The integral of the brightness over the source extension yields the total
source flux density
 |
(63) |
where
 |
[
] |
flux density of source, |
 |
[
] |
brightness as a function of position over source, |
 |
[
] |
infinitesimal solid angle of sky
. |
When the source is observed with an antenna of power pattern (
),
the observed flux density in direction (
) is
 |
(64) |
where
(
) |
[
] |
observed flux density, |
 |
[
] |
brightness as a function of position over source, |
 |
[
] |
normalized antenna power pattern, |
 |
[
] |
infinitesimal solid angle of sky
. |
This integral is a correlation. We now introduce the mirror symmetric of
the antenna pattern to yield a convolution
 |
(65) |
where |
(66) |
The distinction of these two patterns is only important for
non-axisymmetrical cases.