A theoretical discussion of vector pick-up systems for SQUID magnetometers

The magnetic induction field produced by non-homogeneously magnetized samples of arbitrary shape is expanded in terms of a complete set of functions, the vector spherical harmonics. The weighing coefficients of this expansion - the multipole moments - are computed and are given up to fifth order for the most common sample shapes and homogeneous magnetization. The magnetic flux threading a general detection coil is computed analytically and pick-up systems of rotational symmetry as well as transverse systems are discussed. The flux profiles of dipole and higher order multipole moments along the direction of the applied field are plotted for common coil geometries as functions of the sample position. Both the influence of position errors on the flux profiles and the crosstalk between mutually perpendicular components of the dipole vector are analysed.