For a single-field interferometric observation, the dirty map is
obtained by Fourier Transform of the observed visibilities. It is
related to the actual sky brightness distribution
by:
Due to the coupling between the receiver horn and the primary
mirror of the antennas (see Chapter 1 by A. Greve), the
primary beam is, to a good approximation, a Gaussian. Its
FWHM, proportional to the ratio of the wavelength
to the
antenna diameter
, can therefore be used to quantify the
field of view. Note that this size does not correspond to a clear
cut of the map, but to the 50% attenuation level.
Table 17.1 gives the resulting values
for the Plateau de Bure interferometer, for different frequencies. To map regions more
extended than the primary beam width, it is necessary to observe a
mosaic of several adjacent fields. Clearly, due to the
gaussian-shape of the primary beam attenuation, these fields have
to strongly overlap to ensure a roughly uniform sensitivity over
the whole mapped region.
A further complication arises from the lack of the short-spacings
information in the interferometer data set. Due to their diameter, the
antennas cannot be put too close to each other, which results in a
minimal measured baseline (24 m at the Plateau de Bure). Even if projection
effects reduce the effective baselines, a central ``hole'' in the data
distribution in the plane cannot be avoided. As a consequence,
the extended structures (whose visibilities are confined in a small
region in the
plane) are filtered out. The largest structure it
is possible to map with a single-field interferometric observation is
thus even smaller than the field of view, and can be very roughly
estimated by the ratio of the wavelength to the minimal baseline
(Table 17.1).