Time-Averaging Loss

The sampled coherence function (visibility) for objects not located at the phase-tracking center is slowly time-variable due to the motion of the source through the interferometer coherence pattern, so that averaging the samples in time will cause a loss of amplitude. Unlike the bandwidth loss effect described above, the losses due to time averaging cannot be simply parameterized, except for observations at δ = 90^°. In this case, the effects are identical to the bandwidth effect except they operate in the azimuthal, rather than the radial, direction. The functional dependence is the same as for chromatic aberration with Δν/ν₀ replaced by ω_eΔt_int, where ω_e is the Earth's angular rotation rate, and Δt_int is the averaging interval.

For other declinations, the effects are more complicated and approximate methods of analysis must be employed. Chapter 13 of Reference 1 (in Documentation) considers the average reduction in image amplitude due to finite time averaging. The results are summarized in Table 9, showing the time averaging in seconds which results in 1%, 5% and 10% loss in the amplitude of a point source located at the first null of the primary beam. These results can be extended to objects at other distances from the phase tracking center by noting that the loss in amplitude scales with (θΔt_int)², where θ is the distance from the phase center and Δt_int is the averaging time. We recommend that observers reduce the effect of time-average smearing by using integration times as short as 1 or 2 seconds (also see Section 4.5) in the A and B configurations.

Note: The averaging time (in seconds) resulting in the listed amplitude losses for a point source at the antenna first null. Multiply the tabulated averaging times by 2.4 to get the amplitude loss at the half-power point of the primary beam. Divide the tabulated values by 4 if interested in the amplitude loss at the first null for the longest baselines.