FITS world coordinates system

The term FITS stands for Flexible Image Transport System. It allows a user to store data (here an image) and some ancillary parameters (i.e. comments, or astrometry informations of an image) in a file. The ancillary parameters are stored in the top part, the so-called ``header'' of the FITS file. This header is an ASCII text and can be viewed using the commands ``more'' in UNIX or ``type'' in VMS. The actual data is stored in a binary format just after the header. The basic advantage of the FITS file format is that it is or it is supposed to be a stardard. In the extensive tests that we performed using FITS image files from several radio and optical telescopes, we never encountered problems with the image data but only with the astrometry infomation stored in the FITS header. The coordinate unit is the decimal degree. The header stores the coordinates RA and DEC of a specified point of the image (called the reference pixel) in two variables CRPIX1, CRPIX2, as follows:

CTYPE1  = 'RA---TAN'           / first parameter RA  ,  projection TANgential
CTYPE2  = 'DEC--TAN'           / second parameter DEC,  projection TANgential
CRVAL1  =              202.473 / Reference pixel value
CRVAL2  =              47.1967 / Reference pixel value
CRPIX1  =              150.500 / Reference pixel
CRPIX2  =              150.500 / Reference pixel
EQUINOX =              2000.00 /Equinox of coordinates

It also contains the ``roll'' of the image. There are several ways to do that, some official and some not :

• CROTA2 The simplest way is to give CROTA2, the angle between the North and the second axis of the image counted positive to the East, and the coordinate increments CDELT1, CDELT2. The last two are the per pixel increment along RA and DEC. They are included in the header as:

  CDELT1  =         -0.000666667 / Degrees/pixel
  CDELT2  =          0.000666667 / Degrees/pixel
  CROTA2  =              0.00000 / Rotation in degrees.

• CD00n00m Another way is to give the matrix CD00n00m and the increments CDELT1, CDELT2. This matrix is orthogonal (determinant = 1). This is an example:

  CD001001=           0.42355276 /astrometry parameters in DEGREES/PIXEL:
  CD001002=          -0.90587144 /
  CD002001=           0.90587144 /
  CD002002=           0.42355276 /
  CDELT1  =           0.00166667 /Coordinate increment per pixel in DEGREES/PIXEL
  CDELT2  =          -0.00166667 /Coordinate increment per pixel in DEGREES/PIXEL

  CROTA2 can ge given as well, but is redundant since:

        CD11 = cos(CROTA2)  CD12 = sin(CROTA2)
        CD21 = -sin(CROTA2) CD22 = cos(CROTA2)

• CDn_m This is the AIPS standard and is the most accurate method. It is a tranformation matrix and it is the product of CD00n00m by CDELTn:

  CD1_1   = CD001001*CDELT1   CD1_2 = CD001002*CDELT1
  CD2_1   = CD002001*CDELT2   CD2_2 = CD002002*CDELT2

  This is an example:

  CD1_1   =        4.2365384E-01 / DL/DX
  CD1_2   =       -9.0582417E-01 / DL/DY
  CD2_1   =        9.0582417E-01 / DM/DX
  CD2_2   =        4.2365384E-01 / DM/DY

  With this matrix, CROTA2 and CDELT1,CDELT2 are redundant.
• GSSS The GSSS Astrometry structure is described in the STScI Guide Star Survey and stores the coefficients of a polynomial interpolation to the astrometry of the image.

In all previous cases the projection method can be different from tangential (TAN). Often in radio images one finds the sinus (SIN) projection.