SDSS Survey coordinates
The SDSS has two sets of coordinates it uses which are specially designed for the survey geometry. These are described in the Early Data Release paper (Stoughton et al. 2002).
Great circle coordiantes (μ, ν)
The first set is the Great Circle (μ, ν) system, where μ and ν are spherical coordinates (corresponding to RA and Dec) in a system whose equator is along the center of the stripe in question. The stripes in the main survey in the North Galactic Cap are great circles which all cross the survey nodes of (RA, Dec) = (95, 0) and (RA, Dec) = (275, 0) degrees.
The scans are defined by their inclination with respect to the equator, and are indexed by integers n such that the inclination of a stripe is 2.5(n - 10).
The stripes of the main survey in the South Galactic cap are great circles with the same nodes, where the indexing is such that the inclination relative to the survey equator is 2.5(82 - n). The celestial Equator therefore corresponds to stripe number 10 in the Northern Cap and 82 in the Southern Cap. Stripes 1-44 were observed in the North, and stripes 61 to 90 in the South. While the imaging scans of the SEGUE survey are also great circles, they have an assortment of different nodes and are numbered with stripe numbers > 200.
Survey coordinates (η, λ)
The second set is the Survey (η, λ) system. This is simply another spherical coordinate system, where (η, λ) = (0, 90.) corresponds to (RA, Dec) = (275.,0.) and (η, λ) = (57.5,0.) corresponds to (RA, Dec) = (0.,90.). Note also that at (η, λ) = (0.,0.), (RA, Dec) = (185., 32.5). For some reason, although η is constant along great circles, it is referred to as "survey latitude," while λ is referred to as "survey longitude." Also, η runs only from -90. to 90.; the back of the sphere is covered by λ, which runs from -180. to 180. The Survey coordinates are defined such that the "primary" area of a stripe in the north is defined by a rectangle in Survey coordinates which is 2.5 degrees wide in η (coordinate width).
The photometric catalog contains the position of each object in both Great Circle and survey coordinates.
A variation on survey coordinates are the "corrected survey coordinates" (ceta, clambda), which are identical to η and λ, but use the more sensible ranges of -180 to 180 for ceta, and -90 to 90 for clambda.
Survey coordinate transformation software
The idlutils package provides a set of IDL utilities to convert from these coordinates to right ascension and declination and back. These can be consulted for the mathematical relationship between the coordinate systems:
munu_to_radec: convert from Great Circle coordinates to Celestial coordinates
radec_to_munu: convert from Celestial coordinates to Great Circle coordinates
etalambda_to_radec: convert from survey coordinates to Celestial coordinates
radec_to_etalambda: convert from Celestial coordinates to survey coordinates
stripe_to_incl: return the inclination associated with a given stripe number
stripe_to_eta: return the eta value along the middle of a Great Circle stripe number
eta_to_stripe: return the closest stripe center to a given eta value
csurvey2eq: convert from survey coordinates to Celestial coordinates
eq2csurvey: convert from Celestial coordinates to survey coordinates