Aspects concerning the choice of measuring points and specification of parameters needed for a proper determination of magnetic fields

Laplacian fields approximated by a finite series based on an orthogonal set of spherical harmonics are treated. A procedure for estimating the optimal shape of an approximation model, showing not only the variety of degrees but also the highest significant order and a possible order absence of involved field functions, is developed. The restrictions on the distribution of field observations are specified, and a way to ensure a distribution respecting these restrictions that leads to a reduction of necessary field observations is proposed. On the basis of computer simulation, rules for the estimation of the minimal number and distribution of observation points necessary for a proper analysis of a field determination by a particular approximation model are specified. The approach substantially reduces time and calculation effort for magnetic field analysis.