\begin{quotation} {\it Objective:} Measure or set upper limits on the wide-angle contribution of the grating to the LRF, {\it i.e.}, the ``scatter''. Investigate the energy dependance of the scatter and the ability to fit it with a model. {\it Publication(s):} Davis {\it et al.}~\cite{davis98} \end{quotation} \begin{figure} [t] \begin{center} \epsfig{file=H-HAS-SC-7.002.gif.ps,width=16cm} \caption[ACIS-S Scatter: H-HAS-SC-7.002 image] {\small ACIS-S image from test H-HAS-SC-7.002. } \label{fig:acissscatter} \end{center} \end{figure} \subsection{Scattering Data and Results Overview} %{{{ This section describes the phenomenon, gives examples of and summarizes the data sets and presents the analysis results. Several calibration tests were designed to probe the pattern of the scattering and its dependence on energy. The tests were performed at the AXAF X-ray Calibration Facility (XRCF)\cite{weisskopf97}. The double crystal monochromator (DCM) source was used to reduce spectral contributions far away from the central energy. For the first four tests, the DCM was tuned to an W-M emission line from the source. For the remaining tests, the DCM was scanned from 5 keV to 9 keV in 1 keV steps for 5 different data sets. The list of tests is shown in \Table{tbl:tests}. \Figure{1775keVdata} shows the scattering features observed at $1.775$ keV as determined by the extensive Phase G tests. The fractional scattered light integrated over each of several half-order regions at different energies is shown graphically in \Figure{fig:testsum}. More words about the behavior with energy, reference the scattering theory, and comment on how (if at all) it will be included in MARX/models. \begin{quotation} {To-do:} \\ How and do we need to include scatter in our instrument model? \\ \end{quotation} \begin{figure} [ht] \begin{center} \epsfig{file=1.775.ps,height=12cm,angle=270} \caption{\label{1775keVdata} \small Measured HEG scatter at 1.775~keV. The HEG scattering-per-bin normalized to the counts expected in the first order is plotted as a function of diffraction location expressed as a non-integral diffraction order; the bin size here is $0.00716$ orders. Note the strong scattering peaks immediately to the left and right of first order and near second and third orders. ``Half-order'' scattering also appears around $m = 0.5$. } \end{center} \end{figure} \begin{table} [hb] \begin{center} \begin{tabular}[b]{||l|l|l||} \hline Test ID & Detector & Energy(ies) (keV) \\ \hline D-HXH-PO-13.00{2,4,6,8} & HSI & 1.7754 \\ ( 970121/hsi10976{1,3,5,6}.fits ) & & \\ G-H2C-SC-88.00\{1-5\} & ACIS-2C0 & 1.7754\\ H-HAS-SC-7.002 & ACIS-S & 1.3835 \\ H-HAS-SC-7.004 & ACIS-S & 2.035 \\ H-HAS-SC-17.006 & ACIS-S & 5.00, 6.00, 7.00, 8.00, 9.00 \\ \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 {\it et al.}\cite{weisskopf97}.} \end{table} \begin{figure} \begin{center} \epsfig{file=frac_scat_vs_nrg_half.ps,width=16cm} \caption{ \label{fig:testsum} \small This figure shows a summary of the results of the data analysis. The values are normalized to the total of the +1 and -1 order count rates. Due to the systematic errors in background subtraction, bad columns, etc., the fractional scattering at 0.5 order at 1.775 keV has been systematically underestimated -- by as much as a factor of 2 or 3. Error estimates are due to statistical uncertainties only. Note that most scattering fractions are relatively independent of energy above 2.0 keV.