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Astronomical Data Analysis Software and Systems VII
ASP Conference Series, Vol. 145, 1998
R. Albrecht, R. N. Hook and H. A. Bushouse, e
Ö Copyright 1998 Astronomical Society of the Pacific. All rights reserved.
ds.
How to Piece Together Di#racted Grating Arms for
AXAF Flight Data
A. Alexov, W. McLaughlin and D. Huenemoerder
AXAF Science Center; Smithsonian Astrophysical Observatories, TRW,
and MIT, Cambridge, MA 02138
Abstract. The Advanced X­ray Astrophysics Facility's (AXAF) High
and Low energy transmission gratings (HETG, LETG) data require new
tools and data structures to support x­ray dispersive spectroscopy. AXAF
grating data files may be a hundred megabytes (MB) in size, however,
they will typically only be a few MB. We are writing data analysis soft­
ware which can e#ciently process the data quickly and accurately into
wavelengths, orders and di#raction angles for each event. Here we de­
scribe the analysis procedure as well as some of the technical constraints
we had to overcome in order to process the tasks e#ciently.
1. Data Processing
1.1. Standard ACIS/HRC Event Processing
Initial data processing applies transformations from detector to sky coordinates
for each photon in the data set. However, with grating data, additional event
processing must be performed before data analysis can commence.
1.2. Select Zero Order Sources/Find Observed Target
In order to find where the dispersed photons lie, the center of the zero order
source position on the sky must be determined, since this is the origin of the
spectral coordinates. Source detection must not be fooled by emission lines
located away from the center of the field; several methods exist to discriminate
bright emission lines from zero order sources. Primarily, emission lines have
a small variance in the PHA (energy) spectrum, while zero order has a large
variance since it encompasses all of the source energies. Alternatively, the PSF
(Point Spread Function) can be used instead of PHA, to weed out emission
lines. Once zero order source positions are found, the target source is identified
by matching the sky positions with an observation target list.
1.3. Identify Spectrum Parts Geometrically
Grating data events may be categorized by their part of the spectrum. This
is done by creating mask regions for each grating part and by checking every
photon for inclusion within the mask regions. For the HETG grating data, the
relevant parts for each source are: zero order, MEG photons, HEG photons, and
background photons. Regions are defined as rectangles in di#raction coordinates,
169

170 Alexov, McLaughlin and Huenemoerder
in which the zero order is the origin, and one axis is parallel to the spectrum
(dispersion direction), and the other perpendicular to it (cross­dispersion direc­
tion). The width of the rectangle is calculated using the e#ective PSF (mirror
psf, Rowland geometry astigmatism, instrument de­focus, and aspect). These
regions are translated into sky coordinates using each zero order source position,
and by rotating the region by the grating angle (known) plus the mean observed
telescope roll angle. Any event inside the rectangle is then assigned to that part
of the spectrum (HEG or MEG, or LEG). Zero order photons are assigned by
being within some radius of the zero order centroid. Each photon is tagged with
one or more source ID's as well as grating part(s), depending on the number of
regions into which it falls (overlaps).
1.4. Compute Linear Di#raction Coordinates
To calculate the di#raction angle (r) of a photon, work needs to be done in
the geometric system in which the photon was di#racted. The sky coordinates,
which are referenced to the telescope mirror node and therefore independent of
the grating reference node, are only useful for the imaging of zero order and the
filtering of grating arm photons. Grating di#raction coordinates are referenced
to the grating assembly node. Reverting back to the original chip coordinates
(chip number, chip position, grating node and zero order position) allows grating
di#raction coordinates to be calculated for each time interval.
1.5. Compute ``first order'' Wavelengths
Now that di#raction angles have been determined parallel to the dispersion
angle, the basic grating equation, m# = Pr, can be applied to determine m#
for each photon. Here, m is the integral di#raction order, P is the known mean
period of the set of gratings (MEG, HEG, LEG), and r is the di#raction angle.
1.6. Resolve Orders (ACIS only)
The ACIS detector provides moderate spectral resolution via a pulse­height
(PHA, or PI) for every photon. This resolution is enough to determine, with
high confidence, what the spectral order is at any r or m#, since only integral
multiples are allowed at any given position (grating equation, diagram below).
Order sorting is also useful for photons in overlapping mask regions. These
events can be resolved as belonging to one arm/source versus another through
order sorting. Since the HRC detector has no energy resolution, a method has
yet to be determined for resolving orders or any overlapping regions in data
taken by this instrument. The grating equation is used to calculate an estimate
of the grating order (m est), using physical constants and previously calculated
values: m est = Pr(PI)/hc. Here, hc is a physical constant; PI is the ``Pulse
Invariant'' energy from the CCD; r is the calculated di#raction angle; and, P is
the known grating period.
The ACIS instrument response determines the distribution of PI. This in­
formation permits the calculation of an allowed range of m for each photon. If
m est is within this range, then the grating order is equal to the rounded value
of m est. Otherwise, the order is unresolved. For ACIS overlap regions, order is
calculated for each region. If the order can be uniquely identified as belonging
to a single region then it is resolved. Otherwise, the order is left as unresolved.

