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The Rayleigh-Sommerfeld (RS) back-propagation method is accelerated by a modified version of the multilevel nonuniform grid algorithm (MLNG). The algorithm utilizes oblate spheroidal grids to be effective in terms of the number of sampling points that are required for correct reconstruction of the fields measured on quasi-planar surfaces. The method is demonstrated on the example of a parabolic reflector with a surface distortion. A good agreement between the results of the direct RS integration and the proposed method is achieved.

In the noninvasive bio-impedance technique, small amplitude currents are applied to the body and the developing potentials on its surface are measured. This noninvasive technique is used to monitor physiological and pathological processes, which alter the values or the spatial distribution of the electrical impedance inside the human body. A possible application of the bio-impedance technique is monitoring brain cryosurgery procedure--a surgical technique that employs freezing to destroy undesirable tissues. A numerical solver was developed to evaluate the ability of an induced-current bio-impedance system to monitor the growth of the frozen tissue inside the head in simulation. The forward-problem bio-impedance solver, which is based on the finite volume method in generalized two-dimensional (2-D) coordinate systems, was validated by a comparison to a known analytical solution for body-fitted and Cartesian meshing grids. The sensitivity of the developed surface potential to the ice-ball area was examined using a 2-D head model geometry, and was found to range between 0.8 x 10(-2) and 1.68 x 10(-2) (relative potential difference/mm2), depending on the relative positioning of the excitation coil and the head. The maximal sensitivity was achieved when the coil was located at the geometrical center of the model.

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A large class of source imaging methods is based on the radiated field backpropagation, often referred to as antenna holography, which has been widely used for large reflector antenna analysis. In these methods, the field is measured in either the near-or far-field zone of the source, by using a probe whose influence on the measured data is compensated. The measured field is propagated back to the source surface and the resulting reconstructed distribution is compared to the desired one. The comparison allows for the localization of distortions in the source's topography or current distribution. Although back-propagation does not accurately recover the original source distribution, it provides a good approximation of the radiating subspace of source distributions, up to an error due to the truncation of the measurement surface.As a representative example, we analyze parabolic reflector geometries using measurements on a planar surface, at a single frequency. For this case, it is convenient to use the Rayleigh-Sommerfeld integral formulation for backpropagation. Assuming both source and measurement surfaces are discretized by using localized basis functions, the direct numerical evaluation of the backpropagation integral's discretized form is characterized by a computational complexity (CC) of , where is a large parameter, with being the radius of the smallest sphere circumscribing the measurement domain, and -the wavenumber. Aiming to reduce the CC down to , while still being able to reconstruct the field on a concave surface of the reflector, we propose the use of the Multilevel Non-Uniform Grid (MLNG) algorithm (A. Gergel, Y. Brick, and A. Boag, ICEAA 2014, pp. 57-59). The MLNG scheme relies on the sampling of the partial phase-and amplitude-compensated field contributions on optimal sampling grids. The integration (measurement) domain is decomposed hierarchically into smaller sub-domains and non-uniform sampling can be used in a multilevel divide-and-conquer type procedure to capture partial contributions to the overall integral.In this work, we present an MLNG algorithm, for fast field integral evaluation, which makes use of the optimal volumetric sampling schemes in oblate spheroidal coordinates. For this coordinate system, analytical expressions for the phase-and amplitude-compensation and restoration factors are developed, together with optimal sampling criteria for the compensated fields. The performance in terms of accuracy and CC is compared to that achieved with the conventional spherical non-uniform grids. 70 978-1-4799-7817-5/15/$31.00