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MSCGUIDE (Sep98)                 mscred                 MSCGUIDE (Sep98)




            GUIDE TO THE NOAO MOSAIC DATA HANDLING SOFTWARE

                            Francisco Valdes
                             September 1998
                           MSCRED Version 2.0



SECTIONS

1. Introduction
2. Multiextension FITS Files
3. Examining Mosaic Data
    3.1 Displaying the Data
        2.1.1 On-the-Fly (OTF) Calibration
        2.1.2 Real-Time Display with the DCA
    3.2 Examining the Data
    3.3 Examining the Headers
    3.4 Determining Best Focus
4. Data Reductions
    4.1 Some Preliminaries
    4.2 Basic CCD Calibration
        4.2.1  Calibration Data to Obtain At the Telescope
        4.2.2  Preparing Calibration Data
        4.2.3 Pupil Image Removal from Flat Fields
            4.2.3.1 Broadband Data
            4.2.3.2 Narrowband Data
        4.2.4 Object Exposure Reductions
        4.2.5 Pupil Image Removal from Object Data
            4.2.5.1 Broadband Data
            4.2.5.2 Narrowband Data
        4.2.6 Dark Sky or Twilight Sky Flat Fields
        4.2.7 The Variable Pixel Scale and Zero Point Uniformity
    4.3 Coordinate Calibration
        4.3.1 Setting Coordinate Zero Points and Measuring Coordinates
        4.3.2 Matching Coordinate Systems
    4.4 Putting the Pieces Together
        4.4.1 Removing Sky Gradients
        4.4.2 Constructing Single Images
        4.4.3 Matching Intensity Scales
        4.4.4 Making the Final Stack Image



1. INTRODUCTION

This  document  discusses  handling  and  reducing  CCD   mosaic   data, 
particularly  data  from the NOAO CCD Mosaic Imager (referred to here as
the NOAO Mosaic), using IRAF and  the  MSCRED  package.   It  is  not  a
beginner's  guide and assumes some previous experience with IRAF and CCD
reductions.

The first section discusses the mosaic data format and  how  to  use  it
with  IRAF.   This format is more complex than single CCD images because
of the multiple CCDs and possibly multiple amplifiers per CCD.  To  keep
the  data  from each exposure self-contained the multiple CCD images are
stored in a  single  file.   This  multiple  image  per  file  has  many
advantages  but  it does mean that some commands for dealing with images
behave differently.

The second section describes the tools used to examine the mosaic  data.
These tools are used during observing as well as during data reductions.

The  last section describes the reduction of mosaic data.  This includes
basic CCD instrumental calibration and combining mosaic  exposures  into
single images.



2. MULTIEXTENSION FITS FILES

The  data  format  used by the NOAO Mosaic Data Handling Software (MDHS)
is a multiextension FITS (MEF) file.  This format  is  produced  by  the
the  Data  Capture Agent (DCA) when observing with the NOAO Mosaic.  The
MEF file for the NOAO Mosaic currently consists of nine FITS header  and
data  units  (HDU).   The first HDU, called the primary or global header
unit, contains only header information which is common to  all  the  CCD
images.   The  remaining  eight  HDUs,  called  extensions,  contain the
images from the eight CCDs.

The fact  that  the  image  data  is  stored  as  a  FITS  file  is  not
significant.   Starting with IRAF V2.11, FITS files consisting of just a
single primary image may be used in the  same  way  as  any  other  IRAF
image  format.   The  significant  feature  of  the mosaic format is its
multi-image structure.

With multiextension FITS files you  must  either  use  tasks  which  are
specifically  designed to operate on these files as a unit or explicitly
specify the image within the file that is to be operated upon by general
IRAF  image  processing  tasks.   The  tasks  in  the MSCRED package are
designed to operate on the mosaic MEF files and  so  you  only  need  to
specify  the  filename.   For image tasks outside the MSCRED package you
must specify the image in the MEF file using the syntax

    filename[extension]

where "filename" is the name of the  MEF  file.   The  ".fits"  filename
extension  is  optional  provided there is no confusion with other files
with the same basename.   The  image  "extension"  is  specified  either
using  an  extension  name  or the position of the extension in the file
(where the first extension is 1).   The  extension  names  in  the  NOAO
Mosaic  data  are  "im1" through "im8" for the eight CCDs.  For a detail
discussion of the IRAF FITS Image Kernel and the syntax it supports  for
multiextension                FITS               files               see        
      
ftp://iraf.noao.edu/iraf/docs/fits_userguide.ps.Z.

If you forget to specify an  extension  to  a  task  that  expects  only
single  images  you  will get the following error which is your reminder
to include an extension.

    ms> imhead obj012 1
    ERROR: FXF: must specify which FITS extension (obj012)

Two of the most common tasks that require specifying an image  extension
are  DISPLAY  to display a single CCD image (the task MSCDISPLAY is used
to display all the images at once) and IMHEADER to list the header of  a
particular CCD.  So, for example, the following commands might be used.

    ms> display obj012[im2] 1
    ms> imhead obj012[3] l+

Other tasks you may use this way are IMEXAM and IMPLOT.

A  common question is how to specify a list of extensions.  Modification
of  the  syntax  to  allow   wildcard   templates   in   the   extension 
specification   is   under  study.   Currently  you  must  specify  each 
extension explicitly, though the filename itself may be a wildcard;  for
example  the first image in a set of files can be collectively specified
with

    obj*[im1]

There are two methods for specifying some or  all  extensions  in  tasks
that  operate upon lists of images.  One is to make @files.  This can be
done explicitly with an editor.  However  the  PROTO  task  IMEXTENSIONS
can expand MEF files into an @file as in the following example.

    ms> imexten obj012,obj13 > list
    ms> imhead @list

Read  the  help page for further information, additional parameters, and
examples.

Another method is to use the special MSCRED task MSCCMD.  This task  can
be  used  on  the  command  line  or  as  a  simple  interactive command
interpreter.  The idea is that you use the special designations "$input"
and  "$output"  for  task  parameters which allow lists of images.  Then
lists of MEF filenames are specified for the input and output which  are
expanded  and  substituted into the task parameters when it is executed.
For example,

    ms> msccmd "imhead $input l+" input=obj012,obj013

For additional information and examples consult the help page  for  that
task.

Note  that  the  tasks  IMSTAT and IMARITH are so useful and common that
there are specific MSCRED tasks MSCSTAT and  MSCARITH  that  operate  on
all  or  a  subset of image extensions.  So these tasks need not be used
with MSCCMD or with @files.

We conclude with a discussion of  the  special  operations  of  copying,
renaming,  deleting, and reading and writing FITS tapes as they apply to
the mosaic MEF files.  To copy a mosaic file as a unit use COPY,  making
sure  to  explicitly specify the "fits" extension.  If you use IMCOPY it
will expect you to specify a particular extension  and  will  copy  only
that  extension.   While  IMCOPY  is not the way to copy an complete MEF
file the tasks IMRENAME and IMDELETE are the commands for  renaming  and
deleting  these  files; though RENAME and DELETE will also work provided
you are explicit with the extension.  Finally the mosaic data should  be
kept  as  a  MEF  file  and  so  the  special  mosaic tasks MSCWFITS and
MSCRFITS should be used.  The current WFITS and RFITS are  not  intended
for this type of data.



3. EXAMINING MOSAIC DATA

During  observing  a  small  set  of  IRAF commands are commonly used to
examine the data.  This section describes  these  commands.   While  the
discussion  is  oriented  towards  examining  the  data at the telescope
during the course of observing, the tools described here are  also  used
when reducing data at a later time.



3.1 DISPLAYING THE DATA

The  two commands DISPLAY and MSCDISPLAY are used to display the data in
a display server window.  The  display  server  is  a  separate  process
which  must  be  running  before  displaying  the images.  The observing
environment at the telescope will generally  have  the  XIMTOOL  display
server  already  running  with a window on a separate monitor.  If it is
not running for some reason it can be started  with  a  menu  selection.
Away  from  the  telescope you would start XIMTOOL or SAOIMAGE as you do
normally.

The display server must be told what size "frame buffer" to allocate for
holding  the  display  pixels.   This  determines how many pixels may be
loaded at one time.  Note that the display window may  be  smaller  than
this  size  and the display server allows you to move the portion viewed
and zoom/unzoom any region.  If the image size is larger than the  frame
buffer  you can display a portion of the image at full resolution or the
full image at a lower resolution.  The frame buffer size is queried  and
set with the commands:

    ms> show stdimage
    imt4096
    ms> set stdimage=imt2048

There  are  trade-offs  in  the  frame  buffer selection.  A large frame
buffer allows you to have higher resolution for the large mosaic  images
but it uses more memory and takes longer to load.

The  DISPLAY  task  is  used to display individual images in the display
server.  This task is a standard IRAF task about which you  are  assumed
to  have some basic knowledge.  There are many display options which are
discussed in the help page.  The only special factor in using this  task
with  mosaic  data  is  that you must specify which CCD image to display
using the image extension syntax discussed previously.  As  an  example,
to  display  the central portion of extension im3 in the first frame and
the whole image in the second frame:

    ms> display obj123[im3] 1 fill-
    ms> display obj123[im3] 2 fill+

The MSCDISPLAY task is based on DISPLAY with  a  number  of  specialized
enhancements  for displaying mosaic data.  It displays the entire mosaic
observation in a single frame by "filling" each image in a tiled  region
of  the  frame  buffer.   The  default  filling  (defined  by  the order
parameter) subsamples the image by uniform  integer  steps  to  fit  the
tile  and  then  replicates  pixels to scale to the full tile size.  The
resolution is set by  the  frame  buffer  size.   As  mentioned  before,
trying  to  increase  the  resolution  with a larger buffer size has the
penalty of longer display times.  An example display command is:

    ms> mscdisplay obj123 1

The default parameters for MSCDISPLAY are  shown  below.   Many  of  the
parameters  are  the  same  as DISPLAY but there are also a few that are
specific to the task of displaying a mosaic of CCD images  as  indicated
with an asterisk.

