Optimal Sampling in Spherical Near-Field Antenna Measurements by Utilizing the Information Content of Spherical Wave Harmonics

In this article, we propose an efficient method that specifies the minimum number of samples and their locations to measure the spherical near-field (SNF) of antennas utilizing information-theoretic tools. To this end, spherical harmonics are investigated from the information-theoretic point of view. Our study determines the minimum required samples and provides a validation tool to assess the ability of a sampling scheme to recover the antenna characteristics by the measured data. Furthermore, an optimum sampling scheme is proposed by clustering the energy of vector spherical harmonics using the frame theory without any time-consuming iterative, which leads to a highly efficient SNF measurement procedure. The number of samples determined by the proposed method is only 50% of the Nyquist method, which provides significant advantages for storage and processing time. Our method additionally shows a great promise for the recovery of the far-field radiation pattern from near-field samples with the same performance as the Nyquist sampling on a sphere. To derive the proposed sampling scheme with the minimum redundancy, no prior information on the antenna is assumed. Finally, the proposed sampling scheme is validated on measurement data.