\documentclass{article}
\usepackage{spie}
\usepackage{epsfig}
\usepackage{amsmath}

\begin{document}

\title{Spectral Features in the AXAF HETGS Effective Area
using High Signal Continuum Tests}
\author{%
Herman L. Marshall
\and Daniel Dewey
\and Norbert S. Schulz
\and Kathryn A. Flanagan
\skiplinehalf
Center for Space Research, M.I.T.,
Cambridge, MA \hspace{0.5em}02139
}

\authorinfo{Other author information: Send correspondence to HLM:
Email: {\tt hermanm@space.mit.edu}; Telephone:
617-253-8573; Fax: 617-253-8084; WWW:
{\tt http://space.mit.edu/~hermanm/}}

\maketitle

\begin{abstract}
In order to probe for small scale spectral features of the
High Energy Transmission Grating Spectrometer (HETGS) and
the Low Energy Transmission Grating (LETG), we
performed tests at
the AXAF X-Ray Calibration Facility (XRCF) using a very bright
continuum source.  The Electron Impact Point Source (EIPS) was
used with the Cu anode and operated at high voltage and low current
in order to provide a bright continuum at high
energies.  The AXAF CCD Imaging Spectrometer Spectroscopy
detector (ACIS-S) was used to discriminate orders and to provide
high throughput when operated in continuous clocking (CC) mode.
Many spectral features are observed but most of
them are emission lines
attributable to the source spectrum.  We find that the
current models for the HETG efficiency, the LETG efficiency and
the AXAF High Resolution Mirror Assembly (HRMA) effective area
predict very well the observed fine structure near the Au and Ir
M edges where the models are most complex.  Edges in the detector
filter and quantum efficiency (QE) curves are somewhat more
sharply defined in the data than in the current models.

By comparing the
positive and negative dispersion regions, we find no significant
efficiency asymmetry attributable to the gratings and we can
further infer that the QEs of the ACIS-S frontside illuminated
(FI) chips are consistent to $\pm 10$\%.  On the other hand, we
derive the ratio of the QE for the backside illuminated (BI)
chips relative to that of the FI chips and show that it deviates
from the expected ratio.  This deviation may result from grade
differences due to operation in CC mode while most calibration
data are obtained in timed event mode.

\end{abstract}

\keywords{AXAF, grating, calibration, X-ray, diffraction}

\section{Introduction}

Early reports on the efficiencies of the facets used
in the High Energy Transmission Grating (HETG) which will be part
of NASA's Advanced X-ray Astrophysics Facility (AXAF) are summarized by
Dewey et al.\cite{dewey}.  These include tests at a synchrotron
facility that were used to examine details of the efficiency of
small regions on a few reference gratings\cite{polygonmodel}
in order to refine the efficiency model where each grating facet
consists of uniform grating bars whose cross section is a
simple polygon which is approximately trapezoidal.
The HETG Spectrometer
(HETGS) includes the AXAF High Resolution Mirror Assembly (HRMA)
and the focal plane detector, which is usually the AXAF CCD
Imaging Spectrometer Spectroscopy array (ACIS-S).  The model of
the effective area of the HETGS consists of applying the predicted
efficiency of each grating to the effective area of the HRMA at
for that grating, combining with the predicted quantum efficiency
(QE) of the ACIS-S and then summing over all gratings\cite{dewey}.
A similar approach was used to generate the effective area
of the Low Energy Transmission Grating Spectrometer (LETGS),
which consists of the HRMA, LETG and the High Resolution Camera
Spectroscopy array (HRC-S).  Effective area curves, efficiencies,
filter transmissions, etc.
are available from the AXAF Science Center either in the
AXAF Proposer's Guide\cite{prop-guide} or on-line at
{\tt http://asc.harvard.edu}.

In this paper, we describe tests performed at the AXAF X-ray
Calibration Facility\cite{marty} which were designed to verify
the model of the HETGS effective area.  Most of the tests
obtained at the XRCF were designed to illuminate the HRMA with
a monochromatic beam in order to sample one energy at a time.
Reported elsewhere in these proceedings are the results from
HETG efficiency model verification using tests with the EIPS
using non-flight
detectors\cite{dewey98}, tests using the HRC-S as a
detector in order to test the predictions of high order
efficiencies\cite{kathy} and tests using the Double Crystal
Monochromator\cite{schulz} in order to examine the HETGS
effective area at a wide range of energies.
The tests described here employed the Electron Impact Point
Source (EIPS) at high voltage and current in order to obtain
a bright continuum.  The continuum was bright enough to
obtain 100-1000 counts {\em per spectrometer resolution element}
over most of the useful energy range of the spectrometers.
These data could then be used to probe for unexpected
spectral features or deviations near the sharp M edges due
to the iridium on the HRMA and gold in the gratings.
An original purpose of the tests was to test for molecular
contamination on the mirrors by examining the mirror Ir M
edge decrement, so the tests were given the designation ``MC''.

