Primary beam (component) images

As described in the primary beam correction chapter, in most primary-beam correcting modes, WSClean will store 16 separate images for each Mueller-matrix component (e.g. named wsclean-beam-0.fits, wsclean-beam-1.fits, …, wsclean-beam-15.fits). These are difficult to interpret, as e.g. the shape that any one of these images indicates might not reflect the shape of the beam.

To turn a Mueller matrix into something that can be interpreted / validated, one option is to use the 16 images to form the Mueller matrix for each pixel (see below) and multiply this with the vector (0.5; 0.0; 0.0; 0.5). This results in the full Jones sensitivity of the beam. Starting WSClean 3.2, only the components of the Mueller matrix that are necessary for the correction are stored, e.g. with Stokes I imaging, only element 0 and 15 are stored.

Mueller matrix structure

The images form the lower triangle of the Hermitian matrix. For the diagonal elements, only the real value is stored, and off-diagonal elements contain two images: the real and imaginary parts. They’re counted from left to right, top to bottom, so their indices correspond to the following positions:

[0]
[1]+[ 2]i   [ 3]
[4]+[ 5]i   [ 6]+[ 7]i   [ 8]
[9]+[10]i   [11]+[12]i   [13]+[14]i   [15]

This implies for example that the diagonal elements are stored in images named like wsclean-beam-0.fits, wsclean-beam-3.fits, wsclean-beam-8.fits, wsclean-beam-15.fits, and the bottom-left entry of the matrix is split into a real part (wsclean-beam-9.fits) and an imaginary part (wsclean-beam-10.fits).