Data products: General  Astrometry quality overview
A detailed description of the astrometric calibration and the the
resultant accuracy of the astrometry is given in
Pier et al. (2003)
(AJ, or astroph/0211375).
Portions of that discussion are summarized here, and
on the astrometry algorithm
page.
Overall Accuracy
The r photometric CCDs serve as the astrometric reference CCDs for the SDSS.
That is, the positions for SDSS objects are based on the r centroids and
calibrations. The r CCDs are calibrated by matching up bright stars detected
by SDSS with one of two existing astrometric reference catalogs:
 Whenever possible, stars detected on the r CCDs are matched
directly with stars in the
United States Naval Observatory CCD
Astrograph Catalog
(UCAC, Zacharias et al. 2000), an (eventually)
allsky astrometric catalog with a precision of 70 millarcsec (mas)
at its catalog limit of r = 16, and systematic errors of less than 30 mas.
For DR2, stripes 913, 76, 82, and 86 used UCAC.
 If a scan is not covered by the current version of UCAC, then it is
reduced against Tycho2
(Hog et al. 2000), an allsky astrometric catalog
with a median precision of 70 mas at its catalog limit of
V_{T} = 11.5, and
systematic errors of less than 1 mas.
For DR2, stripes 3043 used Tycho2.
For point sources brighter than r = 20, the errors in the calibrations dominate
the centroiding errors.
The accuracy of the calibrations using UCAC are of order 45 mas rms per
coordinate (all errors in this section are quoted as rms per coordinate), with
an additional systematic error of up to 30 mas (due primarily
to systematic errors in UCAC). The accuracy of calibrations using Tycho2 are
of order 75 mas rms with an additional systematic error of order 20 mas
(due to CTE effects in the astrometric CCDs). The rms errors are dominated
by Gaussian distributions of systematic errors which vary on time scales of
one to a few tens of minutes due to anomalous refraction,
and by random errors in the primary reference catalogs.
The accuracy of the relative astrometry of the
u, g, i, and z filters versus the r filter is of order 25 mas rms
for the g, i, and z filters, and 35 mas rms
for the u filter. Systematic errors with magnitude, color, or CCD column
are typically less than 10 mas.
At the survey limit (r = 22), the astrometric accuracy is limited by
photon statistics to approximately 100 mas rms for typical seeing.
Calculating Errors for Individual Objects
The calibrations are performed in great circle coordinates.
The estimated errors in the calibrations are given on a perframe
basis. The calibration errors in great circle longitude and latitude are
given by the attributes muErr and nuErr, respectively
(in arcseconds). These are in the tsField files in the DAS.
These should be added in quadrature with the
centroiding errors for individual objects to give the estimated total error
in the position of a given object. The centroiding errors in great circle
longitude and latitude are given by the attributes objc_rowcErr and
objc_colcErr, respectively (in pixels; these should be multiplied by
the focal plane scale of 0.396 arcseconds/pixel to convert to arcseconds).
These attributes are in the tsObjc files in the DAS.
Astrometric calibrations are generated as a separate set of equations for
each frame, converting frame row (x), frame column (y), and
star color to catalog mean place great circle longitude (μ) and latitude (ν),
in degrees:
for color < (color)_{0}:
x' = x + g_{0} + g_{1} y + g_{2} y^{2} + g_{3} y^{3} + p_{x} color
y' = y + h_{0} + h_{1} y + h_{2} y^{2} + h_{3} y^{3} + p_{y} color
for color > (color)_{0}:
x' = x + g_{0} + g_{1} y + g_{2} y^{2} + g_{3} y^{3} + q_{x}
y' = y + h_{0} + h_{1} y + h_{2} y^{2} + h_{3} y^{3} + q_{y}
μ = a + b x' + c y'
ν = d + e x' + f y'
The transformation from (x, y) to (x', y') corrects for optical
distortions (which, in TDI mode, are a function of column
only) and differential chromatic refraction (DCR). For u and
g frames, DCR is modeled as a linear function of color (ug for u
frames, gr for g frames) for blue stars
[(color)_{0} = (ug)_{0} = 3.0 for u frames,
(color)_{0} = (gr)_{0} = 1.5 for g frames],
and a constant for redder stars. For r, i, and z frames,
DCR is modeled as a linear function of color (ri) for all stars
[(color)_{0} = (ri)_{0} >> 1].
(The DCR corrections are misstated in Pier et al. [2003], where
[ri]_{0} appears in the equations rather than the correct
[color]_{0}, and where the wrong value for
[color]_{0} is given for u frames.)
The corrected frame coordinates (x', y') are then transformed to catalog mean
place great circle coordinates (μ, ν) using an affine
transformation.
The calibration coefficients may be found in the tsField files in
the DAS, where the attribute names are
different than given in the transformation equations above; (color)_{0}
is called riCut;
g_{0}, g_{1}, g_{2}, and
g_{3} are called dRow0, dRow1, dRow2,
and dRow3, respectively;
h_{0}, h_{1}, h_{2}, and
h_{3} are called dCol0, dCol1, dCol2,
and dCol3, respectively;
p_{x} and p_{y} are called csRow and csCol,
respectively; and
q_{x} and q_{y} are called ccRow and ccCol,
respectively.
The calibration equations above yield catalog mean place in great circle
coordinates. To convert these to J2000 celestial coordinates you need to know
the right ascension and inclination of the ascending node of the scan great
circle with respect to the J2000
celestial equator. These are given as the header keywords "NODE" and "INCL",
respectively, in the PDU of the "tsField" file. The celestial coordinates are
then
tan(α_{2000}  α_{0}) = [sin(μ  α_{0})cos ν cos i  sin ν sin i]/[cos(μ  α_{0})cos ν]
sin δ_{2000} = sin(μ  α_{0})cos ν sin i + sin ν cos i
where μ and ν are great circle longitude and latitude,
α_{0} and i are the right ascension and
inclination of the ascending node of the great circle with respect to the J2000
celestial equator, and α_{2000} and
δ_{2000} are J2000 right ascension and declination.
Last modified: Wed Apr 2 18:26:56 CST 2003
