%de 21 (summer solstice, midnight, la serena) (this is IT, Phil!)
%more done on Dec 27th or so
%typos fixed 28 Dec 1pm
%more done on Dec 28th (1st 4-m night morning)
%copy xfered from Chile on Jan 1, 1990
%modifications made after the AAS meeting, Jan 15 1990:
% end itemize problems fixed
% buku aperture photometry stuff added Jan 15/16
% started to make Lindsey's changes Jan 28th
% Next set of changes made Feb. 18th when we SHOULD have been
% off with marcia having a good time.
% more modifications Monday Feb 19
% march 20/21 mods made in Boulder----Lindsey's comments
% march 20/21 mods made in Boulder---beginning of JB's comments
% march 27 mods back in Tucson
% may 11th, fixed the sumed/average read-noise problem!
\documentstyle[11pt,moretext]{article}
\begin{document}
\title{A User's Guide to Stellar CCD Photometry with IRAF}
\author{Philip Massey \and Lindsey E. Davis}
\date{March 29, 1990}
\maketitle
\begin{abstract}
This document is intended to guide you through the steps for obtaining
stellar photometry from CCD data using IRAF.  It deals both with the
case that the frames are relatively uncrowded (in which case simple
aperture photometry may suffice) and with the case that the frames
are crowded and require more sophisticated point-spread-function
fitting methods (i.e., {\bf daophot}).  In addition we show how one
goes about obtaining photometric solutions for the standard stars, and
applying these transformations to instrumental magnitudes.
\end{abstract}
\tableofcontents
\eject
\section{Introduction}
This user's guide deals with both the ``relatively simple" case of
isolated
stars on a CCD frame (standard stars, say, or uncrowded program stars)
and the horrendously more complicated case of crowded field
photometry. We describe here all the steps needed to obtain instrumental
magnitudes and to do the transformation to the standard system.  There
are, of course, many possible paths to this goal, and IRAF provides no
lack of options.  We have chosen to illuminate a straight road, but many
side trails are yours for the taking, and we will occasionally point
these out (``let many flowers bloom").  This Guide is {\it not} intended
as a reference manual; for that, you have available (a) the various
``help pages" for the routines described herein, (b) ``A User's Guide
to the IRAF APPHOT Package"  by Lindsey Davis, and (c) ``A Reference
Guide to the IRAF/DAOPHOT Package" by
Lindsey Davis.  (For the ``philosophy" and algorithms of DAOPHOT, see
Stetson 1987 {\it PASP} {\bf 99}, 111.) 
What {\it this} manual is intended to be is a real
``user's guide", in which we go through all of the steps necessary to go
from CCD frames to publishable photometry. (N.B.: as of this writing
the IRAF routines for determining the standard transformations and
applying those transformations are still being written.)  We outline
a temporary kludge that will work with Peter Stetson's CCDRED VMS
Fortran package.  Hopefully the PHOTRED package currently under
development at Cerro Tololo will be available by Spring 1990, and 
this manual will then be revised. 
  
The general steps involved are as follows: (1) fixing the header
information to reflect accurate exposure times and airmasses,
(2) determining and cataloging the characteristics of your data (e.g.,
noise, seeing, etc.), 
(3) obtaining instrumental magnitudes for all the standard stars
using aperture photometry, (4) obtaining instrumental magnitudes for
your program stars using IRAF/daophot, (5) determining the aperture
correction for your program stars, (6) computing the transformation
equations for the standard star photometry, and (7) applying these
transformations to your program photometry.  We choose to illustrate
these reductions using {\it UBV} CCD data obtained with an RCA chip on the 0.9-m
telescope at Cerro Tololo, but the techniques are applicable to data
taken with any detector whose noise characteristics mimic those of a
CCD.  
 
If you are a brand-new IRAF user we strongly recommend first reading the
document ``A User's Introduction to the IRAF
Command Language" by Shames and Tody, which can be found in Volume 1A
of the 4 blue binders that compose the IRAF documentation. (Actually
if you are a brand-new IRAF user one of us recommends that you find
some simpler task to work on before you tackle digital stellar photometry!)
The procedures described here will work on any system supported by IRAF;
for the purposes of discussion, however, we will assume that you are
using the image display capabilities of a SUN.  If this is true you then
may also want to familiarize yourself with the ins and outs of using
the SUN Imtool window; the best description is to be found in ``IRAF
on the SUN".
 
We assume that your data has been read onto disk, and that the basic
instrumental signature has been removed; i.e., that you are ready
to do some photometry.  If you haven't processed your
data this far yet, we
refer you to ``A User's Guide to Reducing CCD Data with IRAF" by Phil
Massey.
 
\section{Getting Started}
 
\subsection{Fixing your headers}
You're going to have to this some time or another; why not now?  There
are two specific things we may need to fix at this point: (a) Add any
missing header words if you are reducing non-NOAO data, (b) correct the
exposure time for any shutter opening/closing time, and (c) correct the
airmass to the effective middle of the exposure.
 
Two things that will be useful to have in your headers are the exposure
time and the airmass.  If you are reducing NOAO data then you will
already have the exposure time (although this may need to be corrected
as described in the next paragraph) and enough information for the {\bf
setairmass} task described below to compute the effective airmass of the
observation.  You can skip to the ``Correcting the exposure time"
section below.
If
you are reducing non-NOAO data you should examine your header with a
 
\centerline{ {\bf imhead} imagename{\bf l+ $|$ page} }
 
\noindent
and see exactly what information {\it is} there.  If you are lacking the
exposure time you can add this by doing an
 
\centerline{ {\bf hedit} imagename{\bf ``ITIME"} value {\bf add+ up+
ver- show+} }
 
\noindent
If you know the effective airmasses you can add an ``AIRMASS" keyword in
the same manner, or if you want to compute the effective airmass
(corrected to mid-exposure) using {\bf setairmass} as described below,
you will need to have the celestial coordinates key words ``RA" and
``DEC", as well as the siderial-time (``ST"), 
and preferably the coordinate ``EPOCH" and the date-of-observation
(``DATE-OBS"), all of which should have the form shown in Fig.~\ref{header}.

You may want to take this opportunity to review the filter numbers in the
headers, and fix any that are wrong.  If you are lacking filter numbers
you may want to add them at this point.
 
\subsubsection{Correcting the exposure time}
The CTIO 0.9-m has an effective exposure time that is
25-30ms longer than the requested exposure time (Massey et al. 1989 {\it
A.J.} {\bf 97}, 107; Walker 1988 {\it NOAO Newsletter} {\bf No. 13},
20).  First see what "keyword" in your header gives the exposure time:
 
\centerline{
{\bf imhead} imagename{\bf.imh l+ $|$ page} }
 
\noindent
will produce a listing such as
given in Figure~\ref{header}.
\begin{figure}
\vspace{3.2in}
\caption{\label{header}Header information for image n602alu.imh}.
\end{figure}
The exposure time keyword in this header is ``ITIME".  In this case
we wish to add a new exposure time to each of the headers;  we will call
this corrected exposure time
EXPTIME, and make it 25 ms larger than whatever value is listed as
ITIME.  To do this we use the {\bf hedit} command as follows:
 
\centerline{
{\bf hedit *.imh EXPTIME ``(ITIME+0.025)" ver- show+ add+}.}
 
\noindent
An inspection of the headers will now show a new keyword EXPTIME.
(Walker lists a similar correction for the CTIO 1.5-m shutter, but the
CTIO 4-m P/F shutters have a negligible correction.
The direct CCD shutters on the Kitt Peak CCD cameras give
an additional 3.5ms of integration on the edges but 13.0ms in the
center [e.g., Massey 1985 {\it KPNO Newsletter} {\bf 36}, p. 6];
if you have any 1 second exposures you had best correct these by
10ms or so if you are interested in 1\% photometry.)
  
\subsubsection{Computing the effective airmass}
The task {\bf setairmass} in the {\bf astutil} package will compute
the effective airmass of your exposure, using the header values of RA,
DEC, ST, EPOCH, and DATE-OBS, and whatever you specify for the observatory
latitude.  An example is shown in Fig.~\ref{setairmass}.
\begin{figure}
\vspace{2.5in}
\caption{\label{setairmass} The parameter file for {\bf setairmass}.}
\end{figure}
The default for the latitude is usually the IRAF
variable {\bf observatory.latitude}.  To by-pass this ``feature", simply
put the correct latitude in the parameter file
(e.g., $-30.1652$ for CTIO,
$+31.963$ for KPNO; $+19.827$ for Mauna Kea.).
 
\subsection{{\bf imexamine:} A Useful Tool}
 
The {\bf proto} package task {\bf imexamine} is a powerful and versatile task
which can be used to interactively examine image data at all stages of
the photometric reduction process. In this section we discuss and
illustrate those aspects of {\bf imexamine} which are  most useful to
photometrists with emphasis on three different applications of the task:
1) examining the image, for example plotting lines and columns
2) deriving  image characteristics, for example computing the
FWHM of the point-spread function 3) comparing the same region
in different images.
 
The task 
{\bf imexamine} lives within the {\bf proto} package, and you will also need
to load {\bf images} and {\bf tv}.  Then 
{\bf display}  the image, and type {\bf imexamine}.
When the task is ready to accept input the image cursor will begin blinking
in the display window, and the user can begin executing various keystroke
and colon commands.  The most useful data examining commands are summarized
below.  The column, contour, histogram, line and surface plotting commands
each have their own parameter sets which set the region to be plotted and
control the various plotting parameters. All can be examined and edited
interactively from within the {\bf imexamine} task using the
appropriate {\bf :epar} command.
 
\begin{description}
 \item[c] - Plot the column nearest the image cursor
 \item[e] - Make a contour plot of a region around the image cursor
 \item[h] - Plot the histogram of a region around the image cursor
 \item[l] - Plot the line nearest the image cursor
 \item[s] - Make a surface plot of a region around the image cursor
 \item[:c N] - Plot column N
 \item[:l N] - Plot line N
 \item[x] - Print the x, y, z values of the pixel nearest the image cursor
 \item[z] - Print a 10 by 10 grid of pixels around the image cursor
 \item[o] - Overplot
 \item[g] - Activate the graphics cursor
 \item[i] - Activate the image cursor
 \item[?] - Print help
 \item[q] - Quit {\bf imexamine}
 \item[:epar c]  - Edit the column plot parameters
 \item[:epar e]  - Edit the contour plot parameters
 \item[:epar h]  - Edit the histogram plot parameters
 \item[:epar l]  - Edit the line plot parameters
 \item[:epar s]  - Edit the surface plot parameters
 
\end{description}
 
 
Example 1 below shows how a user can interactively
make and make hardcopies of image line plots using {\bf imexamine} and at the same time
illustrates many of the general features of the task.
 
