%+
% Name:
% afterglow_spec_2.0.tex
%
% History:
% 2008 Feb 10, created (v1.0), Glenn E. Allen
% 2008 Feb 11, added cntthresh (v1.1), GEA
% 2008 Feb 12, added maskfile (v1.2), GEA
% 2008 Feb 13, added comments about interleaved mode (v1.3), GEA
% 2008 Jul 23, significantly revised (v1.4), GEA
% 2008 Jul 28, added SAMP_CYC (v1.5), GEA
% 2008 Jul 29, added regwidth (v1.6), GEA
% 2008 Jul 30, minor edits (v1.7), GEA
% 2008 Aug 13, changed a typo in the cntthresh default and min values
% (v1.8), GEA
% 2010 Aug 16, changed some things to \tt (v1.9), GEA
% 2011 Feb 10, added the hot-pixel algorithm, changed equations 10 and 13,
% added a footnote about the series used for equations 10 and 13, added
% the parameters nfpixreg and nfrepeat (v2.0), GEA
%-
\documentclass{article}
\usepackage{changebar}
\usepackage{cxo-memo-logo}
\usepackage[dvips]{graphics}
\usepackage{epsfig}
\usepackage{gea}
\usepackage{pstricks}
\newrgbcolor{red}{1 0 0}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1. Header
\memobasic{
Jonathan McDowell, SDS Group Leader }{
Glenn E.\ Allen, SDS }{
Afterglow {\red and hot-pixel spec} }{
2.0 }{
http://space.mit.edu/CXC/docs/docs.html\#aft }{
/nfs/cxc/h2/gea/sds/docs/memos/afterglow\_spec\_2.0.tex }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2. Tool name
\section{ Afterglows {\red and Hot pixels} }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3. Description
\subsection{ Description }
A cosmic-ray ``afterglow'' is produced when a large amount of charge is
deposited on a CCD by a cosmic ray. Most of the charge is clocked off of the
CCD in a single frame. However, a small amount can be captured in charge
traps that release the charge relatively slowly. As a result, a sequence of
events can appear in a single detector pixel over a few frames as the
trapped charge is released.
To date, two algorithms have been used by the CXC to identify cosmic-ray
afterglows. The first algorithm was implemented in the CIAO tool {\tt
acis\_detect\_afterglow} and used for pipeline processing from the summer of
2000 to the fall of 2004. This algorithm searches for occasions when events
are detected in two or more consecutive frames on the same CCD pixel. While
the events are flagged as potential cosmic-ray afterglows and excluded from
Level 2 event-data files, the corresponding pixels are not included in the
observation-specific bad-pixel file. This algorithm finds many afterglow
events, but at the expense of discarding X-ray events associated with real
astrophysical sources. The fraction of the source events that are discarded
depends on the brightness and variability of a source.
In an attempt to minimize the loss of source events, another algorithm was
developed and implemented in the CIAO tool {\tt acis\_run\_hotpix}, which is
a wrapper around the tools {\tt acis\_find\_hotpix}, {\tt
acis\_classify\-\_hotpix} and {\tt acis\_build\_badpix}. The second
algorithm searches for detector pixels that have an unusually large number
of events that occur over a short period of time. Suspicious pixels are
added to the observation-specific bad-pixel file only if the neighboring
pixels do not have a significant excess of events. This condition helps
insure that events associated with dithered sources are not discarded.
Events associated with afterglows are flagged and excluded from Level 2
event-data files. The newer algorithm has been used for pipeline processing
(and reprocessing) since the fall of 2004. While it is relatively gentle on
astrophysical sources, it does let some afterglows ``slip through the
cracks.'' The afterglow detection efficiency depends on the number of events
in the afterglow. The efficiency declines quickly as the number of events
in an afterglow drops below about eight.
This spec describes a third afterglow-detection algorithm. Like the second
algorithm, it is designed to avoid discarding events associated with real
astrophysical sources. It is also designed to enhance the detection
efficiency for afterglows that have as few as four events. The principal
change between the second and third afterglow-detection algorithms is that
the third algorithm searches for afterglows using the events in a short,
sliding time window instead of using the events from the entire duration of
an observation (\ie, the algorithm searches in three dimensions instead of
two).