The tests proved extremely successful:
we found no unusual features in effective area of the HETGS
and LETGS to a level of about 5\% and found that the models
of the Ir and Au M edges agreed to within statistics in all
cases.  The detailed
Ir M edge structure given most recent HRMA effective
area curve match the data very well but there is a discontinuity
at 2 keV which is not observed.  The data were also used
to show that the positive and negative orders of the gratings
have consistent efficiencies and that the QEs of the frontside
illuminated (FI) CCDs in the ACIS-S are all consistent.  Finally,
using the consistency of the positive and negative orders,
we derive the ratio of the QEs of the backside illuminated (BI)
CCDs relative to the FI CCDs and show that this ratio does not
match the expected ratio of QEs.  The reason for this discrepancy
may be related to a change of event grades because ACIS was
read out in the continuous clocking mode rather than in the
timed exposure mode for which most calibration data exist.
Finally, a pair of new hot columns (or pixels) was discovered that had not
appeared in the preceeding tests.

\section{Observations and Data Reduction}

\begin{table}[b]
\begin{center}
\begin{tabular}{||l|l|l|l||}
\hline
Test ID & Grating & HRMA Shells open & Open Quadrant pattern \\
\hline
H-HAS-MC-3.001 & HETG & 1,3 (HEG subset) & NS, TB\\
H-HAS-MC-3.005 & HETG & 4,6 (MEG subset) & T, N, B, S\\
H-LAS-MC-3.009 & LETG & all & T, N, B, S\\
\hline
\end{tabular}
\end{center}
\caption{
\label{tbl:tests}
This table shows the set of tests used in the data analysis.
For an overview of AXAF calibration, see Weisskopf
et al\cite{marty}.  The HETG high energy gratings (HEGs) have
periods near 2000 \AA\ and are arrayed to receive light
from the inner pair of HRMA mirrors while the HETG medium energy
gratings (MEGs) have periods near 4000 \AA\ and correspond
to the outer mirror pair.  The quadrant pattern represents the
order in which the north (N), south (S), top (T) and bottom (B)
quadrants were opened in order to reduce the telemetry saturation.}
\end{table}

\subsection{General}

The tests that were reduced are given in table~\ref{tbl:tests},
taken at the XRCF on 1997 April 25 between 0341 and 0806 UT.
For each of these tests, the EIPS was fitted with the Cu anode
set to maximum voltage, 20 kV, and minimum current, 0.1 mA, in
order to achieve the highest continuum but keep the total
count rate down without using filters.  In order to prevent
possible radiation induced damage due to the bright zeroth
order image, the detector assembly was ``dithered'' using the
five axis manipulator (FAM).  A serpentine pattern was used.
%whose pattern is given in figure~\ref{fig:dither}.  Long
Long motions in the cross dispersion direction allowed us to
reduce the data in large sections at fixed offset along the
dispersion direction.  Dithering had the advantage of
smoothing over detector gaps and any other features.

%\begin{figure}[t]
%\begin{center}
%\epsfig{file=dither.ps,height=10cm,angle=90}
%\caption{ \label{fig:dither}
%\small
%The pattern of motion executed by the Five Axis Manipulator (FAM)
%during the continuum tests performed at the X-ray Calibration
%Facility (XRCF).  The FAM was moved 25 $\mu$ in facility $Z$
%coordinates every 20 s and 200 $\mu$ in XRCF $Y$ coordinates
%every 820 s.  The HETGS and LETGS dispersion directions are
%nearly parallel to the XRCF $Y$ coordinate.
%}
%\end{center}
%\end{figure}

The ACIS-S was run
in the continuous clocking mode and ``faint'' mode so that
three pulse height values were obtained for each event.
The detector telemetry limit in this mode is about 393
events/s (see the AXAF Proposer's Guide\cite{prop-guide}).
As it was, the source
was so bright that the ACIS-S telemetry limit
was reached easily.  Shell quadrants were closed to reduce
the count rate to a manageable level during the tests and
approximately equal exposure was obtained for all shells.