The {\bf imexamine} task also has some elementary image analysis capability, including
the capacity to do simple aperture photometry, compute image statistics
and fit radial profiles.  The most useful image analysis commands are
listed below.
 
\begin{description}
\item[h] - Plot the histogram of a region around the cursor
\item[r] - Plot the radial profile of a region around the cursor
\item[m] - Plot the statistics of a region around the cursor
\item[:epar h]  - Edit the histogram parameters
\item[:epar r]  - Edit the radial profile fitting parameters
\end{description}
 
Example 2 shows how a photometrist might use {\bf imexamine}
and the above commands to estimate the following image characteristics:
1) the full width at
half maximum (FWHM) of the point-spread function, 2) the background sky level
3) the standard deviation of the background level 4) and the radius at which
the light from the brightest star of interest disappears into the noise
(this will be used to specify the size of the point-spread-function,
e.g.,PSFRAD).
 
Finally {\bf imexamine} can be used to compare images. Example 3
shows how to compare regions in the original image and in the
same image with all the fitted stars subtracted out. The example
assumes that the target image display device supports multiple frame buffers,
i.e. the user can load at
least two images into the display device at once.
 
The {\bf imexamine} task offers even more features than are discussed here and the
user should refer to the manual page for more details.
 
\vspace{12pt}
{\bf Example 1:} Plot and make hardcopies of image lines within {\bf imexamine}.
 
\begin{itemize}
\item {\bf display} the image and then type {\bf imexamine}.
\item move the image cursor to a star and tap {\bf l} to plot the image
line nearest the cursor
\item tap the {\bf g} key to activate the graphics cursor
\item type {\bf :.snap} to make a hardcopy of the plot on your default device
\item expand a region of interest by first moving the graphics
cursor to the lower left corner of the region and typing {\bf E},
and then moving the graphics cursor to the upper right corner
of the region and typing anything
\item type {\bf :.snap} to make a hardcopy of the new plot
\item tap the {\bf i} key to return to the image cursor menu
\item type {\bf :epar l} to enter the line plot parameter set, change the
value of the logy parameter to yes and type {\bf CNTL-Z} to exit and
save the change
\item  repeat the previous line plotting commands
\item type {\bf q} to quit {\bf imexamine}
\end{itemize}
 
{\bf Example 2:} Compute some elementary image characteristics using
{\bf imexamine}.
 
\begin{itemize}
\item {\bf display} the image and then type {\bf imexamine}.
\item move to a bright star and tap the {\bf  r} key
\item examine the resulting radial profile plot and note the final
number on the status line which is the FWHM of the best fitting
Gaussian
\item repeat this procedure for several stars to estimate a good
average value for the FWHM
\item set the parameters of the statistics box ncstat and nlstat
from 5 and 5 to 21 and 21 with  {\bf :ncstat 21} and {\bf :nlstat 21}
commands so that the sizes of the statistics and histogram
regions will be identical
\item  move to a region of blank sky and tap the {\bf m} key to get an
estimate of the mean, median and standard deviation of the
sky pixels in a region 21 by 21 pixels in size around the
image cursor
\item leave the cursor at the same position and tap the {\bf h} key to
get a plot of the histogram of the pixels in the same region
\item tap the {\bf g} key to activate the graphics cursor, move the
cursor to the peak of the histogram and type {\bf C} to print out
the cursor's value.  The ``x" value then gives you a good estimate of
the sky.  Similarly, you can move the cursor to the
half-power point of
the histogram and type {\bf C} to estimate the standard deviation
of the sky pixels.  Tap the {\bf i} key to return to the
image cursor menu
\item compare the results of the h and m keys
\item repeat the measurements for several blank sky regions and note
the results
\item move to a bright unsaturated star and turn up the zoom and
 contrast of the display device as much as possible
\item using the {\bf x} key mark the point on either side of the center
where the light from the star disappears into the noise
and estimate PSFRAD 
\item type {\bf :epar r} to edit the radial profile fitting parameters
and set rplot to something a few pixels larger than PSFRAD
and tap the {\bf r} key
\item note the radius where the light levels off and compare with
the eyeball estimate
\item repeat for a few stars to check for consistency
\item type {\bf q} to quit imexamine
\end{itemize}
 
\noindent
{\bf Example 3:} Overplot lines from two different images.
 
\begin{itemize}
\item {\bf imexamine image1,image2}
\item move the image cursor to a star and type {\bf z} to print the
pixel values near the cursor
\item tap the {\bf n} key to display the second image followed by {\bf z}
to look at the values of the same pixels in the second
image
\item tap the {\bf p} key to return to the first image
\item tap {\bf l} to plot a line near the center of the star and tap
the {\bf o} key to overlay the next plot
\item tap the {\bf p} key to return to the second image and without
moving the image cursor tap the l key again to overplot
the line
\item type {\bf q} to quit imexamine
\end{itemize}
 
\subsection{Dealing with Parameter Files (Wheels within Wheels)}
 
The {\bf daophot} (and {\bf apphot}) packages are unique in IRAF in that
they obtain
pertinent information out of separate ``parameter files" that can be
shared between tasks.  As anyone that
has used IRAF knows, each IRAF command has its own parameter file that
can
be viewed by doing an {\bf lpar} {\it command} or edited by doing an
{\bf epar} {\it command}.
However, in {\bf daophot} and {\bf apphot} there are ``wheels within
wheels"---some of the parameters are in fact parameter files themselves.
For instance, the aperture photometry routine {\bf phot} does not
explicitly
show you the methods and details of
the sky fitting in its parameter file.  
However, if you do an {\bf lpar phot}
you will see a parameter
called ``fitskypars" which
contains, among many other things, the radii of the annulus to be used
in determining the sky value.
You will also find listed ``datapars" (which specifies the properties
of your data, such as photons per ADU and read-noise), ``centerpars"
(which
specifies the centering algorithm to be used), and ``photpars" (which gives
the
size of the digital apertures and the zero-point magnitude).
The contents of any of these parameter files can be altered either by
{\bf epar}ing them on their own or by typing a ``:e" while on that
line of the main parameter file.  If you do the latter, a control-z
or a ``:q" will bring you back. 
For example, to examine or edit {\bf fitskypars}, you can 
do an explicit {\bf lpar fitskypars}
or {\bf epar fitskypars}, or you can do an {\bf epar phot}, move the
cursor down to the ``fitskypars" line, and then type a {\bf :e} to edit
(see Fig.~\ref{wheels}).
\begin{figure}
\vspace{4.2in}
\caption{\label{wheels}Changing the Sky Annulus in {\bf fitskypars}.}
\end{figure}
Confusing?  You bet!
But once you are used to it, it is a convenient and powerful way to
specify a whole bunch of things that are used by several different
commands---i.e., you are guaranteed of using the same parameters in
several different tasks.  If there is only one thing that you want to
change in
a parameter file you {\it can} enter it on the command line when
you run the command, just as if it were a ``normal" (hidden) parameter,
i.e., {\bf phot imagename dannulus=8.} does the same as
running {\bf epar fitskypars} and changing the ``width of sky annulus"
{\bf dannulus} to 8.0.
 
Mostly these things are kept out of the way (``very hidden" parameters)
because you {\it don't} want to be changing them, once you have set them
up for your data.  There are exceptions, such as changing the PSF radius
in making a point-spread function in a crowded field (Sec. 4.6).
However,
you are well protected here if you leave the {\bf verify} switch on.
A task will then give you an opportunity to take one last look at
anything
that you really care about when you run the task.  For instance, if we
had simply run {\bf phot} on an image (we'll see how to do this shortly)
it would have said ``Width of sky annulus (10.)", at which point we
could
either have hit [CR] to have accepted the 10., or we could have
entered a new value.
 
 
\section{Aperture Photometry on your Standards}
 
Standard stars provide a good example of relatively uncrowded
photometry,
and in this section we will describe how to obtain instrumental
magnitudes for your standards using {\bf phot}. 
The basic steps are 
\begin{itemize}
	\item Decide what aperture size you wish to use for measuring your
	standards {\bf (this should be the same for all the frames).} At the
	same time we will pick a sky annulus. 
	\item Set up the various parameter files ({\bf datapars,
		centerpars, fitskypars, photpars}) to have the correct values.
	\item For each frame:
		\begin{enumerate}
		\item Identify the standard star(s) either 
		       interactively using a cursor
			or by using the automatic star finding algorithm
			{\bf daofind}.
		\item Run the aperture photometry program {\bf phot}
		      on each of your standard star frames.
\end{enumerate}
\end{itemize} 
Although the routines you will need to use are available both in the
{\bf daophot} and {\bf apphot} packages, we strongly advise you to run
them from the {\bf daophot} package: the default setup is somewhat different,
and the two packages each have their own data parameter files.

\subsection{Picking an Aperture Size}
Unfortunately, there are not good tools available with IRAF to do this
yet, and we will restrict our discussion here to some of the
considerations before telling you to just go ahead and use a radius that
is something like 4 or 5 times the FWHM of a stellar image; e.g.,
12 or 15
pixels as a radius, assuming you have the usual sort of ``nearly
undersampled" FWHM$\approx3$ data.
You might naively expect (as I did) that you wish to pick an aperture
size
that will ``contain all the light" from your standard stars, but in fact
this is impossible: the wings of a star's profile extend much further
than you imagine at a ``significant" level.  King (1971 {\it Publ.
A.S.P.} {\bf 83}, 199) and Kormendy (1973 {\it A.J.} {\bf 78}, 255)
discuss the fact that on photographic plates the profile of a star
extends out to {\it arcminutes} at an intensity level far exceeding the
diffraction profile; Kormendy attributes this to scattering off of dust
and surface irregularities on the optical surfaces.
Massey {\it et al}.\ (1989 {\bf 97}, 107) discusses
this in regards to CCD's and standard star solutions using the very data
we are using here as an example (which is not exactly a coincidence).
Although the intensity profile falls off rapidly, the increase in area
with radius increases rapidly, and in practical terms Massey {\it et
al.}
found that in cases where the FWHM was typically small (2.5-3 pixels),
increasing the digital aperture size from a diameter of 18 pixels to
one of 20 pixels resulted in an additional 1-2\% increase in light
for a well-exposed star, and that this increase continues
for larger apertures until masked by the photometric errors.
 