{\red Hot pixels are pixels that have an unusually large number of events
during an observation. Pixels that are known to be bad, that have bad bias
values, and that are in a region associated with the ``FEP0'' problem are
excluded from the search for hot pixels. Pixels associated with bias-parity
errors and cosmic-ray afterglows are also excluded, but only during the time
interval of the bias-parity error or afterglow. Pixels that are part of a
known bad column, that are along the edge of a node, or that were previously
identified as being hot are included in the search.
This spec also includes an updated hot-pixel detection algorithm. The
difference between this algorithm and the previous one is that this one is
designed to try to prevent bright sources in the field of view from reducing
the hot-pixel detection sensitivity. }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4. Input
\subsection{ Input }
\begin{enumerate}
\item
A Level 1 event-data file (acis*evt1.fits)
\item
A Level 1 observation-specific bad-pixel file (acis*bpix1.fits)
\item
A Level 1 mask file (acis*msk1.fits)
\item
A Level 1 exposure statistics file (acis*stat1.fits)
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5. Output
\subsection{ Output }
\begin{enumerate}
\item
An updated observation-specific bad-pixel file
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6. Parameters
\subsection{ Parameters }
\begin{enumerate}
\item
{ \tt infile,s,a,"",,,"Name of input event-data file" }
\item
{ \tt outfile,s,a"",,,"Name of output bad-pixel file" }
\item
{ \tt badpixfile,s,a,"",,,"Name of input bad-pixel file" }
\item
{ \tt maskfile,s,a,"",,,"Name of input mask file" }
\item
{ \tt statfile,s,a,"",,,"Name of input exposure-statistics file" }
\item
{ \tt expnowindow,i,h,10,1,100,"Number of frames in the sliding time
window" }
\item
{ \tt probthresh,r,h,0.001,1.0e-10,0.1,"Minimum post-trials significance
of potential after\-glows (\eg, 1 sigma = 0.159, 90\% = 0.1, 2 sigma =
0.0228, 99\% = 0.01 and 3 sigma = \\ 0.00135)" }
\item
{ \tt cntthresh,i,h,4,2,10,"Minimum number of events in an afterglow" }
\item
{ \tt regwidth,i,h,7,3,255,"Size of reference region (\eg, 7~pixels
$\times$ 7~pixels)" }
\item
{ \tt \red nfpixreg,i,h,32,16,256,"Size of region used to calculate the
fluence"}
\item
{ \tt \red nfrepeat,i,h,10,1,30,"Number of iterations during the
calculation of the fluence" }
\item
{ \tt clobber,b,h,"no",,,"Overwrite output file if it exists?" }
\item
{ \tt verbose,i,h,0,0,5,"Amount of messages produced (0=none, 5=a lot)" }
\item
{ \tt mode,s,h,"ql",,, }
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7. Processing
\subsection{ Processing }
In the standard ACIS pipeline, the afterglow-detection algorithm is used
after the bias(es) has been searched for bad bias values, {\red after the
bias-parity error file(s) has been searched for bad pixels and the ``FEP0''
problem,} and before the event data is searched for hot pixels. The
afterglow and hot-pixel detection algorithms are summarized below.
Verify that the {\tt infile}, {\tt badpixfile}, {\tt maskfile}, and {\tt
statfile} exist.
%
If {\tt clobber=no}, then verify that the {\tt outfile} does not exist.
%
Verify that the {\tt infile} has {\tt READMODE}={\tt TIMED}. The afterglow
and hot-pixel detection algorithms are not appropriate for {\tt
READMODE}={\tt CONTINUOUS}.
%
Verify that the values of the parameters {\tt expnowindow}, {\tt
probthresh}, {\tt cntthresh}, {\tt regwidth}, {\tt \red nfpixreg}, and {\tt
\red nfrepeat} are in the valid ranges for these parameters.
%
Note that {\tt regwidth} must be an odd number and
%
{\red that the only valid values for the parameter {\tt nfpixreg} are 16,
32, 64, 128, and 256 (\ie\ those values for which the width of a node in
pixels (256) is an integer multiple of {\tt nfpixreg}).}
\subsubsection{ \red Afterglows }
\begin{enumerate}
\item
Exclude ``invalid'' pixels%
%
\footnote{Here an invalid pixel is one that has ${\tt SAMP\_CYC} = 0$ in
the {\tt maskfile} or that has one or more of the following {\tt STATUS}
bits set in the {\tt badpixfile}.
