The details listed below are from the files kindly supplied to CDS by Dave Monet at the ftp://ftp.nofs.navy.mil/usnoa site. Please refer to http://ftp.nofs.navy.mil/projects/pmm/ for the most recent details about the PMM products.A compression technique adapted to the PMM USNO-A2.0 was used for the CDS installation, keeping the direct access possibilities on a catalog shrinked to 3.6Gbytes.
****************Really Important Stuff**************************************
1) 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 me 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
PO Box 1149 (US Mail Only)
West Highway 66 (FedEx, UPS, etc.)
Flagstaff AZ 86001 USA
Voice: 520-779-5132
FAX: 520-774-3626
e-mail:
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.
2) 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.
3) This file is subject to being updated. We are in the process of moving
the USNO Flagstaff Station Web site from
http://www.usno.navy.mil/nofs
to
http://www.nofs.navy.mil
Please be patient during the transition. This version of the file
was all that I could prepare in time for the CD-ROM distribution.
As changes, mistakes, and additions are processed, the new version
of this file will be available from our Web site.
*********************The Rest Of The Stuff********************************
USNO-A V2.0
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 =========================
1. REFERENCE FRAME
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.
2. STAR NAMES
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.)
3. PHOTOMETRIC CALIBRATION
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.
4. ASTROMETRIC CALIBRATION
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.
5. NUMERICAL REFOCUS
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.
6. EPOCH OF COORDINATES
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.
7. MULTIPLE ENTRIES
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 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.
8. BRIGHT STARS
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.
9. PRETTY PICTURES
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 pictures.
11. SOURCE CODE
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.
-Dave
The following text is copied from the UJ1.0 CD-ROM and gives an overview
of the PMM and its programs. In an attempt to satisfy the serious user
of this catalog, the source code for the PMM is found in the sg1.tar file
somewhere in this CD-ROM set. This file contains the source code for
all pieces of the executable image as well as the key data files used
to calibrate various pieces of the PMM. References to code in this section
point to files in sg1.tar.
Dave Monet is
The Precision Measuring Machine (PMM) was designed to digitize and reduce
large quantities of photographic data. It differs from previous designs
in the manner by which the plates are digitized and in that it reduces the
pixel data to produce a catalog in real time. This section gives an
introduction to the design, hardware, and software of the PMM. For those
wishing to pursue issues in greater detail, the software used to control
the PMM may be found in the directory exec/c24, and all software used to
acquire and process the image data is found in the other directories
under exec/ (processing begins with exec/misc/f_parse).
High-speed photographic plate digitization has been accomplished using
three different approaches. Many machines (APS, APM, PDS, etc.) have
a single illumination beam and a single channel detector. This approach
can offer extremely accurate microdensitometry at slow scanning speeds
(PDS) and has been used by intermediate-speed machines (APS, APM, etc.)
that have produced many useful scientific results. The second approach is
to use a 1-dimensional array sensor, such as the SuperCOSMOS design. These
offer much higher scanning rates but suffer from more scattered light than
true microphotometers. The third approach (PMM) is to use a 2-dimensional
array sensor, such as a CCD. This offers yet higher throughput at the
expense of more scattered light. The 1-D and 2-D designs are new enough
that detailed comparisons with single pixel designs have yet to be done.
Of the three designs, only the 2-dimensional array design separates image
acquisition from mechanical motion. In this approach, the platen is stepped
and stopped, its position is accurately measured, and then a CCD camera takes
a picture of a region of the photographic material. In this manner, the
transmitted light (plates and films) or reflected light (prints) is digitized
and sent to a computer for processing and analysis. The mechanical system
is not required to move the platen in a precise direction or speed while
image data are being taken. Therefore, the mechanical system is much easier
to build and keep operational, and platen sizes can be much larger (a feature
needed to minimize the thermal and mechanical impact of replacing the
photographic materials).
A. Hardware
The PMM design is conceptually simple. The mechanical system executes a
step and stop cycle, and then reports its position to the host computer.
A CCD camera takes an exposure of the "footprint" in its field of view,
and the signal is then read, digitized, and passed to the host computer.
Once the image is in the computer, the mechanical motion may be started
and image processing and mechanical motion can occur simultaneously.
