.
Details are given in RD­9.
ffl The charge transfer efficiency was determined in the lab using long flat
field exposures and analysing the pulse height spectra as a function of
the number of serial and parallel transfers. Due to mechanical stress
near the edges of the devices during the production, the CTI in the 20
columns close to the edges is significantly worse. This is corrected in
the pulse height distributions.
ffl Prior to flight hot columns and pixels were identified. Most of the hot
pixels produce a charge which is just above the set onboard thresholds
for the pixel transfer to the ground. Hence, these 'warm' pixels are
not really hot and their occurance depends also on the set thresholds.
5.2 In­flight verification
During the flight various parts of the RFC response were verified. Using the
flight data the average signal of the dark frames and the gain of the signal
chains (using the on­board calibrators and known emission lines) was veri­
fied (and updated). Also the CTI was updated (using a set of observations
on Mkr 421). This information was only used to update the serial CTE
as the X­rays are recorded for one position in the parallel direction of the
CCD (hence it is impossible to separate the gain from the CTI effects for
the paralllel transfers). It was confirmed that the pre­flight parallel CTI is
consistent with the flight data. Combining these results the CCD redistri­
bution function (the energy scale) is expected to be accurate to 1 %. Some
of these parameters (CTI, dark frames, gain) are regularly monitored and
will be updated to stay within the specified accuracy range.
Detailed analysis of the occurance of hot pixels and columns has indi­
cated their appearance and disappearance over time. Different algoritms
have been identified to reject most of the hot items from the data (see RD­
10 and RD­11). For sources with a very low intensity, it can, however, not
be excluded that at a low level not all 'hot' pixels are rejected. For these low
12

intensity sources this will be more significant. In the spectra (as function
of wavelength) this will translate into a single channel which is significantly
higher than its neighbouring pixels (and not follow the shape of the line
spread function).
Potential contamination on the detectors is monitored by comparing the
countrates for the four on­board calibration sources with their pre­flight
values. As two different source energies are employed (F­K at 0.766 keV
and Al­K at 1.48 keV) a change in their relative intensity would be an
indication of contamination build up (ice) on the cooled detectors. Based
on these ratio's and their abolute intensity there is no reason to assume such
contamination (see RD­12).
Comparison of the spectra of the two RGS instruments revealed two
differences. One global difference which is discussed in some detail in the
section about the effective area. In addition CCD2 at RGS2 showed a ~ 20 %
lower countrate than its two neighbours whereas this was not observed for
RGS1. It was verified that this was not due to an incorrect thickness of the
Al layer by looking at one of the most bright objects on the sky (Canopus, see
RD­13). By comparison of the spectra for a large set of data (PKS2155 and
Mkr421) and looking at the first and second order, a reasonable consistency
between the two instruments was obtained after postulating an additional
40 nm SiO 2 layer on RGS2/CCD2. Although another material cannot be
excluded, this gives a good description of this effect within the expected
accuracies.
Detailed comparison of the CCD redistribution function for a bright
BL Lac (Mkr 421) indicated that the partial event tail was not correctly
described (see RD­15). This tail is due to events which are absorbed close
to the back side of the CCD and loose part of their charge to the surface.
Although the effect on the QE is limited (less than a few %) for bright
sources these tails dominate over the background. Therefore this partial
event tail was included in the CCD model using pre­flight synchrotron data
as reference (see RD­16).
Combining all these results it is expected that the accuracy in the detec­
tor QE is ! 5% for energies above the O­K edge and about 10 % below this
edge provided that the selections in the CCD pulse height are large enhough
(? 90%).
13

