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\begin{document}		
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\begin{titlepage}
\hrule
{\noindent\bf CORONAL DIAGNOSTIC SPECTROMETER}\\
\vspace{-0.7\baselineskip}\\
{\noindent\Huge\bf SoHO}
\vspace{2mm}
\hrule
\vspace{3mm}
\centerline{\bf CDS SOFTWARE NOTE No. 13}
\vspace{3mm}
\hrule
\noindent Version 1.2 \hfill 18 May 1994
\vspace{2mm}
\hrule

\begin{centerpage}

\begin{center}
{\Large\bf PRELIMINARY REPORT ON THE CALIBRATION OF THE VDS FLIGHT DETECTOR}\\
\mbox{}\\
W. Thompson\\
NASA Goddard Space Flight Center\\
Laboratory for Astronomy and Solar Physics\\
Code 682.1\\
Greenbelt, MD 20771, USA\\
\mbox{}\\
thompson@serts.gsfc.nasa.gov\\
pal::thompson
\end{center}

\end{centerpage}

\end{titlepage}

\section{Overview}
\label{overview}

The calibration of the VDS engineering model (EM) detector has been described
previously \cite{thompson:92}.  The flight detector was calibrated in the same
way, except for the following changes:
\begin{enumerate}
\item
The photomultiplier tubes used to monitor the Krypton lamps were operated in a
current measuring photodiode mode between the photocathode and the first
amplification stage.  This gave a steadier and much more repeatable measurement
than the pulse counting mode used during the engineering model calibration.
\item
Additional linearity tests were performed by placing a piece of frosted
magnesium flouride (MgF$_2$) just in front of the lamp.  This acted as a
diffuser, and made the image pattern seen by the detector invariant relative to
the aperture used.  However, it also greatly decreased the amount of light
falling on the detector.  Tests were also done without the diffuser in place,
replicating the test done with the engineering model detector.
\end{enumerate}

Some things still need to be done before the calibration can be considered to
be complete.  In particular, the transmission of the MgF$_2$ window used to
protect the microchannel-plate (MCP) needs to be measured.  This quantity was
measured as 18.5\% transmission for the window used for the engineering model
detector, and we have applied that number for the flight detector.  It will be
remeasured when the MgF$_2$ window currently on the flight detector is returned
to Goddard.

\section{Photometric calibration}

\subsection{Quantum Efficiency}

The absolute quantum efficiency of the VDS detector is controlled by the
microchannel-plate wafer within the Image Intensifier and Converter (IIC)
section of the detector.  The quantum efficience of the MCP was measured by
O.~H.~W. Siegmund at the University of California Space Sciences Laboratory
before delivery to Goddard.  The measured results are shown in Table~\ref{qe}.
\begin{table}
\caption[]
{Detector quantum efficiency as a function of wavelength.}
\label{qe}
\mbox{}\\
\begin{center}
\begin{tabular}{|c|r@{~$\pm$~}l|}
\hline
$\lambda$ (nm)	& \multicolumn{2}{|c|}{Q.E. (\%)} \\
\hline
30.41	& 18.98	& 0.32\\
36.11	& 14.43	& 0.76\\
40.51	& 17.22	& 0.25\\
49.01	& 16.11	& 0.26\\
58.41	& 13.23	& 0.22\\
67.11	& 13.73	& 0.58\\
92.01	&  9.56	& 0.75\\
121.61	&  1.63	& 0.20\\
\hline
\end{tabular}
\end{center}
\end{table}
The quantum efficiency in the wavelength region of interest, 30--65~nm ranges
from 13--19\%.  The low quantum efficiency at the Lyman-$\alpha$ line at
121.61~nm is desirable to reduce the effect of any scattered radiation inside
the spectrograph.

