USNO  A1.0 November 1996
USNO SA1.0 December 1996

This is READ.AST, the file with the discussion of the astrometric calibration
of USNO-A.  Please refer to READ.ME for an introduction to the catalog.


   The astrometric calibration of USNO-A is based on the Space Telescope
   Science Institute's Guide Star Catalog version 1.1, hereinafter GSC.
   This is a temporary calibration, and it will be replaced with a
   calibration to the European Space Agency's Hipparcos and Tycho catalogs
   as soon as they become available (current estimate is June 1997).
   We believe that a typical astrometric error is about 0.25 arcseconds,
   but for stars a few magnitudes brighter than the plate limit and away
   from the corners, the error may be as small as 0.15 arcseconds.
   Coordinates are computed in the system of J2000 at the epoch of the
   survey blue plate.  Proper motions were neither computed for nor
   applied to the coordinates in this catalog.

   Whenever possible, we have adopted Pat Wallace's SLALIB for computing
   quantities associated with position and angle.  Details about these
   routines and permission to use them should be obtained from the
   author at

Source Code:

     binary/acrs - projection of ACRS to survey plate coordinates
     binary/ppm  -    "       "  PPM  "    "     "       "   "
     binary/gscgen -  "       "  GSC  "    "     "       "   "
     newbin/tychogen  "       "  Tycho Input Catalog "  " "  " "
     binary/gsctaff -  Taff-o-grams for various surveys
     binary/autogo - fit POSS-I O to projected GSC
     binary/autoge -  "  POSS-I E "   "   "     "
     binary/autogb -  "  SRC-J    "   "   "     "
     binary/autogr -  "  ESO-R    "   "   "     "
     catalog.tar - electronic version of the various plate logs
     binary/ugapX - the various routines that make the catalog


     Using the reference catalog (GSC1.1) and the information contained
     in the plate log ( and in catalog.tar), SLALIB
     is used to compute the observed place for each catalog star.
     The PMM coordinates are corrected for the nominal cubic distortion
     of the Schmidt telescope (using SLALIB's SLA_PCD, etc.) and
     compared to the projected catalog.  A best fit using up to cubic
     terms is computed and the residuals are saved.  After doing this for
     a significant number of plates, the residuals are binned according
     to their location on the plate, and an approximation for the
     systematic field distortion of the Schmidt telescope is determined.
     (These are called Taff-o-grams in the code in recognition of Larry
     Taff's demonstration of their significance.)  The fitting procedure
     is repeated, this time including the systematic field distortion
     map, and this fit is adopted for the generation of the catalog.

The Individual Plate Solutions:

     For a particular field, the plate log was consulted to get the
     various parameters (date, time, emulsion, etc.) for the plate.
     Unfortunately, there were a substantial number of typographical
     errors in the original versions of these logs, and every effort
     has been made to track down these errors and correct them.  We
     believe that the versions contained in this CD-ROM set are more
     accurate than the ones we started with, and all of the errors
     that we could fix have been fixed.  With the exposure data,
     SLALIB is used to compute the best estimator of where the stars
     should be found.  In order, we used SLA_MAPQK, SLA_AOPQK, and
     SLA_DS2TP to go from catalog to apparent to observed to tangent
     plane coordinates.

     The PMM produces coordinates for each detection in integer hundredths
     of a micron on its focal plane.  Actually, there is a systematic problem
     in the introduction of temperature and pressure into the PMM logic,
     and its version of a micron can be off by as much as one part in
     10^5, but they are sufficiently close to microns for this discussion.
     The coordinates have had the individual platen zero points subtracted,
     and the nominal center of each plate appears at approximately (170,175)
     millimeters.  SLALIB provides a utility for removing the nominal
     pin cushion distortion of a Schmidt telescope, and this correction
     is applied to the raw PMM coordinates.

     With the exception of systematic astrometric errors in the Schmidt
     telescope, the projected catalog and undistorted PMM coordinates
     ought to agree with each other.  The mapping is done using cubic
     polynomials in X and Y, although linear terms are sufficient except
     when doing the full-plate solution.  No sub-plate solutions are used:
     a single fit in X and Y is used to describe the whole plate.  These
     solutions are saved as are the residuals computed for each match between
     the PMM and the reference catalog, and this process is repeated for
     every survey plate.

     When many solutions are available, the residuals are combined
     according to the position of the object on the plate by the
     code in binary/gsctaff.  For USNO-A, a mean distortion pattern
     was computed for each of the three Schmidt telescopes involved.
     However, it is clear from examination of subsets of the data that
     there are significant differences in the shapes of the distortion pattern
     as a function of zenith distance (actually declination but most survey
     plates were taken near enough to the meridian).  In future releases,
     we intend to use zonal versions of this correction.  The residuals
     are binned in a 32x32 grid, and a 2-dimensional smoothing spline is
     used to expand this to a 65x65 grid.  This corresponds to boxes
     about 5 millimeters in size on the plate.

     With the systematic correction determined, the astrometric solution
     is repeated using the same catalog projection but adding the systematic
     correction removal to the pin cushion distortion removal in the
     pre-processing of PMM coordinates before fitting.  Again, a single
     cubic fit in each coordinate is used to describe the entire plate.

Assembling the Catalog:

     Two separate astrometric fits go into each field.  First, the red
     plate is mapped on to the blue plate, and then the blue plate is
     mapped on to the reference catalog.  The code is complicated only
     because of the large number of detections in each field, and the
     importance of applying each fit in the proper order.  This process
     is done in binary/ugap012, and extra software is inserted to verify
     that each step worked properly.  The output of ugap012 is a set of
     rings on the sky that follow from the surveys being taken in rings
     of declination.  Because of the relatively slow response of our
     CD-ROM jukebox that stores the raw catalogs, it takes about a week
     to do this phase of the preparation of USNO-A.

     The rings of various declinations are merged into zones of constant
     width by the code in binary/ugap3.  The zones are examined for
     duplicate detections by the code in binary/ugap4.  This program
     makes a list of all entries to be removed (the TAGs) and saves
     multiple observations of the same object in the sameXXXX.dat file
     for the photometric calibration.  The important routine in ugap4
     is nodup.f which finds the multiple detections.  For USNO-A, the
     radius was taken to be 1 arcsecond.  In the polar regions, the
     xynodup.f routine is used and the double detections are removed in
     coordinates on the tangent plane, and a radius of 15 microns was used.
     Finally, the code in binary/ugap5 removes the TAGged entries and
     produces the final catalog.  This catalog incorporates the astrometric
     calibration, but not the photometric calibration.  Routines to
     check each step appear in binary/ugap3x, binary/ugap4x, and
     binary/ugap5x.  A powerful debugging tool is plotting the entire
     sky because the eye is very sensitive to systematic errors at plate
     boundaries, etc.

     Finally, the code in binary/ugap7 applies the photometric calibration,
     and the code in binary/ugap8 projects the catalog in Galactic
     coordinates.  The partition of the catalog files on the various
     CD-ROMs is done in binary/ugap6.