Systematic optimization of exterior measurement locations for the determination of interior magnetic field vector components in inaccessible regions

An experiment may face the challenge of real-time determination of the magnetic field vector components present within some interior region of the experimental apparatus over which it is impossible to directly measure the field components during the operation of the experiment. As a solution to this problem, we propose a general concept which provides for a unique determination of the field components within such an interior region solely from exterior measurements at fixed discrete locations. The method is general and does not require the field to possess any type of symmetry. We describe our systematic approach for optimizing the locations of these exterior measurements which maximizes their sensitivity to successive terms in a multipole expansion of the field.