Mosaicking

Mosaicking is a particular case of wide-field imaging: The user wishes to observe a given field of view larger than the primary beam size with a sensitivity as uniform as possible.

The targeted field (which area is \ensuremath{A_\ensuremath{\mathrm{map}}}, define by the user) can be divided in a number of independent resolution elements or independent (primary) beams \ensuremath{n_\ensuremath{\mathrm{beam}}}. We have:

  $\displaystyle \ensuremath{n_\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}}
$ (25)
where \ensuremath{A_\ensuremath{\mathrm{beam}}}is the area of the primary beam. It is linked to the telescope full width at half maximum ( \ensuremath{\theta_\ensuremath{\mathrm{}}}) by
  $\displaystyle \ensuremath{A_\ensuremath{\mathrm{beam}}}= \frac{0.8\,\pi\,\ensuremath{\theta_\ensuremath{\mathrm{prim}}}^2}{4\,\ln(2)},
$ (26)
The 0.8 factor represents the truncation of the beam at 20% of its maximum, which is performed during the imaging process.

Note that \ensuremath{n_\ensuremath{\mathrm{beam}}} is not the number of pointed positions that are observed for the mosaic ( $\ensuremath{n_\ensuremath{\mathrm{point}}}> \ensuremath{n_\ensuremath{\mathrm{beam}}}$, see below).

For the sensitivity estimation we assume a standard sampling of targeted field and the on-source time is equally divided between the independent primary beams \ensuremath{n_\ensuremath{\mathrm{beam}}} in the targeted field of view. To first order, we thus yield:

  $\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{...
...n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}}
$ (27)
  $\displaystyle \quad \mbox{with} \quad
\ensuremath{\Delta t_\ensuremath{\mathrm...
...ta_\ensuremath{\mathrm{tel}}}\times \ensuremath{n_\ensuremath{\mathrm{beam}}}}
$ (28)

There are several subtleties in this computation.

In summary, the sensitivity of a Nyquist sampled mosaic is

  $\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{...
...n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}}
$ (36)
  $\displaystyle \mbox{with} \quad
\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}...
...math{\eta_\ensuremath{\mathrm{mos}}}\ensuremath{n_\ensuremath{\mathrm{beam}}}}
$ (37)