WIDE-FIELD IMAGING

The field of view that may be imaged by the VLBA is limited by smearing due to averaging over time and frequency at positions away from the correlator phase center, where the fringes are ``stopped'' (see Bridle & Schwab 1999, upon which this section is based). The maximum field of view is relatively independent of observing frequency in the case limited by bandwidth smearing (chromatic aberration), but depends on observing frequency for time-average smearing. As computing hardware has become more capable, it now is feasible to reduce the averaging in time and in frequency, subject to the maximum correlator output rate of 1.0 MB/s, in order to enable imaging all or part of a wider field of view. Care must be taken to reduce the averaging time and/or spectral channel width in the data output by the correlator, and then to retain these smaller averaging values in subsequent data processing.

A standard set of correlator parameters for VLBA observations of a continuum source would have 16 spectral points per 8 MHz BB channel, and time averaging over 1.97 s. (Correlator averaging times are integer multiples of the fundamental time step of 131.072 milliseconds; see Section 8.) In the limit of short time averaging so that there is no time-averaging loss, the approximate distance from the phase center for a 5% loss in peak amplitude due to bandwidth smearing is given by

$$\theta_{5\%,\Delta\nu}\ \approx\ 4.7\ \biggl({0.5\ {\rm MHz}\over \Delta\nu}\biggr )\ {\rm arcsec},$$ (2)

where $\Delta\nu$ is the width of an individual spectral point in MHz. Equation 2 assumes a Gaussian bandpass with a circular Gaussian taper. In the limit of narrow spectral channels, so that there is no bandwidth smearing loss, the approximate distance from the phase center for a 5% loss in peak amplitude due to time-average smearing is given by

$$\theta_{5\%,\tau}\ \approx\ 2.8\ \biggl({8.4\ {\rm GHz}\ove... ...l({1.97\ {\rm s}\over \tau_{\rm acc}}\biggr)\ {\rm arcsec},$$ (3)

where $\nu$ is the sky frequency in GHz and $\tau_{\rm acc}$ is the correlator accumulation time in seconds. Equation 3 assumes circular coverage in the $u$-$v$ plane with a Gaussian taper, for a source at the celestial pole. Away from the celestial pole, the allowed field of view is somewhat larger, and also depends on direction relative to the phase center, so Equation 3 generally provides a lower limit to the distance from the phase center at which a 5% loss occurs.

For a fixed bit rate in a continuum observation, bandwidth smearing is reduced by using 2-bit sampling rather than 1-bit sampling; this provides approximately the same sensitivity (see Section 14 below) with 1/2 the total bandwidth, or 1/2 the spectral point width for the same correlator output rate. For a 10-station VLBA observation with two 8-MHz BB channels at each of two polarizations, and correlation of all four polarization pairs (RR, RL, LR, and LL), the limiting correlator output rate of 1.0 MB/s is approached (for example) with an accumulation time of 0.26 s and 32 spectral points in each of the 8-MHz BB channels. A rough scaling law for the data output rate from the VLBA correlator in this case is

$${\rm Rate}\ \approx\ 0.87 \biggl({N\over 10}\biggr)^2\ \b... ...biggr)\ \biggl({N_{\rm sp}\over 32}\biggr)\ {\rm MB/s}\ .$$ (4)

If one were to correlate only the parallel hands, RR and LL, Equation 4 would be modified to

$${\rm Rate}\ \approx\ 0.43 \biggl({N\over 10}\biggr)^2\ \b... ...}\biggr)\ \biggl({N_{\rm sp}\over 32}\biggr)\ {\rm MB/s}.$$ (5)

In the two equations above, $N$ is the number of antennas available and $N_{\rm sp}$ is the number of spectral points output by the correlator for each BB channel. For more details on wide-field imaging techniques, see Garrett et al. (1999).