                               I R A F  
            Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mscdisplay

    image   =           root name for image to be displayed
    frame   =        1  frame to be written into
*   (mimpars=         ) mosaic image parameters
*   (check  =       no) check if image is loaded
*   (onepass=       no) load all extensions in one pass?
    (bpmask =      BPM) bad pixel mask
    (bpdispl=     none) bad pixel display (none|overlay|interpolate)
    (bpcolor=      red) bad pixel colors
    (overlay=         ) overlay mask
    (ocolors=    green) overlay colors
    (erase  =      yes) erase frame
    (border_=       no) erase unfilled area of window
    (select_=      yes) display frame being loaded
    (repeat =       no) repeat previous display parameters
    (fill   =       no) scale image to fit display window
    (zscale =      yes) display range of greylevels near median
    (contras=     0.25) contrast adjustment for zscale algorithm
    (zrange =      yes) display full image intensity range
    (zmask  =         ) sample mask
*   (zcombin=     auto) Algorithm for combining z1 and z2 values...
    (nsample=     1000) maximum number of sample pixels to use
    (order  =        0) spatial interpolator order (0=replicate,...
    (z1     =       0.) minimum greylevel to be displayed
    (z2     =    1000.) maximum greylevel to be displayed
    (ztrans =   linear) greylevel transformation (linear|log|none|user)
    (lutfile=         ) file containing user defined look up table

The  mapping  of  the  pixel  values  to  grey  levels includes the same
automatic or range scaling algorithms as in DISPLAY.  This is  done  for
each  image in the mosaic separately.  The new parameter "zcombine" then
selects whether to display each image with it's own independent  display
range  ("none")  or  to combine the display ranges into a single display
range based on the minimum and maximum values  ("minmax"),  the  average
of  the minimum and maximum values ("average"), or the median ("median")
of the minimum and maximum values.   The  independent  scaling  is  most
appropriate  for  raw  data  while the "minmax" scaling is recommend for
processed data which are gain  calibrated.   The  special  value  "auto"
(the  default)  checks if the display data has been flat fielded, either
by separate processing or with on-the-fly  calibration,  and  if  so  it
uses "minmax" scaling and if not it used independent scaling.

The   "mimpars"  (mosaic  image  parameters)  parameter  is  actually  a 
reference to another set of parameters.  The default with  no  value  is
to   use   the  parameters  from  the  parameter  task  MIMPARS.   These 
parameters can be examined and set with  EPAR   either  by  typing  ":e"
when  over  this  parameter in MSCDISPLAY or by running EPAR directly on
this task; i.e. epar mimpars.  The parameters for NOAO Mosaic  data  are
shown below.

                           I R A F  
            Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mimpars

    (extname=         ) extension name pattern
    (exttmpl= _![1-9]![1-9]![1-9].*) extension template

    (xgap   =       72) minimum X gap between images
    (ygap   =       36) minimum Y gap between images

    (process=       no) do calibration processing?
    (oversca=      yes) do line-by-line overscan subtraction?
    (flatfie=      yes) do flat field correction?
    (caldir = mscdb$noao/kpno/4meter/caldir/) calibration directory
    (filter =  !filter) filter

The  "extname"  parameter  is  used  to  select  as  subset of the image
extensions to display.   It  is  a  pattern  to  match  extension  image
names.   For  extensions  such  as  im1, im2, etc. the pattern typically
uses the  character  selection  template  such  as  "[1256]"  to  select
anything  with a 1, 2, 5, or 6 in the name.  The pattern matching syntax
can be found in the help for the task MATCH.

The "exttmplt"  parameter  is  for  use  with  non-MEF  data.   The  gap
parameters   define   the  gap  size  in  the  display.   The  remaining 
parameters are for the on-the-fly calibration discussed below.



3.1.1 ON-THE-FLY (OTF) CALIBRATION

Raw mosaic data can exhibit significant instrumental artifacts which may
interfere  with  inspecting  the  data  prior  to  reductions.  The most
significant artifact is gain variations both within each CCD  image  and
between  the  CCDs.   In  the  simplest case of constant gain variations
between the CCDs the independent display scaling, "zcombine" of none  or
auto,  may  be  sufficient.   But  when there are significant flat field
patterns it may be desirable to apply a quick,  approximate  flat  field
calibration as the data are being displayed.

MSCDISPLAY  can  apply  an  on-the-fly  (OTF)  calibration to raw mosaic
exposures.   This  does  not  change  the  actual  data  files  and  the 
calibration  is  intended  to be quick and approximate.  The calibration
steps performed are a line-by-line bias subtraction using  the  overscan
region  of  the  data  and a division by a flat field.  If the data have
been overscan corrected or flat field  corrected  by  CCDPROC  then  the
task  will  automatically  skip  those  steps.  The title of the display
will indicate if the data have been calibrated by  adding  "[bias]"  for
bias  subtraction  and  "[bias,flat=XXX]"  for bias subtraction and flat
fielding using an OTF flat field called XXX.

The bias subtraction is performed by averaging the overscan pixels in  a
line and subtracting this average from all the pixels in the line.  This
removes the amplifier bias and line-by-line patterns.

The flat field or response calibration is performed by  reading  special
compact  flat  field  calibration  data  which  provides  an approximate
relative response for each pixel in each amplifier  readout.   Depending
on  how  the calibration file is derived this will approximately correct
for  pixel  sensitivity  variations,   gain   variations   between   the 
amplifiers,  sky  illumination  variations,  and any pupil ghost pattern
(as  occurs  with  NOAO  Mosaic  data  from  the  Mayall  (KPNO  4meter) 
telescope).

The  "process"  parameter  in  the  MIMPARS  parameter set shown earlier
selects whether to turn on or off the OTF processing.  If it is no  then
regardless  of  the  "overscan"  or  "flatfield"  parameter  settings no
calibration is applied.  If it is  yes  then  one  or  both  calibration
operations  can  be selected.  Because the MIMPARS parameters can be set
on the command line, it is common to leave the "process"  parameter  set
one  way, say to "no", and then override the value when displaying.  For
example,

    ms> mscdisplay obj023 1 proc+
    ms> mscdisplay flat022 2 proc+ flatfield-

The flat field calibration  requires  special  calibration  files.   The
"caldir"  parameter  defines  a  directory  containing  the  calibration 
files.  This can be a standard directory  or  a  user  directory.   Note
that if a directory is specified it must end with $ or /.

Within  the  calibration  directory  the  calibration  file  to apply is
selected  by  the  "filter"  parameter.   For  automatic  selection   of 
calibrations,  the  calibrations can be selected by the filter string in
the header (or  by  giving  the  same  filter  string  in  the  "filter"
parameter).   To  use  the  filter string in the header the value of the
filter parameter is set to "!<keyword>" where <keyword> is  the  keyword
for the filter string.

Creating  the a calibration directory and calibration files is done with
the task MSCOTFFLAT.  For the NOAO Mosaic  a  calibration  directory  is
provided.   However you can create your own as described in the help for
MSCOTFFLAT.  The "filter" parameter can be set to one of these names.



3.1.2 REAL-TIME DISPLAY WITH THE DCA

During data acquisition the MSCDISPLAY  task  can  be  used  to  display
mosaic  data  as  it  is  being  written  to disk by the DCA.  It begins
execution shortly after the readout begins and displays the  portion  of
the  recorded image which has been written to disk.  It then continually
displays new data which has been written by the DCA until  the  exposure
is completely written to the display.

The  DCA  control panel allows you to select whether to display the data
during readout and how it is to be displayed.  This  includes  selecting
the  OTF  calibration.   One  toggle  is  equivalent  to  the  "process" 
parameter.  If  the  processing  is  turned  on  the  DCA  automatically
selects  only  overscan  bias  subtraction  for non-object exposures and
selects both  bias  subtraction  and  flat  field  division  for  object
exposures.   The "filter" parameter is set by passing through the filter
string from the data acquisition system or by overriding this and  using
the filter menu to select one of the available calibrations.



3.2 EXAMINING THE DATA

The  task  MSCEXAMINE  allows  interactive examination of mosaic images.
It is essentially the same as the standard IMEXAMINE  task  except  that
it  translates  the  cursor  position in a tiled mosaic display into the
image coordinates of the appropriate extension image.  Line  and  column
plots  also  piece  together  the  extensions  at the particular line or
column of the mosaic display.  To enter the  task  after  displaying  an
image the command is:

    ms> mscexam

As  with  IMEXAMINE,  one  may  specify  the  mosaic  MEF filename to be
examined and if it is not  currently  displayed  it  will  be  displayed
using the current parameters of MSCDISPLAY.

It  is important to realize that this task shares the MIMPARS parameters
with MSCDISPLAY.  To get data values back that match what  is  displayed
the  parameters  must  agree  with  those  used to display the data.  In
particular, if the data are display with  OTF  processing  then  MSCEXAM
must  be  told  this  either  by  explicitly setting the process flat in
MIMPARS or setting it on the command line,

    ms> mscexam proc+



3.3 EXAMINING THE HEADERS

There was discussion earlier concerning the use of generic  image  tasks
with  the  NOAO  Mosaic  data.  The tasks IMHEADER and HSELECT fall into
this category.  The two important points to keep in mind  are  that  you
must  specify  either  an  extension  name or the extension position and
that the headers of an extension  are  the  combination  of  the  global
header and the extension headers.