As described in the AXAF Proposer's
Guide\cite{prop-guide}, when the telemetry limit is reached,
CCD buffers fill and data may be lost.  To allow the buffers to
empty in each shell quadrant configuration, the mirrors were
exposed for 15 min
and then closed for 5 min.  Exposure is then determined
by counting frames, since frames are never only partially
lost.  The good frames are determined by examining the average
counts per frame within the time intervals during which the
shutters were open.  These time intervals were then examined
manually to ensure that closed shutter periods were excluded
in the results and to make sure that all good frames were included.
The exposure per frame is given by the time to read
out 512 rows at 10 $\mu$s per column per row and 285 rows per
column, giving 1.459 s.  The exposure was determined for each
CCD separately because the buffers are independent.  The
pixel boundaries of each chip were transformed into wavelengths
by the same method used for the events (see section \ref{sec-evtproc})
and then both sides were added to obtain the exposure functions
shown in figure~\ref{fig:exposure}.

\begin{figure}[t]
\begin{center}
\epsfig{file=exposure.ps,height=15cm,angle=90}
\caption{ \label{fig:exposure}
\small
Exposure as a function of wavelength for each test and
for the positive and negative orders separated.  The
details of the tests are given in table~\protect\ref{tbl:tests}.
Wavelengths are determined from the dispersion relation for
an assumed first order spectrum.  The ACIS-S CCDs start with
S0 on the left and end with S5 on the right.
CCD gaps are apparent; the exposure doesn't go to zero due
to shifting of the detector assembly along the dispersion direction during
the tests.  The zeroth order (and origin) was always on the
S3 CCD, a backside illuminated (BI) CCD.  Several
series of shallow dips result from the elimination of columns
on the S1 (BI) CCD
containing hot pixels and again were shifted to different locations
in wavelength space as the detector was moved.
}
\end{center}
\end{figure}

All events from columns containing hot pixels were eliminated from
the data and from the exposure function.  The hot pixels were most
apparent in detector coordinates because the detector was dithered
during the observations.  Known hot pixels\cite{prop-guide}
were apparent in the first
two observations (3.001 and 3.005) but two new ones showed up in
the LETGS observation (3.009) in columns 225 and 232 of the S3
ACIS-S CCD.  Another, much milder hot pixel showed up at column 670.
The previous hot pixels (columns 383 and 792) were not observed.
The new hot columns (or pixels) are somewhat surprising because
the test 3.009 immediately followed test 3.005 and the ACIS
electonics were not changed.

\subsection{Event Processing}
\label{sec-evtproc}

The overall event processing approach was the same for each test.
First, the details of the dithering were measured and events
were shifted to compensate.  Both the actual FAM shift in XRCF
$Y$ coordinates and the times of the shifts were measured from
the centroids of bright emission lines in detector coordinates.
The Cu-K$\alpha_1$ (8.02783 keV) at $m = +1$ was used for test 3.001, while
the $m = +2$ line was used for test 3.005 and the $m = +3$
line of cu-L$\alpha$ (at 0.9297 keV, or 13.336 \AA) was used
for test 3.009.  These data, shown in
figure~\ref{fig:shift}, indicated that the actual FAM $Y$ shifts for all three
tests were 0.18 mm, compared
to the commanded values of 0.20 mm.\footnote{Irregularities
in the FAM positioning were found in analysis of the HETGS
scattering test\cite{marshall}\cite{davis}.  The sense of the
deviation from the commanded motion was $10\times$ smaller
and had the opposite sign to the deviation determined here,
however.}  The actual time between $Y$ shifts
was observed to be about 561.5 frames, or 819.2 s, which is
consistent with the expected value of 820 s.

\begin{figure}[t]
\begin{center}
\epsfig{file=shift.ps,height=14cm,angle=90}
\caption{ \label{fig:shift}
\small
Centroid of the Cu-L$\alpha$ line (at 13.336 \AA) in detector
coordinates as a function of ACIS frame (in continuous clocking
mode) for test H-HAS-MC-3.005.
{\em Top:} Raw centroids showing the systematic shifts
due to dither, where the detector is moved in the $+Y$ direction
every 820 s, or 562 frames.  {\em Middle:} Centroids are corrected
for shifts of 0.20 mm, which was the commanded value.  Dashed lines
indicate times when the shifts took place.  A residual
trend remains, indicating an error in the dither magnitude.
{\em Bottom:} Centroids are shifted by 0.18 mm at each shift time
to eliminate the secular drift.
}
\end{center}
\end{figure}

Second, event dispersion distances
from zeroth order were computed based on a trial position
for the zeroth order (normally determined by the absolute positioning
of the FAM).  By comparing the positions of lines in the positive
and negative sides, the zeroth order position was measured to
within a detector pixel (24 $\mu$).

