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# 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 Project Book in the section on Survey Strategy.

The first set is the Great Circle (mu, nu) system, where mu and nu are spherical coordinates (corresponding to ra and dec) in a system whose equator is along the center of the stripe in question. The stripes of the survey are great circles which all cross at (ra, dec) = (95, 0). The stripes are defined by their inclination with respect to the equator, and are indexed by integers n such that the inclination of a stripe is -25 + 2.5n. Thus, stripe n=10 corresponds to the Equator. The design is that the area covered by the imaging on a given stripe is a 2.5 degree wide rectangle centered on nu=0 in Great Circle coordinates.

The second set is the Survey (eta, lambda) system. This is simply another spherical coordinate system, where (eta,lambda)=(0,90.) corresponds to (ra,dec)=(275.,0.) and (eta,lambda)=(57.5,0.) corresponds to (ra,dec)=(0.,90.). Note also that at (eta, lambda)=(0.,0.), (ra,dec)=(185.,32.5). For some reason, although "eta" is constant along great circles, it is referred to as "survey latitude," while "lambda" is referred to as "survey longitude." Also, "eta" runs only from -90. to 90.; the back of the sphere is covered by "lambda", 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 eta (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 eta and lambda, but use the more sensible definition ranges of -180 to 180 for ceta, and -90 to 90 for clambda.

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