Time-Averaging Loss

The sampled coherence function (visibility) for objects not located at the phase-tracking center is slowly time-variable due to the changing array geometry, 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. The only simple case exists for observations at $\delta = 90^{\circ}$, where 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 in this case with $\Delta \nu /\nu_0$ replaced by $\omega_e\Delta t_{\rm int}$, where $\omega_e$ is the Earth's angular rotation rate, and $\Delta t_{\rm int}$ 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 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 $(\theta\Delta t_{\rm int})^2$, where $\theta$ is the distance from the phase center and $\Delta t_{\rm int}$ is the averaging time. Since the size of VLA continuum data sets typically is not a limiting factor for modern computers, we recommend that most observers reduce the effect of time-average smearing by using integration times of $3\frac{1}{3}$ seconds (also see Section 3.6) in at least the A and B configurations.

Table 9: Loss vs. Averaging Time for Time Averaging Smearing

	Amplitude loss							.
Configuration	1	.	0%	5	.	0%	10	.	0%
A	2	.	1	4	.	8	6	.	7
B	6	.	8	15	.	0	21	.	0
C	21	.	0	48	.	0	67	.	0
D	68	.	0	150	.	0	210	.	0

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 on the longest baselines.