\vspace*{1.0\baselineskip}
\hbox{
\hspace*{0.25in}
\begin{tabular}{cll}
Bit & Description & {\red Notes} \\ \hline
0 & bad pixel & \\
2 & bias-parity error & {\red only for the duration of the error} \\
3 & bias = 4095 & \\
4 & bias = 4094 & \\
13 & FEP0 problem & \\
{\red 15} & {\red afterglow} & {\red only for the hot-pixel
algorithm and only for the duration of the afterglow} \\
16 & bad bias value & \\
\end{tabular}
}
\vspace*{1.0\baselineskip}
\noindent
%
Note that the {\tt STATUS} bits are numbered from 0 to 31. It is not
necessary to ignore pixels that have bias values of 4096 (\ie, are
missing data) because biases with such problems are adjusted on the
ground. If they are not adjusted, then all events on pixels with a
bias = 4096 are discarded. }
%
from the search.
\item
To improve the performance of the algorithm, perform more than one pass
through the data. In the first pass, potential afterglow events are
identified as suspicious using a minimum set of criteria. Events $i$
and $j$ may be part of an afterglow if the following four conditions are
satisfied.
%
\begin{eqnarray}
{\tt CCD\_ID}_{i} & = & {\tt CCD\_ID}_{j} \label{eqn01}, \\
{\tt CHIPX}_{i} & = & {\tt CHIPX}_{j}, \\
{\tt CHIPY}_{i} & = & {\tt CHIPY}_{j},\ {\rm and} \\
|{\tt EXPNO}_{i} - {\tt EXPNO}_{j}| & \le & {\tt expnowindow}.
\label{eqn04}
\end{eqnarray}
\item
During a subsequent pass through the data, the $i$th, $(i+1)$th,
{\ldots}, $(i+n)$th set of events on a pixel is identified as an
afterglow if each consecutive pair of events in the set satisfies
equations~\ref{eqn01}--\ref{eqn04} and if
%
\begin{eqnarray}
N_{\rm evt}^{\rm aft} & \ge & {\tt cntthresh}, \\
P_{\rm post} & < & {\tt probthresh},\ {\rm and} \\
P_{\rm ref} & \ge & {\tt probthresh}, \label{eqn07}
\end{eqnarray}
%
where the post-trials probability
%
\begin{equation}
P_{\rm post}
=
1 -
\left(
1 - P_{\rm pre}
\right)^{\rm N_{\rm trial}},
\label{eqn09}
\end{equation}
%
the pre-trials probability {\red $P_{\rm pre}$ is given by the series}%
%
\footnote{\red In practice, the series does not extend to infinity.
Each term in the sum is of the form $\mu^{n} \exp(-\mu) / n!$. The last
term is the series is given by $n = N$, where $N$ is the smallest
integer that satisfies the relation
%
\begin{equation}
\frac{\mu^N}{N!} <
10^{-15}
\left[
\frac{1}{2} \frac{\mu^{n_{\rm 0}}}{n_{0}!} +
\frac{\mu^{n_{\rm 1}}}{n_{1}!} + {\ldots} +
\frac{\mu^{N-1}}{(N-1)!}
\right].
\end{equation}
}
%
\begin{equation}
\red
P_{\rm pre}
=
\left[
\frac{1}{2}
\frac{
\left( N_{\rm bgd}^{\rm aft} \right)^{N_{\rm evt}^{\rm aft}}
}{
N_{\rm evt}^{\rm aft}!
} +
\left(
\sum_{n=N_{\rm evt}^{\rm aft}+1}^{\infty}
\frac{\left( N_{\rm bgd}^{\rm aft} \right)^{n}}{n!}
\right)
\right]
e^{-N_{\rm bgd}^{\rm aft}},
\end{equation}
%
$N_{\rm evt}^{\rm aft}$ is the number of events in the potential
afterglow, the number of background events for the potential afterglow
%
\begin{equation}
N_{\rm bgd}^{\rm aft}
=
\frac{ F }{ {\tt SAMP\_CYC}_{\rm aft} }
\left(
\frac{
N_{\rm frame}^{\rm aft}
}{
N_{\rm frame}^{\rm tot}
}
\right),
\end{equation}
%
${\tt SAMP\_CYC}_{\rm aft}$ is the sample cycle for the pixel on which
the potential afterglow occurred,
%
$N_{\rm frame}^{\rm aft}$ is the number of valid frames%
%
\footnote{Here an invalid frame for a CCD is one that is not listed in
the {\tt statfile}. For {\tt TIMED} mode observations, frames with
${\tt EXPNO} < 3$ are invalid. Note that a frame does not have to
include an afterglow event to be included in $N_{\rm frame}^{\rm aft}$.