Third, a wavelength, $\lambda_1$, for each event was computing under the
assumption of first order using the observed dispersion distance
for that event and the grating periods, angles and Rowland distances
derived from previous XRCF measurements\cite{dewey98}.
For the HETGS, the dispersion distances are not directly observed,
only the projection along the XRCF $Y$ axis so the projected
distance was corrected by $\cos \alpha$, where $\alpha$ is the
angle from the dispersion direction to the XRCF $Y$ axis.

Fourth, events are selected by order using the energy, $E$,
computed from the event pulse height.  Events were assigned
to order $m$ if $ | E - hc/(m {\lambda}_1) | < \delta E $, where $h$
and $c$ are the Planck constant and the speed of light,
respectively, and $\delta E$ is 250 eV (or 150 eV in the
case of the LETG observation), larger than
the detector energy resolution.

Finally, events were selected according to CCD grade.
The CCD grades were
determined from the event pulse heights as in timed exposure
mode except that only the 3 pulse heights from the event row were
available instead of a $3 \times 3$ event ``island''.  Thus,
certain ACIS grades were not observed, such as those like
ASCA grade 2 and 6, which are normally included in the event
selection.  Similarly, although grades 1 and 5 are normally
eliminated in processing, since these grades require detecting
corners of the event islands, there were no such grades available.
Thus grading had little effect on the event selection.

\section{Formation and Interpretation of the Continuum Spectra}

A model of the effective area was generated from
a HRMA effective area model recent HETG and LETG efficiency functions,
the ACIS-S flight filter model and the ACIS-S FI QE model.
All data files used here are available from the AXAF Science
Center (ASC) calibration group web page ({\tt
http://asc.harvard.edu/cal/cal.html}) and were derived from
instrument and telescope team characterizations of the AXAF
components.

Because of the high spectral resolution of the grating spectrometers,
it is important to use finely gridded models, especially near
the spectral features such as the Au M and Ir M edges.
The HRMA effective area (EA) was generated by the AXAF telescope
science team and is posted to their web site
({\tt http://hea-www.harvard.edu/MST/mirror/ www/xrcf/hrma\_ea.html}).
They adjusted the model of the EA so that the prediction
would conform to various XRCF measurements
such the SSD continuum data\cite{jeffk} and they incorporated
details of Ir reflectivity based on updated
optical constants\cite{dale,graessle}.  For our purposes, the
gradual variation of EA with aperture size will not have
a significant effect because we are searching for spectrally
small effects, so we used the EA integrated over $2\pi$.
The HETGS and LETGS efficiencies incorporate details of the
Au edges and are described elsewhere\cite{dewey,predehl}.
The ACIS flight filter transmission model was fitted to
synchrotron data\cite{acisqe} and should include fine structure
around the Al and O edges.  The ACIS-S CCD QEs are taken
from detailed QE curves for two ``template'' CCDs: one
FI chip in the ACIS-I array and one BI chip (S3) in the
ACIS-S array\cite{acisqe}; the data from the ASC web page
were supplemented with QE values in the 0.05-0.20 keV range
with data from a fit to BI QEs by the ACIS/MIT team (see
the {\tt QDP} plot of the w134c4r QE
on {\tt http://acis.mit.edu}).

Events were binned into histograms before forming a spectrum.
The source flux, $f(E)$
(in photon cm$^{-2}$ s$^{-1}$ keV$^{-1}$),
is estimated by combining the data from the positive and
negative orders.  Denoting the positive side with $+$ and
the negative side with $-$, the expected number of counts
in a pixel at energy $E$ is given by
\begin{equation}
\begin{split}
C_+ = f A \epsilon_+ T Q_+ t_+ dE \\
C_- = f A \epsilon_- T Q_- t_- dE \\
\end{split}
\end{equation}
where $C_-$ and $C_+$ are the counts in a pixel at energy $E$,
$Q_+$ and $Q_-$ are the QEs of the ACIS-S detectors,
$\epsilon_+$ and $\epsilon_-$ are the efficiencies of the grating
into positive and negative orders and are assumed to be equal
to $\epsilon$,
$A$ is the effective area of the HRMA,
$T$ is the transmission of the ACIS-S optical blocking filter, and
$t_+$ and $t_-$ are the exposure times.
The quantity $dE$ is the
energy width of the pixel based on the derivative of
grating dispersion relation (for orders $|m|$ = 1)
which is very nearly linear:
\begin{equation}
dE = h c E^{-2} P \frac{\delta x}{D} cos(\alpha)
\end{equation}
where $P$ is the grating period, $D$ is the Rowland distance,
and $\delta x$ is the physical size of an ACIS-S pixel, 0.024 mm.
The count spectra for the two sides were combined using an
estimator that is not sensitive to situations where the
counts on one side were small or zero (due to gaps between
CCDs):
\begin{equation}
\hat{f} = \frac{C_++C_-}{A \epsilon T dE (Q_+t_+ + Q_-t_-)}
\end{equation}

