Multiple Phase Centers

The field of view in VLBI observations is very small, around 10-4 of the primary antenna beam area. This restricted interferometer beam arises in the correlation process from smearing at positions away from the correlation phase center, due to averaging in time (with, typically, a 2-second period) and/or across bandwidth ("chromatic aberration'' over, typically, 0.5 MHz spectral resolution). Thus, imaging of targets that are widely spaced in the primary beam requires multiple processing passes in typical correlator implementations. If the visibilities are maintained at high time and frequency resolution, it is possible to perform a u-v shift after correlation, essentially repointing the correlated dataset to a new phase center. However, this approach would require prohibitively large visibility datasets.

DiFX implements multiple u-v shifts inside the correlator, to generate as many phase centers as are necessary, in a single correlation pass. The output consists of one dataset of normal size for each phase center. This mode consumes around three times the correlator resources of a normal continuum correlation, due to the need for finer frequency resolution before the u-v shift, but the additional cost is only weakly dependent on the number of phase centers. For reasonable spectral and temporal resolution requirements (for example, adequate for smearing < 10% at the 50% contour of the VLBA primary beam), 200 phase centers require only 20% more correlator time than 2 phase centers. Extremely high spectral and/or temporal resolution (e.g. for shifts even closer to the edge of the primary beam) carry a higher overhead per additional phase center. This mode thus should be requested only for imaging of three or more sources within any single antenna pointing. The correlator output rate expands proportionally to the number of phase centers.

Correlator memory limits the product of baselines, spectral points, and phase centers for one correlator pass. The current limit is approximately 600 phase centers for the 10 element VLBA at 2 Gbps record rate (512 MHz polarization-summed bandwidth) for dual polarization products. Two correlator passes may be necessary for 600 phase centers with dual polarization products using the 4 Gbps record rate. Full polarization products reduce the maximum number of phase centers per correlator pass by a factor of 2. An unlimited number of phase centers can ultimately be achieved in multiple correlation passes, regardless of record rate or polarization setup.

Multiple phase-center correlation is requested in the NRAO Proposal Submission Tool by setting the "Number of Fields" item in the resource section to the maximum number of phase centers required for any antenna pointing specified in a given resource. The requested spectral resolution and integration time should correspond to the desired initial number of spectral points per data channel (required to minimize bandwidth smearing) and the desired integration between u-v shifts (to minimize time smearing). A resulting expanded output data rate that exceeds the current limit, as well as any required multiple passes, must be justified specifically in the proposal.

SCHED includes facilities to support specification of the actual phase center locations to be used in correlation.

For more details on wide-field imaging techniques, see Bridle & Schwab (1999), and Garrett et al. (1999).