Often  one does not need to list all the headers for all the extensions.
The image title and many keywords of interest  are  common  to  all  the
extensions.   Thus  one  of the following commands will be sufficient to
get header information about an exposure or set of exposures:

    ms> imhead obj*[1] l-                       # Title listing
    ms> imhead obj123[1] l+ | page              # Paged long listing
    ms> hselect obj*[1] $I,filter,exptime,obstime yes 

If you need to list header information from all the extensions then  you
need  to  take the additional step of creating an @file or using MSCCMD.
For example to get the default read noise and gain values for each CCD:

    ms> imextensions obj123 > list123
    ms> hselect @list123 $I,rdnoise,gain yes
            or
    ms> msccmd "hselect $input $I,rdnoise,gain yes" input=obj123

The CCDLIST task in the MSCRED package is  specialized  for  the  mosaic
data.   It  provides  a  compact  description  of the name, title, pixel
type, filter, amplifier, and processing flags.  The "extname"  parameter
may  be  used  to select a particular extension, a set of extensions, or
all extensions.  Because all extensions should generally be at the  same
state  of  reduction  it  may  be  desirable  to  list  only  the  first 
extension.  Like most of the CCD reduction tasks  you  can  also  select
only  a certain type of exposure for listing.  Examples of the two modes
are:

    # Summary for all exposures
    ms> ccdlist *.fits extname=im1
    # Summary for all object exposures
    ms> ccdlist *.fits extname=im1 ccdtype=object
    # List of all extensions.
    ms> ccdlist obj123 extname=""



3.4 DETERMINING BEST FOCUS

Focus sequence frames can be evaluated for the best focus using  MSCEXAM
and the 'r' or 'a' keys.  However, there is a special task for measuring
the sequence of focus images called MSCFOCUS.   This  displays  a  focus
exposure  with  MSCDISPLAY  (if  needed) and then lets you select one or
more bright stars to measure.  This task is customized so that  all  you
need  do is mark the top image in any CCD.  For NOAO Mosaic data, header
information tells the task how many exposures, the spacings between  the
exposures,  and  the focus values.  After the measurements are made they
are displayed and analyzed graphically and written to the  terminal  and
logfile.   This task is the mosaic analog of the KPNOFOCUS and STARFOCUS
tasks for single CCD data.



4. DATA REDUCTIONS

The reduction of CCD mosaic data can be divided into  two  stages.   The
first  is  the  basic calibration of the individual CCDs.  This stage is
similar to reducing data from  single  CCD  exposures  except  that  the
calibration operations are repeated for all the CCDs in the mosaic.  The
only significant difference is that any scaling of an exposure, such  as
in  normalizing  the flat field calibration, must be done uniformly over
all the CCDs.  The details of repeating the calibrations  for  all  CCDs
and  the  scaling  of  the  calibration  data  are  taken care of by the
software and the data format so that these operations  appear  the  same
as with single CCD data.

There  are  some  steps  which are not typical for CCD data with smaller
fields of view or specific to the NOAO Mosaic at the  Mayall  telescope.
At  the  Mayall  telescope  there are reflections off the corrector that
produce a  visible  image  of  the  pupil.   Coating  of  the  corrector
minimizes   this   image   but  it  may  be  desirable  to  remove  this 
instrumental signature which would otherwise cause a small variation  of
the  photometric  zero  point  as  well  as an unwanted visible feature.
There are two sections discussing removal of this feature from the  flat
field  data  and  from  the  object exposures.  If your data is from the
KPNO 0.9 meter telescope or the image is faint enough that it is not  of
concern then you can skip the extended discussion.

A  caveat  about  the  pupil  removal  steps described here is that this
document was written prior to the latest removal of  the  corrector  for
better   anti-reflection   coating.   So  the  NOAO  staff  have  little 
experience with these corrections though earlier  work  has  shown  that
these steps will do a good job.

Another step of the basic CCD calibration stage which has generally been
ignored or forgotten with smaller single CCD  formats  is  the  variable
pixel  scale.   The  large  field  of  view provided by a mosaic and the
optics required to provide it can lead to  a  significant  variation  in
the  pixel  scale.   This  effect is important with the Mayall telescope
and is also present in the NOAO 0.9 meter data to a smaller degree.   It
is likely to be present in other telescopes as well.

When  the  pixel  scale  varies  significantly  the  standard flat field
calibration operation will cause the photometric zero point to vary.   A
simple  calibration  step  can  be  performed  to  remove  this  effect. 
However, if you intend to produce single images from the mosaic of  CCDs
this  step  is  not  necessary  since the resampling operation naturally
accounts for this effect.

The second stage of data reductions is  unique  to  mosaic  data.   This
stage  is  the  combining  of  the  multiple  CCD  images  and  multiple 
exposures into a single image.  Since creating a  single  image  from  a
single  mosaic  exposure  is of marginal value, the thrust of this stage
of the reductions is the combining  of  multiple  exposures  which  have
been  spatially  offset or "dithered" to cover both the gaps between the
individual CCDs and any defects.

The steps required to produce a single deep  integration  from  dithered
exposures  consist  of  accurately registering the images, mosaicing the
exposures into single images with the same spatial  sampling,  measuring
changes in the intensity scale due to variations in transparency and sky
brightness, and combining the individual images into a single deep image
with the gaps and bad pixels removed.



4.1 SOME PRELIMINARIES

The  command  SETINSTRUMENT  is  used  to set default parameters for the
tasks in the MSCRED package  appropriate  to  a  particular  instrument.
For  users of the NOAO Mosaic it is recommended you run this command the
first time you reduce data.  Subsequently you should not do  this  since
it will reset parameters you later changed.

To set the parameters for reducing the NOAO Mosaic data type the command

    ms> setinstrument kpno 4meter CCDMosaThin1 review-

Substitute  "36inch"  for "4meter" if the data is from the Kitt Peak 0.9
meter telescope.

For some of the operations it is useful to specify  lists  of  exposures
corresponding  to  a  dither set.  The examples in this guide show using
@files for dither sets.  An @file is simply a list of filenames.   These
can  be  created in several ways including using a text editor.  One way
is with the FILES command to expand a file template.  For example,

    ms> files obj021,obj022,obj023,obj024,obj025 > field1
    ms> dir @field1
    obj021  obj002  obj003  obj004 obj005



4.2 BASIC CCD CALIBRATION

Basic CCD instrumental calibrations consist of correcting each  CCD  for
electronic  bias  levels, zero exposure patterns, dark counts, and pixel
sensitivities.  A  cosmetic  replacement  of  bad  pixels  may  also  be
included.   For  the Mayall telescope the pupil image due to reflections
off the corrector must  be  removed  from  the  flat  field  and  object
exposures.   An  additional  calibration  is required to correct for the
variable pixel scale across the field  of  view  if  you  intend  to  do
photometry on the individual CCD images.



4.2.1  CALIBRATION DATA TO OBTAIN AT THE TELESCOPE

Good  data  reductions begin with obtaining good calibration data at the
telescope.  This section discusses  the  NOAO  Mosaic  but  the  general
principles   will   apply   to  other  detectors,  though  the  relative 
importance of different calibrations will depend on the quality  of  the
CCDs and the stability of the camera.

The  standard  calibration  data  are  sequences  of  zero exposures and
sequences of dome flat field exposures.   While  dark  count  exposures,
matched  to  the  typical  object exposure times, were important for the
first generation  (engineering  grade)  NOAO  Mosaic,  dark  counts  are
expected  to  be  low  in  the science grade detectors.  Thus dark count
exposures are probably not necessary.

Dome flat fields (dome flats) provide a fair  basic  flattening  of  the
data  to  2%  or  so,  but  sky  flat fields (sky flats) are required to
produce dithered data that can be combined without  introducing  obvious
artifacts.   Good  sky  flats  can  flatten  the  data  to 0.1%.  In our
experience twilight exposures do not work well.  Instead dark  sky  flat
fields  are  derived  from  unregisted object exposures taken during the
night or  run.   If  your  observing  program  consists  of  only  large
extended  objects  or  single  pointings  then you should also take some
dithered exposures of "blank" sky.

At the Mayall telescope there is a pupil  image  caused  by  reflections
off  the  corrector.   For broadband photometry the effects of the pupil
image are small but they can be reduced even further by reduction  steps
to  remove  the  image.   One  useful  calibration for this removal is a
narrowband dome flat field.  The idea is that the narrowband flat  field
has  a more prominent pupil image that can be used as a template for the
much fainter broadband pupil image.

Lastly, good astrometry is required to register  and  stack  the  Mosaic
images.   The NOAO Mosaic data contains previously determined astrometry
recorded in the headers of the raw exposures.  This  is  sufficient  for
most  purposes.   However, for cameras without astrometry or to generate
your own astrometry solutions,  fields  with  a  reasonable  density  of
stars  with  cataloged  accurate  coordinates  must be taken.  Note that
with the new generation of large  astrometric  catalogs  and  the  large
field  of  view of a mosaic, it may be that the object exposures already
contain   sufficient   information   for   deriving   new    astrometric  
calibrations  or corrections.  Note that this guide does not yet discuss
how to create the astrometric coordinate system solutions.



4.2.2  PREPARING CALIBRATION DATA

This section describes how to prepare the basic calibration  data.   The
steps  are  virtually  the same as with the CCDRED package and, in fact,
the command names and parameters are the same.   The  basic  calibration
data  of  zero  level,  dark  count,  and dome flat fields are generally
taken as a  sequence  of  identical  exposures  which  are  combined  to
minimize  the  noise.   A  later  section discusses preparing a sky flat
field calibration using the object exposures.

The calibration exposures are individually reduced by CCDPROC  and  then
combined.   Thus,  it  is necessary to first set the CCDPROC parameters.
Because this task knows which operations are appropriate for  particular
types  of  calibration  exposures  you  can  set  all the parameters for
object exposures.  Below is a  typical  set  of  parameters.   The  main
optional   setting   is   whether  or  not  to  replace  bad  pixels  by 
interpolation, which is purely a cosmetic correction.   However,  it  is
recommended  that  this be done to avoid possible arithmetic problems in
the processing.

                             I R A F  
              Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = ccdproc

    images  =             List of Mosaic CCD images to process
    (output =           ) List of output processed images
    (ccdtype=     object) CCD image type to process
    (noproc =         no) List processing steps only?

    (oversca=        yes) Apply overscan strip correction?
    (trim   =        yes) Trim the image?
    (fixpix =        yes) Apply bad pixel mask correction?
    (zerocor=        yes) Apply zero level correction?
    (darkcor=         no) Apply dark count correction?
    (flatcor=        yes) Apply flat field correction?
    (sflatco=         no) Apply sky flat field correction?

