### Interpretation

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)