6 Line Spread Function and wavelength scale
6.1 Line Spread Function
The line spread function was verified on a number of emission lines as re­
ported in section 4.2 and is consistent with the expectations. Occasionally
features in the spectra are observed which are essentially one CCD bin wide.
These are probably due to the fact that, especially for low intensity sources,
the algoritm to remove the warm pixels is not perfect. Such channels should
be removed. Combining a larger set of data for strong emission lines may
improve the description of the LSF further, but for almost all analysis this
should not affect the results. In the cross dispersion direction the distri­
bution as measured in flight turned out to be broader and this has been
included in our model (see RD­17)
6.2 Wavelength scale
Using flight data for HR1099, Capella and AB Dor, the wavelength scale
was calibrated. The difference between the expected and measured wave­
lengths was minimized by adjusting some pre­flight alignment parameters
(well within the known accuracy of these parameters). The only exception
was the position of the emission lines on RGS1/CCD1 which might be off by
about 150 ¯m. This needs further confirmation. The resulting wavelength
calibration currently shows a random rms residual of ú 8 mš A with occasional
excursions of 20 mš A(RD­5). One should be aware, however, that this has
been proven for a limited dataset only and depends somewhat on the star
tracker accuracy (depending on the number of stars observed an absolute
measurement accuracy of 4 arcsec or better is possible). Careful continued
study may reduce this number further (e.g. incorporating improved knowl­
edge of the astrophysical emission spectrumi, using the information provided
by the OM and/or EPIC).
7 Effective Area
The effective area of the spectrometer at a given wavelength and in a given
spectral order, at a given angle of incidence on the mirrors, consists of the
product of the efficiencies of its various components, integrated over all
angles and pulseheights, times an 'aperture correction' associated with a
given finite integration 'mask' in cross­dispersion/CCD pulseheight space.
14

This aperture correction can be calculated from the known shape of the
PRF.
7.1 Individual Components
The total efficiency of the instrument consists of the following factors:
ffl The efficiency of the mirror module. This item was taken directly from
the mirror calibration program.
ffl The fraction of the focused light intercepted by the gratings. This
fraction was calculated directly using the same raytrace model used to
model the PRF.
ffl The reflectivity of the gratings. Theoretical grating reflectivities were
calculated directly from a numerical solution to Maxwell's equations,
using the Henke optical constants. The free parameters in this model
are the average blaze angle of the grating groove facets, and the slight
deviations from a perfect triangular groove profile.
The blaze angle was constrained using a set of reflectivity calibrations
on a large set of individual gratings obtained with a dedicated X­ray
calibration facility at Columbia University, for a suite of angles of
incidence and wavelengths, and in several spectral orders. This set
was complemented by a very detailed reflectivity calibration on four
gratings at the Bessy synchrotron.
The groove shape was deduced in two steps: a lowest order modulation
on top of the overall triangular shape of the grooves was parameter­
ized in terms of a single sine wave, as suggested by AFM images of
selected grating grooves. Its amplitude was constrained using the set
of reflectivity measurements described above. The effect of higher or­
der modulations of the groove surface is to primarily redistribute the
diffracted light over the lowest couple of diffraction orders. The collec­
tive effect of the higher order modulations was parameterized in terms
of the effective correlation length of the modulations, and their aver­
age amplitude, and these two parameters were constrained from the
measured ratios of the efficiencies in the lowest four diffraction orders
(including zero order) at two different wavelengths.
ffl The effect of vignetting of the dispersed light by neighboring gratings
in the RGA. At dispersion angles larger than the dispersion angle at
15

