A separate great circle coordinate system is defined for each stripe (§ 3.2.2). In these systems, the stripe center is the equivalent of the equator in the equatorial system. Pixel coordinates are corrected for empirically derived optical distortion terms, and the resulting mapping from corrected CCD row and column pixel positions to great circle longitude and latitude is linear to very good approximation. Astrometric solutions are carried out in this coordinate system. One of two reduction strategies is employed depending upon the coverage of astrometric catalogs:
For each r frame, these mappings result in an affine transformation relating corrected pixel positions to celestial coordinates. A secondary catalog is produced from the detections on the r CCDs. This secondary catalog is then matched to centroid positions on the i, u, z, and g CCDs to derive affine transformations in those filters. The transformation also includes terms to correct for differential chromatic refraction and those terms are applied when the colors of objects are known (Table 16). Positions of detected objects given in this EDR have had this correction applied.