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READ.PHT - PMM Photometry for the USNO-A Catalogs

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


   The photometric calibration of USNO-A1.0 is about as poor as one can
   have and still claim that the magnitudes mean something.  The calibration
   process is dominated by the lack of public domain photometric databases.
   In particular, this calibration was done without the final Hipparcos
   and Tycho catalogs, and without the Guide Star Photometric Catalog II.
   We have done the best job we could with the available data, and will
   recalibrate the catalog when significant databases become available.
   We believe that the internal magnitude estimators for stars are probably
   accurate to something like 0.15 magnitudes over the range of 12th to 19th,
   but that the systematic error arising from the plate-to-plate differences
   is at least 0.25 magnitudes in the North and perhaps as large as
   0.5 magnitudes in the South.  Users who are able to locally recalibrate
   USNO-A photometry are encouraged to do so since that will remove the
   systematic errors and leave only the measuring error.

Source Code:

   Useful places to look for pieces of the calibration are the following:

       newbin/piphot - generation of the USNO CCD parallax program magnitudes
       newbin/reversion - mapping the parallax program to individual plates
       newbin/bc1 - mostly obsolete with the exception of generating a
                    couple of input files for bc2
       newbin/bc2 - calibration of the northern sky
       newbin/bc3 - calibration of the southern sky
       binary/ugap4 - find multiple detections of the same object
       binary/ugap7 - apply the calibration to the raw catalog


   The calibration of USNO-A is divided into the calibration of the northern
   sky and then the calibration of the southern sky.  In each case, the
   first step was to compute the plate-to-plate offsets and convert the
   magnitudes from a specific plate into a system that was valid for all
   plates (called the meta-magnitude system).  The second step was to
   compute the transformation from the meta-magnitude system to pseudo-
   photographic magnitudes computed from CCD photometry and the Tycho
   Input Catalog.

The Northern Calibration:

   Removal of the plate-to-plate differences begins with examination
   of the list of all objects found by the code in ugap4 to be multiple
   detections of the same object.  For details, refer to the code, but it
   is sufficient to summarize this process as finding all objects that
   fall within a 1-arcsecond radius of another object.  All objects
   inside this radius were considered to be the same object, and the code
   in ugap4 selects one for the catalog and saves all objects in the
   SAMExxxx.dat file.  Code in bc1 looks at the SAMExxxx.dat files and
   computes the list of plates that overlap other plates and makes
   intermediate files of all stars that overlap a specific plate.
   Code in bc2 (parfit.f) then iterates a solution that starts at a zero
   offset (constant) or a zero offset and unit slope (linear) for each
   plate and computes the best fit for that plate to all of its neighbors.
   At the end of each iteration, all solutions are updated before the
   start of the next iteration.  Typically, the solution is very close
   to the final value after about 5 iterations, but it was allowed to
   run for 17 iterations so that a stable solution was found for all plates.

   The original plan was to allow a linear solution for each plate, but
   after the difficulties encountered in the Southern solution, the solution
   was done allowing only a constant term.  Visual examination of the
   calibration showed that both were essentially similar, so the constant
   one was selected.  The plate-to-plate solutions are found in bc2/calcoef.XX
   files, where XX is the iteration number.  Removal of the plate-to-plate
   offset before application of a transformation between internal and
   external magnitude systems was far more stable than doing the solution
   after such a transformation.  The internal magnitude systems for
   each plate are surprisingly similar.

   Because of the lack of a suitable calibration database, we decided to
   use the B and V magnitudes from the Tycho Input Catalog to calibrate
   the bright end, and to use the V and I CCD photometry done at USNO on
   parallax fields for the faint end.  Henden supplied tables for computing
   the color corrections which he derived from numerical integrations of
   spectrophotometric data and filter response curves.  For Tycho data,
   only stars with B and V were accepted, and the Henden relationships
   were used to compute O(B,V), E(B,V), J(B,V), and F(B,V).  Examination
   of the residuals to the photometric solution indicate that there
   are significant color terms remaining: the O/J solutions show less
   dispersion than the E/F solutions.  To mitigate this problem, Tycho
   stars with B-V less than 0.5 or greater than 1.2 were ignored in the
   final solution.

   The USNO photometric database was complete for V and I, but many stars
   did not have B data.  Because of this, we decided to ignore the B
   data when available, and to base the calibration on the V and I data
   alone.  Dahn supplied a relationship between V-R and V-I, and a crude
   calibration of B-V as a function of V-R was used.  These and the Henden
   tables can be found in newbin/piphot in the various .tbl files.
   Again, this calibration procedure left significant color terms.  The
   E/F calibration shows less dispersion than the O/J calibration.