} \end{center} \end{figure} %\begin{table} %\begin{center} %\begin{tabular}[t]{||c||c|c|c|c|c||} %\hline %Energy & \multicolumn{5}{|c|}{Order range} \\ %(keV) & \multicolumn{5}{|c|}{(fractional power within the given range %$\times$ 10$^{-3}$)} \\ %\hline % & 0.25-0.75 & 0.75-1.25 & 1.25-1.75 & 1.75-2.25 & 2.25-2.75 \\ %\hline %1.384 & 2.97 +/- 0.21 & 2.13 +/- 0.17 & 0.54 +/- 0.09 & 1.08 +/- 0.17 & -- +/- -- \\ %1.775 & 1.05 +/- 0.04 & 4.03 +/- 0.06 & 0.45 +/- 0.03 & 2.83 +/- 0.05 & 1.08 +/- 0.03 \\ %2.035 & 3.56 +/- 0.40 & 1.91 +/- 0.26 & 0.54 +/- 0.15 & 1.51 +/- 0.23 & 0.81 +/- 0.18 \\ %5.000 & 4.26 +/- 0.32 & 2.05 +/- 0.21 & 0.72 +/- 0.13 & 1.28 +/- 0.15 & 1.57 +/- 0.17 \\ %6.000 & 3.48 +/- 0.25 & 2.31 +/- 0.20 & 0.83 +/- 0.11 & 1.18 +/- 0.13 & 1.52 +/- 0.15 \\ %7.000 & 3.53 +/- 0.29 & 2.02 +/- 0.23 & 0.90 +/- 0.15 & 0.96 +/- 0.14 & 1.23 +/- 0.16 \\ %8.000 & 3.80 +/- 0.47 & 2.26 +/- 0.37 & 1.16 +/- 0.26 & 1.13 +/- 0.22 & 1.43 +/- 0.25 \\ %9.000 & 2.31 +/- 0.72 & 3.14 +/- 0.70 & 0.95 +/- 0.44 & 1.09 +/- 0.39 & 2.69 +/- 0.52 \\ %\hline %\end{tabular} %\end{center} %\caption{ %\label{tbl.testsum} %This table shows a summary of the results of the data analysis. %The scattered light is given for five half-order ranges centered every %half order. The values are normalized to $10^{-3}$ %of the total of the +1 and -1 order count rates. Due to the systematic %errors in background subtraction, bad columns, etc., the fractional %scattering at 0.5 order at 1.775 keV has been systematically underestimated %-- by as much as a factor of 2 or 3. Error estimates are due to statistical %uncertainties only.} %\end{table} \clearpage % ---------- begin HSI section \begin{figure} \begin{center} \epsfig{file=scatter.eps,height=9.0cm} \caption[HSI cusp HEG scatter at 1.775 keV] {\small Phase I HEG scatter test. The core of the HSI image of the DCM monochromatic 1.775 keV line in HEG first order is blocked by the HSI cusp (triangular low-count region.) Extending from the cusp along the HEG dispersion axis are scattered 1.775 keV photons. Of order 0.4\% of the line flux is scattered. } \label{fig:scatter} \end{center} \end{figure} \subsection{Phase I HSI Scattering Tests} A test series was developed to search for near line scattering wings (PSF/Outer, Scattering) that would be a concern when measuring absorption features near bright lines. The Double Crystal Monochromator (DCM) was tuned to the bright line W-M$\alpha$ at 1.775 keV in the anode spectrum. The current was turned to the lowest possible value to get a count rate for the total line and then the current was turned to the highest possible value for the scattering test. The image was placed on a detector mask ``cusp'' in order to block the core of the image but allow photons beyond $E/100$ of the target line. Mirror scattering was expected but would be azimuthally symmetric, while grating line scatter was expected preferentially along the direction of dispersion, so would be distinguishable from mirror scattering. After a long integration at high current, a total of 100,000 counts would be obtained from the core of the line (without the blocking cusp), so the test could detect scattered power levels below 0.1\% of peak. The result, Figure~\ref{fig:scatter}, was somewhat surprising at the time: although there was no obvious evidence for power along the dispersion direction near the line, there were clearly significant events dispersed 1-10 mm from the line. In order to verify that the DCM had no significant spectral leakage that could cause the observed effect, we tuned the DCM off of the bright line by only 15 eV. The DCM resolution at 1.775 keV is about 5 eV, so very little power was expected and the current was turned up to its maximum setting. There were no events at the expected dispersion location of 1.775 keV, indicating that it had been suppressed at a level better than one part in $10^5$. We concluded, therefore, that the gratings were incoherently diffracting a modest fraction of the line emission to large dispersion distances. This fraction was estimated at 0.4\% over a 10 mm span. Subsequent modelling and further tests indicated that minor bar location variations could cause an incoherent redistribution of monochromatic light. The grating-bar variations needed can be quite small, of order a few percent of the the distance between bars, Section~\ref{sec:scat_theory}. \begin{quotation} {To-do:} \\ Create normalized scattering plot from HSI data and compare with '2C data (Figure~\ref{1775keVdata}) for normalization check. \\ \end{quotation} \clearpage % ---------- end HSI section \begin{figure}[ht] \begin{center} \epsfig{file=scat_2c_image2.ps,height=10cm} \caption[ACIS-2C image showing HEG scatter at 1.775 keV.] {\small ACIS-2C event plot showing HEG scatter at 1.775 keV. The range shown is 114 rows tall by 1024 columns wide. Zero-order is off the chip to the left, MEG first order is on chip at left and HEG first order is on chip at right. The scattered light from the HEG is visible as the upper-left-to-lower-right diagonal streak through the HEG first order; this is the HEG dispersion direction. Due to the wrapping of the ACIS-2C readout mode used, this scattered light appears to go through the MEG first order. Note that the MEG produces no scattered light as there is no 'lower-left-to-upper-right' streak along the MEG dispersion direction.} \label{fig:scat_image} \end{center} \end{figure} \subsection{ACIS-2C Scattering Tests: G-H2C-SC-88.00\{1-5\}} The W-M$\alpha$ line at 1.7754 keV was the brightest line to which the DCM could be tuned. The shape of the scattering was investigated at this energy using a long integration and the highest DCM current. The test was performed using the backside illuminated CCD in the ACIS-2C\footnote{See {\tt http://space.mit.edu/HETG/acis2c.html} for more details of the ACIS-2C detector} (chip 0), which is a non-flight AXAF detector developed specifically for ground testing and calibration. Five separate exposures of about 900 s each were obtained, shifting by 22 mm between exposures to span a dispersion distance similar to that of the flight detector. The CCD is about 24 mm across, so there was a 2 mm overlap between adjacent exposures. The pixel spacing of the detector was $0.024$ mm, which was precisely measured during fabrication (M. Bautz, private communication). The CCD was operated in a ``fast'' mode where 114 rows of data were obtained every 0.66 s, in order to reduce pile-up near the dispersed orders. The frames are shifted downward by 114 rows after each exposure, so the dispersion lines are ``wrapped''. Event recognition was disabled for the final two rows (wrapped rows were not considered), so there are no events in these two rows (producing a gap that occasionally crosses the dispersion line). For this test, the HETG was used in combination with the DCM set to the bright W M$\alpha$ line at 1.775 keV, and the HRMA with all shells open. The detector is the backside illuminated chip (ID 0, detname was ``w148c4'') in the ACIS-2C detector. The detector was run in 114 row mode, so the integration times were about 0.66 s. In this mode, the MEG and HEG spectra criss-cross through the detector window, Figure~\ref{fig:scat_image}. In order to map the so-called ``scattered'' light out to +3 order, the '2C0 was positioned by the FAM to 5 locations 22 mm apart along the +Y axis. Since the actual level in the lines was not of primary concern, the cores of the dispersed orders were allowed to pile up. The reduction and analysis were done in IDL. The data came in FITS format as the result of second floor processing at the XRCF and was read into IDL using the {\bf mrdfits} routine. Besides the event data, various test- and ACIS-specific FITS keywords were read. The keyword values were used to set system parameters and calibration values such as the detector gain, the grating period, mirror focal length and Rowland distance. The event finding algorithm used in quicklook processing does not process the last two rows of data, even though the charge in these rows is collected. This feature is evident as a 2 pixel wide gap. PH data for each event consisted of 25 values in a 1-D array. The procedure for reducing these observations started with event lists which included the event location in the 114x1024 window, the event time, and pulse heights for the 5x5 event island. \begin{enumerate} \item{Various FITS keywords were read: ONTIME to get the exposure time, OBS\_ID to get the TRW ID, WINSIZE to get the ACIS-2C window size (in pixels), CCD\_ID to get the character setting which chip in the 2C was being used (so the detector name is assigned to ACIS-2C0 to indicate the BI chip in the 2C), DETNAM to get the chip serial number, and TLMAX4 to determine the number of columns allowed. The TRW ID is parsed into components to give the XRCF phase, grating, and detector assembly.