17.1 Introduction

For a single-field interferometric observation, the dirty map $F$ is obtained by Fourier Transform of the observed visibilities. It is related to the actual sky brightness distribution $I$ by:

$$F = D * (B \times I) + N <tex2html_comment_mark>556$$ (17.1)

where $D$ is the dirty beam, $B$ the antenna primary beam, and $N$ a noise distribution^17.1. Hence, an interferometer only measures the product $B\times I$. $B$ is a rapidly decreasing function, and it therefore limits the size of the region it is possible to map. Correcting for the primary beam attenuation (i.e. dividing the map by $B$) is possible, and necessary for a proper estimate of the flux densities, but it does not enlarge the field of view, because of the noise distribution strongly increasing with the distance to the map center after such a correction.

Due to the coupling between the receiver horn and the primary mirror of the antennas (see Chapter 1 by A. Greve), the primary beam $B$ is, to a good approximation, a Gaussian. Its FWHM, proportional to the ratio of the wavelength $\lambda$ to the antenna diameter $\cal D$, 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 $uv$ plane cannot be avoided. As a consequence, the extended structures (whose visibilities are confined in a small region in the $uv$ 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).

Table 17.1: Field of view of the Plateau de Bure interferometer (15 m dishes). The two groups of frequencies correspond to the two receivers that are currently available. The last column gives rough estimates of the size of the largest structure which can be observed.

Frequency	Wavelength	Field of View	Largest structure
(GHz)	(mm)	($''$)	($''$)
85	3.5	58	36
100	3.0	50	31
115	2.6	43	27
215	1.4	23	14
230	1.3	21.5	13
245	1.2	20	12