As mentioned above, emission from the phase center and from points close to it lie approximately in the tangent plane. Polyhedron imaging relies on exploiting this fact by approximating the celestial sphere by a number of tangent planes as shown in Fig. 14.3. The visibility data is phase rotated to shift the phase center to the tangent points of the various planes and a small region around the tangent point is then mapped using the 2D approximation. In this case however, one needs to perform a joint deconvolution involving all tangent planes since the sides lobes of a source in one plane would leak into other planes as well.

The number of planes required to map an object of size can be
found simply by requiring that maximum separation between the tangent
plane and the region around each tangent point be less than
, the size of the synthesized beam. As shown
earlier, the separation of a point degrees away from the
tangent point is
. Hence for critical sampling, the
number of planes required is equal to the solid angle subtended by the
sky being mapped () divided by the solid angle of the
synthesized beam ()

(14.2.8) |

The polyhedron imaging scheme is available in the current version of
`AIPS` data reduction package and the 3D inversion (and
deconvolution) is implemented in the (not any more supported) `SDE` package written by Tim Cornwell et al. Both these schemes, in
their full glory, will be available in the (recently released) `AIPS++` package.