} \item{The chip serial number is used to set the chip gain parameters. For the chip used in these tests, w148c4, no ``official'' values were available, so the gain was set to 0.322 DN per eV, estimated from the PH distribution so that the highest peak would centered at the DCM energy, 1.775 keV.} \item{The 25 PH values were reordered from the subassembly order, which places the center event first, to the flight order, where the center event is 5th in the array. The event PH amplitude is formed as the sum of all 25 PHs. The ``ASCA'' grading criterion is applied to the 3x3 PH data but is not used in processing. The event amplitudes are converted to energy using the chip gain and offset parameters. See figure~\ref{fig:scat_ph} for the pulse height distribution for the entire 5 image data set. The input is monochromatic at 1.775 keV and background is negligible. Thus, the pileup peaks are apparent and there is a tail of incomplete charge collection events below 1 keV. The ACIS-2C0 gain parameters vary significantly over the entire array, so peaks are broad.} \begin{figure} \begin{center} \epsfig{file=scat_pha.ps,height=9.0cm} \caption[Pulse Height Distribution for '2C HEG Scatter Data] {\small Pulse height distribution for the entire five image data set, converted to energy in keV. The input is monochromatic at 1.775 keV, so all features are related to pileup or incomplete charge collection} \label{fig:scat_ph} \end{center} \end{figure} \item{Randomized event chip coordinates by $\pm$ 0.5 pixel.} \end{enumerate} The event positions were randomized within a pixel in order to prevent digitization effects in subsequent analysis, which involved fractional pixel shifts and rotations. The locations were shifted to place the zero point at the 0th order location in facility coordinates and rotated so that the MEG or HEG dispersion direction would be horizontal. Events for each exposure were processed separately due to detector rotations and shifts. \begin{enumerate} \item{Offset by FOA loc (584, 72.8), then rotated -0.58 degrees to convert from chip (real) XY to XRCF YZ. The rotation angle and offset were estimated from the first image where the FAM position was set to (0,0) so that the 0th order image would be centered and the HEG scattering would be horizontal after HEG rotation below.} \item{Offset by FAM Y and Z shifts. Coordinates are now in pixels from 0th order. Subsequent analysis showed that the commanded and reported values, both specifying no motion in Z and 22 mm motions in y only, gave incorrect results.} \item{Rotated XRCF YZ coordinates by the grating dispersion angles (HEG: -5.2 degrees, MEG: 4.7 degrees), determined from the value of the angle of the MEG-HEG bisector, -0.225 degrees and the MEG-HEG opening angle, 9.934 degrees, taken from analysis of Phase I EE data (see Section~\ref{sec:periods_angles}). New coordinates are dispersion $y'$ and cross-dispersion distances $z'$ in pixels. NOTE: The rotation is about the (virtual) 0th order location, not chip FOA, so the rotations are distinguishable (as with HSI).} \item{Coordinates are scaled to physical units (mm) using 24 microns per ACIS pixel.} \end{enumerate} A detector-based energy was computed using the 25 pulse heights and the detector gain, 0.322 eV per DN. In order to reduce background, data were screened to include only events with inferred energies in the 1.3 to 4.4 keV range, which gave events with one or two photons each. The wavelengths for each event, assuming it was dispersed into first order, were computed using the grating equation $\lambda ~=~ | p \sin \beta |$, where $p$ is the grating period (either 4001.13 \AA\ for the MEG or 2000.81 \AA\ for the HEG), $\tan \beta = y' / X_{\rm RS}$, $y'$ is the dispersion distance, and $X_{\rm RS}$ is the Rowland spacing, taken to be 8782.8 mm. See Section~\ref{sec:cip_periods_angles} for a discussion of these values. The events were ``unwrapped'' modulo the 114 row period in order to center the dispersion axis. The unwrapping depends only on the cross-dispersion distance, $z'$: the event $z'$ values are offset by plus or minus $W$ to put them in the range $-W/2 < $z'$ < W/2$, where W $=$ 114 $\times$ 0.024 mm. The events were then combined and binned in 0.05 \AA\ (HEG) or 0.1 \AA\ intervals (MEG). The images are shown in figures~\ref{fig.hegimage} and \ref{fig.megimage}. Background was estimated using a 30 pixel region well away from the dispersed light. The dominant source of background was due to mirror scattering, which is azimuthally symmetric about the 0th order image and all dispersed orders. Many artifacts of the detector are visible but the anomalous scattering is obvious along the HEG direction and is absent along the MEG direction. \begin{figure}[t] \begin{center} \epsfig{file=herman_image_label.eps,width=16cm} \epsfig{file=phot05_tot.ps,width=16cm} \caption{ \label{fig.hegimage} \small This image is the result of binning data from HETGS scattering tests G-H2C-SC-88.00\{1-5\} along the HEG dispersion direction. The anomalous scattering is apparent as the broad, dark horizontal streaks in the image. Wavelength increases to the right from the zeroth order at far left. Three HEG orders are observed as well as MEG orders in between. Note the near coincidence of MEG 4th order and HEG 2nd order about 2/3 of the way from the left end. The diagonal features are due to 2 pixel gaps in the event finding algorithm while vertical features are due to bad pixels masked out or to changes in exposure due to regions of overlap between shifted exposures. Scattering is brightest near the HEG +1 and HEG +2 orders. } \end{center} \end{figure} \begin{figure}[t] \begin{center} \epsfig{file=herman_image_label.eps,width=16cm} \epsfig{file=phot1_tot_meg2.ps,width=16cm} \caption{ \label{fig.megimage} \small An image derived from tests G-H2C-SC-88.00\{1-5\} as in Fig.~\protect\ref{fig.hegimage} but binned along the MEG dispersion direction and binned at 0.1 \AA\ bins (so the image size is about the same as the HEG image). The same detector features are apparent, such as stripes where there are no events. The HEG scattering shows up as steep, wrapped, dark, diagonal lines. No MEG scattering is observed, so stringent upper limits can be set. The faint elliptical image between zeroth and first order is the first order dispersed image of the DCM output at twice the tuned energy. } \end{center} \end{figure} Some of the conclusions that can be drawn from the binned images follow. \begin{enumerate} \item{The MEG shows no detectable scattering. This is evident on many images but no quantitative limits have been measured yet.} \item{The cross-dispersion profiles were fitted with Gaussians of variable location, width, background, and normalization at each wavelength bin for HEG scattered light only in order to diagnose effects of the data reduction procedures. An aperture subtraction technique could not be applied immediately because it was apparent that the initial assumptions about the FAM motion were incorrect. Figure~\ref{fig:scat_centroids} shows results from one reduction run. Fits have been eliminated where unreasonable centroids, widths, or intensities were obtained, causing gaps in the plots. Some bad data points remain, however, and have to be reviewed individually.} \item{A pattern of rotated spectra in each measurement was corrected by applying a rotation in the ACIS-2C0 frame about the FOA. A ``global'' drift remained; centroid values in figure~\ref{fig:scat_centroids} drift downward by about 1.0 arcsec as the wavelength increases from 5 \AA\ to 21 \AA. This drift is corrected with a 0.016 mm Z shift for each 22 mm FAM motion. This drift could be caused by a difference between the FAM and XRCF Y axes (defined in phase C) of 0.04 degrees.