\subsection{CCD offsets}

Each CCD quadrant has a separate offset value associated with it.  Thus, the
data values are guaranteed to be positive.  Table~\ref{offsets} shows the
average offsets for each quadrant.  However, it was found that the offsets
could drift between extremes that were 8~ADC/pixel apart, so that it is
important to have a good value of the local background for each image.  There
was no indication that the offset value changed significantly during the
readout of a single exposure; however, other effects such as scattering could
also affect the local value of the background.  The best way to determine the
local background is to make the data extraction window around a spectral line
wide enough to be able to measure the signal level just outside the line.
However, this has to be confirmed with the detector installed within the CDS
instrument.

\begin{table}
\caption[]
{CCD offset values for the individual readout quadrants.}
\label{offsets}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Quadrant & Average Offset (ADC/pixel)\\
\hline
A	& 217.94\\
B	& 207.47\\
C	& 182.08\\
D	& 179.29\\
\hline
\end{tabular}
\end{center}
\end{table}

\subsection{Throughput}

Tests of the VDS flight detector were done at programmable voltages of 0, 50,
100, 150, 200, 250 in the units used by the EGSE software, e.g.
\begin{quote}
VDS SETPROGVOL 15 $n$
\end{quote}
These correspond to voltages across of the MCP of approximately 600V, 678V,
756V, 834V, 912V, and 990V\@.  Table~\ref{voltage} gives the measurements we
made, based on the housekeeping data, of the correspondence between the
programmable voltage setting and the actual voltage across the MCP wafer.
\begin{table}
\caption[]
{Correspondence between programmable voltage \#15 and MCP voltage}
\label{voltage}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Programmable voltage \#15	& MCP voltage\\
\hline
0	& 602.908\\
25	& 639.109\\
50	& 678.140\\
75	& 717.171\\
100	& 756.202\\
125	& 795.231\\
150	& 834.167\\
175	& 873.198\\
200	& 912.326\\
225	& 951.357\\
250	& 990.486\\
255	& 998.292\\
\hline
\end{tabular}
\end{center}
\end{table}

We define the throughput of the detector as the number of Analog-to-Digital
Conversion (ADC) ``counts'' for each photon that interacts with the MCP\@.  In
essence, this is a measure of the amplification of the detector.  The total
number of ADC units is proportional to the Q.E. times the throughput.
Measuring the throughput requires calibrating the input radiation, which was
done with a NIST photodiode, and adjusting for the MCP quantum efficiency, and
the MgF$_2$ window transparency.  Since some factors are provisional (see
Section~\ref{overview}), the results are only preliminary.

The throughput was measured in two ways.  One method involved putting the
Krypton lamp $\sim$2~m away from the detector, and allowing the light to fall
on the face of the detector without any intervening optics.  The other method
used two off-axis parabolic mirrors to refocus the radiation on the detector.
The first method depends on the amount of radiation per unit area, while the
second depends on the total amount of light.  Each gave similar results, within
the expected errors of the technique.  The average results are shown in
Table~\ref{throughput}.
\begin{table}
\caption[]
{Detector throughput as a function of MCP voltage.}
\label{throughput}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Voltage	& Throughput\\
	& (ADC/photon-event)\\
\hline
600	& 0.240\\
678	& 0.767\\
756	& 2.27\\
834	& 6.25\\
912	& 14.3\\
990	& 32.7\\
\hline
\end{tabular}
\end{center}
\end{table}
Thus, if one wants to tune the VDS detector such that one photon event results
in one ADC ``count'', then the voltage should be set somewhere between 678V and
756V\@.

The VDS detector uses electronic shuttering.  The voltage on the MCP is
switched between the desired voltage during integration and a rest voltage
between integrations.  The rest voltage of the VDS flight detector was measured
as 331V\@.  Although no measurements of the VDS sensitivity were made with the
MCP shuttered off, one can extrapolate the curve in Table~\ref{throughput} and
estimate that the ``off'' sensitivity of the VDS detector is $\ltsim
0.005$~ADC/photon-event.

