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\begin{document}
\title{IDL and DAOPHOT \\ CCD Version }
\author{W.B. Landsman \\ ST Systems Co.}
\date{9 May 1996}
\maketitle
\section{INTRODUCTION}
This document describes an implementation of an early (1984) version of
the DAOPHOT point-source
photometry algorithm into IDL.  Extensive discussions of DAOPHOT are given   
by Peter Stetson both in his April, 1987 P.A.S.P article, as well as in 
the DAOPHOT user's
manual.
This document will
concentrate on the features of the IDL code that differ from standard
DAOPHOT.   

It should be emphasized that the creators of DAOPHOT have no responsibility
whatsoever for the IDL code.  If you want to use ``true'' DAOPHOT, then use
the FORTRAN version.

We have converted the DAOPHOT algorithms into IDL for two main reasons.
\begin{itemize}
\item The IDL version of DAOPHOT can easily be integrated with the IDL 
TV display and plotting package.  The IDL-DAOPHOT procedures can be 
interrupted at any time to print or plot any variable.
In addition, the use of FITS tables allows 
easy transport of the results to other systems. 

\item The IDL-DAOPHOT code can be easily modified or cannibalized 
for other uses.  For example, the Ultraviolet Imaging Telescope (UIT) group 
has modified the IDL code for use with digitized photographic images. 
The procedures MMM and APER have been adapted for use with extended-source 
photometry.  The procedure GETPSF has been used to supply a point
spread function for deconvolution algorithms.    
\end{itemize}

It should also be emphasized that the IDL code was adapted from an early
version of DAOPHOT, and does not include the following recent improvements
to the DAOPHOT code:

\begin{itemize}
\item FIND will ignore bad pixels when convolving the image with
           a Gaussian PSF. 

\item GETPSF will weight stars by their magnitude before combining
           them to create a final PSF.
      
\item A magnitude dependent fitting radius is used in GROUP, allowing
           stars to be broken up into smaller groups.

\item The most recent versions of DAOPHOT allow a spatially dependent
           PSF.

\item The functions of GROUP and NSTAR have been combined into a single
routine named ALLSTAR.  This presumably speeds up the NSTAR calculation
by reevaluating group membership during NSTAR iterations.

\item The early version of DAOPHOT (and the IDL code) could only represent
the PSF as a Gaussian plus residuals.    More recent versions of DAOPHOT
allow the use of other functions besides a Gaussian.

\end{itemize}

There are 4 ways to obtain the output to the IDL-DAOPHOT procedures.  All
the procedures will display their results at the terminal.    The keyword
/PRINT can be set to also write these results to a file with a default name
(e.g.\ aper.prt), or one can set PRINT = `filename' to specify the name of
the output file. 
By supplying sufficient parameters to a procedure, one can
also store the results in IDL output variables.  Finally, a set of IDL
driver procedures exist, beginning with ``T\_'', which perform I/O to FITS 
tables.  For example, the procedure T\_FIND performs the same results as
FIND, but writes the results to a disk FITS ASCII table.     This file can
be read with any FITS table reader, such as the MRDFITS() function in IDL.
  
A typical DAOPHOT sequence would be to run procedures in the following
order.
\begin{description}
\item[SKY] Determine overall sky background for the image.  This value is
needed to help determine a threshold for FIND.
\item[FIND] Find the positive brightness perturbations (i.e.\ stars) that
meet specified sharpness, roundness, and centroid criteria.
\item[APER] Obtain integrated fluxes within circular apertures for source
positions obtained by FIND.  A sky value for each source is also determined,
using pixels within an annulus of specified inner and outer radii.  This
is the only place in the DAOPHOT sequence where sky values are
determined for individual stars.
\end{description}
APER will give correct results, of course, only when the PSF of individual
stars do not overlap.
\begin{description}
\item[GETPSF]  Obtain a point-spread function (PSF) from one or the sum of
several isolated stars.   The PSF is parameterized as a 2-dimensional
gaussian (integrated over each pixel) and a lookup table of residuals.
If desired, the PSF disk file created by GETPSF can be read using the
procedure RDPSF.
\item[GROUP]  Place stars with non overlapping point-spread functions
into distinct groups.
\item[NSTAR]  Simultaneous point-spread function fitting of all stars 
within each group.   In a sense, the purpose of all the previous 
procedures is to obtain the initial conditions to the NSTAR least-squares
fit.   NSTAR will eliminate stars found by FIND that are too faint, or
that merge with other stars.  However, NSTAR cannot add any stars that
were not found by FIND
\item[SUBSTAR]  Take a set of star positions and magnitudes, (usually from
NSTAR), scale and shift the PSF according to each position and magnitude,
and subtract it from the original image.  The subtracted image can be
used to determine the accuracy of the NSTAR fits, or to search for faint
stars that were missed by FIND (e.g.\ because they were hidden in the wings
of a much brighter star.)  In principle, one could run FIND on the subtracted
image, to obtain additional source positions.
\end{description}
\section{Specific Procedures}
This section briefly describes the use of the IDL-DAOPHOT procedures.
The calling sequence is displayed for both the FITS table, as well as
the direct procedure call.  
Optional parameters are placed within square brackets.  
More detailed information on each procedure can be found in the 
documentation header for the individual procedures.   
For many procedures one can set /DEBUG to print out more diagnostics during
execution.