} \item{The total counts in the cross dispersion profiles are given by the integral over the Gaussian, which is proportional to the fitted normalization and the fitted $\sigma$. These data, also shown in figure~\ref{fig:scat_centroids}, show the dispersion peaks expected at multiples of 7.0\AA\ and at the wavelengths halfway between due to the MEG. Bad fits often occur at these locations because the profiles are not Gaussian when the line cores are so dominated by event pileup. The wavelengths are measurably different from the expected values, reaching a maximum deviation of 0.5 \AA\ at the HEG +3 location, expected to be observed at 21.0 \AA. The wavelength errors are eliminated by assuming that the FAM moved 22.25 mm on each step, 1.1\%~too far. The FAM was commanded to move 22.000 mm and FAM log data agree, so the source of the discrepancy is not known at this time.} \begin{figure} \begin{center} \epsfig{file=scat_fit.ps,height=9.5cm} \caption[Fitting Gaussians to the HEG scattered light cross-dispersion profiles.] {\small Fitting Gaussian functions to the HEG scattered light cross-dispersion profiles. {\it Top curve} The centroid location in arc seconds from a fiducial horizontal reference. Note that the centroid drifts downward by about 1.0 arcsec as the wavelength increases from 5 \AA to 21 \AA. {\it Middle curve} The inferred total counts in the Gaussian fits. Scattering peaks appear near 7 \AA, 14 \AA, and 21.2 \AA. Bad fits occurred at the HEG and MEG orders. These should have been at 3.5 \AA\ (or 7.0 \AA\ for the MEG +1), 7.0 \AA\ (HEG +1), 10.5 \AA\ (MEG +3), 14.0 \AA\ (HEG +2, MEG +4), etc. At HEG +3, the line is observed at 20.5 \AA, compared to the expected value of 21.0 \AA, thus wavelengths of orders showed systematic error. The wavelength errors are eliminated by assuming that the FAM moved 22.25 mm on each step, 1.1\% further than the commanded motion. {\it Bottom curve} The fitted Gaussian sigma parameter; good fits give values near 0.5 arc sec (about 2 ACIS pixels, as expected).} \label{fig:scat_centroids} \end{center} \end{figure} \item{For the remaining analysis, a simple aperture extraction method was sufficient because the spectrum was level and smooth. The source aperture was defined to be 2.5 arcsec (5 pix) wide and background was estimated from a region 11-26 arcsec above the source. Figure~\ref{fig:scat_bg_src} shows the count spectra derived in these two regions.} \begin{figure}[p] \begin{center} \epsfig{file=scat_bg.ps,height=8.0cm} \caption[Estimated ``Background'' and the Count Spectra in the Source Region] {\small The estimated ``background'' and the count spectra in the source region. Note that the background increases towards 0\AA~due to mirror scattering from 0th order. The orders show up in background due to mirror scattering and when the MEG image does not land on top of the HEG image; e.g., at 10.5 Å and 17.5 Å. (Note wavelengths have been corrected for the FAM motion error mentioned in figure~\ref{fig:scat_centroids}.)} \label{fig:scat_bg_src} \end{center} \end{figure} \item{Subtracted background and normalized to expected rate in first order of 1700 cps. Figure~\ref{1775keVdata} shows the net scattered light after dividing by the estimated exposure time. There are still background subtraction errors near the MEG and HEG orders but the overall subtraction is good off the lines so that the scattered light is apparent.} \item{Added points at +1, +2, +3 orders affected by pileup in order to make a figure that combines the dominant grating orders from HEG ``coherent'' diffraction with the HEG incoherently diffracted or scattered light. The total scattered light gives 17 count/s and is normalized to the count rate expected from the W-M line in +1 order, which is estimated to be about 1700 count/s. Thus, the total of the incoherently scattered light is estimated to be about 1\% of the power in first order. The scattered light is occasionally detected at values approaching $2 \times 10^{-4}$ of the flux in order +1. The detection limit is about a factor of 20 below this value.