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HETG High­Order Diffraction Efficiency
K.A. Flanagan, N.S. Schulz
Center for Space Research
Massachusetts Institute of Technology
Cambridge, MA 02139
S.S. Murray
Smithsonian Astrophysical Observatory
60 Garden Street
Cambridge, MA 02138
G.D. Hartner, P. Predehl
Max­Planck­Institut fur Extraterrestrische Physik (FRG)
Garching, FRG
ABSTRACT
Measurements at XRCF produced calibration data of the high orders of the AXAF High Energy Transmission Grat­
ings at several energies. These tests provide a necessary complement to the limited set of laboratory high­order
measurements on each of the flight gratings. We present the analysis and results of these measurements made at
XRCF in Phase 2, where the flight detectors, HRC and ACIS, were employed.
Keywords: X­ray, X­ray astronomy, X­ray spectroscopy, transmission grating, calibration
1. INTRODUCTION
The Advanced X­ray Astrophysics Facility (AXAF) includes two transmission grating spectrometers designed for
use with the mirror assembly and with two focal plane detectors to provide high­resolution spectroscopy. The
high­resolution spectrometers, the High Energy Transmission Grating (HETG) Spectrometer and the Low Energy
Transmission Grating (LETG) Spectrometer, consist of individual grating elements on support structures which are
inserted into the optical path behind the AXAF mirrors. In the case of the HETG, these grating elements are of
two types, High Energy Gratings (HEG) and Medium Energy Gratings (MEG). The dispersed spectrum is read out
by one of the two focal plane detectors: the AXAF CCD Imaging Spectrometer (ACIS), and the High Resolution
Camera (HRC). In addition to its imaging capability, ACIS provides moderate spectral resolution. Details of these
instruments are given elsewhere 1;2;3;4 .
All of these flight components -- mirrors, gratings, and detectors -- were subjected to calibration testing at the
X­Ray Calibration Facility (XRCF) at Marshall Space Flight Center 5 . This testing served many purposes, among
them:
ffl compare measurements with predictions arising from calibrations at the subassembly level
ffl provide end­to­end testing of components brought into joint operation for the first time
ffl provide calibration of attributes that were unobtainable at subassembly level (i.e., testing with a subarcsecond
focused beam, testing gratings under full illumination as an assembled array)
ffl examine unexpected behavior revealed by the unique testing configurations and conditions exercised at XRCF
An overview and detailed results of this testing program are given in companion papers at this conference 6;7;8;9;10;11 .
The purpose of this paper is to examine the efficiencies of higher diffraction orders of the HETG gratings in XRCF
measurements taken during Phase 2 with the ACIS and HRC instruments. Since efficiency is a property intrinsic to

