Algorithms: Astrometry

A detailed description of the astrometric calibration is given in Pier et al. (2003) (AJ, or astro-ph/0211375). Portions of that discussion are summarized here, and on the astrometry quality overview page.

The r photometric CCDs serve as the astrometric reference CCDs for the SDSS. That is, the positions for SDSS objects are based on the r centroids and calibrations. The r CCDs are calibrated by matching up bright stars detected by SDSS with existing astrometric reference catalogs. One of two reduction strategies is employed, depending on the coverage of the astrometric catalogs:

1. Whenever possible, stars detected on the r CCDs are matched directly with stars in the United States Naval Observatory CCD Astrograph Catalog (UCAC, Zacharias et al. 2000), an (eventually) all-sky astrometric catalog with a precision of 70 mas at its catalog limit of r= 16, and systematic errors of less than 30 mas. There are approximately 2 - 3 magnituds of overlay between UCAC and unsaturated stars on the r CCDs. The astrometric CCDs are not used. For DR2/DR3, stripes 9-13, 76, 82, and 86 used UCAC.
2. If a scan is not covered by the current version of UCAC, then it is reduced against Tycho-2 (Hog et al. 2000), an all-sky astrometric catalog with a median precision of 70 mas at its catalog limit of V_T = 11.5, and systematic errors of less than 1 mas. All Tycho-2 stars are saturated on the r CCDs; however there are about 3.5 magnitudes of overlap between bright unsaturated stars on the astrometric CCDs and the faint end of Tycho-2 ( 8 < r < 11.5), and about 3 magnitudes of overlap between bright unsaturated stars on the r CCDs and faint stars on the astrometric CCDs (14 < r < 17). The overlap stars in common to the astrometric and r CCDs are used to map detections of Tycho-2 stars on the astrometric CCDs onto the r CCDs. For DR2/DR3, stripes 30-43 used Tycho-2.

The r CCDs are therefore calibrated directly against the primary astrometric reference catalog. FRAMES uses the astrometric calibrations to match up detections of the same object observed in the other four filters. The accuracy of the relative astrometry between filters can thus significantly impact FRAMES, in particular the deblending of overlapping objects, photometry based on the same aperture in different filters, and detection of moving objects. To minimize the errors in the relative astrometry between filters, the u, g, i, and z CCDs are calibrated against the r CCDs.

Each drift scan is processed separately. All six camera columns are processed in a single reduction. In brief, stars detected on the r CCDs if calibrating against UCAC, or stars detected on the astrometric CCDs transformed to r coordinates if calibrating against Tycho-2, are matched to catalog stars. Transformations from r pixel coordinates to catalog mean place (CMP) celestial coordinates are derived using a running-means least-squares fit to a focal plane model, using all six r CCDs together to solve for both the telescope tracking and the r CCDs' focal plane offsets, rotations, and scales, combined with smoothing spline fits to the intermediate residuals. These transformations, comprising the calibrations for the r CCDs, are then applied to the stars detected on the r CCDs, converting them to CMP coordinates and creating a catalog of secondary astrometric standards. Stars detected on the u, g, i, and z CCDs are then matched to this secondary catalog, and a similar fitting procedure (each CCD is fitted separately) is used to derive transformations from the pixel coordinates for the other photometric CCDs to CMP celestial coordinates, comprising the calibrations for the u, g, i, and z CCDs.

Notes: At the edges of pixels, the quantities objc_rowc and objc_colc take integer values.

Errors on RA, DEC available in CAS from DR4 on

There is a new table photAuxAll in the CAS that contain errors and covariances for the right ascension and declination as well as galactic coordinates for all objects (see the CAS Schema Browser entry for photoAuxAll). These errors are calculated by adding the centroiding errors in quadrature with the estimated astrometric calibration errors. The centroiding and calibration errors are calculated in great circle coordinates and are assumed to be uncorrelated in the great circle longitude and latitude directions; the covariance between the right ascension and declination errors is then introduced when transforming the uncorrelated errors in great circle coordinates to the celestial coordinate system.