} \end{enumerate} The exposure time (see \Figure{fig.exposure}) was computed for each wavelength based on the wavelengths of the detector edges for each exposure, and was used to compute count rates as a function of wavelength. The exposure for each wavelength bin was estimated by setting up dummy ``events'' at the chip corners. These events were sent through the same transformations as the photon events. The chip exposure time was added to array elements corresponding to all allowed wavelength bins. Energies were computed from the dummy-event wavelengths. Accumulated exposures for each (overlapping) ACIS-2C0 position. The events were concatenated. Figure~\ref{fig.exposure} gives the resultant exposure time as a function of wavelength, adding all 5 chips. The result was normalized to the estimated count rate of the first dispersed order, which was not directly observed due to significant event pile-up. The zeroth order count rate was estimated by modeling the profile of the trail of the zeroth order image that occurs when the CCD is parallel shifted. The trail receives an exposure of 40 $\mu$ sec per row for each CCD frame and for each window per frame. There were 9 windows (at 114 rows per 1024 row frame) per frame, 100 frames of data (only the first portion was examined) and 25 rows of the 114 row window were combined, giving a total exposure in the trail of 0.9 sec. The one-dimensional profile of the trail region is shown in \Figure{fig.zerotrail}. Fitting two Gaussians to the trail gave about 1200 $\pm$ 100 counts in each component while a detailed model based on the beam normalization detector (BND) data only predicted 1170 in the broad, flat component and 1280 in the Gaussian component. The broad component was modeled as an intensity gradient that varied by a factor of two (as given by the BNDs) across the HRMA aperture and then adjusting the defocus and centroid until a good match was obtained to the observed profile. The normalization was not adjusted but was fixed by the north and south BND count rates.\footnote{See the AXAF Project Science web page {\tt http://wwwastro.msfc.nasa.gov/xray/xraycal/bu/bucat.html} and the figure linked from ``TAP2'', tap2.eps. RunID 112250 shows a good example of the profile of the DCM beam when tuned to a bright line. Additional data taken during the XRCF rehearsal phase with a BND centered in the XRCF vacuum pipe were used to chart the 1.775 keV line and the nearby continuum. Note that the north and south BNDs are placed about 70 cm to either side of the HRMA aperture center while the top and bottom BNDs are centered in XRCF Y coordinates.} Fitting a Gaussian after subtracting the model of the flat component gave 1180 $\pm$ 80 count, so the model agrees well with the data. The first order count rate, $R_{1,HEG}$, was then estimated as $R_{0,HETGS} A_{1,HEG} / (A_{0,HEG}+A_{0,MEG})$, where $A_m$ is the predicted effective area at 1.7754 keV for order $m$ and the grating subset (either HEG or MEG). The model predicts a count rate for HEG 1st order (both sides) of 2980 count/s and 5420 count/s in the MEG 1st order. \begin{figure} \begin{center} \epsfig{file=exposure.ps,height=10cm,angle=90} \caption{ \label{fig.exposure} \small This figure shows the exposure function derived for tests G-H2C-SC-88.00\{1-5\}. Regions where two adjacent observations overlapped show twice the average exposure and there is double exposure near zeroth order as data from the negative dispersion direction is included. } \end{center} \end{figure} \begin{figure} \begin{center} \epsfig{file=profile_fit_submodel.ps,width=10cm,angle=90} \caption{ \label{fig.zerotrail} \small This figure shows the profile of the zeroth order image in test G-H2C-SC-88.001. The profile was obtained by summing 25 rows far from the image centroid so that pile-up would not be a concern. The profile was fitted with three components: 1) {\em dashed line} the pedestal of the profile is dominated by off-line continuum as the beam pattern does