Analysis of the scattered field singularities for optimizing the inverse problems solution

There are many publications concerning the inverse problems. It is known that such tasks have no unique solution. For example, in the given antenna problem there are different current distributions on the different surfaces. The main problem is to obtain the distribution of these currents that produce the minimum reactive field in the near zone so that the whole feeding energy is transmitted into the travelling wave. Such antenna is called a well matched antenna. On the other hand it is known that the travelling wave is analytical everywhere except in the area of singularities of the radiated field. This paper presents a method for visualisation of this area and the singularities in it. The suggestion is that the simple sources placed in the points of the singularities form a well matched antenna. The problem to be solved is as follows. Given the amplitude and phase distribution in far zone, find the corresponding current distribution and the best location that gives a well matched antenna.