The spectra derived from each test are shown in figures
\ref{fig:heg}, \ref{fig:meg}, and \ref{fig:letg}.
The Cu-L line series
(consisting of $\alpha$, $\beta$, $\eta$, $\zeta$, and
$\beta_{1,2}$) is quite prominant in all spectra and makes
it difficult to search for weak features in the 0.8-1.05 keV
region.  The Cu-K$\alpha$ and K$\beta$ lines are apparent
at the high energy end so the nearly featureless continuum
from 1.05 keV to 7.9 keV could be used for the purposes
of this project.  The O-K$\alpha$ and C-K$\alpha$ lines
are also apparent in the MEG and LETG tests
and are somewhat broad.

\begin{figure}[t]
\begin{center}
\epsfig{file=heg_spec.ps,height=17cm,angle=90}
\caption{ \label{fig:heg}
\small
A portion of the spectrum of the source measured
by the HEG portion of the
HETGS (test H-HAS-MC-3.001).  The strong emission lines
were easily identified and
are marked.  The Cu-L lines are broad and have wings that
make modelling difficult near them.
Weak features are identified in figure
\protect\ref{fig:obsmodel}.  The continuum in
the range between the Cu-K and Cu-L lines
is well fitted with a 10th order polynomial
with a few emission lines.
}
\end{center}
\end{figure}

\begin{figure}[t]
\begin{center}
\epsfig{file=meg_spec.ps,height=17cm,angle=90}
\caption{ \label{fig:meg}
\small
Spectrum of the source measured by the MEG portion of the
HETGS (test H-HAS-MC-3.005).
The Cu-L $\alpha$ (0.9297 keV), $\beta_1$ (0.9498 keV),
$\eta$ (0.832 keV), and $\zeta$ (0.8111 keV)
are the strongest lines and O-K$\alpha$ (0.5249 keV) is also
easily detected.  The line observed at 0.465 keV is actually
Cu-L$\alpha$ observed in second order that is picked up in
this first order spectrum due to low pulse height events in
the ACIS pulse height distribution.  An O-K edge feature
is apparent in the 0.53-0.55 keV range.
}
\end{center}
\end{figure}


There are features that can be attributed to high orders
from the strongest lines, in spite of the pulse height
selection.  It appears that these high orders can be
detected because of a low pulse height tail that extends
from the energy of the line down to the background level.
These high order lines are especially noticeable in the
LETGS spectrum (see figure~\ref{fig:letg}).
For example, the Cu-L$\alpha$ line has an energy of 0.9297
keV but there are a significant number of events with
ACIS pulse height energies in the .15 to .45 keV range.
When the emission line is dispersed to $m = 4$, the events
are dispersed to a distance corresponding to 0.31 keV, where
the pulse height selection accepts events in the 0.15-0.45 keV
range.  The pulse height distribution is discussed again
in section~\ref{sec:ratio}.

Comparing the spectra obtained from each grating, we see
that the continuum and line strengths are very similar
but there are systematic deviations.  These differences
are not the subject of this analysis but may be ascribed
to differences between CCD QEs, because each grating places
a specific energy onto a different combination of ACIS-S
CCDs.  In section~\ref{sec:ratio}, we show that there are
systematic deviations from the expected QE curves using data
from within a single grating observation.  This issue
requires further investigation.

