The objective of the photometric calibration process is to tie the SDSS imaging data to an AB magnitude system, and specifically to the ``natural system'' of the 2.5m telescope defined by the photon-weighted effective wavelengths of each combination of SDSS filter, CCD response, telescope transmission, and atmospheric transmission at a reference airmass of 1.3 as measured at APO.
The calibration process ultimately involves combining data from three telescopes: the USNO 40-in on which our primary standards were first measured (see below), the SDSS PT (§ 3.4), and the SDSS 2.5m telescope. At the beginning of the survey it was expected that there would be a single u' g' r' i' z' system. However, in the course of processing the SDSS data, the unpleasant discovery was made that the filters in the 2.5m telescope have significantly different effective wavelengths from the filters in the PT and at the USNO. These differences have been traced to the fact that the short-pass interference films on the 2.5-meter camera live in the same vacuum as the detectors, and the resulting dehydration of the films decreases their effective refractive index. This results in blueward shifts of the red edges of the filters by about 2.5% of the cutoff wavelength, and consequent shifts of the effective wavelengths of order half that. The USNO filters are in ambient air, and the hydration of the films exhibits small temperature shifts; the PT filters are kept in stable very dry air and are in a condition about halfway between ambient and the very stable vacuum state. The rather subtle differences between these systems are describable by simple linear transformations with small color terms for stars of not-too-extreme color, but of course cannot be so transformed for very cool objects or objects with complex spectra. Since standardization is done with stars, this is not a fundamental problem, once the transformations are well understood.
It is these subtle issues that give rise to our somewhat awkward nomenclature for the PT and 2.5m filter systems. The calibration is provisional because the zero points are not quite on an AB system yet. For many purposes the difference between the USNO and the 2.5m systems are of no consequence. We believe that the photometric calibration of the EDR is uniform to of order 3% in , and , and 5% in and (all numbers are rms), while the absolute calibration in Jy is uncertain by as much as 10%.
In this section, we describe the process by which photometric calibration is done (§ 4.5.1), requiring analysis of data from the PT (§ 4.5.2) which is then combined with the 2.5m imaging data (§ 4.5.3). The tests we have carried out to give us confidence in the above numbers and caveats in the calibration are described in § 4.5.4. We do not aim here to give a full pedagogical description of the difficulties of absolute photometry in the SDSS system; that will be presented in papers in preparation.