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README.V20 - README File for the USNO-A2 Catalogs

***Really Important Stuff***

This file is the first level of documentation for the USNO-A2.0
catalog. It discusses the changes between USNO-A2.0 and USNO-A1.0, and
familiarity with USNO-A1.0 is presumed. Should this not be the case,
please start by reading the A1.0 documentation (README.V10 and
associated files) before continuing with this file. Questions and
comments should be directed to

    Dave Monet
    US Naval Observatory Flagstaff Station
    10391 West Naval Observatory Road
    Flagstaff AZ 86001 USA
    Voice: 928-779-5132
    FAX: 928-774-3626

Please understand that the level of support provided will be
commensurate with the level of effort expended. I am too busy to do
your homework for you. E-mail works better than the phone.

If you have been using USNO-A1.0, all you really need to do is
swap the new versions of the .ACC and .CAT files for the old ones. If
you insist on understanding what has changed, you can read the rest of
the documentation, but the new version is intended to be as compatible
as possible with the old one.

***The Rest Of The Stuff***

                  A Catalog of Astrometric Standards

                            David Monet a)
           Alan Bird a), Blaise Canzian a), Conard Dahn a),
 Harry Guetter a), Hugh Harris a), Arne Henden b), Stephen Levine a),
  Chris Luginbuhl a), Alice K. B. Monet a), Albert Rhodes a), Betty
Riepe a), Steve Sell a), Ron Stone a), Fred Vrba a), Richard Walker a)

a) U.S. Naval Observatory Flagstaff Station (USNOFS)
b) Universities Space Research Association (USRA) stationed at USNOFS.

============== Abstract =======================

USNO-A2.0 is a catalog of 526,280,881 stars, and is based on a
re-reduction of the Precision Measuring Machine (PMM) scans that were
the basis for the USNO-A1.0 catalog. The major difference between A2.0
and A1.0 is that A1.0 used the Guide Star Catalog (Lasker et al. 1986)
as its reference frame whereas A2.0 uses the ICRF as realized by the
USNO ACT catalog (Urban et al. 1997).

A2.0 presents right ascension and declination (J2000, epoch of the
mean of the blue and red plate) and the blue and red magnitude for
each star. Usage of the ACT catalog as well as usage of new
astrometric and photometric reduction algorithms should provide
improved astrometry (mostly in the reduction of systematic errors) and
improved photometry (because the brightest stars on each plate had B
and V magnitudes measured by the Tycho experiment on the Hipparcos
satellite). The basic format of the catalog and its compilation is the
same as for A1.0, and most users should be able to migrate to this
newer version with minimal effort.

This file contains a discussion of the differences between A1.0 and
A2.0, and those points not discussed remain unchanged. For
convenience, the documents circulated with the A1.0 catalog are
included in this distribution.

================= Discussion =========================


USNO-A2.0 has adopted the ICRS as its reference frame, and uses the
ACT catalog (Urban et al. 1997) for its astrometric reference
catalog. The Hipparcos satellite established the ICRS at optical
wavelengths, but stars in the Hipparcos catalog are saturated on deep
Schmidt survey plates as are the brighter Tycho catalog
stars. Fortunately, the fainter Tycho stars have measurable images, so
each survey plate can be directly tied to the ICRS without an
intermediate astrometric reference frame. The proper motions contained
in the ACT catalog are more accurate than those in the Tycho catalog,
so the ACT was adopted as the reference catalog. USNO-A1.0 use the
Guide Star Catalog v1.1 as its astrometric reference catalog, and the
availability of the ACT was the driving force behind the compilation
of USNO-A2.0.


USNO-A2.0 continues the policy established for USNO-A1.0 of not
assigning an arbitrary name to each object. Without explicit star
names, the IAU recommendation is to use the coordinates for the
name. Since USNO-A2.0 contains a complete astrometric rereduction, the
coordinates of objects are not the same, so the names for USNO-A1.0
stars are NOT PRESERVED in USNO-A2.0. If you need a name for a star,
you can use either the coordinates or the zone and offset so long as
you are careful to cite USNO-A2.0 as the source.

(If anybody has a clever solution to the problem of star names that
does not waste lots of space or CPU cycles, please let me know.)


The Tycho catalog provides B and V magnitudes for its
stars. USNO-A2.0 uses these and Henden's photometric conversion tables
between (B,V) and (O+E+J+F) to set the bright end of the photometric
calibration for each plate. This is an improvement over USNO-A1.0.

Unfortunately, GSPC-II and other large catalogs of faint
photometric standards are not available, so the faint end of the
photometric calibration came from the USNO CCD parallax fields in the
North, and from the Yale Southern Proper Motion CCD calibration fields
(van Altena et al. 1998) for fields near the South Galactic
pole. Hence, the faint photometric calibration of USNO-A2.0 may not be
any better than for USNO-A1.0. Sorry. When better sources of faint
photometric calibration data become available, new versions of USNO-A
will be compiled.

