X' = x + g 0 + g 1 y + g 2 y 2 + g 3 y 3 + q x Note: At the edges of pixels, the quantities objc_rowc and objc_colc take integer values, contrary to standard practice. 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. 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. 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. In brief, stars detected on the r CCDs, are matched to catalog stars. All six camera columns are processed in a single reduction.
To minimize the errors in the relative astrometry between filters, the u, g, i, and z CCDs are calibrated against the r CCDs. 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. FRAMES uses the astrometric calibrations to match up detections of the same object observed in the other four filters.
The r CCDs are calibrated directly against the primary astrometric reference catalog. There are approximately 2 - 3 magnitudes of overlap between UCAC and unsaturated stars on the r CCDs. Together UCAC2 and r14 cover the whole sky. Outside the UCAC2 area we use an "internal" UCAC data release known as "r14". UCAC2 extends up to around a declination of 41 degrees north. 2000), which has a precision of 70 mas at its catalog limit of r= 16, and systematic errors of less than 30 mas. Stars detected on the r CCDs are matched directly with stars in the United States Naval Observatory CCD Astrograph Catalog (UCAC2, Zacharias et al. The r CCDs are calibrated by matching up bright stars detected by SDSS with the UCAC astrometric reference catalogs. That is, the positions for SDSS objects are based on the r centroids and calibrations. The r photometric CCDs serve as the astrometric reference CCDs for the SDSS.
Portions of that discussion are summarized here. A detailed description of the astrometric calibration is given in Pier et al.
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