It is well known that the scattered field at all points outside the smallest convex support region of a scattering object can be represented in a plane wave expansion (generally known as an angular spectrum expansion) whose plane wave amplitude is linearly related to the objects scattering amplitude and to the plane wave amplitude of the incident wave to the scatterer. This simple linear mapping is shown to lead to a general procedure for constructing a basis set of incident and scattered waves that are ordered according to the scattered field energy Ep . Moreover, the scattered field energy is found to have a critical cutoff p = P0 beyond which it decays exponentially. As a consequence, the scattered field generated by the incident wave generated from modes above the critical cutoff has negligible scattered field energy and, hence, this incident wave does not appear to interact with the scattering ob ject. This talk will review the general theory outlined above and discuss possible applications including the in- verse scattering problem of determining the shape of an ob ject from knowledge of its scattering amplitude. Other applications include constructing incident waves that dont scatter from known ob jects and constructing ob jects that dont interact with a given set of incident waves.