The wireless industry is such that suppliers of antennas have to adapt their designs to requirement changes over a period of just a few months. In these short design cycles time is crucial. Radiation pattern testing of the antennas at various points in this design cycle are nowadays mostly done using spherical near-field techniques, where the tangential electric field is acquired over an imaginary sphere close to, and surrounding, the antenna under test, and this data then transformed into a far-zone radiation pattern. There are some applications where acquisition over a rotationally symmetric surface other than a spherical one would not only reduce test times, but allow equipment cost reductions as well. However, near-field to far-field transformations for finite non-spherical measurement surface shapes are not available. Such a transformation is proposed, implemented and validated in this thesis. It uses the method of moments, customized to a rotationally symmetric surface (body of revolution) to effect this transformation.