It is clear from the spectra that pileup is not a significant
concern when analyzing these data.  The peak count rates in
the Cu-L$\alpha$ and Cu-K$\alpha$
lines gave count rates of order 10 count/s
in the HEG observation.  For an effective frame time of
0.00285 s in continuous clocking mode, we obtain only
0.03 count/frame, for less than 3\% pileup.  For the
continuum regions, pileup is a factor of $>$10 less.
In the LETGS observation, the Cu-L$\alpha$ line gives
somewhat more counts per frame due to the lower resolution;
there is as much as 30 count/s, for at most 10\% pileup
in this line.  Again, the pileup fraction would be less than
1\% for most spectral ranges of interest.

\begin{figure}[t]
\begin{center}
\epsfig{file=leg_spec.ps,height=17cm,angle=90}
\caption{ \label{fig:letg}
\small
Spectrum of the source measured by the LETGS (test H-LAS-MC-3.009).
The Cu-L series is observed in many orders due to the tail of the
ACIS pulse height distribution.  Note that the $m = 2$ lines are
considerably weaker than the $m = 3$ high order lines, as expected
for the LETGS.  The O-K line is apparent, as in the MEG spectrum,
and C-K$\alpha$ is detected as a broad line component under the
$m = 3$ version of Cu-L$\eta$.  Note the residual Cu-K edge at
0.28 keV.
}
\end{center}
\end{figure}

We have not yet computed
a complete model for the source because the goal of the test was
to use the continuum to search for edges and absorption
lines which are not part of the source.  The continuum shape
is not well known {\it a priori} but is not required for our immediate
purpose.  The spectrum was estimated
empirically from the HEG observations
shown in figure~\ref{fig:heg} by fitting a 10th order
polynomial so that we could examine the details of the
edge and emission structure in more detail.  The data
are compared to the model in figure~\ref{fig:obsmodel}.
Several emission lines due to contaminants in the source
are apparent as deviations from the model.  Other deviations
are observed at the Al-K and Si-K absorption edges which
are in the ACIS-S filter transmission model and the
ACIS-S QE model, respectively.  The data indicate that the
edges are somewhat sharper than predicted.  These deviations
are caused merely by interpolating the coarsely
gridded model files.  When more finely computed models
are made available, these edges should be more sharply defined
and will be better modeled.

Another feature that is apparent in figure~\ref{fig:obsmodel}
is a deviation at 2 keV.  This feature is in the model but not
in the data and is caused by a sharp ``edge'' in the HRMA
effective area model.  This edge is not physical and was the
result of patching newly determined optical constants to
older Henke values at this point (R. Edgar, private communication).
The feature should be eliminated in the next update to the
HRMA effective area.

\begin{figure}
\begin{center}
\epsfig{file=obs_vs_model.ps,height=17cm}
\caption{ \label{fig:obsmodel}
\small
Count spectrum for three separate energy ranges of the
test with the HEG portion of the HETGS (test H-HAS-MC-3.001).
Emission line features that are intrinsic to the source are
marked (e.g. Mg-K$\alpha$ at 1.254 keV).  Two absorption edges
are marked (Al-K at 1.559 keV and Si-K at 1.839 keV) where
the model of the ACIS-S filter (Al-K) and the detector (Si-K)
are so coarsely gridded that the edge does not appear as sharply
defined as the data indicate.  The bumps and dips from 2.05 through
2.2 keV are the result of Ir M edges in the HRMA effective area
and those in the 2.2 to 2.6 keV range arise primarily in the
Au M edges of the HEG efficiency curve.  Other sharp features
are due to exposure variations.  A significant deviation from
the model occurs at 2.0 keV where the HRMA effective area has
a feature that is not tracked by the data.
}
\end{center}
\end{figure}

\section{Comparison of Positive and Negative Sides}
\label{sec:ratio}

The ratios of the counts, $R = C_+/C_-$, in the two sides is dependent only
on the QEs and the exposure times as long as the grating efficiency is
the same for positive and negative orders.  All subassembly and XRCF
data to date have shown no differences between positive and negative
efficiencies, so we may examine the ratios of CCD QEs with these data.
We kept track of which CCDs contributed to the ratios so that we could
construct $R(E)$.  When both orders were on FI CCDs, then all model
curves cancel, so that we may test for differences in QEs between
FI CCDs or check for grating positive-negative efficiency differences.
Figure~\ref{fig:fifi} shows the result.  We see that there is
remarkable consistency between FI CCDs, especially in the
1.8-2.8 keV region, once we discount the apparent
discrepancies due to Cu-L lines.  The analysis was designed for
regions where the continuum was varying slowly, so it is not too
surprizing that the L lines show deviations.  These regions should
be reduced separately and the effects of pileup should be
taken into account.

