Fast spherical near-field measurements on arbitrary surfaces by application of pointwise probe correction to compressed sampling schemes

The major disadvantage of Spherical Near-Field (SNF) measurements is their long acquisition time. To calculate the Antenna Under Test's (AUT) far-field radiation characteristics, a sphere containing the AUT must be sampled. Classically, equiangular sampling is chosen, being the resulting sphere heavily oversampled. Since the Spherical Mode Coefficients (SMCs) are usually sparse, an approach to reduce the measurement time of SNF measurements is to undersample the sphere and to reconstruct the SMCs using compressed-sensing techniques. Using a sampling matrix with a minimum mutual coherence for the given bases of the SMCs increases the probability of recovery. The SMCs are defined in the basis of the spherical harmonics or Wigner D-functions, which limits the geometries in which this technique can be applied. In this work, the application of pointwise probe correction for the description of non-spherical surfaces in the Wigner-D basis expansion is suggested. The chosen sampling points are radially projected onto the measurement surface and the new distance to each point is calculated. New equivalent probe response coefficients are calculated per measurement point according to their distance to the AUT. To compensate for different orientations other than the probe pointing to the AUT's minimum sphere's center, the probe's SMCs are rotated to reflect the real orientation of the probe at each point prior to the calculation of the probe response coefficients. Although more computationally demanding than classical probe correction, this technique allows measurements with different, potentially faster geometries and enables the application of compressed sensing to other, non-spherical conventional scanning systems.