For example, if a pixel has afterglow events in frames 100, 101, 104,
107, 109, 113, and 119, and if all of the frames from 100 to 119 are
valid, then $N_{\rm frame}^{\rm aft} = 20$.}
%
in the afterglow,
%
$N_{\rm frame}^{\rm tot}$ is the total number of valid frames for the CCD,
%
the number of trials%
%
\footnote{The estimate of $N_{\rm trial}$ is an upper limit on the
number of trials. The actual number of trials includes only the number
of ``independent'' searches. Since adjacent windows in the sliding {\tt
EXPNO} window overlap, they are not independent. A lower limit on
$N_{\rm trial}$ can be obtained by calculating the number of
nonoverlapping windows. This value is smaller than equation~\ref{eqn11}
by a factor of about $({\tt expnowindow + 1})$. Since a precise value
for $N_{\rm trial}$ can be difficult to determine, equation~\ref{eqn11}
is used because it yields the most conservative (\ie, the largest)
number of trials. }
%
\begin{equation}
N_{\rm trial}
=
\sum_{k}
N_{{\rm pix},k}^{\rm ccd}
\left( N_{{\rm frame},k}^{\rm tot} - {\tt expnowindow} - 1 \right),
\label{eqn11}
\end{equation}
%
$N_{{\rm pix},k}^{\rm ccd}$ is the number of valid pixels$^{1}$ for the
$k$th CCD (\ie, $= 1024 \times 1024$ less the number of invalid pixels),
%
$N_{{\rm frame},k}^{\rm tot}$ is the total number of valid frames for
the $k$th CCD, the probability%
%
\footnote{Unlike the previous afterglow-detection algorithm, the
probability $P_{\rm ref}$ is a pre-trials probability instead of a
post-trials probability. In this case, it is more difficult for events
associated with real astrophysical sources to be identified as
afterglows.}
%
{\red $P_{\rm ref}$} that the event fluence in the reference region is
consistent with the event fluence on the entire node (\ie, that the
potential afterglow {\red or hot pixel} is not part of a dithered
source) {\red is given by the series}$^{2}$
%
\begin{equation}
\red
P_{\rm ref}
=
\left\{
\begin{array}{ll}
\left[
\frac{1}{2}
\frac{\left( N_{\rm bgd}^{\rm ref} \right)^{N_{\rm evt}^{\rm
ref}}}{N_{\rm evt}^{\rm ref}!} +
\left(
\sum_{n=N_{\rm evt}^{\rm ref}+1}^{\infty}
\frac{\left( N_{\rm bgd}^{\rm ref} \right)^{n}}{n!}
\right)
\right]
e^{-N_{\rm bgd}^{\rm ref}},
& (N_{\rm evt}^{\rm ref} > 0)
\\
1
& (N_{\rm evt}^{\rm ref} = 0)
\end{array}
\right.
\label{eqn13}
\end{equation}
%
$N_{\rm evt}^{\rm ref}$ is the total the number of events in the
reference region,%
\footnote{Do not include in $N_{\rm evt}^{\rm ref}$ the events on
the central pixel of the region and, if the region overlaps more than
one node, the events that lie on a different node from the central
pixel.}
%
$N_{\rm bgd}^{\rm ref}$ is given by%
%
\footnote{ Equation~\ref{eqn15} is valid only if all of the valid pixels
in the reference region have the same sample cycle. If, for example,
the reference region contains subsets A and B with $N_{\rm pix,A}^{\rm
ref}$ and $N_{\rm pix,B}^{\rm ref}$ valid pixels and sample cycles ${\tt
SAMP\_CYC}_{\rm ref,A}$ and ${\tt SAMP\_CYC}_{\rm ref,B}$, respectively,
then equation~\ref{eqn15} becomes
%
\begin{equation}
N_{\rm bgd}^{\rm ref}
=
F
\left(
\frac{ N_{\rm pix,A}^{\rm ref} }{ {\tt SAMP\_CYC}_{\rm ref,A} } +
\frac{ N_{\rm pix,B}^{\rm ref} }{ {\tt SAMP\_CYC}_{\rm ref,B} }
\right).
