15.1 Introduction

The dirty map F resulting from a normal, single-field interferometric observation can be described by the equation:

$$F = D * (B \times I) + N %$$ (15.1)

where D is the dirty beam, B the antenna primary beam, I the sky brightness distribution, and N a noise distribution^15.1. The interferometer is only sensitive to the product of the sky brightness distribution by the rapidly decreasing function B. As the noise distribution N is not affected by B, any attempt to correct for the primary beam attenuation (i.e. divide the clean map by B) results in a strongly increasing noise. Hence, the primary beam attenuation limits the size of the region it is possible to map with an interferometer.

Due to the coupling between the receiver horn and the primary mirror of the antennas (see lecture 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 define a ``field of view''. Table 15.1 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 15.1). In the framework of mosaic observations, the short-spacings problem has however to be thought in slightly different terms, because it introduces now artifacts on an intermediate scale (see Sec. 15.5) but also because it can, at least in theory, be partially solved (Sec. 15.2).

 

Table 15.1: Field of view of the Plateau de Bure interferometer: the 15 m dishes have a gaussian illumination, which yields a nearly gaussian primary beam. 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