the gratings, it is natural to use a technique that eliminates dependencies on the properties of the mirrors, detectors,
or X­ray source. The approach taken is to determine the ratio of the higher order to the first order. The results
are compared with subassembly predictions. This approach has several advantages. It is not necessary to know the
incident beam flux, mirror response, or absolute detector efficiency. The beam need not be spectrally pure, since
only dispersed orders are used in this analysis. However, variations in detector uniformity must be considered, as
they can affect the result.
The subassembly calibration of the gratings included very few higher order measurements, and these were all
done on a few isolated portions of the individual gratings. Therefore, XRCF testing was critical to calibration of the
high order efficiency of the assembled grating instrument. In addition, analysis of the data has yielded insight into
both the HRC­I and ACIS­S instruments in aspects that were not fully examined at subassembly level. These will
be discussed further below.
2. SUBASSEMBLY EFFICIENCIES AND ERRORS
Every grating was tested for diffraction efficiency at the subassembly level. Details of the test setup 12 and calibration
test analysis techniques 13 have been given in previous conferences. In subassembly testing, six energies were available:
0.93, 1.254, 1.486, 2.293, 4.511 and 6.4 keV. Among positive and negative orders, a total of 10 to 12 first order
measurements and 7 or 8 second order measurements (depending on the grating) contribute to defining a best­
fit set of grating bar parameters to describe each grating. The model for each grating facet is used to generate
efficiencies at all AXAF energies and orders from ­11 to +11. By summing these efficiencies for all the gratings and
weighting them appropriately for mirror area and vignetting, the predicted efficiency for the assembled grating array
is obtained. Because measured efficiencies were used to obtain the prediction, one might expect these predictions to
be ``reasonable'' at 1st order, ``fair'' at 2nd order but ``poor'' at higher orders. Reflecting this expectation, the error
bars that have been assigned nominally are 5% to 20% for 1st order efficiency (depending on energy), 20% for 2nd
order, 50% at 3rd order and 90% for higher orders. The 1st order error bars and their breakdown by energy are based
on synchrotron tests on a limited number of gratings, where a comparison was made between the synchrotron results
and subassembly predictions. Given that the intensity of higher orders is a strong function of grating bar shape 14 ,
the extension of the subassembly model to very high orders is tenuous, underlining the need for direct measurement
at XRCF.
3. TESTS WITH HRC­I AT XRCF
HETG was tested in combination with the HRC­I in Phase 2 at XRCF. The complete series consisted of one focus
check at 1.254 keV, 33 effective area tests in a defocussed configuration, and one monochromator scan with 4 energies
centered on 1.54 keV. These are listed in Table 1, along with the energy and range of dispersed orders on the detector.
Figure 1 shows the HRC­I with the HEG and MEG grating dispersion pattern at 7 keV. The HRC­I detector is square
and the image of Figure 1 is presented in detector coordinates. The dispersion direction for the gratings is aligned
approximately parallel to a diagonal of the detector, so that the number of orders detected is limited by the detector
size and the intensity of the high orders. In general, the zero order position was displaced from the nominal imaging
aim point in order to minimize accumulated dose in that region. Note that the direction of the bias angle of the
microchannel plate is toward the top in the figure, and is not symmetric with respect to the dispersion direction.
Details of the HRC­I and calibration information are given in this and prior conferences 15;16;17 .
From Table 1 it is evident that HEG 2nd order is only available on the detector for energies of 1.7 keV and
above. For the MEG gratings, 2nd order was suppressed and measurable at only a few energies, but third order was
detectable at 1.49 keV and above. Energies below 1.254 keV were not analyzed for either grating since there were
no higher orders falling on the detector. The breakdown of order by energy is given in Table 2.
3.1. Processing of the Raw Data
The HRC data were processed in several steps. The raw data files were screened for lost major frames, converted
from telemetry format and degapped. Two sets of event lists were then created, with different rejection criteria based
on the saturation levels of the electronics (4096 for the amplifiers and 255 for the pulse height). This approach was
prompted by considering the testing conditions early in Phase 2. In the first day of the HETG + HRC­I tests, the
detector high voltage was set at a relatively high level and there was a considerable number of saturated events. On
succeeding days, the voltage was lowered and the relative number of saturated events decreased. Since saturation can

Figure 1. HETG + HRC­I test at 7 keV. Positive orders are dispersed toward the upper left in the
figure. The large box, top right, is used to estimate detector background. The small boxes around
zero order sample mirror­scattered events. The data have been ``cleaned'' to remove saturated events.
result in incorrect position assignment of the events (of order 1/2 mm or less), two separate analyses were performed
on the data. In the case of ``cleaned'' data, all events with pulse height above 254 or with amplifier value above 4090
were rejected. In the second case, saturated events were included in the analysis (for which the data were termed
``uncleaned'').
A detailed investigation showed that smearing of the image due to electronic saturation did not systematically
affect the result: ratios remained unchanged to within ¸ 3% regardless of whether or not the smeared events were
captured within the counting region. This is understandable since the regions of interest used were large compared
to the position errors due to saturation. However, there was evidence to suggest a higher proportion of saturated
events in bright orders relative to faint orders. (This is currently under study.) If so, when ``cleaned'' data are used,
ratios formed with a bright first order are systematically enhanced (by 10% to 40%). Therefore, since saturated
events represent true X­ray events and their positioning errors do not compromise the analysis, we have chosen to
use the ``uncleaned'' data set throughout. This unusual saturation level 16 as found on the first day of these tests,
was decreased on subsequent days after adjustment of the electronics and has now been eliminated in the flight
instrument.
3.2. Selection of Source and Background Regions
The technique employed for selecting regions of the grating readout was to display each dataset with SAOtng
(SAOimage: The Next Generation 18 ). Each order of interest was captured in a simple rectangular box region, and

