Spherical Wave Expansion With Arbitrary Origin for Near-Field Antenna Measurements

The far-field radiation pattern of an antenna under test (AUT) can be derived via a spherical wave expansion of near-field antenna measurement data. The transformation as well as the measurement time scales with the number of spherical mode coefficients which depends on the radius of the sphere enclosing the antenna. In existing transformation procedures, the radius is measured from the center of the measurement sphere. Thus, the radius increases for an offset-mounted antenna so that more spherical mode coefficients are required to represent the electromagnetic field. In this communication, a procedure is proposed where the origin of the spherical wave expansion can be specified independently of the measurement sphere. With this procedure, the number of coefficients can always be minimized by selecting an expansion origin that minimizes the sphere enclosing the AUT. A translated expansion origin requires to include the probe pointing direction in the probe response constant calculation. This is achieved by Euler rotations of the probe receiving coefficients. The benefits of the procedure are demonstrated by measurements of an offset-mounted AUT.