The signal power received from a sky area in direction
is
(see Fig.2.3 for notations)
over bandwidth
, where
is the antenna power
pattern (assumed identical for both elements, more precisely
with Ai the voltage pattern
of antenna i), and
is the sky brightness distribution
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Two implicit assumptions have been made in deriving Eq.2.14. We assumed incident plane waves, which implies that the source must be in the far field of the interferometer. We used a linear superposition of the incident waves, which implies that the source must be spatially incoherent. These assumptions are quite valid for most astronomical sources, but may be violated under special circumstances. For example VLBI observations of solar system objects would violate the first assumption, while observations of celestial masers could (in theory) violate the second one.
When the interferometer is tracking a source in direction
, with
We thus have