\begin{quotation}

{\it Objective:} Identify the grating facets responsible for the
cross-dispersion outlier images and produce a model to reproduce
the data.

\end{quotation}

\begin{figure}
\begin{center}
\epsfig{file=mis_align_defocus.eps,height=10cm}
\caption[Mis-aligned MEGs: HSI defocused image]
{Defocussed HSI image of the MEG Al-K 3rd order.  Individual 
grating facets are visible here in the two MEG rings of gratings.
At right a blowup shows mis-aligned facets by the doubling up of 
the facet images near the center.
}
\label{fig:mis_align_defocus}
\end{center}
\end{figure}

Surprisingly, the images of MEG Al-K$\alpha$ in third order showed
several additional images at the same dispersion distance as the
Al-K$\alpha$ line, these are the weak features at +400 and -100 in HSI
Z seen in Figure~\ref{fig:mis_aligned}.  The images individually were
2-6\% of the power in the main image.  Several of the images were
displaced in the cross-dispersion direction by 120 microns and a
fourth deviated by almost 400 microns, corresponding to rotations of
the dispersion direction by 7~arc~minutes and 24~arc~minutes,
respectively.  Such large rotations were not expected, based on
subassembly measurements ({\it e.g.}, Figure~\ref{fig:roll_plot}) so
an additional test was devised to confirm this possibility.

A defocussed image of the MEG +3 order Al-K line (Alignement test)
reveals the individual facets, Figure~\ref{fig:mis_align_defocus}.  A
grating mis-aligned in roll will show up as having its image shifted
along the $z'$ axis -- this can be seen for the ``400~$\mu$m
offender'' at around coordinates Y~=~-3~mm, Z~=~+1~mm where the
regular set of grating images has a gap and a doubled facet.  By
analyzing this image 6 MEG gratings were found to be misaligned by 5 to 23
arc minutes.  All of these were from a single fabrication lot.
Further tests have confirmed that fabrication irregularities produced
excess stress gradients in the grating polyimide support structure
leading to inaccurate polarization alignment measurement values.
These ``mis-aligned gratings'' will be explicitly included in our
instrument model.

 The image in Figure~\ref{fig:mis_align_defocus} (TRW ID
D-HXH-AL-27.001, run id 107934, taken 1/7/97, logged as 1/8/97) is MEG
3rd order Al-K defocussed to 65.54 mm.  The main K-alpha line,
satellite line, and K-beta/O-K lines are visible.  The image used is
the raw HSI image and HSI ``gaps'' are visible.

 Each MEG grating creates an image in one of the shells
around the rings.  If a grating is mis-aligned in roll
(``alignement'') its image will move roughly in the +/- Z direction.
The 3rd order MEG Al-K is diffracted $\approx~$55~mm
in the dispersion direction, so a 30 arc minute grating roll results
in a 0.48 mm Z shift. 

 The events in each sector (A through FF) of each shell (1 and 3) have
been converted from facility Y,Z values into R, theta about the ring
center, Figure~\ref{fig:3_ff}.  The events for shell-sector can be view by
plotting the appropriate anglular range (0 degrees is along the +Y
axis, south; positive angles are right-hand rule about X, e.g.,
towards +Z) and radial (shell) range.  The gaps between facets are
generlly visible.  In this theta-R space the cross-dispersion
direction is indicated with an arrow of length 30 arc minutes of
grating roll and pointing in the direction of ``unscrewing'' (+
righthand about +X).  A histogram of counts vs theta helps identify
the gratings, gaps, etc.  The orientation of these plots is as if
standing in the center of the HESS HRMA-side looking radially out
towards the sector: grating 1 of the sector is to the right and
grating 7/9 to the left (larger angles.)

Table~\ref{tab:mis_aligned_megs} presents a list of gratings which
appear to be highly-rolled.  Herman Marshall identified 4 spots in the
Focus Check MEG +3 image in his memo and they are here as well as two
others: one in the Top quadrant (3EE2) that may be visible in the Top
image and one (1E4) that is not clearly visible in South or Bottom but
is is on their boundary and so may be blocked by either shutter.

\begin{table}
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
 run id & Quadrant, hlm feature & $I_{\rm spot}/I_{\rm quad.}$ & 
 roll (arc min.)& HESS ID \\
\hline
\hline
 107463 & Top, -?- (see in image?) &  . &  ~+5   &  3EE2 \\
  107464 &  North, Spot 1 &  5.6 \% &  -8   &  3FF4 \\
  107464 &  North, Spot 2 &  2.3 \% &  +23   &  3FF5 \\
  107465 &  Bottom, Spot 1 &  3.0 \% &  +8   &  3E1 \\
  . &  S/B, -?- (shutter blocked?) &  . &  ~+5   &  1E4 \\
  107466 &  South, Spot 1 &  4.0 \% &  -6   &  1F4 \\
\hline
\end{tabular}

\vspace{0.5cm}

\begin{tabular}{|c|c|c|c|c|c|}
\hline
HESS ID & Grating & Lab ID & Fab ID & Al-K 3rd order & 
 Al-K 1st order \\
\hline
\hline
3EE2 &  ME1411 &  189 &  F07M012 &  1.8-2.0 \% &  17-19\% \\
3FF4 &  MD1312 &  201 &  F07M027 &  2.3-4.9 \% &  6.9-7.8 \% \\
3FF5 &  MD1307 &  195 &  F07M020 &  1.3-1.6 \% &  15-17 \% \\
3E1 &  ME1405 &  185 &  F07M008 &  1.5-1.7 \% &  18 \% \\
1E4 &  ME1402 &  187 &  F07M010 &  1.5-1.8 \% &  15-18 \% \\
1F4 &  MF1502 &  192 &  F07M017 &  1.4-1.6 \% &  18 \% \\
\hline
\end{tabular}
\caption[Mis-aligned MEGs]
{Mis-aligned MEGs.  The upper table provides information
on the identified misaligned gratings and their location on the HESS.
The lower table gives information on the specific grating facets at
these locations.}
\label{tab:mis_aligned_megs}
\end{center}
\end{table}

{\bf Note that all of these gratings are
from Lot F07M !}  In fact these are 6 of the (only) 11 lot F07M gratings
that are on the flight unit.  The other five are: 3EE3, 1FF5, 1F1, 3F5, 3F2.


\begin{figure}
\begin{center}
\epsfig{file=mis_align_3_FFps.ps,height=11cm}
\caption[Shell 3 sector FF Events]
{Shell 3 sector FF Events plotted in radial vs. azimuthal coordinates (top)
and event histogram (bottom).
The 7 gratings in shell 3 sector FF are numbered 1 through 7 from
right to left.  The grating in location 3FF4, bright in 3rd order,
is rotated such that its image has moved left.  The grating in
location 3FF5 has rotated in the other direction by 23 arc minutes
to almost the location of 3FF3. \\
In memory of Tom, grating 3FF1, its diffracted
events visible on the right, is inscribed with ``Thomas H. Markert''
inplace of a grating ID.}
\label{fig:3_ff}
\end{center}
\end{figure}