    (biassec=   !biassec) Overscan strip image section
    (trimsec=   !trimsec) Trim data section
    (fixfile=        BPM) List of bad pixel masks
    (zero   =       Zero) List of zero level calibration images
    (dark   =       Dark) List of dark count calibration images
    (flat   =      Flat*) List of flat field images
    (sflat  =     Sflat*) List of secondary flat field images
    (minrepl=         1.) Minimum flat field value

    (interac=         no) Fit overscan interactively?
    (functio=   legendre) Fitting function
    (order  =          1) Number of polynomial terms or spline pieces
    (sample =          *) Sample points to fit
    (naverag=          1) Number of sample points to combine
    (niterat=          1) Number of rejection iterations
    (low_rej=         3.) Low sigma rejection factor
    (high_re=         3.) High sigma rejection factor
    (grow   =         0.) Rejection growing radius


The overscan correction has two  methods  as  selected  by  the  fitting
function.   A value of "legendre" (or "chebyshev" or "spline3") take all
the  overscan  data  and  fit  a  smooth  function  along   the   column 
direction.   The  "order"  value of 1 shown above fits a single constant
value.  This leaves to  the  zero  level  calibration  to  subtract  any
details  of  line-by-line  structure.   A  value of "mean", "median", or
"minmax" take the mean,  median,  or  mean  excluding  the  minimum  and
maximum  values,  of  the  overscan at each line and subtract that value
from  that  line.   The  other  fitting  parameters  are  ignored.   The 
advantage   of   this  is  that  systematic  line-by-line  patterns  are 
subtracted.  The disadvantage is, since the sample  of  overscan  pixels
is  small  at  each  line,  that  this  can also introduce a statistical
line-by-line pattern.  There is  currently  no  recommendation  for  the
NOAO Mosaic.

The  first  step  is generally to process and combine sequences of zero,
dark,  and  dome  flat  exposures.   This  is  done  using   the   tasks 
ZEROCOMBINE,  DARKCOMBINE,  and FLATCOMBINE.  The combining must be done
in the following order since the processing of  later  calibration  data
requires the preceding calibration data.

    ms> zerocombine *.fits
    ms> darkcombine *.fits
    ms> flatcombine *.fits

Each  of  these  tasks search all the exposures for a particular type so
it is fine to specify all files, though  if  the  file  names  code  the
type,  such  as  "dflatNNN",  then  one  can use that as the wildcard to
shorten the search of all the data.  Also FLATCOMBINE  has  the  feature
that  it will combine the data separately for each filter.  However, you
can use explicit file lists, templates, or @files  to  limit  the  input
files.   The  output  combined  names have standard default values which
the above settings for CCDPROC use.

It is a good idea to first check that the  different  calibration  types
and  filters  are  correctly  identified  by the software.  This is done
using the CCDLIST command

    ms> ccdlist *.fits

Unless you change the parameters "mscred.backup"  and  "mscred.bkuproot"
the  original  raw  files  will be saved in the subdirectory "Raw/".  If
you want to start over, delete the processed  files  and  copy  the  raw
files  back  to  the  working directory.  If disk space is a concern and
you are satisfied with the combined calibration  files  you  can  delete
the  individual  processed  calibration  files.  There is a parameter in
the combining tasks that will delete the individual files  automatically
after processing and combining.



4.2.3 PUPIL IMAGE REMOVAL FROM FLAT FIELDS

NOAO  Mosaic data taken at the Mayall (4meter) telescope include a pupil
image caused by reflections off the corrector.  The  magnitude  of  this
image  is  a function of the filter and the state of the anti-reflection
coatings on the corrector.  It is also a function of  the  total  light,
including  from  outside the field of view, and somewhat on the location
of bright stars.

It might appear at first that one simply divides the object exposures by
the  flat  field  as  is  done for the OTF display calibration.  However
this is not photometrically  correct  because  the  pupil  image  is  an
additive  light  effect  and not a detector response.  Instead the pupil
image must first be removed from the flat field before  applying  it  to
the  object data.  The object data is then corrected after flat fielding
by subtracting the extra light from the pupil image.

The pupil image is removed  from  the  flat  field  by  dividing  by  an
estimate  of the pupil image pattern.  The challenge is to determine the
pupil image contribution in the presence of other flat field structure.

There are two current approaches to obtaining the  pupil  image  pattern
for  removal  from  the  data.   One  is to use data from another source
where the pupil pattern is more easily separated  from  the  flat  field
pattern.   The  second  is  to derive the pattern from the data assuming
something about the form of the pattern.   In  particular,  to  use  the
difference  in  scales  between the larger pupil pattern and the smaller
flat field pattern.  The first approach is preferable  since  it  better
preserves  fine  structure  in  the pupil image but the second is needed
when no other data is available.



4.2.3.1 BROADBAND DATA

For broadband data the recommended procedure is to obtain  a  narrowband
flat  field  exposure.   This  narrowband  exposure will have a stronger
pupil image relative to the flat field pattern and, when the pupil image
is  scaled down to match the broadband image flat field, the errors from
the flat field response will be diminished.

The pupil image is extracted from the narrowband flat  field  using  the
task  MSCPUPIL.   This  task  determines the background levels in a ring
inside and outside the main pupil image and subtracts this background to
produced  the  pupil  image template.  Outside the outer background ring
the template is set to zero.  In effect this  is  like  "scrapping  off"
the pupil image from the exposure.

The relevant parameters are

                           I R A F  
            Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mscpupil

    input   =           List of input images
    output  =           List of output images
    (masks  =      BPM) List of masks
    (type   =     data) Output type
    (xc     =      27.) Pattern center offset (pixels)
    (yc     =       9.) Pattern center offset (pixels)
    (rin    =     300.) Radius of inner background ring (pixels)
    (drin   =      20.) Width of inner background ring (pixels)
    (rout   =    1500.) Radius of outer background ring (pixels)
    (drout  =      20.) Width of outer background ring (pixels)
    (funcin =chebyshev) Inner azimuthal background fitting function
    (orderin=        2) Inner azimuthal background fitting order
    (funcout=  spline3) Outer azimuthal background fitting function
    (orderou=        2) Outer azimuthal background fitting order
*   (rfuncti=  spline3) Radial profile fitting function
*   (rorder =       40) Radial profile fitting order
*   (abin   =       0.) Azimuthal bin (deg)
*   (astep  =       0.) Azimuthal step (deg)
    (niterat=        3) Number of rejection iterations
    (lreject=       3.) Low rejection rms factor
    (hreject=       3.) High rejection rms factor
    (datamin=    INDEF) Minimum good data value
    (datamax=    INDEF) Maximum good data value
    (verbose=      yes) Print information?

The  output  type  is  set  to  "data"  to extract the pupil image after
background subtraction.  The pattern center parameters are offsets  from
the  astrometric  center and the inner and outer radii are measured from
the pattern center.  The default values are for the last measured Mayall
pupil  image.   The  fitting  parameters marked with an asterisk are not
used when extracting the pupil image directly.

The pupil image template is scaled  and  removed  from  the  flat  field
using  the  task  RMPUPIL.   The  removal  is  done  with the arithmetic
operation

        I(out) = I(in) / (scale * I(template) + 1)

where I(out) are the output corrected pixel values, I(in) are the  input
pixel values, I(template) are the pupil image template pixel values, and
scale is the relative scale factor to be applied.   The  parameters  for
the pupil image removal task are

                       I R A F  
        Image Reduction and Analysis Facility
PACKAGE = mscred
   TASK = rmpupil

input   =           Input mosaic exposure
output  =           Output mosaic exposure
template=           Template mosaic exposure
(type   =    ratio) Type of removal
(extname=   [2367]) Extensions for fit
(blkavg =        8) Block average factor
(fudge  =      1.6) Fudge factor
(interac=      yes) Interactive?
(mscexam=       no) Examine corrections with MSCEXAM?

The  "input"  is the broadband flat field, the "output" is the corrected
flat field, and the "template" is the narrowband pupil image produced by
MSCPUPIL.   The  type of removal for a flat field is "ratio" as given by
the equation above.

Determining the optimal scaling of the template pupil image to the input
pupil  image  is normally done interactively.  The task makes a guess at
scaling.  If this task is used non-interactively this will be the  scale
used.   When  the  task  is  used  interactively the input and corrected
mosaic exposures are displayed and then a  query  for  a  new  scale  is
given.   By  repeatedly  adjusting  the  scale  factor  the  best visual
removal can be obtained.  When done the output corrected flat  field  is
created  using  the  last  specified  scale  factor.   Note that to quit
requires entering dummy special values for the scale  factor.   A  value
of  zero  means  to create the final output exposure with the last scale
factor and a value of -1 means to quit without producing any output.

Because this operation is fairly slow and iterative there are some steps
that  can be taken to it speed up.  The "extname" parameter selects just
those extensions to look at.  For NOAO Mosaic data the  default  selects
the  central  four  extensions covered by the pupil image.  The "blkavg"
parameter applies a block average to the input  exposure  and  template.
This  makes the display and iterative corrections faster.  When the best
scale factor  has  been  determined  the  entire  input  image  at  full
resolution  is  corrected  by the full resolution template to create the
output flat field.  If one wants to use the  facilities  of  MSCEXAM  to
evaluate  each  iterative correction then the "mscexam" parameter can be
set.  However, the most powerful estimate for the optimal  scale  factor
is  viewing  the  display  and possibly blinking between the uncorrected
and corrected frames.



4.2.3.2 NARROWBAND DATA

For narrowband data the pupil image template must be  derived  from  the
data itself.  This is done by fitting the data with an axially symmetric
pattern.  The fitting is performed by MSCPUPIL with the parameters

                           I R A F  
            Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mscpupil

    input   =           List of input images
    output  =           List of output images
    (masks  =      BPM) List of masks
    (type   =    ratio) Output type
    (xc     =      27.) Pattern center offset (pixels)
    (yc     =       9.) Pattern center offset (pixels)
    (rin    =     300.) Radius of inner background ring (pixels)
    (drin   =      20.) Width of inner background ring (pixels)
    (rout   =    1500.) Radius of outer background ring (pixels)
    (drout  =      20.) Width of outer background ring (pixels)
    (funcin =chebyshev) Inner azimuthal background fitting function
    (orderin=        2) Inner azimuthal background fitting order
    (funcout=  spline3) Outer azimuthal background fitting function
    (orderou=        2) Outer azimuthal background fitting order
    (rfuncti=  spline3) Radial profile fitting function
    (rorder =       40) Radial profile fitting order
    (abin   =       0.) Azimuthal bin (deg)
    (astep  =       0.) Azimuthal step (deg)
    (niterat=        3) Number of rejection iterations
    (lreject=       3.) Low rejection rms factor
    (hreject=       3.) High rejection rms factor
    (datamin=    INDEF) Minimum good data value
    (datamax=    INDEF) Maximum good data value
    (verbose=      yes) Print information?

