Abstract-Electromagnetic field transformations are important for electromagnetic simulations and for measurements. Especially for field measurements, the influence of the measurement probe must be considered, and this can be achieved by working with weighted field transformations. This paper is a review paper on weighted field transformations, where new information on algorithmic properties and new results are also included. Starting from the spatial domain weighted radiation integral involving free space Green's functions, properties such as uniqueness and the meaning of the weighting function are discussed. Several spectral domain formulations of the weighted field transformation integrals are reviewed. The focus of the paper is on hierarchical multilevel representations of irregular field transformations with propagating plane waves on the Ewald sphere. The resulting Fast Irregular Antenna Field Transformation Algorithm (FIAFTA) is a versatile and efficient transformation technique for arbitrary antenna and scattering fields. The fields can be sampled at arbitrary irregular locations and with arbitrary measurement probes without compromising the accuracy and the efficiency of the algorithm. FIAFTA supports different equivalent sources representations of the radiation or scattering object: 1) equivalent surface current densities discretized on triangular meshes, 2) plane wave representations, 3) spherical harmonics representations. The current densities provide for excellent spatial localization and deliver most diagnostics information about the test object. A priori information about the test object can easily be incorporated, too. Using plane wave and spherical harmonics representations, the spatial localization is not as good as with spatial current densities, but still much better than in the case of conventional modal expansions. Both far-field based expansions lead to faster transformations than the equivalent currents and in particular the orthogonal spherical harmonics expansion is a very attractive and robust choice. All three expansions are well-suited for efficient echo suppression by spatial filtering. Various new field transformation and new computational performance results are shown in order to illustrate some capabilities of the algorithm.

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Imaging is a valuable tool for solving inverse source problems. The achievable image quality is determined by the imaging system. Its performance can be evaluated by using the concept of point spread functions (PSFs). It is common to compute the PSFs using a numerical algorithm. However, in some cases the PSFs can be derived analytically. In this work, new analytical PSFs are presented. The results apply to scalar and dyadic scenarios in 3D originating from acoustics and electromagnetics. Data sets with narrow angular acquisition or complete spherical coverage are considered, where broadband and narrowband frequency domain data is supported. Several visualizations accompany the resulting formulas. Finally, the analytical PSFs are verified using a numerical implementation of the imaging process.

Abstract. The characterization of antenna radiation patterns by transformed near-field measurements requires accurate amplitude and phase data. This represents a problem since expensive measurement equipment is required, especially at millimeter and submillimeter wavelengths (Isernia et al., 1996). Amplitude-only antenna field measurements are theoretically sufficient for the unique determination of antenna far-fields. Therefore, phaseless techniques are of special interest. However, the required field transformations are extremely challenging, since they are nonlinear and strongly ill-posed. In this work, the amplitude-only or phaseless near-field far-field transformation problem is formulated as a nonlinear optimization problem. The linear radiation operator within the nonlinear formulation is evaluated using the fast irregular antenna field transformation algorithm (FIAFTA). A hybrid solution procedure is described which combines a genetic algorithm with an iterative conjugate gradient (CG) search method. Numerical results prove the efficiency and flexibility of the formulation and it is shown that the algorithm remains stable when the noise level in the measurements is moderate. Nevertheless, regularization techniques might be beneficial to further improve the robustness of the algorithm.