\subsection{Exposure time accuracy}

The VDS detector is electronically shuttered by raising and lowering the
voltage on the MCP wafer.  There is a rise and a decay time associated with
this process.  When taking an image, this rise and decay time appears as an
additional amount of effective exposure time, i.e.
%
\mbox{$T\textsub{eff} = T\textsub{exp} + \Delta T$}.
%
These effective decay times were determined by comparing the brightness of
images taken at a variety of exposure times.  The results are shown in
Figure~\ref{time-figure} and in Table~\ref{time-table}.  Also evident from
Figure~\ref{time-figure} is that when the exposure time is low enough, ranging
from 5--20~ms depending on the voltage setting, the MCP voltage never has
enough time to come to its stable value.

\begin{figure}
\caption[]
{Plots of system response versus exposure time, for three MCP voltages.  Also
shown are least-square fits to determine the decay constants shown in
Table~\ref{time-table}.}
\label{time-figure}
\centerline{\psfig{figure=time.eps,width=5in}}
\end{figure}

\begin{table}
\caption[]
{Effective decay times as a function of voltage.}
\label{time-table}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Voltage	& Effective Decay Time (ms)\\
\hline
600	& 274.4\\
834	& 81.0\\
990	& 47.6\\
\hline
\end{tabular}
\end{center}
\end{table}

\subsection{Linearity}

The linearity of the VDS detector was measured by placing a series of
calibrated apertures in the collimated beam between the two detectors.  The
resulting images were compared to a reference image taken with the smallest
aperture and the lowest operating voltage, to ensure that this reference image
was taken under linear conditions.  This test was performed in two ways: with a
diffuser in front of the lamp, and without.

The results of the linearity measurements without the diffuser are shown in
Figure~\ref{linearity}.  One effect that had to be taken into account is that
as different apertures were placed in the beam, the depth of focus of the
measurement system changed.  After a certain point the lamp, which was placed
about an inch behind the focal plane, was essentially in focus.  Thus, for the
larger apertures, only the middle intensity values could be used, as they were
not sensitive to the degree of focus of the lamp.

\begin{figure}
\caption[]
{Plots of system linearity for various MCP voltages.}
\label{linearity}
\centerline{\psfig{figure=linearity.eps,width=5in}}
\end{figure}

Some comment should be made about the differences between these curves and
those reported for the engineering model detector \cite{thompson:92}.  First of
all, in that earlier report the curves were given relative to the number of
photons/pixel/sec impinging on the detector.  Here the numbers are given in
terms of the more useful photon-events/pixel/sec.  These quantities differ by
the MCP quantum efficiency at 123.6~nm, which is $\sim$0.0163.

However, given that, it is evident that these data show more non-linearity than
that reported for the engineering model detector.  When the EM detector was
measured, there was a problem with monitoring the lamp \cite{thompson:92}, such
that the actual lamp brightness was uncertain by as much as a factor of two.
To overcome this problem, the different segments that made up the total
linearity curve were pieced together by hand.  In other words, guesses were
made about how far off the lamp monitor was.  It is possible that this
procedure introduced some error in the linearity curves.  No such correction
needed to be made for the flight detector data.

It was found that if one multiplied the number of photon-events/pixel/sec by
the throughput given in Table~\ref{throughput}, thus generating the predicted
number of ADC/pixel/sec if the detector were linear, then the curves for all
the MCP voltages merge into a single curve.  This is shown in
Figure~\ref{linearity2}

\begin{figure}
\caption[]
{Detector linearity characteristics with system throughput taken into account.
Data from all MCP voltages used are included.  Also shown is a least-square fit
to the data.  See text for details.}
\label{linearity2}
\centerline{\psfig{figure=linearity2.eps,width=5in}}
\end{figure}

We were able to successfully fit the non-linearity characteristics of the
detector using the function:
\begin{equation}
\label{linearity-equation}
F = \frac{R + (R/R_0)^P}{T}
\end{equation}
where $F$ is the number of photon-events/pixel/sec, $R$ is the system response
in ADC/pixel/sec, and $T$ is the throughput from Table~\ref{throughput}.  The
fitted parameters are \mbox{$R_0 = 904.0$} and \mbox{$P = 4.1945$}.  This
fitted curve is shown in Figure~\ref{linearity2}.