Given that you presumably want 1\% photometry or better, what should you
do?  
Well, the fact that photoelectric photometery through fixed apertures
in fact does
work suggests that there is some radius beyond which the same fraction
of
light is excluded, despite variations in the seeing and guiding.  You do
not want to choose a gigantic aperture ($>$ 20 pixels, say) because the
probability of your having a bad pixel or two goes up with the area.
But you do not want to choose too small an aperture ($<$10 pixels, say)
or you will find yourself at the mercy of the seeing and guiding.  Most
photoelectric photometrists will use an aperture of at least 10
arcseconds in diameter, but remember you have one advantage over them:
you are not sensitive to centering errors, since any digital aperture can
be exactly centered. 
If you
have enough standard star observations (I used about 300 obtained over a
10 night run) you can
compute magnitude differences between a large aperture (20 pixels),
and a series of smaller apertures (8, 10, 12, 15, 18) for each filter,
and then see for which radius the difference (in magnitudes) becomes
constant.  Unfortunately, there are no tools currently available within
IRAF for taking the differences between two apertures, or for conveniently
plotting these differences, so you are on your own.  My recommendation
would be that if you have typical data with a
FWHM of $\leq 4$ pixels, that you use something like an aperture of 12 to 15
pixels in radius for your standard stars.  {\bf You can save yourself a lot
of trouble if you simply adopt a single radius for all the standards
from all the nights for all filters.}
  
\subsection{Setting Things Up}
 
As discussed in ``Dealing with Parameter Files" (Section 2.1) we must
setup the parameter files from which {\bf phot} will get the details of
what it is going to do.  The easiest way to do this is to simply
{\bf epar phot}, and on each of the four parameter lists to do a
{\bf :e}.  Mostly we will leave the defaults alone, but in fact you will
have to change at least one thing in each of the four files.
 
\begin{figure}
\vspace{3.5in}
\caption{\label{photdatapars} Parameters for {\bf datapars}.}
\end{figure}
In {\bf datapars} (Fig.~\ref{photdatapars}) we need to specify both
the FWHM
of a star image ({\it fwhmpsf}) and the 
threshold value above sky ({\it threshold}) if we are going to use the
automatic star-finding routine {\bf daofind}; the choices for these
are discussed further below. In order to have
realistic
error estimates for our aperture photometry we need to specify 
the CCD readnoise {\it readnoise} in electrons and the
gain (photons per ADU) for the CCD {\it epadu}.  
In order to
correct the results for the exposure time we need the exposure time
keyword {\it
exposure}. Do an 
 
\centerline{{\bf imhead} {\it imagename} {\bf l+ $|$ page}}
 
\noindent
to see a
listing of all the header information (Fig.~\ref{phothead}).
\begin{figure}
\vspace{4.0in}
\caption{\label{phothead} Header information for std159.imh}
\end{figure}
By specifying the (effective) airmass and filter keywords,
these can be carried along in the photometry file for use when we do
the standards solution ({\it airmass} and {\it filter}).  Finally we use
{\it datamin} and {\it datamax} so we will know if we exceeded the
linearity of the CCD in the exposure, or whether there is some anomalously
low valued pixel on which our star is sitting.
Since the value of the sky on our standard exposures is
probably nearly zero, {\it datamin} should be set to a negative value
about three times the size of the readnoise in {\it ADU's}; e.g., $-3 \times
65. \div 2.25 \approx -90$ in this example.  Note that although we will
later argue that the shape of the PSF changes a little about 20000 
ADU's (presumably due to some sort of charge-transfer problem),
for the purposes of simple aperture photometry we are happy
using 32000 ADU's as the maximum good data value. (We do not really
want to use 32767 as afterall the overscan bias was probably at a
level of several hundred.)
 
\begin{figure}
\vspace{3.0in}
\caption{\label{photcenterpars} Parameters for {\bf centerpars}.}
\end{figure}
In {\bf centerpars} (Fig.~\ref{photcenterpars}) we need to 
change the centering algorithm {\it calgorithm}
from the default value of ``none" to
``centroid".  If the FWHM of your frames are unusually large ($>4$, say,
you would also do well to up the size of {\bf cbox} to assure that the
centering works well; make it something like twice the FWHM. In this
case the FWHM is 3 pixels or a bit smaller, and we are content to leave
it a the default setting of 5 pixels.
 
\begin{figure}
\vspace{2.7in}
\caption{\label{photfitskypars} Parameters for {\bf fitskypars}.}
\end{figure}
In {\bf fitskypars} (Fig.~\ref{photfitskypars})
the only things we must specify are the size and
location of the annulus in which the modal value of the sky will be
determined.  If you are going to use a value of 15 for your photometry
aperture, you probably want to start the sky around pixel 20.  Keeping
the width of the 
annulus large (5 pixels is plenty) assures you of good sampling, but
making it too large increases the chances of getting some bad pixels in
the sky.
 
\begin{figure}
\vspace{2.7in}
\caption{\label{photphotpars} Parameters for {\bf photpars}.}
\end{figure}
In {\bf photpars} (Fig.~\ref{photphotpars}) 
we merely need to specify the size (radius) of the
aperture we wish to use in measuring our standards.
 
\subsection{Doing It}
There are basically two ways of proceeding in running photometry on the
standard stars, depending upon how you are going to identify the
relevant star(s) on each frame.  If you have only one (or two)
standard stars on each frame, and it is always one of the brightest
stars present, then you can avoid a lot of the work and use the
automatic star-finding program {\bf daofind} to find all your standards
and the whole thing can be done fairly non-interactively.  However,
if you are one of the believers in cluster field standards, then you
may actually want to identify the standards in each field using the
cursor on the image display so that the numbering scheme makes sense.
We describe below each of the two methods.  
 
\subsubsection{Automatic star finding}
First let's put the name of each frame containing standard stars into
a file; if you've put the standard star exposures into a separate
directory this can be done simply by a {\bf files *.imh $>$ stands}.
This will leave us with funny default output file 
names for a while (we advise against
including the ``.imh" extension when we discuss crowded field photometry
in the next section), but this will only be true for a short
intermediate
stage. 
 
We want to run {\bf daofind} in such a way that it finds only the
brightest
star or two (presumably your standard was one of the brightest stars
in the field;
if not, you are going to have to do this stuff as outlined below in
the ``Photometry by eye" section).  We will delve more fully into the
nitty-gritty of {\bf daofind} in the crowded-field photometry section,
but here we are content if we can simply find the brightest few stars.
Thus the choice of the detection
threshold is a critical one.  If you make it too low you will find all
sorts of junk; if you make it too high then you may not find any stars.
You may need to run {\bf imexamine} on a few of your images: first
{\bf display} the image, and then {\bf imexamine}, using the ``r" cursor
key to produce a radial profile plot.  Things to note are the
typical full-width-half-maximum and the peak value.  If your sky is
really around zero for your standard exposures, then using a value
that is, say, twenty times the readnoise (in ADU's) is nearly guaranteed to
find only the brightest few stars; do your radial plots in {\bf
imexamine} show this to be a reasonable value?  In the example here we
have decided to use 500 ADUs as the threshold ($20 \times 65 \div 2.25
\approx 500$).
 
Now {\bf epar daofind} so it resembles that of Fig.~\ref{photdaofind}.
\begin{figure}
\vspace{3.5in}
\caption{\label{photdaofind} Parameter file for {\bf daofind}.}
\end{figure}
Go ahead and execute it (Fig. ~\ref{daoout}). 
\begin{figure}
\vspace{3.5in}
\caption{\label{daoout} Screen output from a {\bf daofind} run.}
\end{figure}
Note that since {\it verify} is on that you
will be given a chance to revise the FWHM and detection threshold.  By
turning verbose on you will see how many stars are detected on each
frame.  
%Probably the best way of doing this is to write the output from
%{\bf daofind} into a file; do a
% 
%\centerline{ {\bf daofind @stands $|$ tee starsfound} }
% 
%\noindent
%to put the output into the file ``starsfound" as well as on the screen.
Make a note of any cases where no stars were found; these you will have
to
go back and do with a lower threshold.
 
The run of {\bf daofind} produced one output file named {\it
imagename.imh.coo.1} for each input file.  If you {\bf page} one of
these you will find that it resembles that of Fig.~\ref{photcooout}.
\begin{figure}
\vspace{3.7in}
\caption{\label{photcooout} Output file from {\bf daofind}.}
\end{figure}
The file contains many lines of header, followed by the {\it x} and {\it
y} center values, the magnitudes above the threshold value, the ``sharpness"
and ``roundness" values, and finally an ID number.
In the example shown
here in Fig.~\ref{photcooout} two stars were found: one 2.9 mags
brighter than our detection threshold, and one about 0.4 mag brighter
than our detection threshold.
 
In a few cases we doubtlessly found more than one star; this is a good
time to get rid of the uninteresting non-standards in each field.
If things went by too fast on the screen for you to take careful notes
while running {\bf daofind} we can find these cases now: do a 

\centerline{ {\bf txdump *coo* image,id,x,y yes }}

 
\noindent
to get a listing of the location and number of stars found on each image.
If you have cases where there were lots of
detections (a dozen, say) you may find it easier to first {\bf sort
*.coo* mag} in order to resort the stars in each file by how bright they
are.  Of course, your standard may not be the brightest star in each
field; you may want to keep an eye on the {\it x} and {\it y} values to
see if it is the star you thought you were putting in the middle! 
To get rid of the spurious stars you will need to {\bf edit} each of the
output files (e.g., {\bf edit std148.imh.coo.1} ) and simply delete the
extras.
 
Finally we can run aperture photometry on these frames, using the 
``.coo" files to locate the standard star in each frame.  {\bf epar
phot} until it resembles that of Fig.~\ref{photphot}.
\begin{figure}
\vspace{3.5in}
\caption{\label{photphot} The parameter file for a run of {\bf phot}.}
\end{figure}
Note that we are specifying a {\it single} output file name
(``standstuff" in this example); {\it all} the photometry output will be
dumped into this single file, including things like the airmass and filter
number.  Go ahead and execute {\bf phot}.
You should see something much like that of Fig.~\ref{photrun} on the
screen.
\begin{figure}
\vspace{5.5in}
\caption{\label{photrun} Running {\bf phot} non-interactively
on the standard stars.}
\end{figure}
We will discuss the output below under ``Examining the results".
 
\subsubsection{Photometry by Eye}
In this section we will discuss the case of selecting stars {\it
without}
running the automatic star-finding program, using the image display
window and the cursor.  The first step is to {\bf epar phot} so it
resembles that of Fig.~\ref{photeye}.
\begin{figure}
\vspace{3.5in}
\caption{\label{photeye} Parameter file for {\bf phot} when stars will
be selected interactively.}
\end{figure}
Note that we have replaced the {\bf coords} coordinate list with the
null string (two adjacent double-quotes) and turned ``interactive" on.
 
We need to display the frame we are going to work on in the imtool
window:
 
\centerline { {\bf display std145 1} }
 
\noindent
will display image {\bf std145.imh} in the first frame buffer.
 
Now let's run {\bf phot}.  We are not likely to be {\it too} accurate
with where we place the cursor, so to be generous we will increase the
allowable center shift to 3 pixels; otherwise we will get error messages
saying that the ``shift was too large":
 
\centerline{ {\bf phot std145 maxshift=3.}  }
 
\noindent
(Note that even though {\bf maxshift} is a parameter of {\bf centerpars}
we can change it on the command line for {\bf phot}.) Also note that we
left off the ``{\bf .imh}" extension for a reason: we are going to take
the default names for the output files, and they will be given names
such as {\bf std145.mag.1} and so on. If we had included the {\bf .imh}
extension would would now be getting {\bf std145.imh.mag.1} names.
 
At this point I get a flashing circle in my {\bf imtool} window; I don't
know what you get (it depends upon how your defaults are set up) but
there should be some sort of obvious marker on top of your image.
Put it on the first star you wish to measure and hit the space bar.  The
coordinates and magnitude should appear in the {\bf gterm} window, and
you are ready to measure the next star on this frame.  Proceed until all
the stars on this frame are measured, and then type a ``q" followed by
another ``q".  Display the next frame, and run {\bf phot} on it.
 
When you get done you will have  kerjillions of files.  
 
