In astronomical work the World Co-ordinate System (WCS) describes the relationship
between rectangular pixel co-ordinates of an image and the spherical co-ordinate system of
the sky, in a particular projection (see Section 5.4). The system of co-ordinates used by the
LT will be Right Ascension and Declination (see any standard astronomy text). The Method
of construction of a WCS in a FITS file has still not been met with approval by the
FITS working group. However an exhaustive discussion of WCS, as a proposal for the
FITS standard, is given by Calabretta and Greisen (2000); Greisen (2000); Greisen and
Calabretta (2000). The WCS proposal includes scope for a measurable quantity such the
longitude and latitude in a conventional spherical co-ordinate system which define a direction
in a space (Greisen and Calabretta, 2000).
A WCS is formed by measuring the cartesian co-ordinates, in the tangential plane, of a
known reference point on the celestial sphere. With the pixel scale known it is then possible
to generate the mapping parameters and calculate the spherical coordinates of the other stars
in the frame.
With reference to Figure 5.1; the construction of the WCS in a FITS file is achieved by
specifying (i) a pixel reference point, in cartesian co-ordinates, 
, where 
points to the
East and 
to the North, and (ii) the known celestial co-ordinates of that point in RA and
Dec. Simply, this point can be the centre of the image where the celestial co-ordinates are
known as it is the pointing of the telescope.
This process is integrated with FITS through the keywords shown in Table 5.4 and was
originally proposed by Wells et al. (1981).
| FITS Keyword | Description
|
|
|
|
| | |
| CRVALi | Co-ordinate value at the reference point |
| CRPIXi | Array location of the reference point in pixels |
| CDELTi | Co-ordinate increment at reference point |
| CTYPEi | Axis type (e.g., RA, DEC etc.) |
| CROTAi | Rotation from the standard co-ordinate type |
|
| | |
| Table 5.4: | Keywords original proposed by Wells et al. (1981) to integrate a WCS in to
the FITS environment. |
|
While deliberatively simple in its specification this description is inadequate. It provides for
rotation only in one axis and does not provide for skew. To over come this
Calabretta and
Greisen (
2000);
Greisen (
2000);
Greisen and Calabretta (
2000) have specified a square linear
matrix of side NAXIS:
 | (5.2) |
or
 | (5.3) |
where
pi are the pixel numbers,
ri are the pixel co-ordinates of the reference point (CRPIX
i),
CD
i,j is a co-ordinate transformation matrix,
i is the pixel axis number,
j is the world
co-ordinate axis number and the
xj are the world co-ordinates in physical units. The full
CD
i,j matrix allows for skew and fully general rotations. This method is incorporated in to
FITS using the keywords in Table
5.5
| FITS Keyword | Description
|
|
|
|
| | |
| CRVALjs | Co-ordinate value at reference point |
| CRPIXis | Pixel co-ordinate of the reference point |
| CTYPEjs | Axis type |
| CDj_is | Co-ordinate transformation matrix |
| CUNITjs | Units of CRVALjs and CDj_is |
|
| | |
|
The analogy with the older
FITS headers is:
 | (5.4) |
Once a plane surface has been fitted with a WCS it maybe termed a world canvas - onto
which pixel values or data values may be plotted, in a world co-ordinate system. With an
accurate world canvas stars may be accurately identified by the
PL and matched against the
LT photometric catalogue (see Section
5.9.4), hence correct zeropoint calculations may
occur.
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