In practice, the PMM design is a bit more complicated because it has
two parallel channels for yet higher throughput. The various subsystems
are the following.
a) The mechanical system was manufactured by the Anorad Corporation
of Hauppauge NY to specifications drawn up by USNOFS astronomers
and their consultant William van Altena. Its features include
the following:
i) 30x40-inch useful measuring area.
ii) granite components for stability.
iii) air bearings for removal of friction.
iv) XY stage position sensed by laser interferometers.
v) Z and A platforms for above/below stage instruments.
vi) ball screw motion in X at 4 inch/second maximum speed.
vii) brushless DC motors in Y at 2 inch/second maximum speed.
viii) computer control of all motions.
ix) two laser micrometers mounted on the Z stage to measure
distance to photographic materials.
x) two CCD cameras (discussed below).
In addition, it has a single channel microphotometer system built
by Perkin Elmer, but that system is not used for POSS plates.
It is controlled by a dedicated PC that communicates to
the outside world by an RS-232 interface.
The PMM is housed in a Class 100,000 (nominal) clean room and
the thermal control is a nominal plus or minus one degree
Fahrenheit. Actual performance is much better over the 80
minutes needed to scan a pair of plates. The temperature is
usually stable to +/-0.2 degrees and short term tests show
a repeatability of 0.2 microns over areas the size of POSS
plates. Thermal information is recorded during the scan
and is part of the archive.
b) The images are acquired and digitized by two CCD cameras made
by the Kodak Remote Sensing Division (formerly Videk). Each
has a format of 1394x1037 and a useful area of 1312x1033 pixels.
The pixels are squares of 6.8 microns on a side, have no dead
space between pixels (100 bad pixels in the array (Class 0). A flash analog to digital
converter is part of the camera, and the image is read and
digitized with 8-bit resolution at a rate of 100 nanoseconds
per pixel.
Printing-Nikkor lenses of 95 millimeter focal length are used to
focus the sensor on the photographic plate with a magnification
of 2:1. The resolution of these lenses exceeds 250 lines per
millimeter and they have essentially zero geometric and chromatic
distortion when used at 2:1. The illuminator consists of a
photometrically stabilized light source, a circular neutral
density filter to compensate for the diffuse density of the
plate, a fiber bundle, and a Kuhler illuminator to minimize
the diffuse component of illumination. Each camera's light path is
separate except for the single light source.
c) Each camera has its own dedicated computer and related peripherals.
The digital output of the camera is fed to a 100 megabit
per second optical fiber for transmission to the computer room
where a matching receiver converts it back into an 8-bit wide,
10 megabyte per second parallel digital signal. This signal is
interfaced to a Silicon Graphics 4D/440S computer using an
Ironics 3272 Data Transporter attached to the VME bus. This
system supports the synchronous transfer of 1.4 megabytes in
0.14 seconds with an undetectably small error rate.
The 4D/440S supports DMA from the VME bus into its main memory
without an additional buffer. Once in the computer, the PMM
software (discussed below) does whatever is appropriate, and,
if the user desires, the pixel data can be transmitted across
a fiber optically linked SCSI bus to disk or tape drives located
in the PMM room. This is particularly convenient for the operator.
d) A DEC MicroVAX-II computer acts as system synchronizer, and does
little more than coordinate all steps in the motion and processing.
This operation is not as trivial as it sounds.
e) The user interacts with the PMM using any X-window terminal
by logging into the MicroVAX and starting the control program.
The control program logs into the Anorad PC and each of the
processing computers across RS-232 (it is too old to have X). These
computers open X-windows on the users terminal, and all interaction
with them (including image display) avoids the MicroVAX. A simple
interpretive language was written for the MicroVAX, and plates
are measured by executing sequences of commands. Sequences
may be found in exec/c24/seqNNN.pmm. The sequence for measuring
4 UJ plates is seq485.pmm.
B. Plate Measuring Sequence
The sequence for measuring plates is designed to minimize human intervention.
Each of the two platens holds four POSS plates. While one is being measured,
the other is loaded so that the plates can come to thermal equilibrium.
The measurement sequence consists of the following phases.
a) The camera is positioned over the middle of the plate and the
neutral density filter is set to maximum (D=3.0). A sequence of
fixed length exposures is made as the density is reduced, and
the optimum value for the exposure is found. Due to limitations
of the camera interface, the exposure time has a granularity of
one millisecond and must be in the range of 2 to 127 milliseconds.
