\begin{quotation}
{\it Objective:}  Calculate the relative efficiencies of the
diffracted orders seen in the Phase 2 flight detector data
in order to calibrate the HETG high-order efficiencies.
The use of the two detector's data sets allows likely detector
effects to be separated from HETG effects.

{\it Publication(s):} Schulz {\it et al.}\cite{schulz98},
Flanagan {\it et al.}\cite{flanagan98}
\end{quotation}

\subsection{Overview}

During Phase 2 XRCF testing some 54 HRC-I and ACIS-S EA measurements
were made with the HETG inserted in the beam.  Descriptions and
analyses of these data sets are presented in
Sections~\ref{sec:area_acis} and~\ref{sec:area_hrc}.  The data from
these tests provide a necessary complement to the limited set of
laboratory high-order efficiency measurements on each of the flight
gratings.  Given that the intensity of higher orders is a strong
function of grating bar shape\cite{markert95}, the extension of the
subassembly model to very high orders is tenuous, underlining the need
for direct measurement at XRCF.  In addition, analysis of the data has
yielded insight into both the HRC-I and ACIS-S instruments in aspects
that were not fully examined at subassembly level.

\subsection{HRC-I Data Sets}

  The HRC-I data sets and aspects of their
analysis are described in Section~\ref{sec:area_hrc}.
Blah, blah.

	A detailed investigation showed that smearing of the image due
to electronic saturation did {\it not} systematically affect the
result: ratios remained unchanged to within $\sim 3$\% 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, as mentioned in Section~\ref{sec:area_hrc},
there is evidence to suggest a higher proportion of
saturated events in bright orders relative to faint orders.
If so, then 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 X-ray
events and their positioning errors do not compromise the analysis, we
have chosen to use the ``uncleaned'' data set throughout
this order-ratio analysis.


\begin{table}[h]\centering
\begin{tabular}{|c|c|c|c|c|} \hline\hline
Grating & order ratio  & Typical counting statistics & Assigned Subassy error & deviation from predicted \\ \hline\hline
HEG & 2/1 & 10\% & 20 to 25\% &-10 to -15\%\\ \hline
 & 3/1 & 10\% & 50\% & -35\%\\ \hline
 & 4/1 & 15\% & 90\% & -35\%\\ \hline
 & 5/1 & 20\% & 90\% & -60\%\\ \hline
 & 6/1 & 20\% & 90\% & -60\%\\ \hline
MEG & 2/1 & 15\% & 20 to 25\% & approximately correct\\ \hline
 & 3/1 & 10\% & 50\% & -5\%\\ \hline
 & 4/1 & 20\% & 90\% & +25\%\\ \hline
 & 5/1 & 20\% & 90\% & -25\%\\ \hline
 & 6/1 & 20\% & 90\% & approximately correct\\ \hline
 & 7/1 & 20\% & 90\% & -25\%\\ \hline
 & 8/1 & 30\% & 90\% & approximately correct\\ \hline
 & 9/1 & 30\% & 90\% & -45\%\\ \hline\hline
\end{tabular}
\caption{\small
\label{tab:hrc_order_compare}
Comparison of Predictions with Measured ratios for HETG + HRC-I 
higher orders.} 
\end{table}

\subsection{Discussion of HRC Order Ratios}

	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\ref{tab:hrc_order_compare} 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 are taken 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~\ref{tab:hrc_order_compare}.


\subsection{ACIS-S/HETG Order Ratios}

	Figure~6 shows the +1 to -1 order ratio for HEG as detected by
ACIS-S.  The plot shows significant (up to 35\%) departures from
unity. As discussed previously, these may be due to intrinsic grating
asymmetry or detector nonuniformity.  (Bias angle considerations do
not apply to the ACIS-S.)  However, deviations from symmetry in
Figure~2 with the HRC-I 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 frontside-illuminated (FI) and a backside-illuminated (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, Section~\ref{sec:area_acis}, the quantum
efficiency functions were not yet avaliable for each device and
templates were used for each CCD type. Thus, chip-to-chip
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 HRC-I 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 ACIS-S show much structure and do not
reproduce the systematic reduction relative to predictions as shown
with the HRC-I.

	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.

\subsection{Discussion of ACIS-S/HETG Order Ratios}

The absolute effective areas derived in Section~\ref{sec:area_acis}
in general agree with the expected 
effective area function to quite a high degree. However, there are
significant local deficiencies that remain.  The most prominent
is an apparent drop of effective area for HEG +1 and -1 orders 
below the expected curve at energies above 5 keV, Figure~\ref{hegfirst}.

One possible explanation is a local non-uniformity 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 non-unifomity 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 efficiencies 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 {\it et
al.}\cite{allen98}.  These corrections were used
for the high rate zero-order effective area data,
Figure~\ref{fig:zero_pileup}.  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 show clear fingerprints of these
effects at work, the uncertainty of the beam uniformity issue remains
unresolved and we'll have to calculate and simulate it with \mx 
in Section~\ref{sec:acis_pileup}.

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 focal plane detectors 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\cite{ACISreport97}.  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\cite{propguide}.  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 HRC-I. As discussed earlier, the near-perfect
symmetry of the +1 and -1 orders (to within 5\%) of the HEG with HRC-I
exclude the grating as a contributor to these effects.



\subsection{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,
HRC-I and ACIS-S. We found that:

\begin{itemize}

\item{The symmetry of the +1 and -1 orders of HEG with HRC-I lead to
the conclusion that detector nonuniformity, grating asymmetry and bias
angle effects were small.}

\item{HRC measurements show suppressed higher grating orders for HEG
relative to predictions.  Measurements of the MEG orders agree well
with predictions.}

\item{ACIS-S shows strong detector effects, compatible with grade 
migration and charge loss.}


\item{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.}

\end{itemize}




	Several items remain for future work.  These include:
\begin{itemize}

\item{Investigate the relation between saturation and count rate 
density in HRC-I.}
\item{Quantitative analysis of grade migration and charge loss in ACIS.} 
\item{Incorporate synchrotron high order measurements.}
\item{Examine Phase 1 measurements for high orders and asymmetry.}
\item{Analyze EIPS sources with both detectors and the monochromator 
scan with HRC-I.}
\end{itemize}