\subsection{Examining the Results: the power of {\bf txdump }}
 
Depending upon which of the two methods you selected you will either
have a single file {\bf standstuff} containing the results of all your
aperture photometry, or you will have a file for each frame ({\bf
stand145.mag.1}, {\bf stand146.mag.1} \ldots)containing the stars
on each frame.  In either event the file will pretty much resemble that
shown in Fig.~\ref{photphotout}.
\begin{figure}
\vspace{7.5in}
\caption{\label{photphotout} Output file from {\bf phot}.}
\end{figure}
The file begins with a large header describing the parameters in
force at the time that {\bf phot} was run.  There is, however, a real
subtlety to this statement.  If you had changed a parameter in {\bf
datapars}, say, (or any of the other parameters) between running {\bf
daofind} and {\bf phot}, the header in {\bf phot} will reflect only the
setting that was in force at the time that {\bf phot} was run---in other
words, it does not take the values of what was used for the {\bf
threshold} from the coordinate file and retain these, but instead simply
copies what value of {\bf thresh} happens to be in {\bf datapars} at the
time that {\bf phot} is run.  To those used to the
``self-documenting" feature of VMS DAOPHOT this is a major change!
 
Once we get past the header information we find that there are 5 lines
per star measured.  The ``key" to these five lines of information are
found directly above the measurement of the first star. On the first
line we have ``general information" such as the
image name, the beginning x and y values, the id,
and the coordinate file.  On the next line we have all the centering
information: the computed x and y centers,
the x and y shift, and any centering errors.  On the third line of the
file we have information about the sky.  On the fourth line we have some
information out of the image header: what was the integration time, what
was the airmass, and what was the filter. Note
that {\bf phot} has used that integration time in producing the
magnitude---the exposures are now normalized to a 1.0 sec exposure.
The fifth line gives the actual photometry, including the size of the
measuring aperture, the total number of counts within the aperture, the
area of the aperture, and the output magnitude, photometric error, and
any problems encountered (such as a bad pixel within the aperture).
 
We can extract particular fields from this file (or files) by using the
{\bf txdump} command.  For instance, are there any cases where there
there were problems in the photometry?  We can see those by saying
 
\centerline{\bf txdump standstuff image,id,perror}
 
\noindent
(If you did ``Photometry by eye" you can substitute {\bf *mag*} for {\bf
standstuff}.)
When it queries you for the ``boolean expression" type
 
\centerline{ {\bf perror!$=$"No\_error"} }
 
\noindent
The ``!$=$" construction is IRAF-ese for "not equal to"; therefore, this
will select out anything for which there was some problem in the
photometry. 
 
We can create a single file at this point containing just the
interesting results from the photometry file(s): do a
 
\centerline{ {\bf txdump standstuff
image,id,ifilt,xair,mag,merr yes $>$ standsout} }
 
\noindent
to dump the image name, id-number, filter, airmass, magnitude,
and magnitude error into a file {\bf standsout}.  (Again, if you did
``Photometry by Eye" substitute {\bf *mag*} for {\bf standstuff}).
Unfortunately, what you do with this file is up to you right now until
the standard reductions routines become available.  In the example shown
here we have selected the fields in the same order as used in Peter
Stetson's VMS CCDCAL software, and at the end of this manual we will
describe a (painful) kludge that nevertheless {\it will} let you use
these numbers with that software. 
 
\section{Crowded Field Photometry: IRAF/daophot} 
\subsection{Historical Summary}
 
In the beginning (roughly 1979) astronomers 
interested in obtaining photometry from stars in ``relatively" crowded fields
would make the journey to Tucson in order to use Doug Tody's RICHFLD
program which ran on the IPPS display system. 
RICHFLD allowed the user to define a
point-spread-function (PSF), and then fit this PSF to the brightest star
in a group, subtract off this star, and then proceed to the next
brightest star, etc.  This represented a giant qualitative improvement
over the possibilities of aperture photometry, and allowed stars
separated by a few FWHM's to be accurately measured.  
 
Beginning in 1983, a group of RICHFLD users at the DAO (including
Ed Olszewski and Linda Stryker) began modifications to the ``poorman"
program of Jeremy Mould. This was largely motivated by the
implementation of the ``Kitt Peak CCD" at the prime-focus of the Tololo
4-m, and the idea was to design a crowded-field
photometry
program that (a) allowed simultaneous PSF-fitting,  (b) made
use of the {\it known noise characteristics of a CCD} to do the fitting
in a
statistically correct manner (i.e., to make ``optimal" use of the data),
and (c) to be largely batch oriented.
In mid-1983 Peter Stetson arrived at the DAO, and took over
the effort.  The result was
DAOPHOT, which did all these things and more. 
By 1986 DAOPHOT was well distributed within the astronomical community.
The basic algorithms and philosophy can be found in Stetson 1987 (PASP
{\bf 99}, 111).
 
DAOPHOT (and its companion program ALLSTAR) were not part of a
photometry
package; they were instead stand-alone Fortran
programs which did not deal in any way with the issue of image display
or what to do with the instrumental magnitudes once you had them.  They
were also only supported on VMS, although several ``frozen" versions
were translated into UNIX by interested parties around the country.  
There was therefore
much to be gained from integrating the algorithms of daophot 
with IRAF in order to make use of
the image display capabilities and general tools for manipulating
images.  Also, since many astronomers were now reducing their CCD data
with IRAF, it avoided the necessity of translating the IRAF files into
the special format needed by VMS DAOPHOT.  Dennis Crabtree began this
translation program while at the DAO; it was taken over by Lindsey Davis
of the IRAF group in early 1989, and taken to completion in early 1990.
Pedro Gigoux of CTIO is currently hard at work on the photometry
reduction package, scheduled for completion sometime during the spring.
 
\subsection{{\bf daophot}
Overview}
The steps involved in running daophot are certainly more involved than
in simple aperture photometry, but they are relatively straightforward.
The following sections will lead you through the necessary procedures.
Alternative routes will be noted at some points, and more may be gleaned
from reading the various "help" pages.  A general outline is given here
so that you have some overview in mind; a detailed step-by-step summary
is provided at the end of this section.  
 
\begin{itemize}
\item Before you reduce the first frame, {\bf imexamine}  your data to
determine FWHM's and the radius at which the brightest star you wish to
reduce blends into the sky.  Run {\bf imhead} to find the ``key-words"
in your data headers for exposure times, filter number, and airmass.
Enter these, along with the characteristics of your chip (read-noise,
photons per ADU, maximum good data value) 
into the parameter sets {\bf datapars} and {\bf
daopars}.
\item Use {\bf daofind} and {\bf tvmark} 
to produce a list of x and y positions of most
stars on the frame.
\item Use {\bf phot} to perform aperture photometry on the identified
stars.  This photometry will be the basis of the zero-point of
your frame via the PSF stars. This is also the only point where sky
values are determined for your stars.
\item Use {\bf psf} to define the PSF for your frame.  If your PSF stars are crowded this
will require some iteration using the routines {\bf nstar} and {\bf
substar}.
\item Use {\bf allstar} to do simultaneous PSF-fitting for all the stars
found on your frame, and to produce a subtracted frame.
\item Use {\bf
daofind} on the subtracted frame to identify stars that had been
previously hidden.  
\item Run {\bf phot} {\it on the original frame} to obtain aperture photometry
and sky values for the stars on the new list.
\item Use {\bf append} to merge the two aperture photometry lists.
\item Run {\bf allstar} again on the merged list.
\end{itemize}
When you have done this for your {\it U, B,} and {\it V} frames it is
then time to
\begin{itemize}
\item Use {\bf txdump}, {\bf tvmark}, and the image display
capabilities to come up with a consistent matching between the frames.
If there are additions or deletions then you will need to re-run
{\bf phot} and {\bf allstar} one more time.
\end{itemize} 
Finally you will need to
\begin{itemize}
\item Determine the aperture correction for each frame by subtracting
all but the brightest few isolated stars on your frames and then running
{\bf phot} to determine the light lost between your zero-point aperture
and the large aperture you used on your standard stars.
\end{itemize}
 
\subsection{How Big Is A Star: A Few Useful Definitions}

The parameter files {\bf datapars} and {\bf daopars} contain three
``size-like" variables, and although this document is not intended as
a reference guide, there is bound to be confusion over these three
parameters, particularly among those new to DAOPHOT.  In the hopes
of un-muddying the waters, we present the following.

\begin{description}
\item[fwhmpsf] This is the full-width at half-maximum of a stellar object
(point-spread function, or psf).  The value for {\bf fwhmpsf} gets used
only by the automatic star-finding algorithm {\bf daophot}, unless you
do something very bad like setting {\bf scale} to non-unity.

\item[psfrad] This is the ``radius" of the PSF.  When you construct a PSF,
the PSF will consist of an array that is
$$(2 \times psfrad +1) \times
(2 \times psfrad + 1)$$
on a side.  The idea here is that ``nearly all" of the light of the brightest
star you care about will be contained within this box.  If you were to construct
a PSF with some large value of {\bf psfrad} and then run {\bf nstar} or
{\bf allstar} 
specifying  
a smaller value of {\bf psfrad}, the smaller value would be used.  Making
the {\bf psfrad} big enough is necessary to insure that the wings of some
nearby bright star are properly accounted for when fitting a faint star.

\item[fitrad] This is how much of the psf is used in making the fit
to a star. The ``best" photometry will be obtained (under most circumstances)
if this radius is set to something like the value for the fwhm.

\end{description}

\subsection{Setting up the parameter files ``daopars" and ``datapars" }
 
The first step in using IRAF/daophot is to determine and store the
characteristics of your data in two parameter files called ``datapars"
and ``daopars"; these will be used by the various daophot commands.
In Section 1 we discussed how to deal with parameter files, and 
in Section 2 we went through setting up ``datapars" for the standard
star solutions; at the risk of repeating ourselves, we will go through
this again as the emphasis is now a little different.

 
First inspect your headers by doing an {\bf imhead} imagename {\bf long+
$|$ page}.  
This will produce a listing similar to that shown in Fig.~\ref{newhead}.
\begin{figure}
\vspace{3.0in}
\caption{\label{newhead}Header for image n602alu.imh.}
\end{figure}
The things to note here are (a) what the filter keyword is (we can
see from Fig.~\ref{newhead} that the answer is F1POS; while there is
an F2POS also listed, the second filter bolt was not used and was always
in position ``zero"),
(b) what the effective exposure
time keyword is (EXPTIME in this example), and (c) what the effective
airmass keyword is (AIRMASS in this example).
 
Next you need to examine some ``typical" frames in order to determine
the FWHM ({\bf fwhmpsf}) and the radius of the brightest star for which
you plan to do photometry ({\bf psfrad}).
First {\bf display} an image, and use the
middle button of the mouse (or whatever you need to do on your image
display) to zoom on a few bright stars.  On the SUN the "F6" key will
let you see x and y values.  The ``default" PSF radius is 11 pixels:
are your stars bigger than 23 pixels($23=2 \times 11 + 1$)
pixels from one side to the other?  The FWHM is undoubtably variable
from frame to frame, but unless these change by drastic amounts (factors
of two, say) using a ``typical" value will doubtless suffice.  You can
use the {\bf imexamine} routine to get some idea of the FWHM; do
{\bf imexamine} filename and then strike the ``r" key (for radial
profile) after centering the cursor on a bright (but unsaturated) star.
The last number on the plot is the FWHM of the best-fit Gaussian.
 
