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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 ($B_{\emr {sd}}$) 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, $B_{\emr {primary}}$.
  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) = \cbrace{\mbox{FT}(B_\emr {primary}) \star \mbox{FT}(I_\emr {source})}(u,v)+N.
\end{displaymath} (16)

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 NOEMA is thus ideal as it enables to recover pseudo-visibilities up to 15 m (=30m-15m). 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: Single-dish vs interferometer weight Up: Pseudo-visibility technique Previous: Pseudo-visibility technique   Contents   Index
Gildas manager 2023-06-01