A maximum entropy solution for the undetermined electromagnetic field within a volume

The Gibbs maximum entropy (GME) solution is presented for the problem of estimating the sinusoidal electric field within a given volume of subject to constraints of measured electric field at I/sub 1/ points and zero tangential electric field at I/sub 2/ points. The field is expanded in a set of K solenoidal and perhaps irrotational (curl=0) modes with unknown amplitudes, defined within a convenient volume. Since the number of complex data in the three spatial directions, 3(I/sub 1/+I/sub 2/), is presumed to be considerably less than the number of complex amplitudes K, this is an undetermined problem.