Antenna coupling and near-field sampling in plane-polar coordinates

A probe-corrected vector transmission formula and a rigorous sampling-reconstruction theorem for near-field antenna measurements in plane-polar coordinates are derived from three fundamental theorems of antenna theory: the mutual coupling function between two antennas satisfies the homogeneous wave equation; a receiving antenna can be represented as a differentiator of the incident field; and the mutual coupling function is virtually bandlimited. The rigorous sampling equations are applied to compute the far fields of a circular-aperture antenna sampled in the near field at half-wavelength radial spacing