the number of events within each box was determined. In order to estimate the effects of background and mirror
scattering, several ``background'' regions were selected, as illustrated in Figure 1. The largest box, distant from
the zero order, is assumed to reflect approximately detector backgound. The next largest box, while distant from
the zero order, nevertheless was found to have a higher (¸ 2 times) background rate and is assumed to contain
mirror­scattered photons. The selection of small boxes centered among zero and 1st order had a much higher (¸ 8
times) background rate, which is presumed due to mirror scattering around the zero order.
In the analysis, the simple detector background was used for background subtraction for all orders. This is
appropriate for the distant high orders, but there may be mirror­scattered photons captured within the first order
regions. Mirror scattering is on the 1% level or less, and by using the measured ``scattered rate'', we found that
corrections to the ratios systematically increase it by 0.5% to a few percent, a negligible effect given the counting
statistics and other errors. We have neglected this correction.
3.3. Corrections and Errors
Flat field tests to measure detector spatial uniformity were not performed with the settings used on the day on which
most of the HETG + HRC data were taken. However, the HRC­I was known to be more uniform than on subsequent
days, for which uniformity data are available 16 at 4.5 keV and 1.49 keV. At 4.5 keV, the HRC­I was found to be
uniform to better than 5% over the central region. At 1.49 keV, the detector QE was not as uniform as at the higher
energy, but was flat at the 10% level over the central region 16 out to a radius of 30 to 35 mm. Beyond this radius
the QE dropped by ¸ 20%. No detector uniformity corrections have been applied to the measured ratios.
It has been noted that the bias angle is not symmetric with respect to the dispersion direction. This can result in
an asymmetric detection efficiency of a positive order with respect to its negative counterpart. The angle dependence
of the QE is estimated to result in a difference 19 of at most a few percent, and correcting for bias angle has been
neglected. In order to examine the potential effects of bias angle on the result, the ratio of the +1 order to the ­1
order was taken. Any systematic asymmetry would most likely be ascribed to grating asymmetry in these orders,
detector asymmetry due to bias angle, or to nonuniform QE effects across the detector (known to be small). The
result is given in Figure 2 for the HEG grating, which is more likely than the MEG to show intrinsic asymmetry and
which disperses across more of the HRC­I surface. The plot reflects asymmetry due to all effects: the asymmetry is
obviously very small in comparison with other errors. Thus, neglect of bias angle and detector uniformity corrections
is acceptable. Table 3 gives a summary of the various effects that have been discussed and their impact on the
results.
3.4. HRC Results
Figure 3 shows the expected higher order ratios for the HEG and MEG gratings based on subassembly predictions.
Figure 4 shows the measured HEG ratios for 2nd, 3rd and 4th orders overlaid with the prediction. (Solid points are the
ratios of positive orders, hollow points refer to negative orders. The error bars reflect only counting statistics.) The
5th and 6th order ratios are similar and are not shown. The measurements appear to be systematically suppressed
relative to the predictions. The approximate magnitudes of these deviations are given in Table 4 along with the
typical errors due to counting statistics. Although the departures are within the errors assigned to the predictions,
they exceed the counting statistics and other uncompensated correction effects, and may be deemed to be significant.
Figure 5 shows the measured MEG ratios for 2nd, 3rd, 4th and 5th orders. In general, there is fairly good
agreement with the predictions. Moreover, the higher ratios (orders 6 through 9) are similar, agreeing reasonably
well with the subassembly predictions. These results are summarized in Table 4.
4. ACIS TESTS AT XRCF
During Phase 2, tests of HETG with ACIS­S were performed using electron impact sources and monochromatic
beams. The present analysis is limited to the those tests that employed the double crystal monochromator (DCM),
which have been described in detail in a companion paper 20 . We directly incorporated the results from that study
of absolute effective area to obtain the desired ratios for the present analysis.

