Astrometry

The APS is a high precision measuring machine capable of producing very accurate position measurements. It has a repeatability of 1.6μm in x and 0.9μm in y, corresponding to 0:00.11 and 0:00.06, respectively. However, the final accuracy of any astrometry also depends on the quality of the plates, the centroiding algorithm, and the accuracy and density of the astrometric reference catalogs used. By examining the regions where plate pairs overlap, as well as the positions on the O and E exposures of a given field, we have established that APS object positions are locally accurate to an rms of 0:00.2. Achieving this accuracy over an entire Schmidt plate can be quite difficult. In particular, two basic problems arise when astrometry is attempted on a full Schmidt plate. The bright astrometric standards are badly saturated and are distorted by flare at the plate edges. And second, Schmidt plates suffer from distortions which are especially severe (∼1:005) near their edges (Taff 1989; Taff et al. 1990).

APS astrometry is done in three steps which overcome these problems and obtain a good full-plate astrometric solution.

1. Fitting to the diffraction spikes of bright reference stars.
   We determine the centers of reference stars from the Astrographic Catalog of Reference Stars (ACRS; Corbin & Urban (1988, 1989)) using the intersection of the Schmidt diffraction spikes. This has the important advantage that the derived center is not affected by the very obvious flare and distortions of bright images which occurs in the vignetted region outside of the central 5.4? diameter of each plate. We use the image pixels of each reference star from the threshold densitometry data and fit the ridgelines of the spikes which are clearly visible and easily measured for the faintest reference stars in the ACRS. A linear plate model plus a cubic radial term needed to correct for the difference between the gnomonic and Schmidt projects is used. With this initial solution we achieve an internal rms error of 0:005 to 0:006 in both dimensions.
   
   
2. Corrections for Schmidt plate distortions.
   The positional errors caused by Schmidt plate distortions are sufficiently stable that they can be mapped and removed. By co-adding the astrometric residuals for 50 plates reduced as described above, we have mapped the distortion pattern on the POSS I. Specifically, we have succeeded in fitting it with a relatively simple, axisymmetric analytic function with an rms accuracy of 0:00.07 in each coordinate. This is essentially the machine limit. When the corrections are applied to the reference stars the rms error typically decreases to ∼ 0:00.4.
   
   
3. Astrometry with faint Lick NPM1 stars.
   Most objects in the POSS I Catalog are much too faint (> 12 mag) for diffraction spike centroiding. The Lick Northern Proper Motion (Lick NPM1) Catalog (Klemola et al. 1994) contains numerous faint stars (down to 18 mag) on the FK4 system. Tests made using the ACRS-derived distortion map and a simple median centroider on Lick NPM1 stars gives astrometric solutions with rms ∼ 0:00.25 per coordinate. Using the Lick NPM1 stars plus the distortion corrections, we obtain full-plate solutions with an rms of 0:00.2 - 0:00.3 in RA and Declination. The Lick NPM1 ends at Declination -23°, so for those POSS I fields with field centers south of this and for any fields for which the Lick data are not available, we use the ACRS which typically yields full-plate rms errors of ∼0:00.4. The astrometric positions of both the stars and galaxies are then derived from the median centroid of the background subtracted pixel data. Information about the astrometric solution for each POSS field is included with the archived Catalog.
   
   

This scheme supposes that the distortion pattern determined from the diffraction spike centroids is generic, and will therefore apply to faint objects on the plates. Since we ultimately calculate the astrometric solution using the NPM1 catalog, with the full catalog in hand, we can test this assumption directly by stacking the residuals of the final catalog according to plate location for all the plate solutions. This procedures applied to 533 plates reveals some systematic residuals of the NPM1 positions at the plate edges, but these were typically less than or comparable to the dispersion in the offsets at a given location across all plates (which reflects the combined effects of random measurement errors for individual objects and the stability of the distortion pattern across all plates). Therefore, we conclude that the distortion model based on the diffraction spikes is adequate and is appropriate for use in calculating the final astrometric solution based on median centroids.

After the above steps have produced an astrometric solution, application of the astrometric solution to the median centroids of the catalog objects provides correct positions for stars fainter than m∼12 and for all galaxies. We caution that due to the aforementioned combination of flaring and saturation of brighter stars, a magnitude-dependent - approximately radial - error in the cataloged positions results when the astrometric solution is then applied to the median centroids of bright stars in the outer vignetted region of the plate. Again, galaxies are not affected in this way because such bright galaxies are well resolved and unsaturated. Likewise, brighter stars in the central 5.4° of the plates do not suffer this effect. Although use of the diffraction spike centroids in the main catalog - or application of a magnitude-dependent correction - could remedy this problem, since MAPS emphasizes unsaturated objects we have chosen not to introduce such a dichotomous astrometric scheme.

In order to examine our astrometry for systematic effects, we have compared our positions on 159 POSS I E plates with those of radio sources detected in the FIRST survey (Becker, White, & Helfand 1995). For most plates, the February 1998 version of the FIRST catalog was used. The FIRST coordinates were precessed from J2000 FK5 to B1950 FK4 using the IPAC/JPL precession software suite. The distribution of nearest-associations is modeled as a Gaussian core - representing true associations - and a constant background - representing false associations due to interlopers. Our data indicate that for separations of less than 1-2" the number of true associations overwhelms the number of false associations. Over the entire FIRST catalog we find the Gaussian core to be offset by -0".018 ± 0".003 in Right Ascension and -0".130 ± 0".003 in Declination, in the sense of APS-FIRST. The quoted uncertainties on the offsets are purely statistical. The Gaussian core, representing roughly 20,000 APS-FIRST associations, has a dispersion of 0".52 both in Right Ascension and Declination, consistent with the stated positional accuracy of <1" for FIRST, and our measured astrometric residuals of ∼ 0".3 RMS. As discussed by McMahon, White, Helfand, & Becker (2002) and Ivezic et al. (2002), the majority of optical counterparts detectable on POSS I are resolved galaxies, while some radio sources are themselves extended; both effects will increase the position differences as well as the completeness and reliability of the cross-identifications. However, these issues have little impact on determining the mean astrometric offsets. We also examined whether the above offsets depend on Right Ascension or Declination, but failed to find any convincing trends.