Ill-posedness of inverse problem about mode content determination using far field measurements

The ill-posedness of the inverse problem on determination of mode content in a multimode cylindrical waveguide using far field measurements is investigated in this paper. The radiation patterns of different mode radiated from a conical horn antenna fed by a multi-mode waveguide are calculated. Then the ill-posedness of the inverse problem is investigated by comparing the radiation pattern generated by different hybrid modes. Results show that the inverse problem is severely ill-posed, because the far field at certain positions is not sensitive to the variation of the mode contents. It is difficult to determine the mode content accurately according to the measurements at those positions. After analyzing the change of far-field with the variation of mode content, the positions where measurem