How to Piece Together Di#racted Grating Arms for AXAF 171
1.7. Bin into 1D spectra
Now that the data are complete with identifiers for the part of the spectrum,
di#raction angles, orders, wavelengths, and counts spectra vs # can be created.
These spectra are used for further data analysis (i.e., emission line identification
and flux analysis).
2. Software Solutions
Processing grating data comprised of multiple sources is a non­trivial task. Many
design tradeo#s were considered in attempting to create e#cient and e#ective
analysis software. This section identifies some of the considerations taken into
account when designing the gratings software.
The possibility that parts of di#erent sources may overlap imposes a great
challenge to the data analysis software. All overlapping regions need to be
identified and the software must be able to decompose these regions into the
component source parts. While standard IRAF region software can easily sup­
port overlapping regions of a few sources via region algebra, a mechanism is still
necessary for keeping track of the source parts in a given overlap region. As the
total number of regions (including overlaps) has an exponential growth (5 to
the n for HETG), this method is impractical when dealing with several sources.
For instance, the worst case scenario for 10 HETG sources is over 9.5 million
source parts and overlap combinations to track. Realistic scenarios may contain
approximately 10 sources, but these sources will typically be more spread out
(i.e., Orion Trapezium).
To circumvent this problem, the software has been designed to maintain
tables for all of the parts of each source (resulting in 5n tables for HETG).
Photons are checked for inclusion in each table and source bits are set to indicate
the sources and parts to which the photon may belong. Since the geometry of
the regions being utilized is limited to circles and rectangles, the tables simply
contain sky coordinate range boundaries. To save memory, the axis spanning
the minimum distance for any given source part is o#set to zero and utilized
as the index. For cases where the instrument roll angle equals 45 degrees, the
index axis is arbitrarily chosen as neither of the axes provides an advantage.
3. Future Challenges
AXAF data fields may contain multiple sources. In order to be able to detect,
mask out, coordinate transform, and order sort all these sources correctly is quite
a challenge. We have made the software flexible for the users to be able to specify
source specific characteristics/mask widths and response matrices. We hope that
these extra features will allow severely crowded fields to be scientifically analyzed
in the same context as more common single source fields.
For more details on the AXAF grating flight processing software, see:
http://space.mit.edu/ASC/analysis/L1.5 overview/L15.html
Acknowledgments. We are grateful to Maureen Conroy for initial design
work on the XRCF grating software, which has lead to the flight version. This
project is supported by NASA contract NAS8­39073 (ASC).

172 Alexov, McLaughlin and Huenemoerder
Sample Aspect
Corrected AXAF
Gratings Data
Mask Regions
for the Double
Source Scenario
Data Set Above
1D Spectra
Source #1, HETG
0.0
­0.2
­0.4
­0.6
­0.8 0.2 0.4 0.6 0.8
0.000
0.002
0.004
­0.002
­0.004
meg
overlaps
heg
heg
zero order
source #1
source #2
meg
source #1
source #2
source #2
source #1
meg
zero order
zero order
heg
r : dispersion angle [degrees]
HEG Events in r/d diffraction coordinates
d:cross­dispersion angle
[digrees]
HEG and MEG First Order Counts
Wavelength [Angstroms]
Log
(Counts
per
bin)
[0.05A
bins]
Diffraction Coords
Source #1, HEG
HEG
src #1 heg &
src #2 meg
overlap
HEG 1st order spectrum
MEG 1st order spectrum
Figure 1. Cumulative look at the Processing Steps using Mock Data