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.