We are now ready to do an {\bf epar datapars}.  This parameter file
contains information which is data-specific.  We set {\bf fwhmpsf} to the FWHM
determined above, and we enter the names of the keywords determined from
the header inspection above.  The ``gain" and ``read-noise" are values
you have either determined at the telescope (using the Tololo routines)
or which are carved in stone for your chip.  Choosing the value
for datamax, the ``Maximum good data value",
(in ADU's, NOT electrons) is a little bit trickier.  In the case of
aperture photometry we were satisfied to take the nominal value for
the chip, but point-spread-function fitting is a bit more demanding
in what's ``linear".  The data obtained
here was taken with an RCA chip, and we all know that RCA chips are
linear well past 100,000 e-.  Thus, naively, we would expect that
with a gain of 2.25 that the chip was still linear when we hit the
digitization limit of 32,767 ADU's.  Subtract off 500 for the likely
bias, and we {\it might} think that we were safe up to 32,200.  However,
we would be wrong.  Experience with PSF fitting on these data shows that
something (presumably in those little silver VEB's) has resulted in
these data being non-linear above 20,000 ADU's.  My suggestion here is
to start with the nominal value but be prepared to lower it if the
residuals from PSF fitting appear to be magnitude dependent (more on this
later).  The value for
{\bf datamin}, the
``Minimum good
data value", will be different for each frame (depending what the sky
level is) and there is not much point in entering a value for that yet.
Similarly the value we will use for threshold will change
from frame to frame depending upon what the sky level is.
When you are done your {\bf datapars} should resemble that of
Fig.~\ref{datapars}.
\begin{figure}
\vspace{2.7in}
\caption{\label{datapars} A sample {\bf datapars} is shown.}
\end{figure}
 
Next we will {\bf epar daopars}.  This parameter file contains
information specific to what you want {\bf daophot} to do.  The only things here
we might want to change at this point are the ``Radius of the psf" {\bf psfrad}
(if your experiment above showed it should be increased somewhat), and
you might want to change the fitting radius {\bf fitrad}.  Leaving the fitting
radius to ``something like" the FWHM results in the best SNR (you can
work this out for yourself for a few different regimes if you like to
do integrals).  The ``standard values" are shown in Fig.~\ref{daopars}.
\begin{figure}
\vspace{2.7in}
\caption{\label{daopars} A sample {\bf daopars} is shown.}
\end{figure}.
 
\subsection{Finding stars: {\bf daofind} and {\bf tvmark} }
The automatic star finder {\bf daofind} convolves a Gaussian of
width FWHM with the image, and looks for peaks greater than some
threshold in the smoothed image.  It then keeps only the ones that are
within certain roundness and sharpness criteria in order to reject
non-stellar objects (cosmic rays, background galaxies, bad columns,
fingerprints).  We have already entered a reasonable value for the FWHM
into {\bf datapars}, but what should we use as a threshold?  We expect
some random fluctuations due to the photon statistics of the sky
and to the read-noise of the chip. You can calculate this easily by
first
measuring the sky value on your frame by
using {\bf imexamine} and the ``h" key to produce a histogram of
the data ({\bf implot} and the ``s" key is another way).  In the example
shown in Fig~\ref{hist} we see that the sky value is roughly 150.
\begin{figure}
\vspace{3.6in}
\caption{\label{hist} The {\bf imexamine} histogram (``h" key) indicates
that the sky value is roughly 150.}
\end{figure}
In general, if $s$ is the sky value in ADU, $p$ is the number of
photons per ADU, and $r$ is the read-noise in units of electrons,
then the expected $1\sigma$ variance in the sky
will be 
$$\left(\sqrt{s\times p + r^2}\right)/p$$ 
in units of ADU's.  For the example here we expect
$1\sigma=\left(\sqrt{150.\times 2.25 + 65^2}\right)/2.25=30$ ADU's.
Of course, if you have averaged N frames in producing your image,
then you should be using
$N\times p$ as the gain both here and in the value entered in
{\bf datapars}; similarly the readnoise is really just $r \times \sqrt{N}$.
If instead you summed N frames then the gain is just {\it p} and the
readnoise is still $r\times \sqrt{N}$.
 
In the example shown here the expected $1\sigma$ variation of the sky is
30 ADU's; we might therefore want to set our star detection threshold to
3.5 times that amount.  That won't guarantee that every last star we
find is real, nor will it find every last real star, but it should do
pretty close to that!
 
We should use this opportunity to set datamin in {\bf
datapars} to some value like $s-3\sigma$.  In this case we will set it
to 60.  This is not currently used by {\bf daofind} but will be used
by all the photometry routines.  Fig.~\ref{ndatapars} shows the data
parameters with the appropriate values of threshold and datamin now
entered.
\begin{figure}
\vspace{3.0in}
\caption{\label{ndatapars}  Datapars with {\bf threshold} and {\bf datamin}
entered.} 
\end{figure}
 
We now can {\bf epar daofind} so it resembles that of
Fig.~\ref{daofind}.
\begin{figure}
\vspace{3.0in}
\caption{\label{daofind}  Parameters for {\bf daofind}.}
\end{figure}
Note that although nothing appears to be listed under {\bf datapars} the
default name is ``datapars"; you could instead have created a separate
data parameter file for each ``type" of data you have and have called
them separate names (you could do this by doing an {\bf epar datapars}
and then exiting with a ``:w newnamepar").  This might be handy if
all your {\it U} frames were averages, say, but your {\it B} and {\it V} 
frames were
single exposures; that way you could keep track of the separate
effective gain and readnoise values.  In that case you would enter the
appropriate data parameter name under {\bf datapars}.  As explained earlier,
you could also do a
``:e" on the {\bf datapars} line and essentially do the {\bf epar datapars} from
within the {\bf epar daofind}. 
For normal star images, the
various numerical values listed are best kept exactly the way they are;
if you have only football shaped images, then read the help page for
{\bf daofind} for hints how best to find footballs.

We can now run {\bf daofind} by simply typing {\bf daofind}. 
As shown in Fig.~\ref{daofind} that we were asked for the FWHM and threshold
values; this is a due to having turned ``verify" on in the parameter
set.  This safeguards to a large extent over having forgotten to set
something correctly.  A [CR] simply takes the default value listed.
 
Running {\bf daofind} produced an output file with the (default)
filename of {\bf n602csb.coo.1}.
(Do {\it not} give the {\bf .imh} extension
when specifying the image name, or the default naming
process will get very confused!) We can page
through that and see the x and y centers, the number of magnitudes
brighter than the cutoff, the sharpness and roundness values, and the
star number.  However, of more immediate use is to use this file
to mark the found stars on the image display and see how we did.
If we have already displayed the frame in frame 1, then we can {\bf epar
tvmark} to make it resemble Fig.~\ref{tvmark}.
\begin{figure}
\vspace{2.7in}
\caption{\label{tvmark} Parameter file for {\bf tvmark}.}
\end{figure}
This will put red dots on top of each star found.
 
We can see from Fig.~\ref{dots} that {\bf daofind} did a pretty nice
\begin{figure}
\vspace{7.0in}
\caption{\label{dots} Stars found with {\bf daofind} and marked with
{\bf tvmark}.}
\end{figure}
job.  If we didn't like what we saw at this point we could rerun
{\bf daofind} with a slightly higher or slightly lower threshold---try
varying the threshold by half a sigma or so if you are almost right.
As you may have guessed, subsequent runs will produce output files with
the names n602csb.coo.2, n602csb.coo.3,...
If you are using a very slow computer, or are exceedingly impatient,
 you could have saved some
time by putting a ``c" (say) under ``convolv" in your first run of
{\bf daofind}---this would have saved the
smoothed image as cn602csb.imh, and would drastically reduce
the number of cpu cycles needed to rerun {\bf daofind} with
a different threshold value.
If you really very happy with what {\bf daofind} did but you
just want to add one or two stars at this point, you
can in fact do that quite readily using {\bf tvmark}.  Set the
parameters as in Fig.~\ref{tvmark}, but turn interactive on.  
Position the cursor on top of the star you wish to add and strike
the ``a" key.  Note that this will ``disturb" the format of the file,
but we really don't care; it will still work just fine as the input to
{\bf phot}.
 
Note that it is fairly important that you do a good job at this stage.
If you have used too low a threshold, and have a lot of junk marked as
stars, these fictitious objects are likely to wander around during the
PSF-fittings until they find something to latch onto---{\it not} a good
idea.  However, you also do not want the threshold to be so high that
you are missing faint stars.  Even if you are not planning to publish
photometry of these faint guys, you need to have included them in the
list of objects if they are near enough to affect the photometry of
stars for which you do have some interest.  If you find that varying the
threshold level does not result in a good list, then something is
wrong---probably you have badly over- or under-estimated the FWHM.
When you are close to the ``perfect" value of the threshold, 
changing its value by as little as half a sigma will make a substantial
difference between getting junk and real stars.
 
\subsection{Aperture Photometry with {\bf phot} }
The next step is to do simple aperture photometry for each of the stars
that have been found.  These values will be used as starting points in
doing the PSF fitting, and this is the only time that sky values will be
determined.  
 
{\bf One of the few ways of ``crash landing" in the current
implementation of the software is to forget to reset ``datamin" in the
datapars file before running phot on a new frame.  It is the only
critical parameter which is not queried when verify is turned on.  Therefore,
this is a good time to check to see that ``datamin" is really set to
several sigma lower than the sky value of this particular frame.}
 
The aperture photometry routine {\bf phot} has more parameters than all
the others put together: there are the parameter files 
{\bf centerpars}, {\bf fitskypars}, and {\bf photpars}.  
Fortunately the ``verify"
option frees you from having to look at these, and helps prevent you
from making a mistake. If this is your first pass through DAOPHOT it is
worth your while to do the following:
 
\centerline{ {\bf unlearn centerpars} }
 
\centerline{ {\bf unlearn fitskypars} }
 
\centerline{ {\bf unlearn photpars} }
 
\noindent
If you have used {\bf phot} for measuring standard stars, then this will
reset the defaults to reasonable values for crowded-field photometry; 
in particular, we want to make sure that the centering
algorithm in {\bf centerpars} is set to ``none".  
Do an {\bf epar phot} and make it look like that of Fig.~\ref{phot}.
Since we have the ``verify" switch turned on, we can be happy, not
worry, and simply type {\bf phot}.
{\bf phot} will then prompt you as shown in
Fig.~\ref{phot}.
\begin{figure}
\vspace{7.0in}
\caption{\label{phot} Questions and answers with {\bf phot}.}
\end{figure}
Note that the answers were particularly simple: we told it the name of
the frame we wished to work with, we accepted the default for the coordinate
list (it will take the highest ``version" of image.coo.NUMBER) and the
default for the output photometry list (n602csb.mag.1 will be produced
in this case.)  We accepted the centers from {\bf daofind} as being
``good enough" to not have to recenter (they are good to about one-third
of a pixel, plenty good enough for aperture sizes of 2.5 pixels and
bigger; when we run this routine later on the second pass we would make
a Big Mistake by turning centering on here, so leave it off). 
The sky
values will be taken from an annulus extending from a radius of 10
pixels to a radius of 20 pixels, and it will determine the standard
deviation of the sky from the actual data.  Note that this is probably a
lot closer in than you used on your standard stars; in crowded regions
of variable background keeping this annulus relatively close in will
help.
Finally, we used a measuring
aperture of 3 pixels.  The number of counts within this aperture will be
what defines the zero-point of your frame, as we will see in Section 4.9,
and keeping this value {\it fixed} to some value like your typical FWHM
will keep you safe.
 