Once the optimum neutral density is found, it is kept at that value
for the entire plate. Changes in diffuse density are followed by
changing the exposure time.
b) The Z-stage is fixed at a nominal value, and the plate pair
(1/2 or 3/4) is scanned to obtain the distance between the Z
laser micrometers and the surface of the plate. The XY stage is
positioned at a Y value that will later be used for the digitization
footprints, and then driven at high speed in X. As the stage moves,
the micrometer and the Anorad PC are sampled to determine the
Z distance as a function of X position. This procedure is repeated
for the sequence of Y positions, and the 2-dimensional map of Z
distance is obtained.
c) The camera is positioned over the middle of the plate, and
a sequence of exposures is taken at different values of the Z
coordinate. For each exposure, a measure of the sky granularity is
computed, and interpolation is used to find the Z coordinate that
maximizes the granularity. This establishes the "best" focus in
an impersonal manner, and it appears to be stable to plus or
minus 50 microns in Z.
d) A sequence of frames are taken of the central area of the plate
with increments of 1.0 millimeter between each, and the standard
star finding and centering algorithm is run on each frame.
After all frames have been taken, the nominal value of the plate
scale is used to identify unique stars seen on each of several
frame. Once the set of measures is isolated, software computes
a revised estimate of the plate scale. This revised estimate
can be considered the difference between the layer of the emulsion
that reflected the laser micrometer beam of the reference plate
and of the current plate.
When the plate is scanned, the Z stage is driven to the position appropriate
for each footprint, which is the sum of the "best focus" plus the difference
between the current location and the central location as determined by the
laser micrometers. After the positions have been measured, a linear
expansion is applied to the pixel coordinates for each star to remove the
difference in the (observed-nominal) plate scale. At first glance, this
algorithm seems quite complicated, but determination of the plate scale
is critical to the astrometric integrity of the PMM. To measure to 0.1
arcsecond, the scale must be known to 0.008contribute to uncertainties in the plate scale.
a) No technology better than a laser micrometer was found to
measure the distance between the Z stage and the plate. Unfortunately,
the laser is somewhat sensitive to the reflectance of the surface,
and the range of diffuse densities encountered during the scanning
of the UJ plate of about 0.1 to 2.5 causes an uncertainty of where
the micrometer is measuring. The only competing technology,
touch probes, was considered too risky for use with original POSS-I
and -II plates.
b) The POSS plates are not flat, and no reasonable plate hold-down
mechanism was proposed. This problem is a minor annoyance for
UJ and POSS-II plate because the typical +/- 200 microns could
be removed by software. Unfortunately, the +/-1 or millimeter
seen on the POSS-I plates causes the images to be out of focus,
and a surface following algorithm is required.
Unfortunately, the elaborate focus and scale determination routines developed
to measure POSS-I and POSS-II plates were unreliable for measuring the
UJ plates. Many UJ plates had diffuse densities so low that the sky and
the noise in the sky were extremely difficult to measure. To the human
observers, these plates seem as clear as window glass. Since the UJ exposures
were only 3 minutes, many plates had so few stars in a single footprint
that the scale determination routine got lost. In either case, the error
induced by a lost algorithm was much larger than just measuring the focus on
a good plate and using that value for the UJ plate. This was done, so the
list in the preceding paragraph must be extended.
c) The difference in focus between the current plate and that used
to determine the CCD camera scale is not known. Note that the PMM
should follow the current plate properly since that measurement
is only the difference between the local and central value
determined by the laser micrometer. What is not (or only poorly)
known is the offset at the central location.
C. Image Analysis Algorithms
The mechanical and camera systems serve only one purpose: to deliver image
data to the processing computers. The major precept of the PMM design is to
do all image processing and analysis in real time. It was true when the PMM
was designed, and is still true, that it takes much longer to read or write
an image to storage devices (particularly those for archival storage) than
it does to extract the desired information. Indeed, the original PMM design
had no mechanism for saving the pixels. A substantial amount of thought
and work has gone into the design of the image processing algorithms. This
section gives an overview of the code, and the serious reader is encouraged
to read the source code (located in exec/ and its subdirectories).
When the MicroVAX notifies the computer that the mechanical motion has been
completed, the computer commands one or more exposures to be taken. The
code is written to take 1, 2, 3, 4, or 8 exposures depending on the value
of GRABNORM. The routine exec/misc/f_autoexp is used most often because
it takes the exposures, evaluates the sky background, and will re-take
an exposure with a modified exposure time if certain limits are exceeded.
Since the background is variable, this type of autoexposure routine is
necessary. Note that it does not vary the setting of the neutral density
filter used to illuminate the plate, so it has a limited range over
which it can modify the exposure.