A new algorithm for doing computing the photometric calibration.

a) Since there are 300 or more ACT(==Tycho) stars on each plate,
the computed J+F+O+E magnitude for each star can be computed from
B+V. Given the relatively poor nature of this conversion, subtleties
of the various photometric systems were ignored. Please remember that
all Tycho stars are toasted on deep Schmidt plates, and we were lucky
that PMM could compute decent positions and brightnesses for any of
them. Four solutions were done (O+E+J+F) which fit an offset for each
plate and a common slope for all plates. For example, there were 825
free parameters in the solution for the 824 POSS-I O plates, 824
offsets and 1 slope. This solution isn't quite as good as fitting
individual slopes for "good" plates, but is much more stable than
fitting individual slopes for "bad" plates.

b) There are 215 POSS fields and 42 SERC/ESO fields with faint
faint photometric standards. Again, the ensemble of plates was divided
into 4 solutions (O+E+J+F), and the fit allowed an offset for each
plate but a common value for the linear and the quadratic term. For
example, there were 217 free parameters in the POSS-I O plate
solution, 215 offsets, 1 slope, and 1 quadratic term. Again, this
offers stability at the expense of accuracy on the "good" plates.

c) A number of iterative solutions for using the calibrated plates
to calibrate the rest were tried, and most failed. Finally, a stable
solution was found. For each of the 4 sets of plates, the faint zero
points were fit as a function of the bright zero points. Using this
relationship, the faint zero points for all plates were computed. (We
chose to use the fit instead of the individual solutions for those
plates which had the faint photometric standards.) Note that this
relationship provided the fifth (and final) parameter for the
photometric calibration (i. e., bright offset, bright slope, faint
offset, faint slope, faint quadratic).

Once the coefficients were known for all plates, the overlap zones
on adjacent plates were used to smooth the solution over the whole
sky. In an iterative scheme, the faint mean error for each plate was
computed from all stars in common with other plates, and then the
faint offset was adjusted after all the mean errors were
computed. This algorithm converged in 3 or 4 iterations, and makes the
plate-to-plate photometry as uniform as possible given the paucity of
faint standards.

d) No vignetting function was used.


A startling result of the comparison between PMM and ACT is that
decent astrometry can be done on stars as bright as about 11th
magnitude. Visually, these images have spikes and ghosts, and are not
the sort of images commonly associated with the word
"astrometry". Since there are 300 or more ACT stars on a single
Schmidt plate, each plate can be tied directly to the reference
catalog without an intermediate coordinate system. This solution
includes corrections for systematic errors in the focal plane and for
magnitude equation, and these are discussed below. It should be
emphasized that the raw measures are the same for USNO-A2.0 and
USNO-A1.0, and the difference is in how these are combined to produce
the coordinates found in the catalog.

a) Schmidt telescopes have field-dependent astrometric errors, and
these must be sensed and removed. Because there are hundreds of
reference stars on each plate, the algorithm used was as follows. Data
from the exposure log are used to do the transformation from mean to
apparent to observed to tangent plane coordinates using the relevant
routines from Pat Wallace's SLALIB package. The first set of solutions
finds the best cubic solution between the PMM measures (corrected for
the known Schmidt telescope pin cushion distortion) and the predicted
positions. Once an ensemble of these solutions have been done, the
residuals are accumulated in 5mm by by 5mm boxes of position on the
plate. By combining the residuals from hundreds of plates, the
systematic pattern can be determined with good precision. The second
step is to repeat the cubic fit between predicted and observed
positions after correcting the observed positions using the pattern
determined in the first step. Examination of the systematic pattern
produced by the second step indicated that there was a small residual
pattern that arose from the interdependence of the fixed pattern and
the cubic polynomial fit. A third iteration was done, and the
resulting systematic pattern was consistent with random noise.

The iterative process of determining the systematic pattern of
astrometric distortions was done separately for each telescope in each
color, and intermediate solutions based on zones of declination were
examined for the effects of gravitational deflection. None were found,
so the final patterns were determined through the co-addition of all
plates taken by a particular telescope in a particular color. Hence,
USNO-A2.0 uses 4 specific patterns instead of the single mean pattern
used for USNO-A1.0.

b) Inspection of the astrometric residuals from high declination
fields (where the overlop between plates is large) showed that there
was a significant radial pattern. This, and the analysis of the
residuals from the UJ reductions for the USNO-B catalog, suggested
that magnitude equation was present. This is hardly a surprise because
the images of Tycho stars show spikes, ghosts, and other problems
whereas the faint stars show relatively clean images. The effect is
small to non-existent within a radius of ~2.2 degrees of the center,
and then rises to 1.0 arcsecond at ~3.0 degrees and continues to rise
into the corners. The effect is more or less the same for the POSS-I
O, POSS-I E, and SERC-J plates, but a different behavior was seen for
the ESO-R plates. The source of this different behavior is not
understood, and may indicate a software problem associated with the
different size of the ESO plates (300x300 mm vs 14x14 in).