\subsection{Making the PSF with {\bf psf} }
 
If you are used to the VMS version of DAOPHOT, you are in for a pleasant
surprise when it comes to making a PSF within the IRAF version.
Nevertheless, just because it's easy doesn't mean that you shouldn't be
careful.
 
What constitutes a good PSF star?  Stetson recommends that a good PSF
star meets the following criteria:
\begin{enumerate}
\item No other star at all contributes any light within one fitting
radius of the center of the candidate star. (The fitting radius will be
something like the FWHM.)
\item Such stars as lie near the candidate star are significantly
fainter. (``Near" being defined as, say, 1.5 times the radius of the
brightest star you are going to measure.)
\item There are no bad columns or rows near the candidate star; there
should also be no bad pixels near the candidate star.
\end{enumerate}
 
 
In making a PSF, you wish to
construct a PSF which is free from bumps and wiggles (unless those
bumps and wiggles are really what a single isolated star would look like.)
First off, does it matter if we get the PSF ``right"?  If we had
only isolated stars, then the answer would be no---any
old approximation to the PSF would give you
good relative magnitudes, and there are programs in the literature
which do exactly this.  However, if your stars are relatively isolated
you are not going to gain anything by PSF-fitting over aperture photometry
anyway, so why bother?  If you are dealing with crowded images, then the
PSF has to be right {\it even in the wings}, and for that reason we
construct a PSF empirically using the brightest and least crowded stars
in our frame.
If you are very, very
lucky you will find that your brightest, unsaturated star is well
isolated, and has no neighbors about it---if that's the case, use that
one and forget about the rest.  Usually, however, you will find that
it isn't quite that easy, and it will be necessary to construct the PSF
interatively.  The steps involved will be
\begin{enumerate}
	\item Select the brightest, least-crowded stars for the zeroth-order
	      PSF.
	\item Decrease the size of the PSF radius and fit these stars
	      with their neighbors using {\bf nstar}.  
	\item Subtract off the PSF stars and their neighbors using
	      {\bf substar} to see
	      if any of the PSF stars are ``funny"; if so, go back to
	      the step 1 and start over.
	\item Edit the {\bf nstar} results file ({\bf imagename.nst.N})
	      and delete the entries for the PSF stars.  You are left
	      with a file containing the magnitudes and positions of just
	      the neighbors.
	\item Subtract off just the neighbors using this file as input
	      to {\bf substar}.  Display
	      the results, and examine the region around each PSF star.
	      Are the neighbors cleanly removed?
	\item Increase the PSF radius back to the original value.
	      Construct an improved PSF using the new frame (the one with the
	      neighbors gone.)
        \item Run {\bf nstar} on the PSF stars and their neighbors again, and
	      again subtract these using {\bf substar}.  Examine the results.
	      If you are happy, proceed; otherwise, if the neighbors need
	      to be removed a bit more cleanly go back to step 4.  
\end{enumerate}
 
First {\bf display} the frame, and put dots on all the stars you've found
using {\bf tvmark} as discussed above.  Next {\bf epar psf} and make sure
it looks like that of Fig.~\ref{psfparams}.
\begin{figure}
\vspace{2.5in}
\caption{\label{psfparams} Parameter file for {\bf psf}}
\end{figure}
We have set this up so we can choose the stars interactively from the
display window.
 
Next run {\bf psf}.  The defaults that you will be asked to {\bf verify}
are probably fine, but pay particular attention to {\bf psf radius}
and {\bf fitting radius}.  The {\bf psf radius} should be as large
as you determined above (11 usually works well on ``typical" CCD
frames whose star images have FWHM's $\approx 3$).  The ``fitting radius"
should be relatively generous here---maybe even larger than what you
want to use on your program stars.  A reasonable choice is approximately
that of the FWHM. 
 
You will find that the cursor has turned into a circle and is sitting
on your image in the display window.  Position it on a likely looking
PSF star, and strike the ``a" key. You will be confronted with a mesh
plot that shows the star and it surroundings.  To find out more
about the star (such as what the peak data value is you can type
an ``s" while looking at the mesh plot.  To reject the star type an
``x", to accept the star type an ``o".  In the latter case, you will
next see a mesh plot that
shows you the star with a two-dimensional Gaussian fit removed from the
star.
Again, exit this with a ``o".  If you don't find these mesh
plots particularly useful, you can avoid them by setting {\bf showplot=no}
in the {\bf psf} parameters (see Fig.~\ref{psfparams}).  
At this point you will be told what the star number was, what the
magnitude was, and what the minimum and maximum data values within
the PSF were.   (If you picked a star whose peak intensity was greater
than ``datamax" it will tell you this and not let you use this star.)
When you are done selecting stars, type a ``w" (to write the PSF to
disk) followed by a ``q". 
 
If in making the PSF you noticed that there were stars you could have
used but didn't because they had faint neighbors not found in the earlier
step of star finding, you can add these by hand by simply 
running {\bf tvmark} interactively and marking the extra stars.  First
{\bf epar tvmark} so it resembles that of Fig.~\ref{tvmark}. Then:
 
\centerline{ {\bf display n602csb 1} }
 
\centerline{ {\bf tvmark 1 n602csb.coo.1 interactive+} }
 
\noindent
 
Striking the ``l" key will mark the stars it already knows about onto
the display (as red dots this time around); positioning the cursor on the
first star you wish to add and type an ``a".  When you are done adding
stars exit with a ``q" and re-run {\bf phot}.
 
Now that you have made your preliminary PSF, do a {\bf directory}.  You'll
notice that in addition to the image {\bf n602csb.psf.1.imh} that the
{\bf psf} routine has also added a text file {\bf n602csb.psg.1}.  If
you {\bf page} this file you will see something like that of Fig.~\ref{psg}.
\begin{figure}
\vspace{3.5in}
\caption{\label{psg} The ``point spread function group" file 
{\bf n602csb.psg.1}}
\end{figure}
This contains the aperture photometry of each PSF star plus its neighbors,
with each set constituting a ``group".  Running the psf-fitting photometry
routine {\bf nstar} will fit PSF's to each of the stars within a group
simultaneously.
 
Before we run {\bf nstar}, however, we must decide what psf radius to use.
Why not simply keep it set to the value found above (e.g., something like 11
pixels)?  The answer to this is a bit subtle, but understanding it will
help you diagnose what is going wrong when you find a PSF going awry (and
don't worry, you will).  Let's consider the case that you construct a PSF
from a single star with one neighbor whose center is 12 pixels away from
the center of the PSF star, and let's have the PSF radius be 11 and the PSF
fitting radius be 3. The PSF looks something like that of Fig.~\ref{bump}.
\begin{figure}
\vspace{5.0in}
\caption{\label{bump} The zeroth order PSF of a star with a neighbor 12 pixels
away.}
\end{figure}
The light from the neighbor star ``spills
over" into the PSF. 
 
What happens when you try to fit two PSF's simultaneously?  The bump from the
PSF of the brighter star sits within the fitting radius of the fainter star,
and it is the sum of the PSF's which are being fit to each star (that's
what ``simultaneous" means).  Thus there is an ``implicit subtraction" of
the fainter star simply from fitting the bumpy PSF to the brighter star,
and the brightness of the fainter star will be underestimated.  The way
to avoid this is to see that the PSF of the brighter star does not come
within the fitting radius of the fainter star, and {\it that} we can 
accomplish easily by truncating the PSF size to something like the separation
of the two stars minus the fitting radius.  Thus in the example here
we would want to fit the two stars using PSF's that were only ($12-3=9$)
pixels in radius. It's true that there may still be light of the PSF
star beyond this radius, but that will matter only if the PSF star is still
going strong when you get within the {\it fitting radius} of the fainter
star.  
 
Now that we understand all that, run {\bf nstar}.  Specify the appropriate
image name for ``image corresponding to photometry" and  give it
the ``.psg" file {\bf n602csb.psg.1} for the ``input group file".
Remember to decrease
the {\bf psf radius} when it tries to verify that number.  {\bf nstar}
will produce a photometry output file {\bf n60csb.nst.1}.
You can
subtract the fitted PSF's from these stars now by running {\bf substar}.
Again, {\bf verify} the PSF radius to the smaller value.  When the routine
finishes, {\bf display} the resultant frame {\bf n60csb.sub.1.imh} and
take a look at the PSF stars...or rather, where the PSF stars (and their
neighbors) were.  Are they subtracted cleanly?  Does one of the PSF
stars have residuals that look the reverse of the residuals of the others?
If so, it would be best to reconstruct the PSF at this point throwing out
that star---possibly it has a neighbor hidden underneath it, or has something
else wrong with it.  Are the variations in the cores of the subtracted image
consistent with photon statistics?  To answer this you may want to play
around with {\bf imexamine} on both the original and subtracted images,
but if the stars have cleanly disappeared and you can't even tell where
they were, you are doing fine. 
 
The worst thing to find at this point
is that there is a systematic pattern with position on the chip.  This
would indicate that the PSF is variable.  There is the option for making
a variable PSF, but the assumption is that the PSF varies smoothly in x
and
y; usually this is not the case.  (In the case of the non-flat TI chips
the variations are due to the potato-chip like shape.)  If you {\it do}
decide the PSF is variable, be sure to use plenty of stars in making the
PSF.  As it says in the ``help page",
twenty-five to thirty is then not an unreasonable number.  If that
doesn't scare you off, nothing will.
 
If the brightest stars have residuals that are systematically different than 
those of the fainter stars, maybe that chip wasn't quite as linear as you
thought, or perhaps there are charge transfer problems.  This proved to
be the case for the RCA CCD data being reduced here.  In Fig.~\ref{yuko}
we show the residuals that result when we based our PSF on a star whose
peak counts were 30000 ADUs.  
Empirically we found that stars with peaks of 18K ADUs (a mere 40K electrons)
were safe to use, with the result that the dynamic range of our data
was simply not quite as advertised.  Although the PSF function broke down
above 18K, the chip remained ``linear" in the sense that aperture photometry
continued to give good results---the total number of counts continued to
scale right up to the A/D limit of 32,767 ADUs (72K electrons after bias
is allowed for).   This appears to be a subtle charge transfer
\begin{figure}
\vspace{7.0in}
\caption{\label{yuko} A ``before" and ``after" pair of images, where the
PSF was constructed with a star that was too bright.  Note the systematic
residuals for the two bright stars.  A ``bad" PSF star would result in a
similar effect; however, in these data we found that there was always a
systematic effect if the PSF stars were about 18000 ADU.}
\end{figure}
problem.
 
