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Algorithms to merge single-dish and interferometer information

The measurement equations of a single-dish and an interferometer are quite different from each other. Indeed, the measurement equation of a single-dish antenna is

\begin{displaymath}
I_\emr {meas}^\emr {sd} = B_\emr {sd} \star I_\emr {source} + N,
\end{displaymath} (12)

i.e. the measured intensity ( $I_{\emr {meas}}^{\emr {sd}}$) is the convolution of the source intensity distribution ( $I_{\emr {source}}$) by the single-dish beam ($B_{\emr {sd}}$) plus some thermal noise, while the measurement equation of an interferometer can be rewritten as
\begin{displaymath}
I_\emr {meas}^\emr {id} = B_\emr {dirty} \star \cbrace{B_\emr {primary}.I_\emr {source}} + N,
\end{displaymath} (13)

i.e. the measured intensity ( $I_{\emr {meas}}^{\emr {id}}$) is the convolution of the source intensity distribution times the primary beam ( $B_{\emr {primary}}.I_{\emr {source}}$) by the dirty beam ( $B_{\emr {dirty}}$) plus some thermal noise. $B_{\emr {sd}}$ has very similar properties than $B_{\emr {primary}}$ and very different properties than $B_{\emr {dirty}}$. In radioastronomy, $B_{\emr {sd}}$ and $B_{\emr {primary}}$ both have (approximately) Gaussian shapes. Moreover, the fact that we will use the single-dish information to produce the short-spacing information filtered out by the interferometer implies that $B_{\emr {sd}}$ and $B_{\emr {primary}}$ have similar full width at half maximum. Now, $B_{\emr {dirty}}$ is quite far from a Gaussian shape with the current generation of interferometer (in particular, it has large sidelobes) and the primary side lobe of $B_{\emr {dirty}}$ has a full width at half maximum close to the interferometer resolution, i.e. much smaller than the FWHM of $B_{\emr {sd}}$.

Merging both kinds of information obtained from such different measurement equations thus asks for a dedicated processing. There are mainly two families of short-spacing processing: the hybridization and the pseudo-visibility techniques.



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Next: Hybridization technique (``feathering'') Up: Short and Zero spacings Previous: Principle   Contents   Index
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