Active compensation of magnetic field distortions based on vector spherical harmonics field description

An analytic solution to the magnetostatic inverse problem in the framework of vector spherical harmonic basis functions is presented. This formalism is used for the design of a spherical magnetic field compensation system and its performance is compared with an already existing rectangular coil system. The proposed set of spherical coils with 15 degrees of freedom achieves a shielding factor of 1000 or better in a large part of the volume enclosed by the coils for a dipolar type external perturbation.