\begin{quotation}
{\it Objective:}  Calculate the relative efficiencies of the
diffracted orders as seen in the Phase II flight detector data.
This analysis is to calibrate the HETG order ratios.
\end{quotation}

During Phase II some 54 HRC-I and ACIS-S EA measurements were
made with the HETG inserted in the beam.

\subsection{DCM-HETG-HRC-I Efficiency Ratio}

That the XRCF data will support a 3\% relative and 10\% absolute HETGS
calibration is better domonstrated with a DCM-HETG-HRC data set,
Figure~\ref{fig:hrc_dcm}.  Here, the DCM was tuned to energies in the
1.5 to 7 keV range (TRW IDs G-HHI-EA-7.030 to '48, and 
 '99.059 to '61).  At each energy the ratio of counts detected in
the HEG and MEG plus-first orders to the counts detected in the
combined HEG and MEG zero order was computed.  This ratio depends
primarily on the HETG zero-order and first-order efficiencies and
secondarily on the HRMA effective areas and the HRC-I spatial
uniformity:

\begin{equation}
{\frac{R_{\rm 1st}}{R_{\rm 0}}}(E) = 
{\frac{
QE_{\rm HRC}(E,\vec{X_M})  \sum_{s=1,3} A_{s}(E) G_{s}(E,1) ~~+~~
QE_{\rm HRC}(E,\vec{X_H})  \sum_{s=4,6} A_{s}(E) G_{s}(E,1)
}{
QE_{\rm HRC}(E,\vec{X_0})  \sum_{s=1,3,4,6} A_{s}(E) G_{s}(E,0)
}}
\end{equation}

\noindent where $QE_{\rm HRC}(E,\vec{X_*})$ is the quantum efficiency
of the HRC-I at the different
detected spatial regions (MEG 1st, HEG 1st, and zero orders)
and the other terms have been previously defined.

\begin{figure}
\begin{center}
\epsfig{file=hrc_dcm_ratio.eps,height=14cm}
\caption[DCM-HETG-HRC-I 1st to 0 order ratio vs. E]
{DCM-HETG-HRC data: ratio of first orders to zero-order.}
\label{fig:hrc_dcm}
\end{center}
\end{figure}