Integral equation formulation for probe corrected far-field reconstruction from measurements on a cylinder

A novel and numerically efficient method of far-field evaluation from measurements taken on a cylinder is based on the representation of both the antenna and the probe fields as superpositions of plane waves. A system of two integral equations are established whose unknown functions are the azimuthal and elevation components of the antenna pattern and whose known terms are the set of measurement data taken with two different probes-the second probe in most practical instances being simply the same probe with a different geometrical orientation. The equations express the known data-for each angular position of the antenna under measurement-as the integrals of the products of the corresponding components of the unknown antenna and known probe patterns multiplied by a phase term. The convolutional nature of the integral equations makes their solutions straightforward. If, as is virtually always the case, the probe has small or moderate size so that the axis of rotation of the antenna mount is in the far field of the probe, the intervention of asymptotic techniques makes the solution numerically very efficient. The agreement of calculated and experimental patterns is excellent.