Another problem related to taking an exposure is the presence of holes, tears,
and the area around the sensitometer spots. Typically, the POSS plate sky
background has a diffuse density larger than two, but where the emulsion is
absent or hidden from the sky, the density can be very close to zero.
These regions cause gross saturation of the CCD camera, and its behavior
becomes extremely non-linear, even to the point of having decreasing
signal level with increased exposure. To avoid this, the routine
exec/misc/f_toasted takes a very short exposure to test for this condition
before the normal exposure sequence is started.
Flat field processing is done in the traditional manner, using bias and
flat frames taken under controlled circumstances. The CCD cameras are
quite linear and uniform, and the flat field processing does little more
than take out the non-uniformities in the illuminator. Pixel data are
converted from unsigned bytes into floating point numbers during the
flat field processing, and all steps in the image analysis and reduction
software are applicable to non-photographic data.
The image processing is divided into a hierarchy based on accuracy,
and there are three levels. The first, called the blob finder, is charged
with finding areas that need further processing, and doing this with a
relatively coarse accuracy of +/-1 pixel. The second is invoked to refine
this guess to an accuracy of +/- 0.2 pixel and to provide improved estimators
for the object's size and brightness. The third step is non-linear least
squares processing, which produces the accurate estimators for image
position, and moment and other image parameters. Each is discussed in
greater detail in the following paragraphs.
a) Blob finding: Many different algorithms have been proposed to
find blobs in an image. (I prefer to use "blob" instead of "star"
since we do not know in advance what sort of an object we have
found.) The PMM algorithm was designed for very high speed.
It is based on the concept that finding an image requires neither
the spatial resolution nor the intensity resolution required to
measure accurate image parameters. The first step of the blob
finder is to block average the input image by a size PARMAGNIFY
which can take on values of 1, 2, or 4, but all experience indicates
that 4 is acceptable for PMM processing of POSS plates. (The driver
for this processing is in exec/pfa124subs/bmark2_N.f where N
takes on the values of 1, 2, or 4.) The larger the value of PARMAGNIFY,
the faster the blob finder will operate.
With PARMAGNIFY determined, the block average TINY image is computed
and then subjected to a median filter to produce the SKY image
of similar size. The histogram processing of the sky image determines
the dispersion of the sky, a scaler that will be applied to the
whole image. Then, the sky image and the sky dispersion are used
to generate the DN1P image, an image whose pixel values are 1
if the TINY image was greater or equal to the SKY pixel plus
PARSIGMA times the sky dispersion, or 0 if not. If the DN1P pixel
is set to 1, the corresponding SKY pixel is set to zero indicating
that it should not be used to compute local sky values.
Another picture of reduced size is computed as well. The
DN2P pixel is set to 1 if the TINY pixel is greater or equal
to PARSAT, a number that represents the level at which an image
is considered to be saturated. In practice, the number is about
230 instead of the maximum possible value of 255 that comes from
the camera A/D converter.
The logic behind the TINY, SKY, DN1P, and DN2P is the following.
Most computers take many cycles to compute an IF statement, and
these tend to negate look-ahead logic needed to make software
execute quickly. By making images whose values are 0 or 1,
additions and multiplications can replace many IF statements,
and thereby increase the speed of the code. Our experience is
that automatic blob finding is very expensive (slow) because of
the complexity of the algorithm, and our efforts to run it in
parallel mode were unsuccessful. Hence, optimization was needed
in this part of the code to keep its bandwidth high.
Given TINY, SKY, DN1P, and DN2P, blob finding can begin. The
algorithm is based on the concept that we wish to find
isolated, mostly circular objects. The algorithm considers a
circular aperture and computes the area and perimeter based on
the pixel values in either the DN1P or DN2P image. The area is
the number of pixels that meet or exceed the detection
criterion inside of the aperture, and the perimeter is the
number of such pixels that cross from inside the aperture to
outside the aperture. A detection is triggered when the area
has a non-zero value and the perimeter is zero. This means
that a blob has been isolated. Once a blob has been detected,
its location and coarse magnitude are tallied and the pixels in
DN1P or DN2P are set to zero so that it will not be detected
again.
This algorithm can be expedited in a variety of ways. First,
the central pixel is tested to see if it is one. If not, the
aperture is moved to the next pixel. This test corresponds to
the assertion that the night sky is dark, and that a substantial
number of pixels will be fail the detection threshold test.
