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Hansen T.B.,Seknion Inc.
International Journal of Antennas and Propagation | Year: 2012

The system-matrix method for higher-order probe correction in spherical near-field scanning is based on a renormalized least-squares approach in which the normal matrix closely resembles the identity matrix when most of the energy of the probe pattern resides in the first-order modes. This method will be stressed-tested in the present paper by employing probes for which up to 49% of the pattern energy resides in the higher-order modes. The condition number of the resulting normal matrix will be computed, and its distance from the identity matrix displayed. It is also shown how the condition number of the normal matrix can be further reduced. Copyright © 2012 Thorkild B. Hansen. Source


Analytic continuation of Gegenbauer's addition theorems produces a diagonal Gaussian translation operator for the fast multipole method (FMM) in three dimensions. The Gaussian beams affect only the translation operator, and as usual the field computation is performed with plane waves. Sampling theorems determine the plane-wave sampling rate required by the Gaussian translation operator. The formulation is based on an exact identity, so arbitrarily high accuracy can be achieved. The required sampling rate depends not only on the diameter of the source and receiver regions but also on the actual locations of the sources and receivers within those regions. The directionality of the Gaussian translation operator makes it possible to disregard a large fraction of the plane-wave translations. Numerical simulations reveal that for general source-receiver geometries the required number of plane-wave translations grows linearly with the diameter of the source-receiver groups. © 2013 Elsevier B.V. Source


An exact complex-space extension of the plane-wave Gegenbauer formula leads to a diagonal Gaussian translation operator for the fast multipole method (FMM) in two dimensions. The Gaussian beams are confined to the translation operator, and the fields are transmitted through plane waves as usual. The regions where the real source and receiver points can reside depend on the beam sharpness. As the beam gets sharper, the transverse dimensions of these regions get smaller. An arbitrarily high accuracy can be obtained with the Gaussian translation operator. The Gaussian translation operator makes it possible to disregard a large fraction of the plane-wave translations. The required sampling rate depends not only on the diameter of the source and receiver regions but also on the actual locations of the sources and receivers within those regions. For some common source-receiver geometries, the required sampling rate is below that of the standard translation operator. For other source-receiver geometries, the required sampling rate is greater than that of the standard translation operator. The theory is validated through numerical examples. © 2013 Elsevier B.V. Source


Hansen T.B.,Seknion Inc.
IEEE Transactions on Antennas and Propagation | Year: 2014

A new exact plane-wave expansion is presented for general time-harmonic electromagnetic fields radiated by an arbitrary finite source region in three dimensions. The plane-wave expansion employs a directional spectrum that is proportional to the far-field pattern of the source. The directionality is achieved through an exact representation that involves a beam parameter, which determines the sharpness of the spectrum. When the beam parameter is set to zero, the new expansion becomes identical to the plane-wave expansion employed in the fast multipole method. The expansion is exact for observations points all the way up to the source region and includes evanescent waves. An antenna-antenna transmission formula follows straightforwardly. Numerical examples demonstrate that the new plane-wave expansion requires fewer plane waves than previously derived plane-wave expansions. © 2014 IEEE. Source


Hansen T.B.,Seknion Inc.
IEEE Transactions on Antennas and Propagation | Year: 2014

A diagonal Gaussian translation operator for the time-harmonic fast multipole method (FMM) in two dimensions is examined numerically. The Gaussian translation operator depends on a beam parameter that determines its sharpness. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard FMM translation operator. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The required number of plane waves depends strongly on the actual source-receiver locations, not just on the diameter of the source and receiver regions. © 1963-2012 IEEE. Source

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