the blaze wavelength in first order, a fraction of the dispersed light is
vignetted by the next grating in the RGA. This factor can be calculated
analytically. A number of gratings were replaced with stiffening braces
in the RGA design, and the small correction factor associated with the
difference in vignetting for gratings next to these braces was calculated
with the raytrace code.
ffl The quantum efficiency of the CCD detectors. These are calculated
based on the Henke absorption coefficients for the known and mea­
sured thicknesses of the various components in the CCD (Si thickness,
MgF 2 isolation layer and Al filter). These were verified by a set of
independent lab measurements. By applying a model for the pulse
height redistribution, the QE can be determined for varying selections
in this data space. Various other corrections such as gain and CTI are
directly applied to the measured data before they are compared with
the models using the instrument response.
7.2 Estimated Accuracy of the Pre­flight Effective Area Model
The effective area model, based on the product of the calibrated models for
the various components, has no free parameters, and a direct comparison to
the effective area as measured at the Panter Long Beam facility therefore
yields a direct estimate of the accuracy of the model. To carry out this
comparison, we used the effective area model to predict the effective area
specifically for the Long Beam Test geometry. Measurements are available
at Si K, Al K, Mg K, Cu L, Fe L, and O K. We find that the agreement
between the model and the measurements is better than 5% at wavelengths
longer than 9 š A in first order, and better than 10% in second order. First
order efficiency appears to be systematically underpredicted at wavelengths
shorter than 9 š A, by up to 15% at Si K (the shortest wavelength at which
we have calibration data). The fact that this latter discrepancy arises at
the shortest wavelengths indicates that it is most likely due to a systematic
deviation in the grating reflectivity model, which is very sensitive to small
changes in the blaze angle and groove profile in this wavelength range. Note
that there might also be a small contribution arising from a systematic in the
mirror reflectivity. As one approaches the Au M edge, any systematic error
in the modeling of the reflectivity of Au appears raised to the third power in
the RGS efficiency. We deferred a final assessment of this systematic until
the in­flight verification of the instrument performance (see below).
16

Third order measured efficiencies show discrepancies of up to a factor
2 with respect to the model. These discrepancies are most likely due to a
combination of factors, such as the breakdown of the large­angle scattering
model used to calculate the aperture corrections, and the extreme sensitivity
of the higher spectral order efficiencies to small details of the groove shape.
Given the very good performance of the model in predicting the lowest
two diffraction order effective area's, it appears futile to try and find the
modifications that will also force agreement with third order, especially in
view of the fact that the precise effective area of this order is not likely to
be a decisive factor in any meaningful astrophysical investigations.
7.3 In­flight Verification
In flight verification of the effective area consists of two steps.
In step 1, we verify the 'relative' behavior of the effective area model,
i.e. we compare the changes in the effective area as a function of the off­axis
angle of the source, and the spectral order, as measured and as predicted by
the model. This procedure is independent of any assumptions concerning
the shape and absolute flux of the spectrum of the astrophysical source.
Tests of the off­axis behavior of the effective area on bright continuum
targets (primarily 3C273) vindicate the model: rms deviations between ob­
served and predicted behavior ! ¸ 5% on the brightest target. As had been
expected, deviations do appear at short (– ! ¸ 9 š A) wavelengths, and the
simple interpretation is that the grating reflectivity model is inadequate at
these wavelengths, resulting in the ! ¸ 20% underprediction of the area in
first order shortward of 9 š A.
Step 2 will consist of a verification of the absolute effective area, most
likely through a systematic cross­calibration with all other suitable spec­
trometers on XMM­Newton and Chandra. This work is in progress.
The RGS efficiency appears to exhibit an absorption feature at the O K
edge, which was not seen in the laboratory calibration. Direct interpretation
of the feature as absorption due to oxides in the system seems natural, but
has problems. The absorption edge wavelength does not appear to coincide
with the measured wavelengths of the oxygen photoelectric absorption edges
in any of the natural oxides that might occur in a CCD; moreover, to ex­
plain the depth of the edge (ú 30%) would appear to require oxide surface
densities that are unrealistically (but not impossibly) large. We therefore
17