Next, explicit logic tests for small blobs. The logic contained
in exec/blob/find124_N tests for all radius one and two pixel events,
and special cases of 4 pixel events. The routine exec/blob/find3_N
tests for all possible 3 pixel events. These cases are worth
the effort because the apparent stellar luminosity function
tells us that the vast majority of stars in the catalog will be
faint (small), and that the processing for small blobs needs
to be optimized.
The processing is completed by examining the DN1P or DN2P image
with progressively larger apertures, until all blobs are
found or until an unreasonably large aperture is needed, which is
an indicator either that a very bright object is in the field or
there is something wrong with the image. In all cases, blob
finding has been completed.
As the blobs are detected, the routine exec/blob/plproc_N attempts
to divide the blob into sub-blobs if required. This is not a
true deconvolution because we have transmission and not intensity.
This routine is intended to separate almost distinct blobs found
in the outskirts of other blobs, and does not do a good job
splitting close double stars. For the parameters used in UJ1.0,
the splitter is far too aggressive and tends to break up well
resolved objects into a series of distinct blobs. This is an
area for algorithm development before beginning the scans of the
deep Survey plates.
Once the list of blobs has been assembled, the TINY, SKY, DN1P, and DN2P
are no longer used. All further processing refers to the full resolution
DATA image. In addition, the code shifts from scaler to parallel operation
because it can consider each blob as a separate entity. Silicon Graphics
implements parallel processing with the DOACROSS compiler directive
for the pfa (Power FORTRAN Accelerator) compiler. Its function is to
assign the next step of the DO statement to the next available CPU.
This algorithm is quite effective for processing stars because it means
that a big, complicated star will occupy one CPU for a while, but the
other CPUs can continue processing other stars. Efficiencies between
3.5 and 3.8 were seen on the 4 CPU 4D/440S computer.
b,c) Coarse and fine analysis are carried out sequentially by
exec/fsubs/multiproc. The first step in done by exec/fsubs/proccenscan
which examines the blob along 8 rays and determines the size and
center of the blob. Then, the blob is fit by a circularly
symmetric function by the routine exec/fsubs/marg and then various
other image description parameters (moments, gradient, lumpy,
etc.) are computed and packed into integers.
The function selected was B + A/(EXP(z)+1) where
z = c*((x-x0)**2 + (y-y0)**2 - r0**2). (Perhaps this is more
familiar when called the Fermi-Dirac distribution function.)
Because the PMM uses transmitted light, faint images look
something like a Gaussian, but bright images have flat tops because
they are saturated. Hence, the desired fitting function needs to
transition between these two extremes in a smooth manner. A large
number of numerical experiments were made, and they can be
summarized by the following points.
i) The production PMM code takes the sky value from
the median SKY image rather than letting it be a free
parameter in the fitting function. The failure mode
for many normal and weird objects was found to be
an unreasonably large value for the sky and a correspondingly
tiny value for the amplitude. Fixing the sky forces the
function to fit the image, and this is much more robust than
letting the sky be a fit parameter.
ii) Allowing the function to have different scale lengths
in X and Y was found to be numerically unstable for too
many stars. With 6 free parameters in the exponent, chi
squared can be minimized by peculiar and bizarre combinations
that bear little resemblance to physical objects.
iii) Iteration could be terminated after 3 cycles without
serious damage. If the object could be fit by the function,
convergence is rapid and the parameter estimators at the
end of the 3rd iteration were arbitrarily close to those
obtained after many more iterations. If the object could not
be fit by the function, the parameters obtained after 3
iterations were just as weird as those obtained with
more iterations.
iv) The best image analysis debugging tool was to subtract
the fit from the DATA image and display the residuals
as the PMM is scanning. This allows the human observer
to get a good understanding of the types of images that
are processed correctly, and where the analysis algorithm
fails. This mode of operation is not possible on plate
measuring machines that do not fit the pixel data.
Therefore, a 5 parameter, circularly symmetric, fixed sky function
was fit to all detections, and the position determined by this
function is reported as the position of the object.
Since most other high speed photographic plate measuring machines
compute image moments, the PMM computes these as well. Our
experience is that the image moments are less useful for star/galaxy
separation than quantities obtained from least squares fitting,
and the positions determined from the first image moments are
distinctly less accurate than those determined by the fit.
In addition, the image gradient, effective size, and a lumpiness
parameter are also computed since these may assist in star/galaxy
separation. All parameters are packed into 13 integers by the
routine exec/fsubs/marg, and that code should be consulted for
information concerning the proper decoding of these values.