The first step is to read an image and header (e.g.\ with READFITS)
into IDL variables, which we shall call here IMAGE and IMG\_HDR.  
(An image header is needed only for the FITS table calling sequence.)
\subsection{SKY}
{\tt SKY,IMAGE,[SKYMODE,SKYSIG]} \\

Obtains the overall skylevel of an image by applying the procedure MMM
to approximately 4000 uniformly spaced pixels.  MMM (Mean, Median, Mode)
is sophisticated sky background algorithm that assumes that the sky 
contamination (i.e.\ stars) gives predominantly {\em positive} deviations
from the true value.
The only need for the sky intensity in subsequent 
procedures is to 
determine the threshold detection limit in FIND.
\subsection{FIND}
{\tt FIND,IMAGE,[X,Y,FLUX,SHARP,ROUND,HMIN,FWHM, ROUNDLIM, SHARPLIM]} \\
{\tt T\_FIND,IMAGE,IMG\_HDR, FITSFILE}  \\ 
   
FIND will output the X and Y centroids, an appoximate flux (in magnitudes
relative to the threshold intensity)
and the sharpness and roundness index, for all local enhancements meeting
the threshold, sharpness, roundness, and centroid criteria.  Default
sharpness (0.2-1.0) and roundness (-1.0 - 1.0) limits are used if not
supplied.  FIND will print the number of sources rejected by each criterion,
to help determine whether the supplied parameters are appropiate. 
Note that the FIND algorithm is not a good one for identifying galaxies
or HII regions, since non-stellar objects are discriminated against in the
search.
           
FIND requires the user to supply an
approximate FWHM (in pixel units, not necessarily integral) for the image,
and an intensity threshold,
HMIN, above background.  Appendix II of the DAOPHOT manual describes
how to choose the intensity threshold to obtain a desired significance
level (e.g.\ 3.5 sigma) for the sources detected by FIND.
One is required to know the readout noise, RONOIS, and photons per
analog digital unit PHPADU for the CCD (needed for computing Poisson
statistics).  For a single (not coadded) image 
the threshold is determined as follows.
\begin{enumerate}
\item The random noise per pixel is computed from the sky level (found by
SKY) and the readout noise.
\begin{center}
random noise = {\tt SQRT(PHPADU$\ast$SKYMODE + RONOIS$^2$)}
\end{center}
\item After a FWHM (in pixels) 
has been supplied, FIND will print a value called the
``Relative Error''.  This is simply a scaling factor to convert the standard
error of one pixel, to that for detecting a point source.  For example,
the relative error = 1.06 and 0.79, respectively, for FWHM of 2.0 and 6.0
pixels
\item The 1 sigma random noise should be multiplied by the ``Relative error''.
This value should then be mulitiplied by the desired detection significance
(i.e. multiply by 3 for 3-sigma detection significance.)    
\end{enumerate}

The Gaussian convolution in FIND cancels out any large-scale variations
in the sky brightness.  However, FIND does not identify any variation 
in the {\em errors} (or fluctuations) in the sky brightness across an image.   
In this latter case, the detection significance of a supplied threshold 
may vary across the image.

FIND requires a large amount of virtual memory to perform the convolution.
This is because the Gaussian convolution requires REAL*4 data for both
input and output (even if your image array is INTEGER*2).  
\subsection{APER}
{\tt APER,IMAGE,X,Y,MAG,ERRAP,SKY,SKYERR,[PHPADU,APR,SKYRAD,BADPIX, /FLUX]} \\
{\tt T\_APER,IMAGE,FITSFILE,[APR,SKYRAD,BADPIX]} \\

APER performs circular aperture photometry, linearly weighting pixels
that are partially wihin the aperture radius.
The user must supply a set of aperture radii, an inner and
outer sky radius, and low and high bad pixel values.   
For each position (X,Y) found by FIND, APER will determine a sky value
and uncertainty, and the sky-corrected magnitude and uncertainty 
within each aperture.   Relative magnitudes are computed from the aperture flux,
FLUX in data units 
\begin{center}
{\tt MAG = 25 - 2.5$\ast$ALOG10(FLUX)} 
\end{center}
so that an aperture flux of 1 data unit is assigned a magnitude of 25.
If the /FLUX keyword is set, then APER will not convert to magnitudes.

