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 astro-ph/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) all-sky 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 9-13, 76, 82, and 86 used UCAC.
If a scan is not covered by the current version of UCAC, then it is reduced against Tycho-2 (Hog et al. 2000), an all-sky 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 30-43 used Tycho-2.

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 Tycho-2 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 per-frame 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.

Calibration Equations

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 + g₀ + g₁ y + g₂ y² + g₃ y³ + p_x color
   y' = y + h₀ + h₁ y + h₂ y² + h₃ y³ + p_y color

for color > (color)₀:
   x' = x + g₀ + g₁ y + g₂ y² + g₃ y³ + q_x
   y' = y + h₀ + h₁ y + h₂ y² + h₃ y³ + 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 (u-g for u frames, g-r for g frames) for blue stars [(color)₀ = (u-g)₀ = 3.0 for u frames, (color)₀ = (g-r)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 (r-i) for all stars [(color)₀ = (r-i)₀ >> 1]. (The DCR corrections are mis-stated in Pier et al. [2003], where [r-i]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; g₀, g₁, g₂, and g₃ are called dRow0, dRow1, dRow2, and dRow3, respectively; h₀, h₁, h₂, and h₃ 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.

Transformation from Great Circle Coordinates to J2000 Celestial Coordinates

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(α₂₀₀₀ - α₀) = [sin(μ - α₀)cos ν cos i - sin ν sin i]/[cos(μ - α₀)cos ν]
   sin δ₂₀₀₀ = sin(μ - α₀)cos ν sin i + sin ν cos i

where μ and ν are great circle longitude and latitude, α₀ and i are the right ascension and inclination of the ascending node of the great circle with respect to the J2000 celestial equator, and α₂₀₀₀ and δ₂₀₀₀ are J2000 right ascension and declination.

Last modified: Wed Apr 2 18:26:56 CST 2003

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