\begin{figure}
\begin{center}
\epsfig{file=fifi.ps,height=10cm,angle=90}
\caption{ \label{fig:fifi}
\small
Ratio of the count rates from 30 pixel regions at the same
dispersion distance from zeroth order but on two different
frontside illuminated (FI)
CCDs in the ACIS-S array.  The different symbols indicated which
grating data set was used to obtain the ratio.  The ratios are
comfortably close to unity for most of the energy range so that
any deviations can be ascribed to variations of QE between
FI CCDs.  Data from regions near the Cu-L lines should be
discounted because the analysis is very sensitive to the
exact placement of the integration window around the emission
lines.  The analysis was designed primarily for regions where
the spectrum varies slowly.
}
\end{center}
\end{figure}

The ratio of the fluxes determined for the BI CCDs could also be
compared to those determined in the FI CCDs.  The estimated fluxes
already include the ratio of the BI to FI QEs.  Figure~\ref{fig:bifi}
shows this ratio computed for each grating set.  There are very
significant, systematic deviations: 15-20\% in the 2-4 keV band, 
10-40\% in the .5-.8 keV band, and differences greater than a
factor of 2 below 0.35 keV.  The FI QE in the latter region is
extremely small and falling rapidly, so it is perhaps not too
surprizing that there may be errors there.  The fact that the
QE ratio may be measured there may be more surprizing.

The deviations elsewhere, and especially in the 2-4 keV range, are
more disturbing.  Although investigations are in progress, we
have identified an effect that may have bearing on this problem.
In figure~\ref{fig:pha}, we show the pulse height distribution
for events detected by the S3 (BI) CCD and dispersed to a location
consistent with energies in the range of 3.0 to 4.0 keV.  The
figure shows that there is a tail to the pulse height distribution
(PHD) that contains a significant number of events and which deviates
dramatically from the expected PHD measured from timed exposure mode
data.  This difference could arise from the inherent limitation of
the on-board processing of continuous clocking mode event data.  If
an event is split such that a significant fraction of the charge
appears in an adjacent row, then the event can be detected as two
different events when operating in the continuous clocking mode.


\begin{figure}
\begin{center}
\epsfig{file=bifi.ps,height=10cm,angle=90}
\caption{ \label{fig:bifi}
\small
Ratio of the exposure and QE corrected fluxes from 30 pixel
regions where the count
rate from one side with a BI CCD is compared to that of
a FI CCD on the opposite side at the same
dispersion distance from zeroth order.
The different symbols indicated which
grating data set was used to obtain the ratio.
This ratio indicates difficiencies in the ratios of the
QE models for BI and FI chips.
Investigations to explain the observed differences
are currently focussed on the differences in event grade
assignation between continuous clocking mode and the
timed exposure mode normally used in calibration.
As in figure~\protect\ref{fig:fifi}, data points which are
near or include the Cu-L lines should be discounted.
Similarly, there is a point at Cu-K$\alpha$ that is
likely to be badly computed.
}
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\epsfig{file=pha.ps,height=7cm}
\caption{ \label{fig:pha}
\small
Pulse height distribution (PHD) for a region of the S3
(BI) CCD selected from events whose dispersion corresponds
to the 3-4 keV range, assuming $m = 1$ (taken from test
H-HAS-MC-3.001).  The peak in the 3-4 keV band is expected
but the tail that extends to extremely low pulse heights
contains much more power than expected.  Normally, in
timed exposure mode, of order 1\% of events would appear
in a small peak at 1.74 keV, which is the Si-K escape
peak.  The escape peak is not visible in this plot because
it appears to have been swamped by events with partial
charge collection.
}
\end{center}
\end{figure}

\section{Conclusion and Further Investigations}

These tests provided data that nicely validated the effective
area model fine structure near known edges, so that we may
be confident that spectral features in the spectrometer can
be modelled adequately for observations after AXAF is
launched.  Concerns arise regarding the HRMA effective area
model near 2 keV that will be addressed by the telescope
science team.  In addition, we noted problems that may result
from event loss.

One prospective reanalysis of the data would be to attempt
to identify events that are actually associated with split
events which were not recognized by the ACIS on-board
processor.  These events could be combined to improve
the pulse height distribution so that the QEs of the BI
and FI chips might be more closely comparable to that of
timed exposure mode.  Very little calibration data were
taken in the continuous clocking mode but these data
must be examined and modeled to see if the apparent
QE differences we find can be explained.

There are grating observations of continuum
sources that have yet to be reduced and analyzed.
In one test, ACIS was read out in timed exposure mode, so
we may be able to compare with the results from these
observations.  Pileup is expected to be more prevalent,
however.  Another series of tests involving continuous
clocking mode employed the carbon EIPS anode, so data will
be available for searching for features in the 0.8-1.1 keV
region.  A preliminary examination of the data\cite{dewey}
showed slightly different contaminants than observed in
these copper anode tests.

