When u talk about the spectral content you likely mean the aperture field spectrum, i.e. , the Fourier Transform of the aperture field. As you probably know this spectrum is related to the radiation pattern...practically IT IS the radiation pattern, unless a cosine term and the proper (u,v) -> (theta, phi) substitution.
Anyway, when you know the aperture spectrum you know essentially the directivity of the antenna...so..you know how it irradiates the power in to the space.
In coclusion, from the spectrum of the aperture fields, u can characterize almost completely the radiative behaviour of the antenna.
Bye