Theoretical development of laboratory techniques for magnetic measurement of large objects

Equations that relate magnetic gradiometric measurements over a closed surface to the prolate spheroidal multipole moments of an object can be used to remove the uniform inducing field of a magnetic calibration facility´s coil system, along with the Earth´s background field, from the signature of a large test object without requiring it to be moved. This paper presents an example that shows how the equations can be used to determine the optimum number, orientation, and position of gradiometers for accurate extrapolation of the object´s field signatures. In addition, it gives generalized boundary conditions that guarantee unique extrapolations of magnetic field, up to an additive constant, from a closed measurement surface instrumented only with gradiometers