We also did linearity tests with a frosted MgF$_2$ diffuser in front of the
lamp.  These measurements only went out to about 100~photon-events/pixel/sec,
and showed that the detector acted linearly within this range at all voltage
settings.

\subsection{Flat-field response}

The flat field response of the VDS detector was measured by illuminating the
detector with a lamp placed $\sim$2~meters away.  The light was allowed to fall
directly onto the detector with no intervening optics.  A series of apertures
could be placed in front of the lamp to control the amount of illumination.
Measurements were made with the detector in three different positions in the
beam, to remove any artifacts caused by the illumination pattern.

A typical flat-field pattern is shown in Figure~\ref{flat}.
\begin{figure}
\caption[]
{Flat field pattern of the VDS detector.  The image intensity has been
stretched to enhance the contrast.  The box illustrates the part of the
detector that will be used during flight.  The percent RMS deviations for the
data in this box are given in Table~\ref{flat-table}.}
\label{flat}
\centerline{\psfig{figure=flat.eps,width=5in}}
\end{figure}
This image was produced by averaging together images taken at the three
different test positions, rejecting any pixels that were significantly
different from the corresponding pixels of the other two images.  This greatly
reduces the effects of artifacts in the input illumination caused by the light
having to pass through the MgF$_2$ window.  Note that each quadrant has a
slightly different amplifier gain in the CCD electronics.  The box drawn on the
image shows the part of the detector that will be used during flight.
Table~\ref{flat-table} gives the percent RMS deviations from perfect flatness
for the data in this box as a function of MCP voltage and CCD quadrant.
\begin{table}
\caption[]
{Percent RMS deviations for the portion of the VDS detector that will be used
during flight, as a function of CCD quadrant and MCP voltage.}
\label{flat-table}
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\cline{2-5}
\multicolumn{1}{c}{}	& \multicolumn{4}{|c|}{Quadrant} \\
\hline
Voltage	& A	& B	& C	& D\\
\hline
600	& 6.1	& 10.2	& 6.9	& 9.0\\
678	& 5.3	& 9.6	& 6.0	& 8.2\\
756	& 6.1	& 9.5	& 6.7	& 8.6\\
834	& 7.1	& 10.2	& 7.6	& 9.4\\
912	& 7.9	& 12.0	& 8.3	& 10.7\\
990	& 8.3	& 12.7	& 8.3	& 11.3\\
\hline
\end{tabular}
\end{center}
\end{table}

When the IIC is operated past its linear regime, the flat field characteristics
of the detector change.  This is illustrated in Figure~\ref{flat-nonlinear}.
\begin{figure}
\caption[]
{Blowup of part of the flat-field pattern of the VDS detector operated beyond
its linear regime.  The image intensities have been stretched to enhance the
contrast.}
\label{flat-nonlinear}
\centerline{\psfig{figure=flat_nonlinear.eps,width=5in}}
\end{figure}
Two hexagonal structures can be seen in this image.  The larger hexagons
outlined in thin dark lines are due to the fiber optic faceplate at the back of
the IIC\@.  The somewhat smaller hexagonal pattern outlined in more diffuse
bright lines come from the MCP wafer.  They are much less evident when the
detector is operated within its linear regime.  We have been able to model this
by allowing the factor $R_0$ in equation~\ref{linearity-equation} to vary as a
function of position.

