As discussed before, the and
co-ordinates of an antenna are a
function of time and continuously change as earth rotates generating
the
-coverage. To improve the signal-to-noise ratio as well
as reduce the data volume, the visibility function
is
recorded after finite integration in time (typically 10-20s for
imaging projects) and the average value of the real and imaginary
parts of
are used for average values of
and
over the
integration time. Effectively then, the assigned values of
and
for each visibility point is evaluated for a time which is wrong
from the correct (instantaneous) time by a maximum of
where
is the integration time.
In the map domain, the resulting effect can be visualized by treating
the resulting map from the time average visibilities as the average
for a number of maps made from the instantaneous (un-averaged)
visibilities. The baseline vectors in the -domain follow the
loci of the
-tracks (which are parabolic tracks) and rotate at an
angular velocity equal to the that of earth,
. Since a
rotation of one domain results into a rotation by an equal amount in
the conjugate domain in a Fourier transform relation, the effect in
the map domain is that the instantaneous maps also are rotated with
respect to each other, at the rate of
. Hence, a point
source located at (
) away from the center of the map would get
smeared in the azimuthal direction. This effect is same as the
smearing effect due to finite bandwidth of observations, but in an
orthogonal direction.