also explored an alternative effect, contamination of the optics (mirrors and
gratings). A thin layer of oxygen­bearing material would modulate the re­
flectivity through a thin film interference effect (absorption shortward of
the edge, and slightly enhanced reflectivity longward of the edge due to the
anomalous dispersion close to the edge). This explanation has the attractive
property that a relatively small amount of material could account for the
effect, since any modulation in the reflectivity potentially appears raised to
the third power in the RGS efficiency (two bounces on the mirrors, one on
the gratings). But an interpretation in terms of contamination of the optics
also has problems in that the detailed shape of the feature does not match
the predicted reflectivity change very well, if we use the nominal Henke
optical constants of oxygen. More work is required using more accurate op­
tical constants in the vicinity of the edge, as well as in considering possible
statistical distributions of the contaminant layer thickness.
Finally, there appears to be an systematic offset between the efficiencies
of the two spectrometers that was not seen in the ground calibration (RGS 1
less efficient than RGS 2 varying as a function of exit angle from the gratings,
fi, see RD­20 for details). Given the homogeneity of the grating and CCD
selection for the two separate spectrometers, it is inconceivable that this
offset is due to a systematic difference in efficiency at the component level.
Likewise, there are no independent indications that the two mirror modules
differ in efficiency by such amount. The efficiency ratio between the two
spectrometers appears to be independent of wavelength, and exhibits a linear
dependence on dispersion angle, which suggests a geometric vignetting effect,
possibly by a misplaced baffle in the telescope tube (although the required
shift appears to be rather large). In the absence of any other constraints
on the origin of this effect, we have chosen to reduce the model efficiency
of RGS 1 ad hoc by a reduction factor, linear in dispersion angle, ranging
from 1.0 at the lowest dispersion angle (fi = 0:038rad), to 0.8 at the largest
dispersion angle (fi = 0:075rad).
8 Background in the RGS
For most of the bright sources the background in RGS is of minor im­
protance, especially when the periods with high solar activity are rejected.
For these periods the background varies typically between 0.002 and 0.008
counts/s/ š A for the full CCD and is further reduced when applying selections
in the cross dispersion direction.
18

The other instrumental components (onboard calibration source, weak
fluoresence lines, and some residuals due to the characteristics of the elec­
tronics as well as the particle background due to solar activity can be rea­
sonably modelled (see RD­18 and RD­19 for details). These models were
essentially derived from the Lockman hole observations and only limited
information about the variations in this background are available.
19

A References
Below a list of relevant documents is given for further details
RD­1 The reflection grating spectrometer on board XMM­Newton, A&A
365, L7­L17, 2001
RD­2 XMM mirror module performance and interface requirements, in­
ternal ESA document RS­PX­00258, issue 8
RD­3 the measured XMM telescope PSF compared to the simpel model
in the Columbia raytrace code, RGS­COL­CAL­00­003, dd Oct
11, 2000
RD­4 Tuning and assesmet of the RGS LSF model approproate for the
response matrix generation, RGS­COL­CAL­01­002
RD­5 wavelength scale: the second pass, RGS­COL­CAL­00­011
RD­6 Preliminary in­flight assessment of the RGS wavelength response,
RGS­COL­CAL­00­003, dd feb 17, 2000 (same id as RD­3)
RD­7 a simple CCD pulse height model, RGS­SRON­CAL­ME­98/010
RD­8 CCD homogeneity, RGS­SRON­CAL­ME­98/011
RD­9 inflight CCD PHA model and gains
RD­10 hot pixel/column rejection, RGS­COL­CAL­00­015
RD­11 Description of an algorithm to find bad pixels/column, RGS­
SRON­CAL­99­007
RD­12 In­flight cal­sources status, RGS­SRON­CAL­00­cv1
RD­13 Comparison of RGS1/RGS2 on more data for RGS2/CCD­2, RGS­
SRON­CAL­01­cv1
RD­14 Analysis of Canopus UV measurement, RGS­SRON­CAL­00­cv7
RD­15 Effective area verification: CCD response, RGS­SRON­CAL­00­
003
RD­16 modification of the CCD redistribution by adding a flat partial
events tail, RGS­SRON­CAL­00­cv8
RD­17 RGS cross dispersion PSF, XMM­CCF­REL­45
RD­18 exposure to exposure variation of the RGS background, RGS­
SRON­CAL­00­002
RD­19 model for the RGS background II, RGS­COL­CAL­00­012
RD­20 comparison of RGS1/RGS2 effective areas, RGS­SRON­CAL­00­
cv5
RD­21 measurement of CCD homogeneity, RGS­SRON­CAL­99­009
20