\section{Resolution}

The limiting resolution due to the Nyquist frequency of the $21 \times 21$ CCD
used in the VDS detector is 23.8~lp/mm.  The VDS Flight detector is able to
resolve standard Air Force resolution targets down to this limiting resolution,
as can be seen in Figure~\ref{aft}.
\begin{figure}
\caption[]
{Image taken with the VDS detector of a standard Air Force 1951 resolution test
target:  (b) is a blow-up of (a) showing groups 4 and 5.  The images have been
stretched and contrast-enhanced to show detail.}
\label{aft}
\begin{center}
\mbox{} \psfig{figure=aft1.eps,width=5in} \mbox{}\\
\mbox{}\\
(a)\\
\mbox{}\\
\mbox{} \psfig{figure=aft2.eps,width=5in} \mbox{}\\
\mbox{}\\
(b)
\end{center}
\end{figure}
A square-wave modulation transfer function (MTF) derived from the image in
Figure~\ref{aft} is shown in Figure~\ref{mtf}.
\begin{figure}
\caption[]
{Square-wave modulation transfer function based on an image of an Air Force
resolution target.  The solid line represents the resolution in the horizontal
direction, and the dashed line is for the vertical direction.}
\label{mtf}
\centerline{\psfig{figure=mtf.eps,width=5in}}
\end{figure}
Curves for both vertical and horizontal resolution are shown---they are very
similar within the limits of the technique.  The measurement was only taken out
to a spatial frequency of $\sim$20~lp/mm as it was found to be difficult to
estimate the value of the MTF at the Nyquist frequency from the data.

\section{Dark current}

Since the VDS detector is designed to work at a CCD temperature of -70~C, it
has very low dark current characteristics.  Also, since the MCP has no
photocathode, it produces very few thermal electrons, even though it is
uncooled.  Table~\ref{dark} gives the dark current characteristics of the VDS
flight detector, determined by comparing images taken with the lamp off at long
exposure times to those taken at short exposure times.  However, these numbers
are uncertain, since the effect was so small.

\begin{table}
\caption[]
{Dark current characteristics of the VDS flight detector.}
\label{dark}
\begin{center}
\begin{tabular}{|c|c|}
\hline
MCP Voltage	& Dark current (ADC/pixel/s)\\
\hline
600		& 0.0039\\
990		& 0.011\\
\hline
\end{tabular}
\end{center}
\end{table}

\section{Noise}

\subsection{Readout noise}

The readout noise characteristics of the detector depend to some extent on the
electromagnetic environment in which it sits.  Typically there was an RMS
deviation of 1.5--2~ADC/pixel.  However, there was electromagnetic interference
from the ground support equipment picked up in some of the (non-flight) cabling
external to the vacuum tank, which caused the RMS deviation in quadrant C (and
occasionally A) to be
elevated to approximately 5.5~ADC/pixel.  It was determined that this effect
could be neutralized by moving and/or shielding the cables, which resulted in
the readout noise determinations shown in Table~\ref{readout-noise}.

\begin{table}
\caption[]
{Readout noise for the four CCD quadrants.}
\label{readout-noise}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Quadrant	& RMS deviation (ADC/pixel)\\
\hline
A	& 1.67\\
B	& 1.52\\
C	& 1.88\\
D	& 1.41\\
\hline
\end{tabular}
\end{center}
\end{table}

\subsection{Statistical Variation}

The dominant sources of noise in the VDS detector are the Poisson statistics
inherit in the photons themselves, and the ``shot'' noise produced within the
image intensifier.  This latter term represents the amount of variability in
the amplification process, also known as the pulse height distribution, which
is a strong function of the voltage across the MCP\@.  For a given MCP voltage,
both the Poisson statistics and the shot noise should be proportional to the
square root of the number of photons collected.

To measure the dark current, a series of five images were taken as rapidly as
possible.  This procedure was repeated for different MCP voltages, and for
different intensity levels.  Care was taken to ensure that the intensity levels
were within the linear range of the detector for the current MCP voltage.