Note that this only differs from  the  previously  shown  parameters  by
setting  the "type" parameter to ratio.  Because the template is derived
from the data itself there is no need  to  use  RMPUPIL  to  iteratively
determine  a scale factor.  The "output" parameter is the corrected flat
field.

The corrected narrowband flat field will show some artifacts  from  fine
structure  in  the  pupil image.  However, a large fraction of the pupil
image will be removed.  Later reduction steps of  applying  a  sky  flat
field  and  combining  with  dithering further eliminate effects of this
approximate solution to the pupil image.



4.2.4 OBJECT EXPOSURE REDUCTIONS

At this point you will have some subset of  combined  zero  level,  dark
count,  and  flat  field  calibration  data.   The  calibration  data is
applied to the object exposures, either in bulk or as  observations  are
completed, using the task CCDPROC.  The command is simply

    ms> ccdproc <files>



4.2.5 PUPIL IMAGE REMOVAL FROM OBJECT DATA

The  pupil  ring image in the object exposures is removed by subtraction
since this is excess light.   Again this is only required for data where
the  pupil  image  occurs, such as from the Mayall telescope.  The tasks
for modeling and removing the image are the same  as  for  removal  from
the flat field except that the "type" parameter is set to "difference".



4.2.5.1 BROADBAND DATA

Probably  the best subtraction will be obtained by using the pupil image
template from a narrowband flat field.  This would be the same  as  used
for  the  flat  field and extracted from the narrowband flat field using
MSCPUPIL with "type = data".   The  subtraction  is  carried  out  using
RMPUPIL with "type = difference".

An  alternative, since the pupil image is weak and the fine structure is
unimportant, is to use MSCPUPIL with "type = difference" to determine  a
smooth  large  scale  ring  pattern  and subtract it from the data.  The
iterative sigma rejection and the "datamin" and "datamax" parameters are
used  to  eliminate smaller scale astronomical objects in the field from
affecting the background fits and  the  ring  profile  fits.   For  this
application  the  "abin"  parameter  should be set to a value such as 30
degrees and the "astep" parameter to a smaller value such as 5 degrees.

The main advantage of this  method  is  that  no  iterative  scaling  is
required  since  the  fit is done directly to the data.  The difficulty,
though, is if  there  is  a  bright  star  or  fairly  extended  object,
particularly  in  the  inner  background ring, then the fit will be poor
and the subtraction will show gross artifacts.

The last alternative, and the one to use if there is no narrowband  flat
field  for  the  template  and  the  field has bright stars which affect
fitting directly to the data, is to make a "sky flat"  to  generate  the
pupil  image  template.   This  is  done as described in the section for
creating a sky flat.  Once the sky flat is created with the pupil  image
then  MSCPUPIL  is  used to separate the pupil image from the background
and RMPUPIL is used to scale and subtract  the  image  from  the  object
exposures.   Note  that  after  the pupil image is subtracted then a new
sky flat should be created.



4.2.5.2 NARROWBAND DATA

For narrowband data the two alternatives  described  for  the  broadband
data  are  used.   The  first is to fit and subtract a smooth ring model
from each object exposure using MSCPUPIL.  This is the same as described
for  removing  the  pupil  image  from  the flat field except the "type"
parameter is set to difference.  The second is  to  create  a  sky  flat
from  disregistered  exposures, extract the pupil pattern with MSCPUPIL,
and then subtract it from each object exposure using RMPUPIL.



4.2.6 DARK SKY OR TWILIGHT SKY FLAT FIELDS

You will notice that there are two flat field corrections which  can  be
performed  by  CCDPROC.  The first one is for an initial flat field such
as the dome flat obtained at the beginning  of  the  night,  a  standard
flat  field  from a previous night or run, or a final combined dome flat
and sky flat from some other night or run.  The second  is  for  a  dark
sky  or twilight sky flat field prepared from the object exposures after
they have been calibrated with the first flat field.

Sky flat fields are created by combining object exposures  with  objects
removed  by using data in each pixel that is only sky.  In principle one
could use exposures of the twilight  sky  but  our  experience  is  that
these  do not work well.  You are welcome to take some exposures and try
using them.  We have found that dark sky flat fields  derived  from  the
object exposures do work quite well.

Mosaic  observations already typically dither a field.  One will do even
better by combining observations from other fields.  The more data  used
the  better  the  resulting  sky  flat  will  be. The main criterion for
including  data  is  to  avoid  observations  contaminated  by   varying 
background  light from the moon or scattered light from bright stars off
the field.  Of course, another factor  that  has  to  be  considered  is
whether  a  field has a very large extended object which appears in many
of the observations.  These will not be useful.

The  sky  flat  field  is  created  using  the  task  SFLATCOMBINE  with 
parameters  selected  to  reject  objects  appearing above a median.  We
don't have much experience with creating sky  flats  currently  so  some
experimentation  with parameters may be required.  Below is one possibly
set of parameters.

                             I R A F  
              Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = sflatcombine

    input   =             List of images to combine
    (output =      Sflat) Output sky flat field root name
    (combine=    average) Type of combine operation
    (reject =  avsigclip) Type of rejection
    (ccdtype=     object) CCD image type to combine
    (subsets=        yes) Combine images by subset parameter?
    (scale  =       mode) Image scaling
    (statsec=           ) Image section for computing statistics
    (nkeep  =          1) Minimum to keep (pos) or maximum to reject (neg)
    (nlow   =          1) minmax: Number of low pixels to reject
    (nhigh  =          1) minmax: Number of high pixels to reject
    (mclip  =        yes) Use median in sigma clipping algorithms?
    (lsigma =         6.) Lower sigma clipping factor
    (hsigma =         3.) Upper sigma clipping factor
    (rdnoise=    rdnoise) ccdclip: CCD readout noise (electrons)
    (gain   =       gain) ccdclip: CCD gain (electrons/DN)
    (snoise =         0.) ccdclip: Sensitivity noise (fraction)
    (pclip  =       -0.5) pclip: Percentile clipping parameter
    (blank  =         1.) Value if there are no pixels
    (grow   =         3.) Radius (pixels) for neighbor rejection

This task is a combination of CCDPROC to first process  the  images,  if
they  have  not  previously  been  processed, and COMBINE to combine the
offset images with rejection of object pixels.  A new  feature  of  this
task  is  the  "grow"  parameter  which  now  provides a two dimensional
circular rejection of pixels around pixels  rejected  by  the  rejection
algorithm.   Whatever  rejection algorithm is used it is likely that the
best results will be when  the  clipping  sigmas  are  non-symmetric  as
shown  above.   Note  that  a very low rejection threshold or very large
grow radius will make the task quite slow.

After producing a good sky flat that has no evidence of objects  it  may
be  applied  directly  to  the data by using it as the second flat field
correction.

    ms> ccdproc <files> sflatcor=yes sflat=Sflat*

Note that the object exposures  used  in  creating  the  sky  flat  will
already  have  been processed except for the application of the sky flat
so CCDPROC will only apply the sky flat field calibration.

The  sky  flat  field  includes   corrections   at   all   scales   from 
pixel-to-pixel   sensitivity  variations  to  large  scale  illumination 
differences.  If the signal-to-noise is poorer than the dome flat  field
you  might wish to apply a filtering/smoothing operation to the sky flat
data thus  relying  on  the  dome  flat  field  for  the  pixel-to-pixel
sensitivity  calibration  and  the  sky  flat  field  for  larger  scale 
illumination corrections.  There are a  number  of  filtering  tasks  in
IRAF.   A  median  is  a  good  filter and there is the choice of a ring
median or box median.  To apply one of  these  general  filtering  tasks
you would use MSCCMD to run it on all the CCDs

    ms> msccmd
    msccmd: median $input $output 10 10
    Input files: SflatV
    Output files: SflatMedV
    msccmd: q

Because  the object exposures are first processed with the dome flat (or
other flat field) you would normally  run  CCDPROC  again  on  the  data
using  the sky flat and any observations that have not been processed at
all will use both the dome flat and the sky flat.  However, if you  want
to  make  a single flat field to apply to raw data, say if starting over
or using it for a second night, you  can  combine  the  two  flat  field
corrections  into  a single flat field to be used as the only flat field
correction.  This is done by  multiplying  the  two  flat  fields  using
MSCARITH

    ms> mscarith FlatV * SflatV FinalflatV



4.2.7 THE VARIABLE PIXEL SCALE AND ZERO POINT UNIFORMITY

A  key assumption in the traditional reduction of CCD images is that the
pixel scale is uniform and that a properly reduced blank sky image  will
have  a uniform and flat appearance.  Unfortunately, this is not correct
when the pixel scale varies over the field.  In the  case  of  the  NOAO
Mosaic  at the Mayall telescope, the pixel scale decreases approximately
quadratically from the field  center,  with  the  pixels  in  the  field
corners  being  6%  smaller  in  the radial direction, and 8% smaller in
area.  Pixels in field corners thus would properly detect  only  92%  of
the  sky  level seen in the field center, even with uniform sensitivity.
At the same time the same number of  TOTAL  photons  would  be  detected
from  a  star regardless of how many pixels the PSF would be distributed
over.  Forcing the sky to be uniform over the image has the  deleterious
effect  of  causing  the  photometric  zeropoint  to vary from center to
field  corners  by  8%.   Note  that  this  effect  is  different   from 
vignetting  where  the  flux  actually delivered to the image margins is
less than that at the center, an effect that IS corrected  by  the  flat
field.