APER will not compute a flux if one of the 
following conditions holds:
\begin{itemize}
\item The aperture exceeds the edge of the image
\item A sky value could not be determined (e.g. if MMM requires too many
      iterations), or the sky exceeds the gross intensity within the 
      aperture
\item At least one pixel within, or partially within, the aperture radius
      is ``bad''.                              
\end{itemize}

If a flux could not be computed, the star is assigned either a flux
of -100. or a magnitude of 99.9.
Although APER will output results in either flux units or magnitudes,
the subsequent procedures GETPSF and NSTAR will require their input in
magnitudes.
\subsection{GETPSF}                         
\begin{tabbing}
GETPSF,IMAGE, \=   \kill
{\tt GETPSF,IMAGE,X,Y,MAG,SKY,} \\
\>  {\tt  [RONOIS,PHPADU,GAUSS,PSF,IDPSF,PSFRAD,FITRAD,PSFNAME]} \\
{\tt T\_GETPSF,IMAGE, FITSFILE,[IDPSF,PSFRAD,FITRAD,PSFNAME]} \\
\end{tabbing}
                                                      
GETPSF requires the positions (X,Y) found by FIND, and the magnitude,
MAG and sky values, SKY, found by APER.  The PSF determined by GETPSF
is represented by a 5 element vector GAUSS, containing the best-fit
bivariate gaussian parameters, and by a lookup array of residuals.
The user must supply the index numbers of the stars to be used to create
the PSF.   Ideally, the PSF stars should be isolated, free of bad pixels, 
and free of any saturated pixels.
GETPSF will also store the PSF as an STSDAS (modified FITS) disk image.
(In order to view the PSF, one must recombine the residuals with the Gaussian;
this can be done with the procedure RDPSF.)

\subsection{GROUP}
{\tt GROUP,XC,YC,RMAX,NGROUP} \\
{\tt T\_GROUP, FITSFILE,RMAX}     \\
                          
GROUP will assign a group number to each star with position (XC,YC).
The user must supply a value of RMAX, the radius at which two stars
are considered to be just overlapping.  Stetson suggests setting RMAX
equal to the radius of the brightest star {\em plus} the fitting radius
to be used in NSTAR.  The idea is that the pixels used to fit the PSF
to a star will only be contaminated by stars with the same group number.

The IDL code for GROUP is extremely elegant (only 7 lines long!)  However,
it is approximately half as fast as the equivalent FORTRAN.

\subsection{NSTAR}
\begin{tabbing}
NSTAR,IMAGE \= \kill
{\tt NSTAR,IMAGE,ID,X,Y,MAG,SKY,GROUP,} \\
\>    {\tt  [PHPADU,RONOIS,PSFNAME,MAGERR,ITER,CHISQ,PEAK, /VARSKY]} \\
{\tt T\_NSTAR,IMAGE, FITSFILE,[PSFNAME,GROUPSEL, /VARSKY]} \\
\end{tabbing}

NSTAR will simultaneously fit the PSF to all stars within a given group.
Three parameters are determined for each star - the (X,Y) position, and
the magnitude, MAG.  As initial conditions to the least-squares fit, NSTAR
requires the (X,Y) positions obtained from FIND, and the magnitudes, MAG
obtained from APER.   The sky values obtained from APER are taken as fixed
parameters.  Other required inputs are the GROUP vector created by GROUP,
and the name of the PSF file created by GETPSF.   

The DAOPHOT user's manual describes the moderately sophisticated star-rejection
algorithm used by NSTAR.   Basically, a star is rejected if (1) it merges
with a brighter star, (2)  it is more than 12.5 magnitudes fainter than
the PSF star, or (3) its brightness  is less than the 2-sigma noise level.
Upon output, the vector ID will contain the ID numbers of the stars that
were {\em not} rejected.

NSTAR has three output vectors that describe the quality of the fit.
CHISQ gives the chi-square of the fit for each star per degree of freedom,
and should be close to 1, {\em if  proper values of the readout noise
and photon per analog digital unit were supplied}.  
PEAK (called SHARP by Stetson) determines
whether the star is broader or narrow than the PSF.  Isolated stars should
have PEAK approximately equal to zero, while extended sources (galaxies,
unresolved binaries) will have PEAK greater than zero.  Finally, NITER
gives the number of iterations required for the fit.  If NITER = 50, then
the least-squares solution did not converge for at least one star in the
group.

NSTAR is the most CPU-intensive step in the DAOPHOT sequence and should
usually be done in batch.  The CPU time required depends exponentially
(I would guess) on the size of the group.   
The T\_NSTAR call allows one to select specific
groups to process through the vector GROUPSEL.  
\subsection{SUBSTAR}
{\tt SUBSTAR,IMAGE,X,Y,MAG,[ID,PSFNAME]}  \\
{\tt T\_SUBSTAR,IMAGE, FITSFILE,[ID, PSFNAME, /VERBOSE]} \\

SUBSTAR will subtract the PSF, scaled to each star's magnitude, MAG, 
from positions specified by the vectors (X,Y).  Note that IMAGE
will be modified to contain the star-subtracted image, so be sure to 
have a duplicate copy if the original is needed.
If desired, then only a subset of stars, specified by the ID vector,
will be subtracted.
                   
\end{document}                                        
