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Precise knowledge of magnetic fields is crucial in many medical imagingapplications like magnetic resonance imaging or magnetic particle imaging (MPI)as they are the foundation of these imaging systems. For the investigation ofthe influence of field imperfections on imaging, a compact and uniquerepresentation of the magnetic fields using real solid spherical harmonics,which can be obtained by measuring a few points of the magnetic field only, isof great assistance. In this manuscript, we review real solid harmonicexpansions as a general solution of Laplace's equation including an efficientcalculation of their coefficients using spherical t-designs. We also provide amethod to shift the reference point of an expansion by calculating thecoefficients of the shifted expansion from the initial ones. These methods areused to obtain the magnetic fields of an MPI system. Here, the field-free-pointof the spatial encoding field serves as unique expansion point. Lastly, wequantify the severity of the distortions of the static and dynamic fields inMPI by analyzing the expansion coefficients.

Unique Compact Representation of Magnetic Fields using Truncated Solid Harmonic Expansions