On the relationship between the physical aperture and the scattered power from a receiving antenna

In the application of the Poynting Theorem around a receiving antenna, the total power leaving the surface enclosing the antenna is a result of interference between the incident and scattered fields. An incident power is subject to the choice of a physical aperture, that is not uniquely defined. The only term that is independent of the choice of the physical aperture is seen as a combination of the self scattering term, resulting from sources over the antenna, and a cross term that involves both scattered and incident field. The way to determine a physical aperture is quite subjective.