In  practice,  the photometric effect of the variable pixel scale can be
ignored  provided  that  the  reduced  images  will   be   part   of   a 
dither-sequence  to  be  stacked later on.  As discussed below, prior to
stacking the images  they  first  must  be  re-gridded,  which  produces
pixels  of  essentially  constant  angular scale.  This is done with the
MSCIMAGE task, which re-grids the pixels and has a  "flux  conservation"
option  that can scale the pixels photometrically by the associated area
change.  If this  function  is  disabled,  then  "improperly"  flattened
images  will  have  a  uniform  zero point restored.  In short, the flat
field adjusted (if inappropriately) for the different  pixel  sizes,  so
MSCIMAGE  would  then  do  no  further  adjustment.   Stars would be too
bright in the corners of the flattened images,  but  after  re-gridding,
their  total  fluxes  would be seen to be scaled down to the appropriate
values.

If the mosaic CCD images are to be analyzed individually,  as  might  be
done  for standard star fields, then after the flat field reductions are
complete the differential scale effects must be  restored.   At  present
we  are  developing  a routine in the MSCRED package to do this, without
actually re-gridding the image.  The correction process is  simple;  the
scale  at  any  point  in  the  Mosaic  field  is already known from the
astrometry so one just calculates  and  multiplies  by  the  correction.
The  final image would appear to have a variable sky level, but would be
photometrically uniform.



4.3 COORDINATE CALIBRATION

For some projects the basic flux calibrated CCD  exposures  may  be  all
that   is   required.    However,  if  you  want  to  obtain  coordinate 
information or combine multiple exposures which are dithered on the  sky
or  taken with different filters, you must calibrate the celestial world
coordinate system (WCS) of the data.  This may be done  in  an  absolute
or  relative sense; an absolute calibration ties the data coordinates to
catalog  coordinates  while  a  relative   calibration   ties   multiple 
exposures to the same coordinates.

Determining  the WCS from scratch is a complicated business and requires
special observations of astrometry fields.   However,  for  NOAO  Mosaic
data   a   standard   coordinate   calibration   determined  earlier  is 
automatically inserted into your data by the data  capture  agent.   The
default  coordinate  system  is  sufficiently accurate for most purposes
and just requires some small adjustments as described below.   To  piece
a   single   exposure   into  a  single  image  that  does  not  require 
registration to any other data you may use the default WCS and skip  the
WCS calibration steps.

The  WCS  is  a  mapping  from  pixels  in  the mosaic data to celestial
coordinates relative to a reference point on  the  sky.   The  reference
point,  or  zero  point, is set using the telescope pointing coordinate.
The telescope pointing is generally off by a  small  amount,  though  it
could  be  completely  wrong in some hardware/software error situations.
In addition, differential atmospheric refraction introduces  small  axis
scale  changes  and  rotations,  which  are significant due to the large
field of view of the mosaic even during the  course  of  single  set  of
dithered  exposured.   Putting  observations from different filters onto
the same coordinate system also requires mapping  small  scale  changes,
since  currently  there  is  only a single standard WCS solution derived
through one filter.  [In the future filter dependent solutions  will  be
made available.]

The  WCS  calibration  operations  consist  of  adjusting  the  standard 
coordinate system calibration to  a  desired  zero  point  and  applying
small  axis  scale  changes  and  rotations.  This is done using objects
(usually stars) in the exposures.  Unlike a full WCS calibration,  which
requires  a high density of stars with accurate catalog coordinates, the
adjustments to the default WCS calibration require only a  few  objects;
only one objects is needed to provide a zero point correction.

The  WCS adjustments are determined by specifying coordinates for one or
more objects in the data.   The  coordinates  can  be  obtained  from  a
reference  catalog  or, more commonly, by measuring coordinates from one
reference exposure to which other exposures are to be  "registered".   A
combination  of  using  a catalog coordinate for one object in the field
to set the zero point in a reference exposure  and  then  measuring  the
positions  of  other  stars  in  the  reference image based on that zero
point calibration may also be done.

The two tasks you will use are MSCZERO and MSCCMATCH.  MSCZERO  is  used
to  interactively  set  the  zero  point  of  the  coordinates, register
multiple exposures closely, and generate a  list  of  coordinates  in  a
reference  exposure  to  which  other  exposures  in  a  dither  set are
registered.  MSCCMATCH finds objects at the  positions  specified  by  a
list  of coordinates and determines corrections for the zero point, axis
scale change, and axis rotation.



4.3.1 SETTING COORDINATE ZERO POINTS AND MEASURING COORDINATES

MSCZERO is an interactive display task for mosaic exposures that  allows
measuring  coordinates  and  adjusting  the  WCS  zero  point.  The task
parameters are shown below.  The last set of parameters  (starting  with
"ra") are for the task to query and maintain lists.

                             I R A F  
              Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = msczero

    images  =             List of mosaic exposures
    (nframes=          2) Number of frames to use
    (logfile=    default) Log file for measurements

    ra      =             RA (hours)
    dec     =             DEC (degrees)
    update  =        yes  Update WCS zero point?
    (fd1    =           )
    (fd2    =           )

The  task  displays  each exposure in the list, in turn, and responds to
cursor key commands.  You can go forward and backward through the  input
list  or  quit  at  any  point.   The exposures are displayed by cycling
through the specified number of frames starting with  the  first  frame.
As  an  aid  to  efficiency,  if  the  exposure is already loaded in the
appropriate frame then the display step is skipped.

This task has several  uses  (type  '?'  to  get  the  list  of  command
options):

    1. Set the WCS zero point by specifying the coordinate of a star.
    2. Create a list of coordinates for use with MSCCMATCH and MSCIMATCH.
    3. Report coordinates at the cursor position.

It  may  be  that  the  WCS zero points, based on the telescope pointing
coordinates, are accurate enough that you can use this task  on  only  a
reference  exposure  to  generate  a  list  of  coordinates for use with
MSCCMATCH and  MSCIMATCH.   However,  because  it  is  fairly  quick  to
explicitly check and set the zero point of all the exposures in a dither
set  to  the  same  coordinate  for  a  common  reference  star,  it  is 
recommended you do this first.

To  check  and  set  the zero points for a set of dithered exposures run
MSCZERO with a list of the exposures

    ms> msczero @field1

After the first exposure is displayed either find  a  reasonably  bright
unsaturated star which will be in all the exposures or find a star whose
coordinate is known from a catalog such as the HST Guide  Star  Catalog.
Move  the  cursor  to the star and type 'z' (zero) to invoke a centering
algorithm.  Note that even though  the  exposure  may  be  displayed  at
lower  resolution  the  centering is done with the full resolution data.
The task will then tell you what it thinks the  coordinate  is  and  ask
you  for  a  new coordinate.  The first time 'z' is typed it will prompt
with the measured coordinate and thereafter  it  will  prompt  with  the
last  entered  value.   If  you are referencing all the exposures to the
first exposure in the list accept the  measured  coordinate  (and  write
the  value  down  in case you need it later) otherwise enter the desired
coordinate.

Note that all further  measurements  of  the  image  will  automatically
apply  the  measured  zero  point correction but the exposure WCS is not
actually updated until you type 'n' (next) or 'q' (quit).  If  you  want
to  print coordinates without changing the zero point correction use the
space bar or 'c' (center) to center on an object and print the  centered
coordinate.

If  you  changed  the  WCS  zero  point you will be shown the zero point
offsets and given the option to update the WCS in  the  data  file  when
you  type  'n'.   Then  the next exposure in the list will be displayed.
Find the same star and type 'z' again.  Since it will  retain  the  last
entered   coordinate  you  should  only  need  to  accept  the  prompted 
coordinates.  When you have  done  this  for  all  the  exposures  their
coordinate systems will be registered at least at that point.

The  WCS  in  the  dither  set  may still not be registered over all the
field due to refraction effects.   Also  the  intensity  scales  of  the
dithered  exposures  may  not be the same due to changes in transparency
and sky brightness.  These effects are calibrated  by  matching  objects
throughout  the  field in position and brightness.  This requires a list
of coordinates tied to one of the dithered  exposures  as  a  reference.
Usually the first exposure in the set is used as the reference.  MSCZERO
is used to create a list from objects in the reference exposure.

    ms> msczero obj021

Select objects, usually stars, throughout the field  and  type  'x'  for
each  one.  This will center on the object and and record the coordinate
in a logfile.  The default logfile name "default"  creates  a  log  file
beginning  with  "Coords." and followed by the name of the exposure.  In
the example this will be "Coords.obj021".

To be useful for coordinate  matching  this  list  should  have  a  good
number  of  stars, say three or four from each CCD, with emphasis on the
field edges but allowing for the dithering.  For the intensity  matching
you  want to have stars with a range of brightness (though not saturated
or extremely faint) and which are  mostly  isolated  so  that  a  region
around  them  may  be  used  for  sky.  The lists for the coordinate and
intensity matching do not have to be the same but it  is  reasonable  to
just create one list.



4.3.2 MATCHING COORDINATE SYSTEMS

The  task  MSCCMATCH  determines  and applies a linear correction to the
WCS to match objects, generally stars,  in  an  exposure  to  a  set  of
reference   celestial   coordinates.    This  correction  maintains  the 
detector geometry and optical distortions while adjusting for changes in
apparent  sky  position  such  as produced by atmospheric refraction and
telescope pointing errors.  The linear correction  consists  of  a  zero
point  shift, scale changes in the right ascension and declination axes,
and rotations of the axes.

To use this task you need a list  of  reference  celestial  coordinates,
right  ascension  in  hours  and  declination in degrees, and the mosaic
exposure coordinate system must be relatively  close  to  the  reference
coordinate  system.   The  default  WCS  plus  telescope pointing may be
close enough, but if not you would use  MSCZERO  to  register  the  zero
points  at  some  point in the exposures.  Since it is relatively simple
to register a set of dithered exposures to a common  star  with  MSCZERO
this is recommended procedure before using MSCCMATCH.

The  reference  coordinates should cover all of the mosaic field of view
to  be  sensitive  to  the  small  rotation  and  scale  effects.    The 
coordinate  list  might  be obtained from a catalog or measured from one
of the exposures to which other overlapping exposures will  be  matched.
For  the  purposes  of making a well aligned stacked image from a set of
dithered exposures one generally  uses  one  of  the  exposures  as  the
source of the reference coordinates.

