## Source and observed flux density

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.