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Next: Conversion to Standard Celestial Up: Sky Images Previous: From Pixel to Physical Deprojection

  The plane coordinates in physical units represent a projection of the celestial sphere. This projection is not unique, and different projections may be useful for different purposes. Maps of the earth, for example may be Mercator, equal-area, or some other projection, depending on the intended use. In this step, the projection is reversed, and the plane coordinates are transformed back to the projected sphere.

AIPS memo 27 (Greisen 1983) identified four common choices, which are discussed here because of their wide use. For three of these four projections, the choice for the tangent point, the point common to the celestial sphere and the plane on which it is projected, is arbitrary. AIPS adopted the convention that the reference pixel, given by the values of CRPIXn, is at this tangent point. If the tangent point of the projection is outside the image, then the values of the CRPIXn will be outside the data array. Note that the values of the CRVALn do not change between images in different regions of the same projection.

In the TAN (tangent) or gnomic geometry, the projection of a point of the celestial sphere onto the plane is found by extending the line from the center of the sphere to the point on the tangent plane. This projection is common in optical astronomy. In the SIN (sine) or orthographic geometry, common in radio aperture synthesis, the projection point is on the perpendicular between the point on the sphere and the surface of the tangent plane. In the ARC geometry, the projection point is on an arc passing through the point on the sphere and the tangent plane, with the center of the arc at the reference point. This projection preserves angular distances. It is the natural projection of Schmidt camera imagery, such as the Palomar Sky Survey, and is also used in single-dish radio telescope mapping. GC note that the NCP geometry discussed in the AIPS memo, a projection onto a plane perpendicular to the North Celestial Pole used by the Westerbork Synthesis Radio Telescope and a few other east-west radio interferometers, can be treated as a special case of the orthographic (SIN) projection. The SIN and TAN projections are special cases of the perspective zenithal projections, which are generated from a point and carried through from the unit sphere to the plane of projection.

The proposal adopts the notation that has been used in AIPS, using the last four characters of the value field of the CTYPEn keywords to identify the projection. Table 4.1 shows the codes for the projections described above.

Table:4.1 Common Projections
-TAN tangent
-SIN sine
-ARC arc

GC define 25 projection codes in all, including the spherical cube projection used by the COBE project (CSC). Many standard projections are special cases of these 25. The -NCP designation of the original AIPS memo is no longer used. For each projection they provide the transformation equations and a diagram.

The following indexed keyword is reserved under this proposal for defining projections:

PROJPn (floating) is the nth projection parameter. Projection parameters are additional quantities that are must be specified in order to define the projection completely. The specfic meaning of the keyword or keywords is defined separately for each projection. Many projections do not need these additional parameters.

GC call the deprojected coordinate system that results from this step the native coordinates.

next up previous contents
Next: Conversion to Standard Celestial Up: Sky Images Previous: From Pixel to Physical