While this relationship was derived using a particular experimental setup,
it yields a result that only characterize the state of the antenna. As
usual in thermodynamics, the state is independent on the exact setup. This
implies that the relationship is valid independent on the way it was
yielded.
Nevertheless the demonstration is useful to understand that the solid angle
that we have to consider in this relationship is the beam area, i.e., the
coupling of the antenna to all direction in
. It is then
possible to rewrite this relationship as
 |
(81) |
Using the definition of the aperture efficiency, we yield
 |
(82) |
As
and |
(83) |
we yield
 |
(84) |
The factor
defines the coupling of the optics to the sky, which
can be computed with Gaussian optics. Its value is typically
. Finally, the Ruze theory indicates that the aperture efficiency is
linked to the RMS
of the deviation of the telescope surface to a
perfect parabola as
 |
(85) |