## Effective aperture and aperture efficiency

Let's define the effective aperture of an antenna, , through the relationship between the received spectral power and the sky brightness

| (99)

This definition is based on Eq. with the assumption that the power pattern is independent of infinitesimal surface area of the receiving antenna in order to be able to factorize the integral on this infinitesimal surface area. Moreover the factor 1/2 corresponds to the case where the radiation is incoherent and unpolarized, and the receiver is only sensitive to one polarization.

This effective aperture corresponds to the fraction of the power density of a plane wave that is intercepted by the antenna. It has the unit of a surface [ ]. It thus resembles a cross-section in particle physics. We thus define the aperture efficiency, , as the ratio of the effective aperture by the geometric aperture of the antenna

where | (100)