4.1. Order Ratios
Figure 6 shows the +1 to ­1 order ratio for HEG as detected by ACIS­S. The plot shows significant (up to 35%)
departures from unity. As discussed previously, these may be due to intrinsic grating asymmetry or detector nonuni­
formity. (Bias angle considerations do not apply to the ACIS­S.) However, deviations from symmetry in Figure 2
with the HRC­I detector are less than 5%, on a par with detector uniformity. Thus, grating asymmetry cannot
be expected to account for the structure seen in Figure 6. These arise from variations within the detector. The
jumps seen at 1.7 keV and 2.9 keV coincide with points at which one of the orders traverses a boundary between
a frontside­illuminated (FI) and a backside­illuminated (BI) device. Between these energies, the +1 and ­1 orders
are both captured on FI chips, but outside that range the one order falls on a BI chip, the other falls on a FI chip.
It is clear that this strong residual structure, due to the detector, will complicate interpretation of the higher order
ratios. It is worth remembering that in the analysis 20 , the quantum efficiency functions were not yet avaliable for
each device and templates were used for each CCD type. Thus, chip­to­chip discontinuities would be expected at
this level of analysis.
Figure 7 shows the HEG 2nd, 3rd, 4th and 5th order ratios. Ratios between positive orders are denoted with
filled boxes, whereas those between negative orders are marked by hollow boxes. In each one of these plots, there
is a strong enhancement above 7 keV. Since it is common to all four order ratios, it likely arises from a supression
of first order effective area. From the 2nd order ratio, it is clear that this feature is far stronger it the ­2/­1 ratio
(where the ­1 order is captured by a FI device) than in the +2/+1 ratio (where the +1 order lands on the S3 chip,
a BI device). The 3/1 ratio agrees generally with the HRC­I results over the energy range of 3 to 5 keV, but then
the ratio is enhanced above 5 keV and shows other structure. In general, the HEG ratios with ACIS­S show much
structure and do not reproduce the systematic reduction relative to predictions as shown with the HRC­I.
Figure 8 shows the MEG 3rd, 5th, 7th and 9th order ratios. The 3rd and 5th orders show enhancements above
5 keV, but there appear to be some smooth regions (2.5 to 4.5 keV) which agree reasonably well with predictions.
The features that have been noted can be traced to detector effects (grade migration, charge loss and ``blooming'')
which will be discussed below.
4.2. Discussion of ACIS results
The effective areas presented by Schulz et al. 20 show that in general the measurements agree with the expected
effective area function to quite a high degree. However, there are significant local deficiencies that remain. The most
prominent (see Figure 11 of Schulz et al. 20 ) is an apparent drop of effective area for HEG +1 and ­1 orders below
the expectation at energies above 5 keV.
One possible explanation given in that paper was a local non­uniformity effect in the beam to which the HEG,
because of its smaller aperture, would be more susceptible than the MEG. (In the MEG such a drop is not significantly
visible in the data.) However, the observed drop in HEG area sometimes exceeds 10%, which would need a quite
strong local non­unifomity in the beam. This is unlikely since the DCM beam at higher energies has been measured
to be very uniform overall. In addition, if beam nonuniformities were the cause, the 2nd order effective area would
also show this deficiency, but it does not.
A more plausible explanation, which we are currently investigating, are deficiencies in the CCD quantum efficien­
cies caused by grade migration and lost charge effects at high energies and high fluences (cts/s/cm 2 ). This has been
described in detail by Allen et al. 7 Similar corrections were used by Schulz in order to correct deficiencies observed
in the zero order effective area. The effects are triggered by the higher fluence at XRCF, which causes events to
overlap more often and forces a migration into higher number grades in the event detection algorithm. At even higher
energies, charge cloud overlaps may prevent the detection of the event. Again, the HEG is more susceptible to these
effects since the fluence in the HEG image at XRCF is generally higher than in the MEG image (recall that the HEG
mirror shells are of smaller diameter). Although the first order areas presented in Schulz show clear fingerprints of
these effects at work, the uncertainty of the beam uniformity issue remains unresolved.
A comparison of the higher orders to the first order has an advantage over the effective area analysis in that
beam uniformity issues are removed -- only effects caused by the science instruments are left. Since a quantitative
evaluation is still in progress, we restrict ourselves for now to a merely qualitative description of effects and emphasize
that the following interpretations should be treated with caution.

