Transition from the parabolic problem to the flat one and phantom

Abstract

Reduction of three-dimensional conical problem to two-dimensional (cylindrical, flat) has played a big role in the development of electromagnetic theory and its use in antenna technology. A similar result can be obtained by reducing the parabolic problem to the flat one. In this article the relations between the coordinates of the two systems are derived, and a condition allowing the transition is described.

The results are applied to the solving problem of the phantom shape and dimensions influence on the measurement results of the electric field generated by an external source outside of the phantom shell.