\end{equation}
}
%
\begin{equation}
N_{\rm bgd}^{\rm ref}
=
\frac{F}{\red {\tt SAMP\_CYC}_{\rm ref}}
N_{\rm pix}^{\rm ref},
\label{eqn15}
\end{equation}
%
{\red ${\tt SAMP\_CYC}_{\rm ref}$ is the sample cycle for the pixels in
the reference region},
%
$N_{\rm pix}^{\rm ref}$ is the number of valid pixels%
%
\footnote{For the purposes of calculating $N_{\rm pix}^{\rm ref}$, the
central pixel of the region (\ie, the pixel on which the potential
afterglow occurred) is invalid as are pixels that lie on a different
node from the central pixel. Other pixels are considered invalid if they
satisfy the usual conditions.$^{1}$
}
%
in the {\tt regwidth}~pixel $\times$ {\tt regwidth}~pixel reference
region surrounding the pixel with the potential afterglow, and the
nominal fluence $F$ is computed as follows.
%
\begin{enumerate}
\item
For each {\tt \red nfpixreg}~pixel $\times$ {\tt \red
nfpixreg}~pixel region $l$ of the node,%
%
\footnote{Equation~\ref{eqn17} is valid only if all of the valid
pixels in the region have the same sample cycle. If, for example,
the region contains subsets A and B with $N_{\rm evt,A}^{l}$ and
$N_{\rm evt,B}^{l}$ events on $N_{\rm pix,A}^{l}$ and $N_{\rm
pix,B}^{l}$ valid pixels and sample cycles ${\tt SAMP\_CYC}_{l,{\rm
A}}$ and ${\tt SAMP\_CYC}_{l,{\rm B}}$, respectively, then
equation~\ref{eqn17} becomes
%
\begin{equation}
F_{l}
=
\frac{
{\tt SAMP\_CYC}_{l,{\rm A}} N_{\rm evt,A}^{l} +
{\tt SAMP\_CYC}_{l,{\rm B}} N_{\rm evt,B}^{l}
}{
N_{\rm pix,A}^{l} + N_{\rm pix,B}^{l}
}.
\end{equation}
}
%
\begin{equation}
F_{l}
=
{\red {\tt SAMP\_CYC}_{l}}
\frac{
N_{\rm evt}^{l}
}{
N_{\rm pix}^{l}
},
\label{eqn17}
\end{equation}
%
where {\red ${\tt SAMP\_CYC}_{l}$ is the sample cycle for region
$l$},
%
$N_{\rm pix}^{l}$ is the total number of valid pixels$^{1}$ in the
region, and
%
$N_{\rm evt}^{l}$ is the total number of events on these pixels
during the entire observation.
%
\item
Select the regions where $F_{l}$ is greater than zero and less than
two times the mean value of the set of $F_{l}$s.
\item
Calculate the median value, $F_{\rm med}$, of the selected values of
$F_{l}$.
\item
Calculate the root-mean-square, $F_{\rm rms}$, of the selected values.
\item
Select the regions where $F_{l}$ is greater than zero, is greater
than or equal to $F_{\rm med} - 2 F_{\rm rms}$, and is less than
$F_{\rm med} + 2 F_{\rm rms}$.
%
\label{stepf}
\item
Calculate the median of the selected values.
\item
Calculate the root-mean-square of the selected values.
\label{stepg}
\item
Repeat steps~\ref{stepf}--\ref{stepg} an additional ${\red {\tt
nfrepeat}-1}$ times (\ie, a total of {\tt \red nfrepeat} times).
\item
Set $F$ equal to the value of $F_{\rm med}$ from the last iteration.