From each series of five images a mean and standard deviation were calculated
for each CCD pixel.  The results are illustrated by the curves in
Figure~\ref{statistics1}.
\begin{figure}
\caption{Statistical variation based on a pixel-by-pixel analysis of sequential
images.}
\label{statistics1}
\centerline{\psfig{figure=repeatability1.eps,width=5in}}
\end{figure}
However, a careful examination of Figure~\ref{statistics1} together with the
information in Table~\ref{throughput} reveals that the measured RMS deviations
are actually smaller than Poisson statistics predict they should be for all but
the 600V trace, by as much as a factor of $\sim$4 for the larger MCP voltages.
There are two possible reasons why this may be:
\begin{enumerate}
\item
The absolute calibration of the VDS detector, represented by
Table~\ref{throughput}, could be off.  This may be either because the NIST
photodiode is less sensitive than supposed, or because the MgF$_2$ window is
more transparent than assumed.  Additional measurements on these components of
the test setup should allow us to determine whether either or both of these is
the case.
\item
Some property of the VDS detector acts to suppress the variability of any
individual pixel.
\end{enumerate}

One possible effect that could produce the effect discussed in the second item
above is the resolution of the VDS detector.  The effect of the IIC and lens
sections of the detector is such that each detected photon produces a
``splash'' of light on the CCD\@.  This splash has a full-width half-maximum of
$\sim$30~$\mu$m, which is somewhat larger than the CCD pixel size of 21~$\mu$m.
Thus, each pixel is affected to some degree by the pixels surrounding it.  To
determine whether or not this could explain the discrepency, we did Monte Carlo
simulations of the VDS detector, and found that the RMS deviation of this
simulated data was indeed suppressed by about a factor of two.

We then attempted to recover the true statistical properties of the image by
adding together bins of pixels, of sizes \mbox{$4 \times 4$}, \mbox{$8 \times
8$} and \mbox{$16 \times 16$}.  We theorized that these ``superpixels'' would
be largely shielded from the effect discussed above.  This appeared to be
successful with the simulated data, which was suppressed by only 20\%
relative to Poisson statistics when compressed by 4 in both dimensions.  When
applied to the VDS data, it appeared that convergence was achieved when the
compression factor was 8, and increasing this to 16 had no additional effect.
Figure~\ref{statistics2} shows the result of the \mbox{$8 \times 8$}
compression, with the resulting averages divided by 64, and the standard
deviations divided by 8 (i.e.\ we made the assumption that the deviations
scale as $\sqrt{N}$) so that a direct comparison can be made with
Figure~\ref{statistics1}.

\begin{figure}
\caption[]
{Derived statistical variation based on sums of \mbox{$8 \times 8$} pixels.
See text for details.  The resulting averages are divided by 64, and the
standard deviations are divided by 8 so that a direct comparison can be made
with Figure~\ref{statistics1}.}
\label{statistics2}
\centerline{\psfig{figure=repeatability2.eps,width=5in}}
\end{figure}

The traces for MCP voltages 600V and 678V do not appear in
Figure~\ref{statistics2} because it was discovered that an additional effect
was contributing to the statistics of those images.  Examination of the image
totals demonstrated that there was an overall brightness change from image to
image at 600V and 678V that wasn't present in the images taken with higher MCP
voltages.  Two possible causes were examined: either the CCD offset was
changing when these images were made, or the IIC amplification was changing.
Since the statistical properties of these effects are global rather than local,
they are not amenable to the pixel-summing procedure outlined above.

Further examination of the images led to the conclusion that the amplification
was changing.  Table~\ref{stability} gives the estimated RMS stability of the
VDS detector as a function of MCP voltage.
\begin{table}
\caption[]
{Estimated root-mean-square stability of the VDS throughput, in percent.}
\label{stability}
\begin{center}
\begin{tabular}{|c|c|}
\hline
Voltage	& Stability\\
\hline
600	& 1.26\\
678	& 0.39\\
756	& 0.055\\
834	& 0.083\\
912	& 0.088\\
\hline
\end{tabular}
\end{center}
\end{table}
The value for 990V seemed to be dominated by the low level of light during the
test, rather than an intrinsic property, so it is not reported here.

\section{Scattered Light}

The scattered light characteristics of the VDS detector were measured in two
different ways---as light scattered into small distances from the image, and
light scattered into a diffuse background.

