\subsection{Source Spectra and Efficiency Measurements}

\begin{quotation}
{\it Objective:} Use the HSI images of the various source lines
to create a grating-derived high resolution spectrum of the source.
\end{quotation}

During Phase I calibration the HSI detector\cite{evans97}
provided imaging capability at high event rates.   Companion HSI
exposures were taken for most of the FPC/SSD effective area tests
expressly for the purpose of being able to see the dispersed images
that the focal plane aperture was sampling.  Through application
of the grating equation these images also yield high-resolution
spectra of the sources; Fe-L and Ti-K HRMA-grating-HSI spectra are
shown in Figures~\ref{fig:FeL_spectra}
and ~\ref{fig:TiK_spectra}.

  The model spectra plotted in these figures consist of a Kramer
continuum\cite{dewey94} plus a number of Gaussian lines with widths
and intensities set to approximate the HSI-measured spectra.  The line
energies are fixed at tabulated values for identified lines.
Comparison of the measured and modeled spectra has been done by eye,
facilitated by the use of normalized cummulative plots, examples
of which are shown at the bottom of Figures~\ref{fig:FeL_spectra} and
\ref{fig:TiK_spectra}.  Generally we have spectra of these lines with all three
AXAF gratings.  Because of the high spectral resolution of
the HRMA-grating systems, the actual line widths and shapes can
be resolved for many lines especially with the MEG and HEG
gratings, {\it e.g}, the Fe-L and O-K lines
here.  Other lines, like the Ti-K lines shown in Figure~\ref{fig:TiK_spectra},
are narrower than the instrument resolution and are modeled
as delta functions.

Source spectra from grating-HSI observations are available
at: \\
{\tt http://space.mit.edu/HETG/xrcf\_sources/sources.html}

\begin{figure}
\begin{center}
\psfig{file=E-HXH-3D-10.007_compare.ps,width=17.0cm}
\end{center}
\caption[Ti-K : HEG-HSI spectrum and model]
{
Ti-K line: HEG-HSI Spectrum and Model.  {\it Top}: Measured Ti-K flux
spectrum, calibrated by nominal parameters for the HRMA, HEG, and HSI;
the Ti-K$\alpha$ and Ti-K$\beta$ lines are well resolved by
the HEG dispersion.
A model spectrum (solid) is plotted with the HEG-HSI-derived spectrum.  {\it
Bottom}: The data (dashed) and model (solid) spectra are compared by
plotting the cummulative (integrated) normalized flux within the
observed energy range.  This plot provides a measured {\it vs.}
modeled comparison of the relative line and continuum fluxes in spite
of spectra differences, {\it e.g.}, here the measured and modeled line
widths differ.
}
\label{fig:TiK_spectra}
\end{figure}


\begin{figure}
\begin{center}
\center{\hskip0.01in \vbox{\psfig{file=hsi_FeL_hist.ps,width=15.0cm}}}
\vskip0.3in
\psfig{file=D-LXH-3D-11.030_compare.ps,width=17.0cm}
\end{center}
\caption[Fe-L line: LEG-HSI Spectrum]
{
Fe-L line: LEG-HSI Spectrum and Model.  {\it Top:} The High Speed Imager
(HSI) positioned at the location of the LEG first-order for the
Fe-L$\alpha$ line; the detected events are binned by their
location along the dispersion axis
($Y_{\rm xrcf}$).  {\it Middle}: The counts spectrum is converted
to a flux {\it vs.} energy spectrum using nominal calibration parameters for
the HRMA, LEG, and HSI.  A smooth model spectrum (see text) is plotted
with the LEG-HSI spectrum.  {\it Bottom}: The data (dashed) and model spectra
(solid) are compared by plotting the cummulative (integrated) normalized flux
within the observed energy range.  This plot provides a
comparison of the relative line (abrupt jumps) and continuum (sloping regions)
fluxes
in spite of data-model variations in line location,
width, and overall normalization, {\it e.g.}, the small difference in
measured {\it vs.} modeled energies due to inaccurate HSI position analysis.
}
\label{fig:FeL_hsi_dispersion}
\label{fig:FeL_spectra}
\end{figure}

\clearpage

\subsection{Beam Uniformity Effects on Efficiency Measurements}

\begin{quotation}
{\it Objective:} Evaluate the effect of non-uniform illumination
on ``grating-in grating-out'' efficiency measurements in Phase I
and on relative efficiency measurements in Phase II.
\end{quotation}