During subassembly testing of the ACIS instrument, fluences were low and grade migration and lost charge effects
were not observed 21 . Although the focused beam at XRCF increases the fluence, the higher order grating efficiencies
are low enough that fluences in these orders drop below those of subassembly testing. Thus, grade migration and
lost charge effects should not be noticed in any order other than 1st. Key indicators for grade migration and charge
loss effects are the ratios of the lower orders to the first orders. (Higher order ratios will have poor counting statistics
and large uncertainties.) Figures 7a and 8a show the HEG 2nd to 1st order ratio and the MEG 3rd to 1st order
ratio. The solid line indicates the prediction. Clearly, in both figures the ratios start to deviate from the prediction
above 5 keV, suggesting a deficiency in the 1st order effective area. Here the HEG, as expected, shows the strongest
deviations. Above 5 keV we probably see the effects of grade migration, and above 7 keV the additional effect of
charge loss. The latter effect is more pronounced in the negative order ratio (empty squares) where the 1st order
appears on a FI device, as compared to the positive ratio (filled squares), where the 1st order appears on a BI device.
This is consistent with the related effect of 'blooming' caused by high energy events in FI devices; it is not seen in BI
devices 22;23 . The effects are also observed in the HEG 3rd and MEG 5th order ratios. At higher orders, the ratios
follow the predictions nicely, however the data show significant scatter due to poor counting statistics.
We can rule out the possibility that these effects are caused by the grating itself, because they are not observed
in analogous measurements with the HRC­I. As discussed earlier, the near­perfect symmetry of the +1 and ­1 orders
(to within 5%) of the HEG with HRC­I exclude the grating as a contributor to these effects.
5. CONCLUSIONS
We have examined the ratios of higher grating orders with respect to the first order for Phase 2 tests of HETG with
the flight instruments, HRC­I and ACIS­S. We found that:
ffl The symmetry of the +1 and ­1 orders of HEG with HRC­I lead to the conclusion that detector nonuniformity,
grating asymmetry and bias angle effects were small.
ffl HRC measurements show suppressed higher grating orders for HEG relative to predictions. Measurements of
the MEG orders agree well with predictions.
ffl ACIS­S shows strong detector effects, compatible with grade migration and charge loss.
ffl Subassembly fluences were too low to trigger charge migration and charge loss effects in ACIS. These calibration
tests, and the ratio technique we have employed, have provided useful means for probing these detector effects.
Several items remain for future work. These include:
ffl Investigate the relation between saturation and count rate density in HRC­I.
ffl Quantitative analysis of grade migration and charge loss in ACIS.
ffl Incorporate synchrotron high order measurements.
ffl Examine Phase 1 measurements for high orders and asymmetry.
ffl Analyze EIPS sources with both detectors and the monochromator scan with HRC­I.
6. ACKNOWLEDGMENTS
We thank D. Dewey and H. Marshall for helpful discussions. We are grateful to Andrea Prestwich for assistance
with data reduction techniques. We are indebted to Eric Mandel for providing assistance with an updated version
of SAOtng for use in this analysis. We thank Eric Fischbach for assistance with manuscript preparation. This work
was prepared under NASA contracts NAS8--38249 and NAS8--39073.

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2 4 6
0.7
0.8
0.9
1
1.1
1.2
energy (keV)
HEG +1/­1 ASYMMETRY with HRC­I
Figure 2. Ratio of +1 to ­1 for HEG grating on HRC­I. In general, departures from unity are expected to be caused
by intrinsic grating asymmetry, detector nonuniformity or bias angle effects.
5 10
0.5
1
1.5
2
wavelength (Angstroms)
HEG +1/­1 ASYMMETRY with ACIS­S
Figure 6. Ratio of +1 to ­1 for HEG grating on ACIS­S. Structure is due to detector effects.

2 4 6 8
0
0.05
0.1
0.15
0.2
0.25
energy (keV)
PREDICTED HEG RATIOS with 1st ORDER
+3/+1
+5/+1
+2/+1
+4/+1
2 4 6 8
0
0.05
0.1
energy (keV)
PREDICTED MEG RATIOS with 1st ORDER
+3/+1
+5/+1
+2/+1
+4/+1
Figure 3. Expected ratios of orders 2 through 5 with respect to 1st order for HEG (top) and MEG (bottom). These
are based on subassembly calibrations.