The analysis of the UJ plates (like POSS-II J except with a 3
minute exposure) shows a similar behavior when the Tycho stars are
subdivided into bins of <9, 9, 10, 11, and 12 magnitude. Since the
nominal difference between UJ and POSS-I is something like 4
magnitudes, the effect was assumed to be zero for stars fainter than
15 and rises linearly until it becomes the same for all stars brighter
than 11. This is an empirical correction, and more work needs to be
done to verify its behavior.


The most common mode for the PMM to mis-measure a plate is that it
does not determine the distance between the camera and the plate
accurately. The PMM starts by using the granularity of the emulsion as
a signal for setting the focus (i.e., minimum background smoothness),
and then does 15 exposures separated by 0.5 millimeters to compute the
actual pixels per millimeter. In many cases, this algorithm is not
sufficient, and the raw scans have relatively large astrometric
errors, and show a sawtooth pattern in the residuals.

Since PMM saves many more data than are contained in this catalog,
it is possible to refocus the plate after the scan. To do this, the
known positions of the ACT stars are fit as a function of the new Z
distance between the camera and the plate. Minimization of these
residuals indicates what the proper focus should have been, and then
the entire set of raw measures are corrected for this effect. In
general, this processed tightens the histogram of the number of plates
as a function of the astrometric error. The good scans are unaffected
but the bad scans get better. This algorithm has been applied to all
plates used in USNO-A2.0.


In USNO-A1.0, the coordinates were computed from the positions
measured on the blue plate (O or J), so they were J2000 at the epoch
of the blue plate. For USNO-A2.0, we believe that the uncertainties in
the positions are no longer dominated by systematic errors, so it
makes sense to average the blue and red positions. Hence, USNO-A2.0
coordinates are J2000 at the epoch of the mean of the blue and red
exposure. For POSS-I plates, this difference is trivial because the
plates were taken on the same night. For SERC-J and ESO-R, there can
be a significant epoch difference between the blue and red plate, and
stars with small proper motions will be affected. Note that stars with
large proper motions will be selectively deleted from the SERC-J+ESO-R
portion of the sky because they will fail the test of blue and red
positions within a 2 arcsec radius, and that this omission depends on
the epoch difference of the plates for the individual fields.


We have done our best to remove multiple entries of the same star,
but they still remain. The improved astrometric reduction decreased
the number of stars in the catalog by about 0.8% (about 4 million
stars), but this reduction is masked by the increase in the number of
stars associated with moving the north/south transition from about -33
degrees to about -17.5 degrees. In the north/south overlap zone,
double entries are generated for stars with large proper motions since
if they were detected in each survey separately but moved far enough
to escape the double detection removal algorithm. There shouldn't be
too many of these, but they may be obvious because they are
statistically brighter than the typical catalog entry.


Images for stars brighter than about 11th magnitude are so
difficult to measure that their computed positions may differ with the
correct position by more than the 2 arcsecond coincidence radius used
in the reductions. For really bright stars, all that appears are an
ensemble of spurious detections associated with diffraction spikes,
halos, and ghosts. To make USNO-A2.0 a useful catalog, bright stars
were inserted into it so that the catalog is a better representation
of the optical sky. For may applications, it is better to know that a
bright star is nearby than it is to insist that the poorly measured
objects be deleted from the catalog. In compiling USNO-A2.0, a list of
all ACT stars that were correlated with PMM detections was kept. For
these stars, USNO-A2.0 contains the PMM position, not the ACT
position, and the flag bit is set to indicate the correlation. In the
compilation process, all uncorrelated ACT stars were inserted into the
catalog using the ACT coordinates. However, ACT is not complete at the
bright end because it omits stars with low astrometric quality. Hence,
a final pass inserted all Tycho stars that do not appear in the ACT
catalog at the Tycho position. According to the documents published
with the Tycho catalog, every effort was made to make it complete at
the bright end, even for stars with low astrometric quality.

Note that one should not use the coordinates of ACT and Tycho stars
presented in USNO-A2.0 for critical applications. ACT stars appear at
the epoch of the plate, but because the proper motions for the non-ACT
Tycho stars are unreliable, these stars appear at the epoch of the
Tycho catalog.


The all-sky pretty pictures generated from USNO-A2.0 used an
algorithm to reduce the over-density of southern stars that arises
from the fainter limiting magnitudes of the SERC-J and ESO-R
plates. This was done by using a random number generator and omitting
the star if the random number was less than 0.45. That is to say, the
southern over-density is not quite a factor of 2 more objects per unit
area than found from the northern surveys. Again, all objects are in
USNO-A2.0 and the over-density was removed to make the pretty


As with USNO-A1.0, we have published the source code for all
computations and for all calibration. The compilation code is in
ALPHA13.TAR in the directories ./newbin/procN. The code for the
numerical refocus is in NEWBIN.TAR ./newbin/newz0 and for the fixed
pattern removal in ./newbin/tycho2xtaff.

The code is published as a service to those who wish to understand
USNO-A2.0 and not so that we can be ripped off. Please respect the
intellectual property rights contained in the source code, and do not
make us wake up the lawyers.

Enjoy! If you use USNO-A2.0 for neat stuff, drop me an e-mail.

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