MSCCMATCH  operates  on  a  set of input mosaic exposures; each in turn.
For an exposure it converts each input celestial coordinate to  a  pixel
coordinate  in  one  of  the  extensions  using the current WCS.  If the
coordinate does not fall in any extension the coordinate  is  not  used.
The  pixel  coordinate is used as a starting point for the APPHOT.CENTER
task.  If the centering fails for some reason, such as the object  being
too  near  the edge or the final position being too far from the initial
position, the coordinate is not used.  For  those  objects  successfully
found  a  fit is made between the original celestial coordinates and the
measured coordinates expressed as arc seconds from the exposure  tangent
point.   The  fit  is  constrained  to  yield some combination of shift,
scale change, and rotation for each of the  celestial  coordinate  axes.
These  parameters  are  then used to update the exposure WCS so that the
adjusted  measured  coordinates   best   agrees   with   the   reference 
coordinates.

The task parameters are shown below.

                               I R A F  
                Image Reduction and Analysis Facility
    PACKAGE = mscred
        TASK = msccmatch

    input   =               List of input mosaic exposures
    coords  =               Coordinate file (ra/dec)
    (nfit   =            4) Min for fit (>0) or max not found (<=0)
    (rms    =           2.) Maximum fit RMS to accept (arcsec)
    (maxshif=           5.) Maximum centering shift (arcsec)
    (fitgeom=     rxyscale) Fitting geometry
    (update =          yes) Update coordinate systems?
    (interac=          yes) Interactive?
    (fit    =          yes) Interactive fitting?
    (verbose=          yes) Verbose?
    accept  =          yes  Accept solution?

The  input  is  a  list  of  mosaic  exposures  and  a file of reference
celestial coordinates.  The exposures should all include  a  significant
number of objects from the list of coordinates.

The  task  can  be  run  interactively or non-interactively based on the
"interactive"  parameter.   In  interactive  mode  you  can  graphically 
interact  with  the  fitting  (selected  with  the  "fit" parameter) and
accept or reject a  fit  based  on  the  printed  fit  parameters.   The
fitting  is  done  using the task GEOMAP and the interactive mode allows
you to view the distribution of coordinates, residuals verses the  input
coordinates,   delete  bad  values,  and  possibly  change  the  fitting 
constraints (see the help for GEOMAP for more information).

The linear  transformation  may  be  constrained  by  the  "fitgeometry"
parameter  as  described  in the help for GEOMAP.  This may be desirable
if there are only a few coordinates  or  if  you  want  to  impose  some
physical  assumption.   Note  that the effects of atmospheric refraction
actually do cause independent scale changes and  rotations  in  the  two
axes so the default "rxyscale" should be used.

There   are  some  constraints  which  are  placed  on  the  task.   The 
"maxscale" parameter limits how far the objects may be  found  from  the
initial   coordinates.    This  constraint  protects  against  incorrect 
identifications and tells the centering routine how much of the image to
look  at.  This parameter should be as small as possible consistent with
the errors in the WCS.  If you  first  zero  the  coordinates  then  the
objects  should  be  found quite close to the initial coordinates.  When
the "verbose" parameter is set the results  of  the  centering  will  be
printed  consisting  of  the  image  extension  name,  the  final  pixel 
coordinates, the shift in pixel coordinates from the initial value,  and
the  formal  uncertainties in the pixel coordinates.  If an error occurs
one of the error codes from  APPHOT.CENTER  will  be  reported  such  as
"BigShift"  for  objects  with too big a shift from the initial position
and "EdgeImage" for objects to near the edge of the image.

The "nfit" parameter requires a certain  number  of  coordinates  to  be
included  in  the  fit.  If specified as a negative number the parameter
is interpreted as a maximum number that may be lost from the input  list
due  to  being  off  the  exposure or failing to be centered.  The "rms"
parameter requires that the final RMS of the  residuals  about  the  fit
for each axis be less than a certain value.



4.4 PUTTING THE PIECES TOGETHER

This   section   tells   you   how  to  make  single  images  from  each 
multiextension exposure and how to combine sets of dithered images  into
a  final  deep  image  free  from  gaps  and  artifacts.  Obtaining good
results depends on having well-flattened data, a uniform sky,  a  dither
pattern  that  samples  the  gaps  and bad regions of the detectors, and
accurately registered world coordinates.  Most difficulties  are  caused
by  variable  sky conditions or scattered light within a dither sequence
or the data used to create a sky flat.



4.4.1 REMOVING SKY GRADIENTS

Any sky level  mismatches  when  combining  dithered  exposures  produce
artifacts  in the final image.  The three sources of such mismatches are
sky gradients, sky level differences between the  CCDs,  and  sky  level
differences  between  exposures.   While  the  flat  field  calibration, 
particularly with a sky flat, should remove differences  in  sky  levels
between CCDs, in practice there may still be small errors.  And the flat
field will not deal with sky gradients across the large field  of  view.
Exposure-to-exposure  sky  brightness  variations can be dealt with at a
later stage but even this is tricky.

The best final result is obtained by fitting  a  low  order  surface  (a
plane  or quadratic) to the sky and subtracting it from each CCD of each
object exposure at this stage.  This will force the sky to be  zero  for
all  CCDs  and  all exposures.  Note that if one wants to preserve a sky
level for statistical reasons it is possible to add a  uniform  constant
after  the subtraction to all the data (or add the constant to the final
dither stacked image).

To fit and subtract a sky and sky gradient the combination  of  IMSURFIT
and  MSCCMD  is used.  With IMSURFIT use the option to fit to medians in
large blocks to remove the effects of objects.

    ms> msccmd
    msccmd: imsurfit $input $output xo=2 yo=2 type=resid xm=100 ym=100 
    Input files: obj*
    Output files: obj*
    msccmd: q

In this example the  input  and  output  are  the  same,  replacing  the
original  by  the  sky  subtracted  data,  but one can create new output
files if desired.  Note that x and y orders of 2 correspond to  a  plane
and orders of 3 correspond to a quadratic surface.



4.4.2 CONSTRUCTING SINGLE IMAGES

Making  a  single  image  from  a mosaic exposure is done by mapping the
pixels from each extension to a single uniform grid on the sky.  The WCS
calibrations  described in previous sections provide this.  For making a
single image from a single exposure the WCS calibration is not  critical
and  the  default  WCS  is  sufficient.  For combining multiple dithered
exposures all the exposures must be registered to  a  common  coordinate
system, either relative to one reference exposure or to a set of catalog
stars, and each exposure must be resampled to the same final  coordinate
system.

The  task  that  makes  single images from mosaic exposures is MSCIMAGE.
Its parameters are shown below.


                             I R A F  
              Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mscimage

    input   =           List of input mosaic exposures
    output  =           List of output images
    (referen=         ) Reference image
    (pixmask=      yes) Create pixel mask?
    (verbose= )_.verbose) Verbose output?

                        # Resampling parameters
    (blank  =       0.) Blank value
    (interpo=   linear) Interpolant for data
    (minterp=   linear) Interpolant for mask
    (fluxcon=       no) Preserve flux per unit area?
    (ntrim  =        7) Edge trim in each extension
    (nxblock=     2048) X dimension of working block size in pixels
    (nyblock=     1024) Y dimension of working block size in pixels

                                    # Geometric mapping parameters
    (interac=       no) Fit mapping interactively?
    (nx     =       10) Number of x grid points
    (ny     =       20) Number of y grid points
    (fitgeom=  general) Fitting geometry
    (functio=chebyshev) Surface type
    (xxorder=        4) Order of x fit in x
    (xyorder=        4) Order of x fit in y
    (xxterms=     half) X fit cross terms type
    (yxorder=        4) Order of y fit in x
    (yyorder=        4) Order of y fit in y
    (yxterms=     half) Y fit cross terms type

An output image is created for each input mosaic exposure.   The  output
image  is  created  with  a  coordinate  system defined by the specified
"reference" image.  If no reference image is specified  then  the  first
input  mosaic  exposure  is  used  to  define  a  simple  tangent  plane 
coordinate system with optical distortions removed, and that  coordinate
system  is used for all the input mosaic exposures.  The important point
is that for a set of dithered exposures all the output  images  must  be
created  with  the  same  coordinate  system  grid  so  that they may be
combined by simple integer shifts along the image axes.

The normal usage is to specify all the mosaic exposures in a dither  set
as  the  input,  give  a  matching  list of output images, and leave the
reference image unspecified.  If all the exposures in a dither  set  are
not  done  at  the  same  time  then you must specify one of the earlier
output images as the reference image to continue to  create  the  output
images on the same coordinate grid.

The  output  images  are  created with a size that just covers the input
data and initially filled with the specified "blank" value.  This is the
value  that  the  mosaic gaps will have in the final output image.  Then
each extension is resampled into the  appropriate  part  of  the  output
image.   The  coordinate  mapping  is  generated  by  GEOMAP  using  the 
geometric mapping parameters  which  you  don't  need  to  change.   The
resampling  is  done  with  the  specified  interpolation function.  The
small rotations in the CCDs produce edge  effects  in  the  interpolated
output  pieces  so a small trim is required to eliminate these.  [At the
time this document was prepared the  best  value  for  the  new  science
grade NOAO Mosaic had not been determined.]

Linear  interpolation  is  the  fastest and most straightforward.  Other
interpolation   functions   are   available.    In    particular    sinc  
interpolation  is  now  available  as  an  add-on option (see the MSCRED
installation instructions).  Experience with  sinc  interpolation  shows
that   it  is  not  overly  slow  and  does  provide  improved  results; 
particularly with maintaining the  statistical  characteristics  of  the
sky  noise.  The "minterpolant" parameter allows using a faster and more
local interpolation function for the mask.  This is particularly  useful
when  using sinc interpolation of the data to allow flagging only around
the actual bad  pixels  and  not  extending  out  as  far  as  the  sinc
interpolation does.

It  is  useful for the later combining step to make bad pixel masks that
reflect the interpolation and resampling from  the  input  data.   These
may  be  created  by setting the "pixmask" parameter.  If this parameter
is set and the input mosaic data have bad pixel  masks  defined  through
the  header  BPM  keywords  (default bad pixel masks are provided in the
NOAO Mosaic data) then the masks will be  interpolated  in  exactly  the
same  way  as  the  data.   The  interpolated  masks  will appear in the
working directory with names related to the output image names and  with
the  output  images  containing the BPM keyword pointing to these masks.
The input bad pixel masks are assumed to have zero  for  good  data  and
one  for  bad  data  and  the  output  masks have zero for good data and
values between zero and ten thousand for bad data.   The  value  is  the
result  of  interpolation and reflects the relative contribution of good
and bad data.