We will assume that you have gotten the PSF to the point where
the cores of the stars disappear cleanly, although there may be residuals
present due to the neighbors.  Our next step is to get rid of these neighbors
so that you can make a cleaner PSF.  Edit the {\bf nstar} output file
{\bf n602csb.nst.1} and delete the lines associated with the PSF stars,
leaving only the neighbors behind.  You can recognize the PSF stars, as
they are the first entry in each group.  When you are done with this
editing job, re-run {\bf substar}, using the edited ``.nst" file as the
photometry file.  Again in running {\bf substar} make sure you {\bf verify}
the PSF radius to the smaller value you decided above.  Examine the results
on the image display.  Now the PSF stars should be there but the neighbors
should be cleanly subtracted.  Are they?  If so, you are ready to proceed.
If not, re-read the above and keep at it until you get those neighbors
reasonably well out of the frame.
 
We can now run {\bf psf} on the subtracted frame---the one with only the
neighbors gone.  We have added some noise by doing the subtraction, and
so we should reset {\bf datamin} to several sigma below the previously
used
value. We are going to have to do more typing this time when
we run it, as the defaults for things will get very confused when we
tell it that the ``Image for which to build PSF" is actually
{\bf n60csb.sub.1}.  For the ``Aperture photometry file" we can tell
it the original photometry file {\bf n602csb.mag.1} if we want, or
even the old ``.psg" file {\bf n602csb.psg.1} since every star that
we are concerned about (PSF star plus neighbor) is there.  Go ahead
and give it the next `version" number for the ``Output psf image"
{\bf n602csb.psf.2} and for the ``Output psf group file" 
{\bf n602csb.psg.2}.  
We can of course do this all on the command line:
 
\centerline{ {\bf psf n602csb.sub.1 n602csb.mag.1 n602csb.psf.2
n602csb.psg.2 datamin=-150.} }
 
\noindent
An example is shown in Fig.~\ref{psf1}.  
{\it This time make sure you take the
large psf radius.}
\begin{figure}
\vspace{7.0in}
\caption{\label{psf1} Making the first revision PSF using the frames with the
neighbors subtracted. Compare this to Fig. 23, which shows the
same region before the neighbors have been removed.}
\end{figure}
Make a new PSF using the cursor as before.
 
How good is this revised PSF?  There's only one way to find out: run
{\bf nstar} on the original frame, this time keeping the psf radius large.
Then do {\bf substar} and examine the frame with both the PSF stars and
neighbors subtracted.  Does this show a substantial improvement over the
first version?  Now that you have a cleaner PSF it may be necessary to repeat
this procedure (edit the {\bf n602csb.nst.2} file, remove the PSF stars,
run {\bf substar} using this edited file to produce a frame with the
just the neighbors subtracted this time using a better PSF, run {\bf psf}
on this improved subtracted frame) but probably not.
 
\subsection{Doing the psf-fitting: {\bf allstar}.}
The next step is to go ahead and run simultaneous PSF-fitting on all
your stars, and produce a subtracted frame with these stars removed.
To do both these things you need only run {\bf allstar}.  The defaults
are likely to be right: see Fig.~\ref{allstar}.
\begin{figure}
\vspace{3.5in}
\caption{\label{allstar} Running {\bf allstar}.}
\end{figure}
As you may imagine, {\bf allstar} produces a photometry file
{\bf n602csb.als.1}, and another subtracted image: {\bf imagename.sub.N}.
 
Display the subtracted frame, and blink it against the original.  Has
IRAF/daophot done a nice job?  If the stars are clearly gone with a few
hidden ones now revealed, you can be proud of yourself---if the results
are disappointing, there is only one place to look, and that is in the
making of the PSF.  Assuming that all is well, it is now time to 
add those previously hidden stars into the photometry.  
The easiest way to do this is to run {\bf daofind} on the subtracted
image. 
Set the value of {\bf datamin} to a value several sigma lower
than what you had used earlier in case the subtraction process generated
some spuriously small values, and you will want to {\it increase} the
value of threshold by 1 or 2 sigma above what you used previously.
Why?  Because the subtraction process has certainly added noise to the
frame, and if you don't do this you will be mainly adding spurious
detections.  Use {\bf tvmark} as before to examine the results of {\bf
daofind}; remember that the coordinate file name will be 
{\bf imagename.sub.N.coo.1} this time around.  If you are really close,
but want to add a couple of stars, re-run {\bf tvmark} on this file
using
{\bf interactive+}; this will allow you to add (and delete) coordinates
from the file.
 
Now run {\bf phot} using this new coordinate file as the input list.
However, you do want to use the {\it original} frame for this photometry;
otherwise the sky values for the newly found stars will be very messed
up owing to the many subtracted images.  A new aperture photometry file
{\bf n602csb.mag.2} will have been produced.  Use {\bf append} to 
concatenate these two files: {\bf append n602csb.mag.1,n602csb.mag.2
n602csb.mag.3}.  You can now re-run {\bf allstar} using this combined
photometry file as the input.
 
\subsection{Matching the frames}
In the example here we have been reducing the {\it B} frame of 
a set of {\it UBV}.  Once all three frames have been reduced it is often
necessary to do a little fiddling. Have the same stars been identified
in each group?  In many cases you don't want the same stars to have been
identified in each clump---afterall, some stars are red, some are blue
(that's presumably why you are doing this afterall, right?), but in some
cases you may find that a clump was identified as three objects on the
{\it U} and the {\it V} frames and clearly should have been three on the
{\it B} frame but instead is four or two. What to do?
 
Using {\bf tvmark} it is relatively easy to set this right.  First we
need to use {\bf txdump} to produce a file for each frame that can be
displayed.  Do something like an 
 
\centerline{ {\bf txdump n602csu.als.2 $>$ tvu}}
 
\noindent
followed by an 
 
\centerline{ {\bf txdump n602csb.als.2 $>$
tvb}} 
 
\noindent
and a 
 
\centerline{ {\bf
txdump n602csv.als.2 $>$ tvv}}
 
\noindent
In each case select {\bf xc,yc} and use
{\bf MAG!=INDEF} as a selection criteria.  Thus you will then have three text
files that contain only the x's and y's of the stars with photometry.
 
Next display the three frames ({\bf display n602csu 1}, {\bf display
n602csb 2}, {\bf display n602csv 3}) and put colored dots up to denote
the different allstar stars: 
 
\centerline{ {\bf tvmark 1 tvu color=204 inter-},}
 
\centerline{
{\bf tvmark 2 tvb color=205 inter-},}
 
\noindent
and 
 
\centerline{ {\bf tvmark 3 tvv color=206
inter-}}
 
\noindent
will give pleasing results.  Zoom, pan, register, and blink
around the frames until you are convinced that you really do want to
add or delete a star here or there.  If you want to add or delete a star to the
{\it U} frame list, do a 
 
\centerline{ {\bf tvmark 1 tvu color=203 inter+}}
 
\noindent  
You are
now in interactive mode, and centering the cursor on the star you want
to add and striking the ``a" key will append the x and y value of the
cursor the tvu list.  Similarly, striking the ``u" key
will delete a star from the list if you are using IRAF v2.9 or later.  
(For earlier versions you are just going to have to do a little
editing by hand, good luck!) The star you add or delete will have
a white dot appear on top of it. 
If you need to switch to a different coordinate file, simply exit the
interactive {\bf tvmark} with a ``q" and re-execute it specifying, for
example, {\bf tvmark 3 tvv color=203 inter+}. 
 
When you are done with adding and deleting stars, then it is time to
redo the photometry.  Do a {\bf phot n602csu coords=tvv datamin=100}
in order to generate new aperture photometry and sky values.  These
can then be run through {\bf allstar}, and the procedure repeated for
each
of the frames.
 
\subsection{Determining the Aperture Correction}
 
The zero-point of your magnitudes have been set as follows.  When you
ran {\bf phot} using a small aperture (3 pixels in the example above)
magnitudes were defined as -2.5 * log{(Counts above sky)/(Exposure
time)} + Const.
(The constant Const was hidden away in {\bf photpars} and is the
magnitude assigned to a star that had a total of  one ADU per second 
within the measuring aperture you used.)  When you defined your PSF the
magnitudes of the PSF stars determined from the aperture photometry were
then used to set the zero-point of the PSF.  However, your standard
stars were presumably measured (if you did things right) through a much
larger aperture, and what we must do now is measure how much brighter
the PSF would have been had its zero-point been tied to the same size
aperture used for the standard stars.  
 
We need to determine the aperture correction from the brightest, 
unsaturated stars (so there will still be reasonable signal above sky
at the size of the large aperture); if you can pick out stars that are
reasonably well isolated, so much the better.  If this sounds vaguely
familiar to you, you're right---this is basically what you did for
selecting PSF stars, and these would be a good starting point for
selecting stars for determining the aperture correction.  Ideally you
would like to use at least five such stars, but since when is data
reduction ideal?  Nevertheless, it is in the determination of the
aperture correction the largest uncertainty enters in doing CCD
photometry on crowded fields.
 
We will first need to pick out the brightest, isolated stars and then
to subtract off any stars that might affect their being measured through
the large ``standard star" aperture (e.g., something like 15 pixels).
To do this we need good photometry of any of these neighbor stars, and
we describe two ways to do this (1) the very long complicated way, and
(2) the very short easy way:
 
\begin{enumerate}
 
\item {\bf Method 1: Using the image display}
We can also use {\bf tvmark} to mark the stars that we wish to use for
aperture photometry.  First we should remind ourselves what are multiple
stars and what aren't: {\bf display} the image, and then use {\bf
tvmark} to mark the stars with {\bf allstar} photometry:
 
\centerline{ {\bf display n602csb 1} }
 
\centerline{ {\bf txdump n602csb.als.2 xc,yc yes $>$ tvb} }
 
\centerline{ {\bf tvmark 1 tvb color=204 interact-} }
 
\noindent
Now go through and mark the stars you want to use as the aperture
correction stars {\it plus any neighbors that might contribute light
to a large aperture centered on the bright stars:}
 
\centerline{ {\bf tvmark 1 bapstars color=203 interact+ }}
 
\noindent
Use the ``a" key to generate a list ({\bf bapstars}) of the approximate
{\it x} and {\it y} positions of these stars.  Next run this list
through {\bf phot} to generate improved centers and good sky values:
 
\centerline{ {\bf phot n602csb bapstars bapphot calgor=``centroid" } }
 
\noindent
Next run the photometry output file {\bf bapphot} through {\bf group}:
 
\centerline{ {\bf group n602csb bapphot default default crit=0.2} }
 
\noindent
This will have generated a ``group" file {\bf n602csb.grp.1}.
 