2 4 6
0.02
0.04
0.06
0.08
0.1
energy (keV)
HEG 2/1 with HRC­I, plus and minus orders
2 4 6
0.02
0.04
0.06
energy (keV)
HEG 3/1 with HRC­I, plus and minus orders
Figure 4. Measured HEG ratios for 2nd,3rd, and 4th orders with HRC­I. The solid curve represents the predicted
ratios. Hollow points indicate ratios of negative orders, and solid points refer to positive orders. The error bars are
due to counting statistics. The measurements systematically fall below predictions.

2 4 6
0.01
0.02
0.03
energy (keV)
HEG 4/1 with HRC­I, plus and minus orders

Run ID TRW ID Energy HEG orders MEG Orders Comments
i0810621 G­HHI­EA­7.048 7.0 +6 to­6 +3 to ­5
i0811327 G­HHI­EA­99.059 7.0 +4 to ­4 +3 to ­5
i0810657 G­HHI­EA­7.047 6.3 +6 to ­5 +8 to ­5
i0811342 G­HHI­EA­99.060 6.3 +4 to ­4 +8 to ­3
i0810725 G­HHI­EA­7.046 5.76 +5 to ­5 +8 to ­5
i0811356 G­HHI­EA­99.061 5.76 +4 to ­4 +5 to ­5
i0810804 G­HHI­EA­7.045­1 5.66 +5 to ­5 +8 to ­9
i0810756 G­HHI­EA­7.045 5.66 +5 to ­5 +5 to ­7
i0810831 G­HHI­EA­7.044 5.48 +5 to ­4 +7 to ­5
i0810855 G­HHI­EA­7.043 5.32 +5 to ­4 +7 to ­8
i0810916 G­HHI­EA­7.042 5.25 +5 to ­4 +8 to ­7
i0810936 G­HHI­EA­7.041 5.13 +4 to ­4 +5 to ­5
i0810950 G­HHI­EA­7.040 5.05999 +4 to ­4 +6 to ­5
i0811005 G­HHI­EA­7.039 4.96 +4 to ­4 +5 to ­7
i0811019 G­HHI­EA­7.038 4.9 +4 to ­4 +7 to ­8
i0811037 G­HHI­EA­7.037 4.8 +4 to ­4 +7 to ­5
i0811054 G­HHI­EA­7.036 4.59999 +4 to ­4 +7 to ­5
i0811114 G­HHI­EA­7.035 4.51 +4 to ­4 +7 to ­5
i0811132 G­HHI­EA­7.034 4.0 +4 to ­4 +7 to ­7
i0811155 G­HHI­EA­7.033 3.5 +3 to ­3 +7 to ­6 MEG 2 overlaps HEG 1. Not corrected.
i0811238 G­HHI­EA­7.032 2.29 +2 to ­2 +4 to ­4
i0811414 G­HHI­EA­7.031 1.95 +2 to ­1 +4 to ­4
i0811434 G­HHI­EA­7.030 1.7 +2 to ­1 +3 to ­3
i0940311 G­HHI­EA­9.018 1.48693 +3 to ­3 MEG only. Has contaminant line..
i0911019 G­HHI­EA­6.002 1.254 +2 to ­2 MEG only. EIPS ­ broad line.
i0911034 G­HHI­EA­6.003 1.254 +1 to ­1 HEG only. EIPS ­ broad line.
i0910739 G­HHI­FC­1.003­Q1 1.254 +1 to ­1 +2 to ­2
i0910817 G­HHI­FC­1.003­Q2 1.254 +1 to ­1 +2 to ­2
i0910854 G­HHI­FC­1.003­Q3 1.254 +1 to ­1 +2 to ­2
i0910931 G­HHI­FC­1.003­Q4 1.254 +1 to ­1 +2 to ­2
i0940337 G­HHI­9.019 1.17595 +1 to ­1 MEG only. W contaminant line.
i0811452 G­HHI­10.003 1.54 +1 to ­1 +3 to ­2 Energy scan; analysis pending.
i0940357 G­HHI­9.020 0.95996 Not analyzed
i0902304 G­HHI­6.004 0.9297 Not analyzed. MEG only.
i0902318 G­HHI­6.006 0.9297 Not analyzed. HEG only.
i0940427 G­HHI­9.021 0.75996 Not analyzed
i0901229 G­HHI­6.005 0.705 Not analyzed
i0940505 G­HHI­9.022 0.70499 Not analyzed
i0900251 G­HHI­6.001 0.5249 Not analyzed. MEG only.
i0900336 G­HHI­6.001­b 0.5249 Not analyzed. MEG only. Contains O.
Table 1. Summary of HETG + HRC­I higher order data.

