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In this paper, we apply a recently developed 3D source reconstruction algorithm to perform antenna diagnostics on a planar array configuration. The test case is a planar X-band slot array measured in a spherical near-field facility and two slots were intentionally covered during the measurement campaign to test the performance of the algorithm. These measured data have previously been analyzed in [1] using two different methods for planar back-projection. For the purpose of comparison, results obtained with a planar reconstruction method based on conversion of spherical waves are also presented.

A multilevel computation scheme for time-harmonic fields in three dimensions will be formulated with a new Gaussian translation operator that decays exponentially outside a circular cone centered on the line connecting the source and observation groups. This Gaussian translation operator is directional and diagonal with its sharpness determined by a beam parameter. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard fast multipole method translation operator. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The use of the computation scheme will be illustrated through a near-field scanning problem where the far-field pattern of a source is determined from near-field measurements with a known probe. Here the Gaussian translation operator improves the condition number of the matrix equation that determines the far-field pattern. The Gaussian translation operator can also be used when the probe pattern is known only in one hemisphere, as is common in practice. Also, the Gaussian translation operator will be used to solve the scattering problem of the perfectly conducting sphere.

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined.Index Terms-Fast multipole method, higher order basis functions, integral equations.

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