The inverse problem in the magnetic diffraction of Josephson junctions

The determination of the critical current distribution in a Josephson junction is an important practical problem which is potentially capable of providing information about the local junction morphology. One possible approach is based on the magnetic diffraction pattern of the Josephson junction. Since the magnetic diffraction pattern may be expressed as the modulus of the Fourier transform of the current distribution in the junction, the problem of determining the current distribution is equivalent to retrieving the phase information which is lost when taking absolute values. This paper constitutes an analysis of this inverse problem specifically in relation to the determination of the current distribution from the magnetic diffraction pattern. Algorithms developed for similar inverse problems from other fields are examined to determine their applicability to this problem. It is proved that in some special cases the problem may be solved uniquely. In more general cases the density of possible solutions is studied to determine the conditions under which a unique solution might be found by an extension of the experimental procedure.