The  "fluxconserve"  parameter  applies  a  pixel  area  correction   if 
selected.   As  discussed  earlier,  standard flat fielding distorts the
flux per unit area in pixels of different projected size by making  them
have  the  same flux per pixel.  In effect this applies half of the flux
conservation operation by adjusting the pixel values  without  adjusting
the  pixel  sizes.  MSCIMAGE does the second half by adjusting the pixel
sizes.  So for standard flat fielded data, the usual route to  making  a
combined  dithered  image, the flux conservation parameter should not be
used to arrive at a proper final flux per unit  area  in  the  resampled
data.   Flux  conservation  would  only be used if the input mosaic data
has previously been corrected back to proper flux per unit area  through
adjustment  of  the  flat  field  or  data  for  the variable pixel size
inherent in the mosaic coordinate system.

Below are two examples; one using prepared @files and  one  illustrating
advanced usage of filename templates.

    ms> mscimage @dither1 @outdither1 pixmask+
    ms> mscimage obj02![2-5]* %obj%mos%02![2-5]* pixmask+

In  the  second  example  the  input  template expands to obj022.fits to
obj025.fits and the output template matches the input template using the
first part of the %% substitution field and then replaces the "obj" with
"mos" to give output images mos022.fits to mos025.fits.



4.4.3 MATCHING INTENSITY SCALES

When stacking dithered exposures  (the  single  images  created  in  the
previous  step)  to  fill  in  the mosaic gaps and remove bad pixels and
cosmic ray events it is  critical  that  the  intensity  scales  of  the
images  match.   Otherwise  you will see artifacts from the gaps, places
with bad data, and around objects as the combined intensity level  jumps
when  data  from an exposure is missing or rejected.  Also the rejection
algorithms require that the image intensities  match  both  at  the  sky
level and in the objects.

There  are two parameters that must be determined to match the intensity
scales.  One is a additive offset caused by sky  brightness  variations.
The  second  is a multiplicative scale change caused by transparency and
exposure time variations.  Matching the intensity scales for  a  set  of
dithered  exposures consists of determining values for these two scaling
parameters relative to a reference exposure  and  setting  them  in  the
image  headers.   The actual adjustment of the pixels values occurs when
stacking the exposures.

The intensity matching values are  determined  by  the  task  MSCIMATCH.
The task parameters are shown below.


                           I R A F  
            Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mscimatch

    input   =           List of images
    coords  =           File of coordinates
    (scale  =      yes) Determine scale?
    (zero   =       no) Determine zero offset?
    (box1   =       21) Inner box size for statistics
    (box2   =       51) Outer box size for statistics
    (lower  =       1.) Lower limit for good data
    (upper  =    INDEF) Upper limit for good data
    (niterat=        3) Number of sigma clipping iterations
    (sigma  =       3.) Sigma clipping factor
    (interac=       no) Interactive?
    (verbose=      yes) Verbose?

The  input  is  a  list  of images to be matched and a file of celestial
coordinates (RA in hours and DEC in degrees) to  use  in  computing  the
matching parameters.  The input images are the single images constructed
from the mosaic exposures for a set of dithered observations.

The parameters "scale"  and  "zero"  select  whether  to  determine  the
multiplicative  scale,  the zero level offsets, or both.  If the sky has
been subtracted at an earlier  stage  (as  recommended)  then  only  the
multiplicative  scale  difference needs to be determined.  The advantage
of subtracting the sky  earlier  is  that  scale  determination  becomes
better  constrained.   Also determining the sky from photometry (as done
by this task) is less robust than the surface fitting which uses all  of
the sky data.

The  scaling  parameters  are determined by measuring the mean flux in a
set of matching regions between each input image.  The  centers  of  the
regions  are  specified  by  their  celestial  coordinates.  The list of
coordinates should consist of the positions of  objects  in  the  field.
These  objects  should span a range of brightness.  As noted previously,
you would normally use the same coordinate list as used with  MSCCMATCH,
which  is  generally  obtained  using MSCZERO.  However, you can use any
IRAF task that produces a list  of  celestial  coordinates  from  images
with  a  WCS.   One  possibility  is  to  use  RIMCURSOR  on  one of the
displayed single images with the "wcs" parameter set to "world" and  the
"wxformat"  set  to  "%.2H"  to  produce right ascension values in hours
instead of degrees.

The now accurately aligned coordinate systems in the images are used  to
identify  the  matching  pixel  coordinate  center  in  each image.  The
regions to be measured consist of square boxes of  the  specified  sizes
about  the  pixel  coordinate center.  There are two boxes, an inner box
and an outer box which excludes  the  inner  box.   The  box  sizes  are
intended  to  define  photometry  apertures  for  the objects and nearby
background.  It is not critical that they exactly  fit  the  objects  or
that  the objects necessarily be stars but this is usually how they will
be set.  Because of possible PSF variations  the  inner  box  should  be
large enough include all the light from stars over the whole data set.

If  the inner box is not fully contained in the input or reference image
that box is not used for that pair.  Similarly the  outer  box  must  be
fully  contained  in the images but if only the outer box is outside one
or both images the measurement for the inner box may still be used.

In order to exclude regions that include the gaps or bad data in one  or
both  of the pair of images all pixels in a box must have values between
the specified good data limits.  Those regions with values  outside  the
limits are eliminated from the intensity matching.

The  mean  fluxes  in  each  region  are  used to simultaneously fit the
relations

    mean_j = A_ij + B_ij * mean_i

for all i and j where i and j are any pair of images.   These  equations
are  constrained  by  the  fact  that  the  scaling  from  image i to j,
followed by the scaling from image j to k, must agree with  the  scaling
from  image  i  to image k.  The final scaling coefficients reported and
stored in the image header are A_1j and B_1j, which  correspond  to  the
scalings to the first image in the input list.

The  task will attempt to reject photometry points which are discrepant.
If the task is  run  interactively  it  will  also  show  plots  of  the
photometry  flux  in  one  image  verses  another.   It  does  this  for 
sequential pairs of images.  Points can be deleted in  these  plots  and
they  will  be  excluded  from  the  data  used to determine the scaling
parameters.

When the task is done determining  the  scaling  factors  they  will  be
printed  and  a  prompt  issued to accept or not accept the results.  If
the scaling parameters  are  accepted  then  the  keywords  MSCZERO  and
MSCSCALE  are  recorded  in  the  input  image  header when the "update"
parameter is set.  Note that the reference image is assigned  values  of
0 and 1 for these header keywords.



4.4.4 MAKING THE FINAL STACK IMAGE

After  MSCIMAGE  produces  single  images of each of the dithered mosaic
exposures with a common coordinate system grid, a final image is created
with  the  task MSCSTACK.  The task MSCIMATCH is generally used to match
the intensity scales of the images before this step as described in  the
previous  section.   However,  for quick reductions or for other reasons
the images may be stacked either with no  intensity  matching  or  using
the  "scale"  and  "zero"  options of MSCSTACK.  The task parameters are
shown below.

                             I R A F  
              Image Reduction and Analysis Facility
    PACKAGE = mscred
       TASK = mscstack

    input   =             List of images to combine
    output  =             Output image
    (plfile =           ) List of output pixel list files (optional)

    (combine=     median) Type of combine operation (median|average)
    (reject =       none) Type of rejection
    (masktyp=       none) Mask type
    (maskval=         0.) Mask value
    (blank  =         0.) Value if there are no pixels

    (scale  =  !mscscale) Image scaling
    (zero   =   !msczero) Image zero point offset
    (weight =       none) Image weights
    (statsec=           ) Image section for computing statistics

    (lthresh=         1.) Lower threshold
    (hthresh=      INDEF) Upper threshold
    (nlow   =          1) minmax: Number of low pixels to reject
    (nhigh  =          1) minmax: Number of high pixels to reject
    (nkeep  =          1) Minimum to keep (pos) or maximum to reject (neg)
    (mclip  =        yes) Use median in sigma clipping algorithms?
    (lsigma =         3.) Lower sigma clipping factor
    (hsigma =         3.) Upper sigma clipping factor
    (rdnoise=         0.) ccdclip: CCD readout noise (electrons)
    (gain   =         1.) ccdclip: CCD gain (electrons/DN)
    (snoise =         0.) ccdclip: Sensitivity noise (fraction)
    (sigscal=        0.1) Tolerance for sigma clipping scaling corrections
    (pclip  =       -0.5) pclip: Percentile clipping parameter
    (grow   =          0) Radius (pixels) for 1D neighbor rejection

This task is a simple variant  of  COMBINE  that  registers  the  images
using  the  coordinate  systems and has the default threshold parameters
set to ignore values below one DN based on the default "blank" value  in
MSCIMAGE  for  the gaps.  If you have also generated bad pixel masks for
the resampled images you can exclude them as well by setting  "masktype"
to "goodvalue".

The  real art in using this task is deciding how to scale and reject bad
data not covered by the bad pixel masks.  A  "combine"  of  "median"  is
the  simplest  but  it  does  not  optimize  the signal-to-noise for the
number of images.  If you "average" the data you will probably  want  to
apply a rejection algorithm such as "avsigclip".

Careful  flat  fielding  will make each separate image have the same sky
level  across  the  different  CCDs.   However,  the  sky   levels   and 
transparency  may  still  be  varying from exposure to exposure.  If you
simply combine such data you will see imprints of the gaps.   So  it  is
generally  a  good  idea  to  scale  the images.  This is done using the
"scale" and "zero" parameters which can be set to header keyword values,
files  containing  the  values,  or  special  values  to  compute  image 
statistics in a particular region of the data.  The  recommended  method
for  scaling  is  to use the intensity matching task MSCIMATCH described
in the previous section and use the image header keywords  MSCSCALE  and
MSCZERO produced by that task.

An example of using this task to create a final image is given below.

    ms> mscstack @field1 Field1 combine=average rej=avsigclip


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