The nominal Full Width Half Maximum (FWHM) of a LOFAR Station beam is determined using the equation
where λ denotes wavelength and D denotes the station diameter. The value of α1 will depend on the tapering intrinsic to the layout of the station, and any additional tapering which may be used to form the station beam. No electronic tapering is presently applied to LOFAR station beamforming. For a uniformly illuminated circular aperture, α1 takes the value of 1.02, and the value increases with tapering (Napier 1999).
The Field of View (FoV) of a LOFAR station is defined by
The number of pointings to cover 2π steradians of sky in a Nyquist sampled way (on a square grid) is approximately 64800/FoV. After the weighted combination of the different pointings, the effective sensitivity will be better by a factor 1.5. Hence, one can choose to sample at slightly less than Nyquist to increase surveying speed.
Table 1 and Figure 1 summarize the FWHM, the FoV, for the different layouts of LOFAR stations .
Table 1 Primary beams (FWHM) and Field of View for the three configurations of LOFAR stations.
Figure 1 Primary beams (FWHM) as a function of frequency for the different station configurations. The curves are labeled by the type of LOFAR antenna field, whether LBA or HBA, as well as by either core, remote or international. The effective size of each field is also indicated in meters.
The angular resolution of the LOFAR array, calculated as the full width half maximum (FWHM) of the synthesized beam in radians, is given by
where λ is the observing wavelength, L denotes the longest baseline, and α2 depends on the array configuration and the imaging weighting scheme (natural, uniform, robust, ...). Values of the resolution of LOFAR based on a value of α2=0.8, which corresponds to uniform weighting scheme for the Dutch array can be found in Table 2.
Note: The numbers on the table below are indicative. For example in the NL the maximum baseline of ~82 km is only at a North-South direction. At the east-west direction the resolution is significantly lower; currently the maximum east-west baseline is ~21 km.
Table 2. Indicative resolution of the LOFAR array with frequency (see text for details).
Figure 2. Effective spatial resolution as a function of frequency for different subsets fo the LOFAR array.