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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

| (5.6)

i.e. the measured intensity ( ) is the convolution of the source intensity distribution ( ) by the single-dish beam ( ) plus some thermal noise, while the measurement equation of an interferometer can be rewritten as

| (5.7)

i.e. the measured intensity ( ) is the convolution of the source intensity distribution times the primary beam ( ) by the dirty beam ( ) plus some thermal noise. has very similar properties than and very different properties than . In radioastronomy, and both have 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 and have similar full width at half maximum. Now, 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 has a full width at half maximum close to the interferometer resolution, i.e. much smaller than the FWHM of .

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.

Subsections

- Hybridization technique
- Pseudo-visibility technique
  - General description
  - An important subset: The zero spacing
  - Single-dish vs interferometer weight
- Comparison

Next: Hybridization technique Up: Short spacings (RUN UV_SHORT Previous: Short spacings (RUN UV_SHORT Contents Index