\chapter{XRCF Efficiency and Effective Area Measurements}
\label{chap:xrcf_eae}

\section{Overview}

The role and purpose of the various XRCF efficiency
and effective area tests are discussed here.

\subsection{Diffracted Order Sign Convention}

\fbox{\begin{minipage}{5in}
{\it Note}: By convention the sign of a diffracted order is given by
the corresponding sign of the image location reported by the
detection system:
\begin{itemize}
\item[ ] {Phase 1, HXDS}~--~the $m=+1$ order is in the $+Y_{\rm xrcf}$
direction
\item[ ] {ACIS-2C}~--~the $m=+1$ order is in the $+Y_{\rm xrcf}$
direction
\item[ ] {ACIS, HRC}~--~the $m=+1$ order is in the $+Y_{\rm Det}$
direction, that is in the $-Y_{\rm xrcf}$ direction
\end{itemize}
\end{minipage}}


\subsection{Divide and Conquer}

One of the key calibration activites to be carried out at the XRCF is the
measurement of the effective area of the AXAF.  For the HETGS this effective
area depends on the performance of the HRMA, HETG, and ACIS-S, that
is:

\begin{equation}
A_{hetgs}(E,m,{\rm mode}) = \sum_{s=1,3,4,6} A_s(E) ~G_s(E,m)
~QE_{acis}(E,\vec{X},{\rm mode}).
\end{equation}

\noindent where the three contributing elements are the HRMA single shell
effective areas ($A_s$), the effective HETG grating efficiencies
($G_s$) for the mirror shells, and the ACIS-S photon detection
efficiencies ($QE_{acis}$).  Here $E$ denotes the dependence on
energy, $m$ the diffraction order, $mode$ the event identification in
the CCD (here, for example, we will consistently use the sum of ASCA
grades 0,2,3,4,6 and TE-mode), and the $\vec{X}$ dependences from
spatial dependencies in the detector array, i.e FI/BI efficiencies and
gap locations between the devices.

Figure~\ref{hrmaarea} shows the total AXAF HRMA on-axis effective area
at XRCF and its contributing single shell areas. Mirror shells 1 and 3
cut off at energies around 5 and 6.5 keV, while shells 4 and 6 extend
up to 7 and 9 keV. The decrease near 2 keV is due to the iridium
M-edge in the reflective mirror coating. The effective area sum,
equation 1 above, then adds s = 1 and 3 for the MEG area and 4 and 6
for the HEG area.

\begin{figure}
\psfig{file=hrma_effarea.ps,height=11cm}
\caption{\small HRMA effective areas, the straight line shows the total area, followed by
the ones for each shell (courtesy of the AXAF MST).}
\label{hrmaarea}
\end{figure}

The grating efficiencies have been determined from laboratory
measurements, Section~\ref{sec:xgef_meas}, where the
diffraction efficiency of each flight grating was measured at several
energies and orders and positions within each
facet. Figure~\ref{hetgeff} show the predicted efficiencies for MEG and
HEG. Displayed are the zeroth order (solid line) and the 1st and 3rd
positive order in MEG, and the 1st and 2nd order in HEG, which are the
dominant orders for each grating.

\begin{figure}
\psfig{file=meg_effic.ps,height=10cm}
\psfig{file=heg_effic.ps,height=10cm}
\caption{\small MEG (top) and HEG (bottom) efficiencies as a function of energy, from subassembly data 
analysis.} 
\label{hetgeff}
\end{figure}


In general each CCD device has its own characteristics. However, since
not all quantum efficiency functions are yet avalable, we have to use
templates for each CCD type. Figure~\ref{aciseff} shows the quantum
efficiencies for the FI device in I3 of the imaging array versus the
BI device in S3 of the spectroscopy array. The functions already
include the transmission characteristics of the flight filters. The
use of these templates is reasonable since FI devices are quite
similar and we only expect systematic deviations of the order of
5$\%$. The difference between the two BI devices (S1, S3) should not
be significantly larger. However, as we will show during the analysis,
the differences are visible in the data.

\begin{figure}
\psfig{file=acis_effic.ps,height=9cm}
\caption{\small Effective efficiencies (quantum efficiency $\times$ filter transmission) as a function
of energy for the FI device I3
in ACIS-I and for the BI device S3 in ACIS-S (courtesy of the MIT ACIS team).}
\label{aciseff}
\end{figure}