\noindent 
Finally (!) run this group file through {\bf nstar}:
 
\centerline{ {\bf nstar n602csb default default default} }
 
\item {\bf Method 2: Using the ``.psg" files}
If you used a goodly number ($>3-5$, say) stars in
making the PSF, then we will simply use these stars as the aperture
correction stars.  Your last {\bf nstar} run should have produced an
``{\bf .nst}" file that contains good photometry for the PSF stars {\it
and} their neighbors. (If you don't remember if you did this, run {\bf
nstar} using the ``{\bf .psg}" as the input group file.)  Note that this
method relies upon the assumption that the sum of the psf radius and psf
fitting radius is about as large as the size of the large aperture you
will use, so that all the important neighbors have been included in the
point-spread-function group, but this is probably a reasonable
assumption.
 
\end{enumerate}
 
Now that we are done with the preliminaries (!!),
we now want to produce two files: one of them containing only the
neighbors that we wish to subtract off, and another containing only the
bright isolated stars which we want to use in computing the aperture
correction.  To do this we will use {\bf group} to divide up the ``{\bf
.nst}" file (we could simply use the editor but that would be a lot of
work).  First we will use {\bf txdump} on the {\bf nstar} file to see the magnitude
range covered by the PSF stars and their neighbors: hopefully there
won't be any overlap.  To do this try
 
\centerline{ {\bf txdump n602csb.nst.3 id,group,mag yes} }
 
\noindent
In the example shown in Fig.~\ref{grouping} we see that the PSF stars
\begin{figure}
\vspace{2.0in}
\caption{\label{grouping} The three PSF stars and their groups.}
\end{figure}
have magnitudes of 13.9, 15.0, and 16.5 in the three groups; all the
neighbor stars are fainter than 17.0.  Thus we can use {\bf select} 
to create a file containing the
photometry of the faint stars:
 
\centerline{ {\bf select n602csb.nst.3 n602csbsub} }
 
\noindent 
and answer {\bf MAG$>$17.0} when you are queried for the ``Boolean
expression".  This will put the photometry of the stars you wish to get
rid of into the file {\bf n602csbsub}.  Next do an 
 
\centerline{ {\bf txdump n602csb.nst.3 xc,yc $>$ n602csbap} }
 
\noindent
and answer {\bf MAG$<$17.0} in response to ``Boolean expression".  This
will put the {\it x} and {\it y} values of the stars we wish to use for
the aperture correction into the file
{\bf n602csbap}.  Next subtract the stars in the first file:
 
\centerline{ {\bf substar n602csb n602csbsub} }
 
\noindent and accept the defaults.  This will result in the subtracted
image {\bf n602csb.sub.N}.  It is this file on which we wish to run
the aperture photometry to determine the aperture correction:
 
\centerline{ 
{\bf phot n602csb.sub.N n602csbap n602csbapresults apertures=3.,15. annulus=20. dannu=5.} }
 
\noindent
You will see something like Fig.~\ref{apcor1} on your terminal.
In this example we've made the assumption that the aperture size that
set your zero-point in making the PSF was 3 pixels (i.e., what you used
with {\bf phot} Way Back When), and that the aperture size used on your
standard stars was 15 pixels.
\begin{figure}
\vspace{3.0in}
\caption{\label{apcor1} The aperture correction run of {\bf phot}.}
\end{figure}
It is time to drag out your hand calculator.  Using all three stars we
find an average aperture correction of $-0.371$ with a standard
deviation of the mean of 0.012 mag; given the large range in magnitude,
I might have been tempted to ignore the two fainter stars and keep the
aperture correction based only upon the brightest star (the frame is
sparsely populated, and there isn't a whole heck of a lot else we can
do).  By an amazing coincidence, the aperture correction based just on
the brightest star is also $-0.371$.
 
 
\subsection{{\bf daophot} summary}
\begin{itemize}
\item Set up {\bf datapars} and {\bf daopars}.
	\begin{enumerate}
	\item Do an {\bf imhead} on some image and note the keywords for the
	filter position, the effective exposure time, and the effective
	airmass.
	\item Use {\bf display} and {\bf imexamine} on a few frames to 
	determine the typical full-width-half-max
	of stars and what would be a good
	value to use for the radius of the psf (i.e., what radius will
	contain the brightest star for which you wish to do photometry.)
        \item Enter these into {\bf daopars} (psfrad) and {\bf datapars}
	(header key words, fwhm).  Also check that the correct values
	are entered in {\bf datapars} for the gain (photons per ADU)
	and read-noise (in electrons), as well as the ``maximum good data
	value".
	\end{enumerate}
\item Find stars.
	\begin {enumerate}
	\item Do an {\bf implot} or {\bf imexamine} to determine the sky
	level on your frame.  Calculate the expected $1\sigma$ error.
	\item Enter the sky value minus 3$\sigma$ as your value for
	{\bf datamin} in {\bf datapars}.
	\item Run {\bf daofind} using as a threshold value 3 to 5 $\sigma$.
	\item Use {\bf tvmark} to mark the stars found ({\bf imagename.coo.1}).
	If you need to, rerun {\bf daofind} with a larger or small
	threshold.
	\end {enumerate}
\item Run aperture photometry using {\bf phot}.  
\item Generate a PSF. Run {\bf psf} and add stars using the ``a" key.  Try
      to select bright, uncrowded stars. Then:
	\begin {enumerate}
	\item Run {\bf nstar} using the file {\bf imagename.psg.1} as the
	``input photometry group" file.  If there are neighbors, be sure
	to decrease the psf radius as explained above.
	Run {\bf substar}  (also using the smaller sized psf radius)
	and display the
	resultant subtracted frame {\bf imagename.sub.1}.  Do the residuals
	of the PSF stars look consistent, or is one of them funny?  If need
	be, start over. 
	\item Remove any neighbor stars by editing the PSF stars out of the
	``.nst"  file, and rerunning {\bf substar}.  Run
	{\bf psf} on the subtracted file, using the normal psf radius again.
	You will have to over-ride the defaults for the input and output file
	names now that you are using the subtracted image.  Rerun {\bf nstar}
	on the original frame using the normal psf radius and the revised
	PSF. Run {\bf substar} and display the results.  Are the PSF stars
	nicely removed, and do the areas around the PSF stars look clean?
	It may be necessary to remove neighbors again using this revised
	PSF.
	\end {enumerate}
\item Run {\bf allstar}.  Display the subtracted frame and see if your stars
	have been nicely subtracted off.
\item Run {\bf daofind} on the subtracted frame, using a value for 
       {\bf threshold} which is another $\sigma$ or two larger than before,
       and a value for {\bf datamin} which is several $\sigma$ lower than
       before.  Use {\bf tvmark} to examine the results, and if need be
       run {\bf tvmark} interactively so that you may add any extra stars.
\item Run aperture photometry using {\bf phot} {\it on the original frame},
      using the new coordinate list produced above.
\item {\bf append} the two aperture photometry files.
\item Run {\bf allstar} using the combine photometry file.
\item Repeat all of the above for each frame in your ``set" (e.g., all short
      and long exposures in each filter of a single field, say.
\item Use {\bf txdump} to select the stars from the allstar files which
      have magnitudes not equal to ``INDEF".  Mark these stars using
      {\bf tvmark}, and then use the capabilities of the image display
      and {\bf tvmark} to match stars consistently from frame to frame.
      Rerun {\bf phot} and {\bf allstar} on the final coordinate lists.
\item Determine the aperture corrections.
\item Transform
	to the standard system (see the next section) and then
      publish the results.
\end{itemize}
\section{Transforming to the Standard System}
 
This section will eventually tell you how to easily and painless obtain
the transformation equations for going from your instrumental magnitudes
to the standard system, and how to apply these transformation equations
to your program fields.  Unfortunately, the IRAF routines for doing this
are still under construction.
In the meanwhile, we are providing here a kludge solution that can be
used by initiates of Stetson's VMS CCDCAL routines.  If you haven't been
made a member of the club yet, and don't feel like waiting until the
IRAF routines are become available before you get results, then I would
recommend getting a hold of the good Dr. Stetson and bribing him until he
offers to send you a copy of CCDCAL.  There is an excellent manual that
comes along with it, and we will not attempt to repeat any of that
material here.
 
\subsection{Standard Star Solution}
First we will describe how to get output good enough to fool
the CCDCAL software into believing the photometry was produced by CCDOBS
(for the standard magnitudes), and what modifications need to be made
to CCDSTD.FOR
 
On the standard file do a {\bf txdump standstuff lid,ifilt,xair,mag,merr
$>$ foolit} to dump the star number, filter number, airmass, and
instrumental magnitudes and errors into the file {\bf foolit}.
Unfortunately, you are now going to have to edit this file and stick in
the star name (in what ever form you have it in creating the library of
standard stars with CCDLIB) in place of the image name and star ID.
(These were simply placed in the file to help guide you).  While you are
at it, line up the filter numbers, airmasses, and magnitudes into nice,
neat columns.  When you get done, stick in a line at the top that gives
the number of instrumental magnitudes and their names, using a
i1,13x,n(6x,a6) format.  For instance, in the case shown here there
are 3 instrumental magnitudes, U, B, and V.  Finally, the filter numbers
have to be edited so they agree with these (e.g., they must denote 
instrumental magnitude 1, 2, and 3...now aren't you sorry you didn't
decide to wait until the IRAF routines were finished?).  In
Fig~\ref{groan} we show an example of the ``before" and ``after" file.
\begin{figure}
\vspace{3.5in}
\caption{\label{groan}The output of {\bf txdump} and the final file
ready for {\bf ccdstd}.  Note the switching of the filter number ``5"
with  ``1".}
\end{figure}
 
CCDOBS.FOR itself now needs to be modified.  Search for line statement
``1120" (which will say JSTAR=JSTAR+1).  Add a line that sets the
integration time to 1 (tint=1.).  Modify the READ statement as shown
in Fig.~\ref{ccdobs}, and finally modify the 213 FORMAT statement
so it actually matches your data file.
\begin{figure}
\vspace{2.5in}
\caption{\label{ccdobs} Modifications to CCDOBS.FOR}
\end{figure}
You should now be able to compile, link, and run this modified
version of CCDOBS and have it work on your standard star data.
 
\subsection{Program Stars}
The work required for faking ``CCDCAL" is actually a lot less. The data
files are easily produced.  Do a
 
\centerline{{\bf txdump n602csu.als.2
id,xc,yc,mag,merr,nit,chi $>$ csu} }
 
\centerline{{\bf txdump n602csb.als.2 id,xc,yc,mag,merr,nit,chi $>$
csb}}
 
\centerline{{\bf txdump n602csv.als.2 id,xc,yc,mag,merr,nit,chi $>$
csv}}
 
\noindent
answering {\bf MAG!=INDEF} to ``boolean expression" each time.  
These three files ({\bf csu}, {\bf csb}, {\bf csv} can be used
with CCDCAL once a single modification is made to CCDCAL.FOR: on
statement number 2020 change the format to ``free format", e.g.,
2020 IF(NL(IOBS).NE.2) READ(2,*,END=2040).  When CCDCAL queries
you for an integration time, be sure to tell it 1.0, as your data have
already been corrected for exposure times. 
 
\section{Acknowledgements}
We are grateful to Jeannette Barnes and Carol Neese for critical
readings of this document, although final blame for style and content
of course rests with the authors.
\end{document}