Filter functions for computing multipole moments from the magnetic field normal to a plane

A technique for calculating the magnetostatic multipole moments (and therefore complete biomagnetic information) from measurements of the normal component of the magnetic field on a plane is described. The technique involves multiplying the measured values by a set of unique filtering functions and integrating. A new formulation and method for calculating the filtering functions is introduced. The method uses expansions in basis sets and matrix inversion. Proofs are given of the nonsingularity of the matrices. Computer simulations of the application of the technique to a circular current loop and a current dipole in a spherical conductor are described.