   With the ensemble of pseudo-photographic magnitudes for standard stars,
   the relationship between the meta-magnitude and the standard magnitude
   system was done by newbin/tcapply.  The algorithm attempts to find a
   ridge line between the two systems, and then to fit a smoothing spline
   to it.  This solution is provided to the user (newbin/bc2/tcnodes.?)
   who can examine, correct, and extrapolate it as appropriate.  These
   new nodes (newbin/bc2/tcedit.?) are then fit with the smoothing spline
   and the final lookup tables (newbin/bc2/tclut.?) are produced.  Although
   the blue and red solutions are done by the same code, they are completely
   independent of each other.

   It is possible for the PMM to produce magnitudes that don't make sense.
   In particular, the total flux can be zero or negative should the estimator
   of local sky contain some sort of contamination.  These fluxes are
   mapped into 50.0 for the case of zero flux, and 50.1 through 75.0 for
   the case of negative flux.  In the latter case, the flux is negated before
   taking the logarithm and 50 is added to the result.  These magnitudes
   are ignored during the calibration process and passed directly from
   the PMM to the final catalog.  At best, they serve as flags that something
   was wrong with a particular image.

The Southern Calibration:

   The first step of the southern calibration is the same as that for the
   northern calibration, the removal of the plate-to-plate offsets.
   This is done in newbin/bc3/parfit and makes files soucoef.XX in a
   manner very similar to the northern solution.  However, the first
   solution that allows a constant and slope for each plate was seen
   to quadratically grow for the red (F) solution but not the blue (J)
   solution.  This was traced to a small but significant correlation between
   limiting magnitude and declination which drove the numerical instability.
   Solving for only a plate-to-plate offset showed the same instability.
   Therefore, an extra routine (newbin/bc3/damper.f) was inserted to
   remove this term after each iteration.  The blue solution with and
   without this term was examined and found to be essentially the same,
   so we have some confidence that the red solution is reasonable, too.
   The source of this correlation is unknown, and should disappear with
   the inclusion of more calibration data.

   The calibration of the meta-magnitude system in the southern solution
   was made more difficult because there are no USNO parallax fields
   south of -20.  Instead, a boundary condition that the southern and
   northern solutions should agree in the -30 degree zone was used.
   The list of same stars found by binary/ugap4 was used to identify those
   objects with northern and southern magnitudes, and the calibrated
   northern magnitudes were combined with the Tycho Input Catalog pseudo-
   J and F magnitudes to provide the calibrators for the southern
   meta-magnitude system.  Because of all of the difficulties associated
   with the apparently incomplete removal of color terms based on broad
   band photometric indices, the decision was made to ignore differences
   between J and O, and F and E.  This is a crude approximation, but one
   that was forced by the lack of appropriate calibration databases.
   As with the north, the calibration of the meta-magnitude system starts
   with nodes computed from a ridge line, and ends with a lookup table
   computed from nodes supplied by the user.  The code is in newbin/bc3
   and is nsapply.f, nsnodes.?, nsedit.?, and nslut.? in a manner similar
   to the northern solution.

Other Matters:

   The Schmidt telescope vignetting function was ignored.  Indeed, there
   are three such functions, but the lack of a suitable calibration database
   makes it almost impossible to solve for these functions from PMM data.
   The choice of zero vignetting function follows from Henden's analysis
   of the UJ1.0 data in which he could not independently verify the
   Palomar Schmidt vignetting function adopted by the Guide Star Catalog.
   Henden's analysis showed only a marginally significant function, and
   it was substantially smaller than that developed for the GSC.

   The northern calibration must be done first because of the reliance
   of the southern calibration on it.  Both are then copied to binary/ugap7
   where they are applied to the uncalibrated catalog and same files.
   Various other programs verified that the calibration was applied

   The distinction between galaxy magnitudes and stellar magnitudes was
   ignored.  This followed from the lack of star/galaxy separation
   information for POSS-I plates.  The reductions being developed for
   USNO-B include star/galaxy separation, but they rely on the improved
   signal to noise ratio offered by the fine grain emulsions.

   Future releases of USNO-A will incorporate improved photometric
   calibration algorithms.  The release of the Tycho catalog in 1997
   will offer a dramatic improvement in the calibration of the bright
   end of the catalog as well as the transition from saturation
   around 12th magnitude.  The release of GSPC-II will provide an important
   calibration database for the intermediate stars, especially in the south,
   but more work is needed to extend the calibration to 20th magnitude
   and beyond.
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