The brightness observed in direction (
) is the flux density
observed in this direction divided by the typical beam area
 |
(67) |
where
(
) |
[
] |
observed brightness, |
 |
[
] |
actual brightness as a function of position over source, |
 |
[sr] |
typical beam area, |
 |
[
] |
normalized antenna power pattern, |
 |
[
] |
infinitesimal solid angle of sky
. |
The typical beam area is an ambiguous notion. Indeed, there are
three different solid angles that can be used in this formula: The antenna
beam solid angle (
), the forward beam solid angle
(
), or the main beam solid angle (
)
It is trivial to show that
 |
(71) |
At IRAM, the observed brightness obtained after a single-dish
calibration are by default computed using the forward beam solid angle.