Spherical Near Field to Far Field Transformation Algorithm for Offset-Mounted Antennas on Metallic Ground

With regard to the spherical near-field measurement of on-board and airborne antennas, the floor of the test site is mostly replaced by metallic plane, which not only facilitates the movement of large carriers but also narrows the test space. However, it will lead to difficulty in recovering the spherical mode coefficients (SMC) of the antenna under test (AUT) from the superimposed near field on the upper hemisphere, extrapolating the far field in free zone. Furthermore, due to physical constraints, the AUT will generally deviate from the scan center, inducing an increment of the required samples for solving SMC. Therefore, a transformation algorithm is proposed in this paper, which can be applied to the near field on the measurement sphere of the offset antenna above the PEC plane to acquire the three-dimensional radiation characteristics in free space at a lower oversampling rate. The boundary conditions of the electric field of the PEC plane are fulfilled by imposing the image principle on the spherical modes. With the introduction of rotation and translation operators, the relationship of SMC in the global and eccentric coordinate system is investigated, enabling the algorithm to effectively minimize the quantity of unknown SMC. Moreover, when combined with the igloo sampling grid, the oversampling rate for retrieving SMC can be further decreased, thus shortening the measurement time. While the test site contains metallic ground, the numerical results demonstrate the capability of the presented method to derive the SMC of the offset antenna and extrapolate the far field in free space.