not fill the mirror aperture and the detector was (unintentionally) placed slightly out of focus; 2) {\em dotted line} a Gaussian which approximates the pattern produced by the DCM when tuned to a source emission line; and 3) the uniform background is primarily due to mirror scattering. } \end{center} \end{figure} Detector and grating order artifacts were eliminated after close examination of the raw data. MEG orders 1, 3, and 5 caused systematic errors at 3.5, 10.5, and 17.5 \AA\ while HEG orders 1, 2, and 3 required excising data at 7, 14, and 21 \AA. The excised regions were generally 0.3 \AA\ wide and no scattering due to the grating was apparent in these regions. Bad exposure corrections due to the 2 row gap were eliminated near 4.3, 11.2, 2.2, and 18.4 \AA\ while bad columns in the detector required eliminating data near 18.95, 1.30, and 8.85 \AA. The result is shown in \Figure{1775keVdata}. The total scattered light from 0th order through 3rd order is 1.00$\pm$0.01 \% of HEG first orders based on this data set. A similar analysis of the MEG data shows no significant detections of scattered light. There are systematic background subtraction errors as the HEG scattered light contributed to the background. Nevertheless, the MEG scattered light density never appears to exceed a value of 5$\times 10^{-6}$ per 0.014 order. The total scattering is difficult to estimate given the systematic errors but appears to be less than 5$\times 10^{-5}$ between orders 1 and 3 while the comparable HEG scattering is 6$\times 10^{-3}$. \clearpage \subsection{ACIS-S Scattering Tests: H-HAS-SC-7.002, 7.004, and 17.006} The ACIS-S was used in phase H for these scattering tests, so there were no problems associated with windows or shifting of the detector. In the first test, the DCM was tuned to the W M$_\zeta$ 1.384 keV line. In the second test, the DCM was tuned to the W M$_\gamma$ 2.035 keV line. For the third test, the DCM was scanned from 5.00 keV to 9.00 keV in 1.00 keV steps. The HETGS dispersion relation constants derived from phase C data were verified to a part in 2400 using the first data set. The data reduction steps were essentially identical for these tests except that for H-HAS-SC-17.006 time selections were needed to separate the periods when the DCM energy was constant. In addition, for the last test only, the five axis mounts (FAM) that moves the ACIS-S relative to the HRMA was positioned at Y=0.25 mm in XRCF coordinates. The ACIS-S was run in the timed event mode so there was no ambiguity between MEG and HEG. The DCM current was set at the highest possible value, which caused significant pile-up in the dispersed orders and made zeroth order readout trail bright enough to measure in order to estimate the beam flux. The trail was somewhat fainter than in the tests taken at 1.775 keV, so total counts in a 3 column region starting 200 rows on either side of the zeroth order image were compared to a similar region rotated 15$^{\circ}$ from the vertical. The exposure time in the zeroth order trail was $40\mu$s/row/frame $\times(1024-2\cdot200)$ rows, or $25$ms per frame. Events were selected so that the energy derived from the ACIS pulse height was within 100 eV of the expected value. The event positions were transformed using the grating constants into wavelengths and a simple extraction was performed using a window 0.2 mm wide around the dispersed events while background was measured in a region 0.2 to 0.8 mm from the dispersion line. An additional rotation of -0.13$^{\circ}$ was required to make more horizontal dispersion lines; this rotation could be either in the ACIS to XRCF coordinate frame or could be a residual error in measuring the HETG to XRCF coordinate frame. Data near 0th order were eliminated from the final results as background measurements failed to account for the azimuthal symmetry of the 0th order (mirror) scattered light. Data near orders were also eliminated in general. The results are shown in figures~\ref{fig:en0-2} and \ref{fig:en3-6}. %}}}