These data can still be examined in a bit more detail for
possible features in the O-K to Cu-L$\zeta$ energy range,
spanning from about 0.5 keV to 0.8 keV.  The details of
the O-K edge structure have been measured at a synchrotron
using polyimide filters similar to those used in the MEG,
so these details should be incorporated into the HETGS
grating efficiency curves.

\section{Acknowledgments}

This work was supported in part by NASA under the HETG contract
NAS-38249 and the
AXAF Science Center contract to the Smithsonian Astrophysical
Observatory, NAS8-39073.

\begin{thebibliography}{9}
\bibitem{dewey}
Dewey, D., et al, ``Towards the Calibration of the HETGS Effective
Area,'' in Grazing Incidence and Multilayer X-ray
Optical Systems, Proc. SPIE, vol 3113, pp 144-159, 1997.
\bibitem{polygonmodel}
T.H. Markert et al, ``Modeling the Diffraction Efficiencies of the AXAF
High Energy Transmission Gratings'', in EUV, X-Ray, and Gamma-Ray
Instrumentation for Astronomy VI, Proc. SPIE, vol 2518, pp 424-437, 1995.
\bibitem{prop-guide}
``NASA Advanced X-ray Astrophysics Facility Proposer's Guide,''
AXAF Science Center technical document ASC.TD.402, 1997.
\bibitem{marty}
Weisskopf, M.C., et al, ``Calibration of the AXAF Observatory:
Overview,'' in Grazing Incidence and Multilayer X-ray
Optical Systems, Proc. SPIE, vol 3113, pp 2-17, 1997.
\bibitem{dewey98}
Dewey, D., Drake, J.J., Edgar, R.J., Michaud, K.,
and Ratzlaff, P., ``AXAF Grating Efficiency Measurements with
Calibrated, Non-imaging Detectors,''
these proceedings.
\bibitem{kathy}
Flanagan, K.A., Hartner, G.D., Murray, S.S., and Predehl, P.,
``HETG High Order Diffraction Efficiency,''
these proceedings.
\bibitem{schulz}
Schulz, N.S., Dewey, D., and Marshall, H.L.
``Absolute Effective Areas of the HETGS,''
these proceedings.
\bibitem{marshall}
Marshall, H.L., et al, ``Towards the Calibration of the HETGS Line
Response Function,'' in Grazing Incidence and Multilayer X-ray
Optical Systems, Proc. SPIE, vol 3113, pp 160-171, 1997.
\bibitem{davis}
Davis, J., Marshall, H.L., Dewey, D., and Schattenburg, M.
``Analysis and Modeling of the Anomalous Scattering in the AXAF HETGS,''
these proceedings.
\bibitem{jeffk}
Kolodziejczak, J.J., et al., ``Uses of continuum radiation in the
AXAF calibration, '', in Grazing Incidence and Multilayer X-ray
Optical Systems, Proc. SPIE, vol 3113, pp 65-76, 1997.
\bibitem{dale}
Graessle, D.E., Burek, A.J., Fitch, J.J., Harris, B., Schwartz, D.A.,
and Blake, R.L., ``Optical constants from synchrotron reflectance
measurements of AXAF witness mirrors - 2 to 12 keV, ''
in Grazing Incidence and Multilayer X-ray
Optical Systems, Proc. SPIE, vol 3113, pp 52-64, 1997.
\bibitem{graessle}
Graessle, D.E., Blake, R.L.,
Burek, A.J., Dyson, S.E., Fitch, J.J., Schwartz, D.A.,
and Soufli, R., ``Modeling of synchrotron reflectance
calibrations of AXAF iridium-coated witness mirrors over 2-12 keV, ''
in X-ray Optics, Instruments, and Missions,
Proc. SPIE, vol 3444, 1997.
\bibitem{predehl}
Predehl, P., et al, ``X-ray Calibration of the Low Energy
Transmission Grating Spectrometer: Effective
Area,'' in Grazing Incidence and Multilayer X-ray
Optical Systems, Proc. SPIE, vol 3113, pp 172-180, 1997.
\bibitem{acisqe}
Bautz, M.W., Nousek, J., Garmire, G., and
the ACIS instrument team, ``Science Instrument Calibration Report for
the AXAF CCD Imaging Spectrometer (ACIS)'', available at
{\it http://wwwastro.msfc.nasa.gov/xray/axafps.html}, 1997.
\end{thebibliography}

\end{document}