One important step in this process is the division of XRCF testing
into Phase 1 and Phase 2.  In Phase 1 more traditional X-ray detectors
are used to test the HRMA and HETG.  In this phase it is useful to
consider the {\it optic effective area (OEA)} which represents the
ability of the optics to collect photons at energy $E_{\rm line}$ into
order $m$.  This quantity does not include the detector quantum
efficiency and so is a property of the optics only:

\begin{equation}
OEA_{2\pi}(E_{\rm line},m) = {\frac{\rm focal~plane~photons/s~in~line{\rm -}order}
{\rm source~flux~in~line}}~~~
[{\frac{\rm photons/s}{\rm photons/cm^2s}} = {\rm cm^2}]
\label{equ:oea_defn}
\end{equation}

\noindent Note that we get the usual ${\rm cm}^2$ units, as for example
in the HRMA-only effective area analysis\cite{kellogg97}.  The
subscript ``$2\pi$'' (steradians) is used to indicate that this is the
effective area over the full focal plane (half sphere) behind the HRMA
and includes all structure in the diffracted order, {\it e.g.}, LEG
support structure pattern.  Low-level scattering by the HEG,
Sections~\ref{sec:scat_theory} and~\ref{sec:scatter}, is not
considered a contribution to these integer diffraction orders,
however.  From a prediction or modeling point of view, the optic
effective area for the mirror-grating combination is calculated from
the following terms:

\begin{equation}
OEA_{2\pi}(E_{\rm line},m) = \sum_{s=1,3,4,6} A_s(E_{\rm line}) 
~G_s(E_{\rm line},m)
\label{equ:oea_model}
\end{equation}
\noindent where the terms have been defined in Section~\ref{sec:intro_effic}.
Going a step further, the ratio of optic effective areas can be
used to measure the grating diffraction efficiency $G_s(E_{\rm line},m)$
itself.

\subsection{Test Strategy}

The 1st-order HRMA-HETG effective area curves can be divided (somewhat
arbitrarily) into 5 regions where different physical mechanisms govern
the effective area of the optical (mirror-grating) system:

\begin{itemize}
\item[ ] {\it below 1 keV}~--~The polyimide membrane of
the gratings is dominating the area changes, with edges due to C,
N, and O.
\item[ ] {\it 1-2 keV}~--~The phase effects of the grating cause an
increasing enhancement of the diffraction efficiency.
\item[ ] {\it 2-2.5 keV}~--~Edge structure from the mirror (Ir) and
grating (Au) dominates, sharply reducing effective area.
\item[ ] {\it 2.5-5.5 keV}~--~Effective area is slowly varying, with some
low-amplitude Ir and Au edge structure.
\item[ ] {\it 5.5-10 keV}~--~The mirror reflectivity and grating efficiency
are decreasing rapidly with energy.
\end{itemize}

Table XXX summarizes the various XRCF efficiency and effective
area tests that have been carried out and presents their role in our
overall effective area calibration strategy.
  Most of the tests carried out 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{flanagan98} and tests using the Double
Crystal Monochromator\cite{schulz98} in order to examine the HETGS
effective area at a wide range of energies.  In contrast, a set of tests
employed the Electron Impact Point Source (EIPS) at high voltage and
current in order to obtain a bright continuum. 
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''.

\clearpage

\section{Alignment Tests}
\label{sec:align}
\input{pre_align}

\clearpage

\section{XRCF Source Characteristics}
\label{sec:xrcf_sources}
\input{draft_xrcf_sources}

\clearpage

\section{Efficiency: Phase 1, Fixed Energies}
\label{sec:effic_phase1}
\input{draft_eae_phase1.tex}

\clearpage

\section{Efficiency: Phase 1, Monochromator Scans}
\label{sec:effic_mono}
\input{pre_effic_mono}

\clearpage

\section{Efficiency: ACIS-2C Data}
\label{sec:effic_2c}
\input{pre_effic_2c}

\clearpage

\section{Absolute Effective Area with ACIS-S}
\label{sec:area_acis}
\input{draft_area_acis}

\clearpage

\section{Relative Effective Area: Molecular Contamination}
\label{sec:effic_mc}
\input{draft_mc.tex}

\clearpage

\section{Effective Area with HRC-I}
\label{sec:area_hrc}
\input{draft_area_hrc}

\clearpage

\section{Efficiency: High-Order Efficiency Measurements}
\label{sec:effic_highorders}
\input{draft_highorders.tex}