The Data and Astrometric Solutions

The original plate images are composed of 14000 x 13999 pixels. To allow fast access to any portion of the plates, the images were divided into blocks of 500 x 500 pixels (500 x 499 for the last row) that were compressed separately. The GetImage image extraction software allows any arbitrary section of a plate to be extracted; only the blocks that are needed for the requested section are uncompressed.

All the extracted plate images have header. These header contain a FITS-like description of the plate scans. Keywords other than those for standard FITS headers describe the details of the plate scans, including a polynomial solution for mapping X,Y pixel coordinates on the plate to right ascension and declination. The polynomial form of the astrometric solutions is identical to that adopted for the GSC(versions 1.0 and 1.1). The solutions for plates that were not desheared or dechopped are indeed the GSC V1.0/1.1 solutions. A new astrometric solution was computed for the 48 plates that were processed through our deshearing ordechopping algorithms.

The following information is provided for those who wish to compute object coordinates once a subimage has been uncompressed.

The origin convention adopted in generating the astrometric solutions is that the X, Y coordinates of the lower left hand corner of the lower left hand pixel in a 14000 x 13999 pixel image are (1.0, 1.0). Therefore, the center of the lower left hand pixel is (1.5, 1.5). This is contrary to the FITS standard(and the expectations of some popular image analysis packages) which define the center coordinates of the origin pixel to be (1.0, 1.0). If using software that expects pixel centers to have integral coordinate values, a (+0.5, +0.5) offset should be added to the measured X, Y coordinates prior to computing celestial coordinates. Failure to do so could result in a ~ 1.2" position error.

One also must assure that any image display software properly sets the absolute values of the origin coordinates for the particular subimage being processed. Some image display packages generate only relative coordinates (ie.the origin is always (0, 0) or (1, 1), and, consequently, gross position errors could be introduced. The proper X, Y coordinates of the lower left hand corner of the lower left hand pixel for any given subimage are stored in the keywords CNPIX1 and CNPIX2, respectively.

To compute an equatorial position ( J2000 ) from pixel coordinates X, Y, computed with respect to the origin of the full 14000 x 13999 pixel image!!, one must first convert X, Y to units of mm from the plate center x, y:

    x = (Xc - Px*X) / 1000
    y = (Py*Y - Yc) / 1000
where Xc and Yc are the plate center coordinates in microns (assigned to keywords PPO3 and PPO6, respectively, in the FITS header) and Px and Py are the x and y dimensions of a pixel in microns (assigned to keywords XPIXELSZ and YPIXELSZ,respectively, in the FITS header).

One then constructs the standard coordinates xi, eta (x^2 = x*x):

   xi  = A1*x + A2*y + A3 + A4*x^2 + A5*x*y + A6*y^2 + 
         A7*(x^2 + y^2) + A8*x^3 + A9*x^2*y + A10*x*y^2 + 
         A11*y^3 + A12 x*(x^2 + y^2) + A13*x*(x^2 + y^2)^2
   eta = B1*y + B2*x + B3 + B4*y^2 + B5*x*y + B6*x^2 + 
         B7*(x^2 + y^2) + B8*y^3 + B9*x*y^2 + B10*x^2*y + 
         B11*x^3 + B12*y*(x^2 + y^2) + B13*y*(x^2 + y^2)^2
where A1, ..., A13 are assigned to keywords AMDX1, ..., AMDX13 and B1, ...,B13 are assigned to keywords AMDY1, ..., AMDY13. The keywords AMDX14, ...,AMDX20 and AMDY14, ..., AMDY20 are not currently used. The standard coordinates, as computed above, will be in units of arcseconds.

Finally, the J2000 celestial coordinates alpha, delta (in radians) are computed from the standard coordinates as follows:

   alpha = arctan [(xi/cos(Dc))/(1 - eta*tan(Dc))] + Ac

   delta = arctan {[(eta + tan(Dc))*cos(alpha-Ac)] / [1 - eta*tan(Dc)]}
where Ac is the plate center right ascension (assigned to keywords PLTRAH,PLTRAM, and PLTRAS) and Dc is the plate center declination (assigned to keywords PLTDECSN, PLTDECD, PLTDECM, and PLTDECS).

Attention! The variables Ac,Dc, xi, and eta must be converted to radians before using the above expressions! If alpha < 0, one must add 2 pi to its value to get the correct right ascension.