\end{enumerate}
%
\item
Each potential afterglow that satisfies the criteria in equations
\ref{eqn01}--\ref{eqn07} is written to the {\tt outfile} with
%
\begin{equation}
{\tt TIME}
=
{\tt TIME}_{\rm start} -
{\tt TIMEPIXR} \times {\tt TIMEDEL} -
{\tt FLSHTIME}
\end{equation}
%
and
%
\begin{equation}
{\tt TIME\_STOP}
=
{\tt TIME}_{\rm stop} +
(1 - {\tt TIMEPIXR}) \times {\tt TIMEDEL},
\end{equation}
%
where ${\tt TIME}_{\rm start}$ and ${\tt TIME}_{\rm stop}$ are the {\tt
TIME}s in the {\tt statfile} that are associated with the start and stop
{\tt EXPNO}s of the afterglow and {\tt TIMEDEL}, {\tt TIMEPIXR}, and
{\tt FLSHTIME} are keywords in the {\tt statfile}. The contents of the
{\tt badpixfile} are also copied to the {\tt outfile}. Note that it is
possible, albeit unlikely, for more than one afterglow to occur on the
same pixel during an observation.
\end{enumerate}
\subsubsection{ \red Hot pixels }
{\red
\begin{enumerate}
\item
Exclude ``invalid'' pixels$^{1}$
\item
A pixel is identified as hot if
%
\begin{eqnarray}
P_{\rm post} & < & {\tt probthresh}\ {\rm and}
\label{eqn20}
\\
P_{\rm ref} & \ge & {\tt probthresh},
\label{eqn21}
\end{eqnarray}
%
where the post-trials probability $P_{\rm post}$ is given by
equation~\ref{eqn09}, the pre-trials probability $P_{\rm pre}$ is given
by the series$^{2}$
%
\begin{equation}
P_{\rm pre}
=
\left[
\frac{1}{2}
\frac{
\left( N_{\rm bgd}^{\rm hot} \right)^{N_{\rm evt}^{\rm hot}}
}{
N_{\rm evt}^{\rm hot}!
} +
\left(
\sum_{n=N_{\rm evt}^{\rm hot}+1}^{\infty}
\frac{\left( N_{\rm bgd}^{\rm hot} \right)^{n}}{n!}
\right)
\right]
e^{-N_{\rm bgd}^{\rm hot}},
\end{equation}
%
$N_{\rm evt}^{\rm hot}$ is the number of events on the potential hot
pixel,
%
\begin{equation}
N_{\rm bgd}^{\rm hot}
=
\frac{ F }{ {\tt SAMP\_CYC}_{\rm hot} },
\end{equation}
%
${\tt SAMP\_CYC}_{\rm hot}$ is the sample cycle for the potential hot
pixel,
%
the number of trials
%
\begin{equation}
N_{\rm trial}
=
\sum_{k}
N_{{\rm pix},k}^{\rm ccd},
\label{eqn25}
\end{equation}
%
$N_{{\rm pix},k}^{\rm ccd}$ is the number of valid pixels$^{1}$ for the
$k$th CCD (\ie, $= 1024 \times 1024$ less the number of invalid pixels)
and
%
the probability $P_{\rm ref}$ that the event fluence in the reference
region is consistent with the event fluence on the entire node is given
by equation~\ref{eqn13}.
\item
Each potential hot pixel that satisfies the criteria in equations
\ref{eqn20} and \ref{eqn21} is written to the {\tt outfile}. The
contents of the {\tt badpixfile} are also copied to the {\tt outfile}.
\end{enumerate}
}
Once the afterglow and hot-pixel detection algorithms have been used, the
tools {\tt acis\_build\_badpix} and {\tt acis\_process\-\_events} are used
to mark the pixels adjacent to such pixels as bad and to set the appropriate
{\tt STATUS} bit for events associated with afterglows (16 of 0--31) and hot
pixels (4 of 0--31), respectively.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8. Caveats
\subsection{ Caveats }
\begin{enumerate}
\item
Although it may not be optimum to do so, the afterglow and hot-pixel
detection algorithms are applied separately to the primary and secondary
data for interleaved mode observations.
\item
The algorithms are not applied to the data for continuous-clocking mode
observations.
\item
The choices of default values for the parameters {\tt expnowindow}, {\tt
\red probthresh}, {\tt cntthresh}, {\tt regwidth}, {\tt \red nfpixreg},
and {\tt \red nfrepeat} may not be optimum.
\item
{\red Add {\tt TIME} and {\tt TIME\_STOP} to the last step of the
hot-pixel algorithm.}
\end{enumerate}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9. Finish
\end{document}