\subsection{Small angle scattered light}

The amount of light scattered into a small area around a feature was measured
using the engineering model detector \cite{thompson:92}.  The measurement was
based on light generated from small scratches on the front surface on the MCP,
which is why the test could not be duplicated with the flight detector.
Attempts to measure the scattering using slit and pinhole images turned out to
be dominated by scattering within the test apparatus.

The measurements showed that a spectral line image would produce scattered
light at the level of $\sim 10^{-3}$ of the line's peak intensity, out to a
distance of $\sim$60~pixels.  This is shown in Figure~\ref{scattered}, which is
reproduced from the engineering model report \cite{thompson:92}.
\begin{figure}
\caption[]
{Scattered light measurements displayed as line-spread functions.  The dashed
line is taken from measurements around hot spots on the engineering model MCP
(see text).  The solid represents the measurements based on imaging a slit onto
the detector, and is contaminated by scattering within the MgF$_2$ protective
faceplate.  The plots are normalized to unity at the origin---the solid line
exhibits saturation in the CCD.}
\label{scattered}
\centerline{\psfig{figure=halo.eps,width=5in}}
\end{figure}

\subsection{Large angle scattered light}

The diffuse background produced by scattered light within the VDS detector was
measured by looking at the brightness of the image corners outside of the IIC
active area when the entire VDS was illuminated.  This brightness was about
13\% of the brightness of the image itself, most of which cannot be accounted
for by the small angle effect discussed above.  If one divides by the total
number of pixels contributing to this diffuse background, one comes to the
conclusion that the amount of scattered light in any one pixel is proportional
to \mbox{1--$2 \times 10^{-7}$} of the total signal measured in all the pixels
taken together.  It is felt that this represents scattered light within the
section of the detector between the IIC and the lens.

\section{Conclusions}

\subsection{Dynamic Range}

The full well capacity of the Tektronix CCDs used in the VDS detector were
typically about 150,000~e$^-$.  However, the actual upper limit on the data
returned from the flight detector was imposed by the 12~bit A/D converter,
which had an upper limit somewhat below the CCD full well capacity.  Combining
this information with the data on readout noise (Table~\ref{readout-noise}),
one obtains that the dynamic range of the VDS flight detector in a single
exposure is $\sim$2000:1.  A greater dynamic range can be achieved by taking
multiple images with different exposure times.

\subsection{Photometric calibration}

Converting an image taken with the VDS detector into a photometric flux is a
multistep process.  First, the local background must be estimated and
subtracted from the data.  Next, the linear flat field response must be removed
from the image (Figure~\ref{flat}).  After that, the exposure time must be
adjusted to take into account the rise and decay times of the electronic
shutter (Table~\ref{time-table}), and convert the image into ADC/pixel/sec.  At
this point a correction can be made for the effects of non-linearity, using
equation~\ref{linearity-equation} with $T$ taken from Table~\ref{throughput},
\mbox{$P = 4.1945$}, and $R_0$ being a function of position.  After that the
detector quantum efficiency (Table~\ref{qe}) and the efficiency of the CDS
optics can be taken into account.

Figure~\ref{success} shows this procedure applied to one of the lamp images
taken during calibration.  The raw image (a) displays all the effects discussed
above, including nonlinearity inducing a honeycomb pattern onto the image.  The
processed image (b) shows that these effects can be calibrated out to show what
the actual lamp pattern looks like.

\begin{figure}
\caption[]
{Image taken with the VDS detector of the illumination pattern of the Krypton
resonance lamp used during the calibration tests.  Image (a) shows the raw
image taken by the detector.  Image (b) shows the same image after the
calibration process had been applied.  The intensities have been stretched to
show detail.}
\label{success}
\begin{center}
\mbox{} \psfig{figure=success_a.eps,width=5in} \mbox{}\\
\mbox{}\\
(a)\\
\mbox{}\\
\mbox{} \psfig{figure=success_b.eps,width=5in} \mbox{}\\
\mbox{}\\
(b)
\end{center}
\end{figure}

\bibliography{vds_report}

\end{document}
