Investigation of Different Matrix Solver for Spherical Near-Field to Far-Field Transformation

The calculation of the spherical mode spectrum for the near-field to far-field transformation can be efficiently calculated by the use of the Fourier transform. However, this method requires an equiangular sampling over the sphere. This limitation can be overcome if the transmission equation is reformulated as a system of linear equations. The paper presents and compares different methods such as the least squares method and two iterative algorithms. It is shown that using a linear equation system does not reduce the accuracy of the calculated mode spectrum. Further it is pointed out that the flexibility can be used to apply arbitrary sampling grids and results for random sampling are presented. In conclusion it is motivated to replace the Fourier transform by a linear equation solver in order to improve the spherical near-field to far-field transformation.