D. Catalog Products
The distribution of PMM data should begin and end with the distribution of
the raw catalog files. Unfortunately, cheap recording media are incompatible
with the bulk. So far, over 440 CD-ROMs are needed to store these data, and
the scanning is not yet done. Perhaps the digital video disk will make this
problem go away. Until them, the PMM program will attempt to generate
useful catalogs that contain subsets of the parent database.
USNO-A:
These catalogs are intended to be used for astrometric reference. They
contain only the position and brightness of objects, and ignore such
useful parameters as proper motion and star/galaxy classification. These
are objects that measured well enough on each of two plates to pass the
spatial correlation test based on a 2-arcsecond entrance aperture.
V1.0 contains RA and Dec, and takes its astrometric calibration from
GSC1.1 and is photometric calibration from the Tycho Input Catalog and
from USNO CCD photometry.
V1.1 is derived from V1.0 by using SLALIB to transform RA/Dec to
Galactic L/B. The catalog is arranged in zones of B and is sorted on L.
Because of intermediate storage requirements, the lookup tables between
V1.1 and the GSC will not be computed.
V2.0 is planned for late summer of 1997 after ESA releases the Hipparcos
and Tycho catalogs. The astrometric calibration will be made with
respect to Tycho, and Tycho will be used to calibrate the bright end
of the photometry. Should STScI release GSCP-II (or significant chunks
of it), this improved photometric calibration will be included, too.
USNO-B:
This catalog will extend USNO-A in several key areas. It will contain
star/galaxy separation information and will contain proper motions.
Note that these quantities will be computed from J/F plate data, so
USNO-B will be incomplete in the north according to the production
schedule of POSS-II, and proper motions will be impossible south of
-42 due to missing second epoch survey data. Proper motions in the
-36 and -42 zones can be computed from the Palomar Whiteoak extension.
In addition, the plan is to use spatial coincidence data from the
O+J and E+F survey comparisons to supplement the O+E requirement
needed by USNO-A. Hence, there should be many more entries, and the
limiting magnitude for objects with peculiar colors will be much deeper.
UJ1.3 and beyond:
The UJ plates (3-minute IIIa-J on POSS-II field centers) provide a
useful set of astrometric standards at intermediate brightnesses.
To the extent possible, UJ will be kept current and made available
to those who request it.
Pixels:
The PMM pixel database is approaching 5 TBytes. Each of the PMM
detections contains a pointer back to the frame and position of
the pixel that triggered the detection loop. Current USNO policy
is to release the pixel database as soon as there is a reasonable
way to do so. Users with a particular urgency can contact Dave
Monet and make a special request for access, but the logistics of
searching and retrieving a specific frame from the archive on 8-mm
tape will preclude all but the most important requests.
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.
Summary:
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
Strategy:
Using the reference catalog (GSC1.1) and the information contained
in the plate log (possi.cat and south.cat 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.
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.
Summary:
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
Strategy:
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
properly.
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.
The original catalog consisted in 24 files, one for a 7.5° strip in declination. Each file was extended to a directory, named N000...N8230 and S0000...S8230, i.e. with the same conventions as those used for the GSC Catalog.
In each of these directories, there is one file for 30min (i.e. 7.5° at the Equator) in right asension; the total number of files is therefore 24×48 = 1152 files, with an average number of 20,000 (near the poles) to 800,000 objets per file. In each of these files, the range of the coordinates is then restricted to 7.5°, i.e. a maximal value of 2,700,000 when the coordinates are expressed in their original units of 10mas. The final grouping allowed to reduce one record to 7 or 8 bytes (the mean is close to 7).
The resulting catalog occupies only 3.6Gbytes, including all transformation and query software; the full 526×106 objects are tested in about 45 minutes (i.e. 5µs per object) on a Sparc-20 (72MHz).
A few benchmarks made on a Sparc-20 (72MHz) give the following average elapsed times (between 15 and 70for a search by position on the catalog, keeping the 10 closest stars (actually performed on the USNO-A1.0 which was converted in April 1997 with an almost identical software):
=========================================================================
Search Tested stars Time required Reading time
Radius (') per target (s) for 1 star (microsec)
-------------------------------------------------------------------------
2.5 14153 0.09 6.4
10.0 66394 0.24 3.6
30.0 201351 0.67 3.3
=========================================================================
A client/server access to the PMM USNO-A2.0 Catalog – as well as to other catalogues – is also available via the findpmm2 program which is part of the cdsclient package.
François Ochsenbein, <&CDS.home>
<&Viz.tailmenu /srv/httpd/Pages/VizieR/pmm/usno2.htx "index">