On the physical meaning of the model of two uncoupled isotrops

From first principles, we show that two non-isotropic radiators with a specific and uniquely determined far-field pattern can be modeled consistently as two uncoupled isotropic radiators, provided one is willing to accept a non-linear distortion of the geometry. This shows that the, per se, non-physical model of uncoupled isotrops can have physical meaning in correctly describing the behavior of special non-isotropic radiators. The necessary distortion of geometry and its consequences are discussed.