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General description

In this family, the single-dish information is heavily processed before merging with the interferometric information. The basic idea is to produce from the single-dish observations pseudo-visibilities similar to the ones that would be produced by the interferometer if they were not filtered out.

  1. The Single-Dish measurements are re-gridded and then FFTed into the $uv$ plane.
  2. The data are deconvolved of the single-dish beam ( $B_\ensuremath{\mathrm{sd}}$) convolution by division by its Fourier Transform (truncated to the antenna diameter).
  3. The data are FFTed back to the image plane and multiplied by the interferometer primary beam, $B_\ensuremath{\mathrm{primary}}$.
  4. The result is FFTed again in the $uv$ plane where the visibilities are sampled on a regular grid.
  5. In the case of a mosaic, the two last operations are performed for each pointing center.
Using the properties of the Fourier transform, we can rewrite the measurement equation of an interferometer as
\begin{displaymath}
V(u,v) = \ensuremath{\displaystyle\left\{ \mbox{FT}(B_\ensu...
...ar \mbox{FT}(I_\ensuremath{\mathrm{source}}) \right\}}(u,v)+N.
\end{displaymath} (5.10)

This equation means that the visibility measured by an interferometer at the spatial frequency $(u,v)$ is the convolution of the Fourier transform of the source intensity distribution by the Fourier transform of the primary beam. Hence, to get pseudo-visibilities truly consistent with interferometric visibilities, we must be able to reliably compute the convolution by the Fourier transform of the primary beam. This implies that we can compute pseudo-visibilities only for spatial frequencies lower than $D-d$. The use of the IRAM-30m to produce the short-spacing information of the PdBI is thus ideal as it enables to recover pseudo-visibilities up to 15 m ( $=30\,\mbox{m}-15\,\mbox{m}$). Once the pseudo-visibilities have been computed, they are merged with the interferometric visibilities and standard imaging and deconvolution are then applied to the merged data set.


next up previous contents index
Next: An important subset: The Up: Pseudo-visibility technique Previous: Pseudo-visibility technique   Contents   Index
Gildas manager 2024-03-29