Order HEG Energy range MEG Energy range Comments
2 1.7 to 7.0 1.254, 1.7, 1.95, 2.29 not sufficiently detectable at other energies
3 3.5 to 7.0 1.48693 to 7.0
4 4.0 to 7.0 1.95 to 6.3 not sufficiently detectable at 7.0
5 5.25 to 7.0 3.5 to 7.0
6 6.3 and 7.0 only 3.5 to 6.3 except 5.13
7 3.5 to 5.76 except 5.05999, 5.13
8 4.9, 5.25, 5.32, 5.66, 5.76, 6.3
9 5.66 only
Table 2. Energy ranges of the measured HETG + HRC­I higher orders.
Error magnitude Comments
Counting Statistics 10% to 30% (see Table 4) accounted for in analysis
Background subtraction up to 3%, systematic only detector background used
bias angle few percent neglected
detector QE nonuniformity 5 to 10% within 35 mm radius; edges drop by 20% neglected
Event saturation 10 % to 40% systematic accounted for: all events included
Table 3. Corrections, Systematic Effects and Errors for HETG + HRC­I
Grating order ratio Typical counting statistics Assigned Subassy error deviation from predicted
HEG 2/1 10% 20 to 25% ­10 to ­15%
3/1 10% 50% ­35%
4/1 15% 90% ­35%
5/1 20% 90% ­60%
6/1 20% 90% ­60%
MEG 2/1 15% 20 to 25% approximately correct
3/1 10% 50% ­5%
4/1 20% 90% +25%
5/1 20% 90% ­25%
6/1 20% 90% approximately correct
7/1 20% 90% ­25%
8/1 30% 90% approximately correct
9/1 30% 90% ­45%
Table 4. Comparison of Predictions with Measured ratios for HETG + HRC­I higher orders.

2 4 6
0.01
0.02
0.03
0.04
energy (keV)
MEG 2/1 with HRC­I, plus and minus orders
2 4 6
0.05
0.1
energy (keV)
MEG 3/1 with HRC­I, plus and minus orders
Figure 5. Measured MEG ratios for 2nd,3rd, 4th and 5th orders with HRC­I. The measured values agree fairly well
with the predictions.

2 4 6 8
0.05
0.1
0.15
0.2
0.25
energy (keV)
HEG 2/1 with ACIS­S, plus and minus orders
2 4 6 8
0.05
0.1
0.15
0.2
energy (keV)
HEG 3/1 with ACIS­S, plus and minus orders
Figure 7. Measured HEG ratios for 2nd, 3rd, 4th and 5th orders with ACIS­S.

2 4 6 8
0.02
0.04
0.06
0.08
0.1
energy (keV)
HEG 4/1 with ACIS­S, plus and minus order
2 4 6 8
0.01
0.02
0.03
energy (keV)
HEG 5/1 with ACIS­S, plus and minus order

2 4 6 8
0.05
0.1
0.15
0.2
energy (keV)
MEG 3/1 with ACIS­S, plus and minus orders
2 4 6 8
0.02
0.04
0.06
0.08
energy (keV)
MEG 5/1 with ACIS­S, plus and minus orders
Figure 8. Measured MEG ratios for 3rd, 5th and 7th and 9th orders with ACIS­S.

2 4 6 8
0.01
0.02
0.03
0.04
energy (keV)
MEG 7/1 with ACIS­S, plus and minus orders
2 4 6 8
0.005
0.01
0.015
0.02
energy (keV)
MEG 9/1 with ACIS­S, plus and minus orders