The radiative near- and far-field regions are characterized by the approximations made to the integrals [Eq. (1)].

 (1)

The radiative near-field region lies between the near field, with no approximations, and the far-field region. In both approximations the field (observation) distance r is substituted for |r − r| in the amplitude term. The vector potentials reduce to

  (2)

We handle the phase term differently in the two regions. First, we expand the phase term in a Taylor series,

 where ˆr is the unit vector in the field point direction. We retain the first two terms for the far-field approximation and the vector potentials become

   (3)

where we have combined k, the propagation constant, with the unit vector ˆr:

The magnetic vector potential integral parallels Eq. (3) as in Eq. (2). In the radiative near-field zone approximation the terms in r 2 are retained and we obtain the following integral for the electric vector potential:

  (4)

No clear boundary between the three regions exists because the fields are continuous. Common boundaries are

where L is the maximum dimension on the aperture.