Boberg, MarijaMarijaBobergKnopp, TobiasTobiasKnoppMöddel, MartinMartinMöddel2025-04-012025-04-012025-03-03European Journal of Applied Mathematics (in Press): (2025)https://hdl.handle.net/11420/55009Precise knowledge of magnetic fields is crucial in many medical imaging applications such as magnetic resonance imaging (MRI) or magnetic particle imaging (MPI), as they form the foundation of these imaging systems. Mathematical methods are essential for efficiently analysing the magnetic fields in the entire field-of-view. In this work, we propose a compact and unique representation of the magnetic fields using real solid spherical harmonic expansions, which can be obtained by spherical t-designs. To ensure a unique representation, the expansion point is shifted at the level of the expansion coefficients. As an application scenario, these methods are used to acquire and analyse the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as the unique expansion point.en1469-44252025Cambridge University Presshttps://creativecommons.org/licenses/by/4.0/magnetic fields | magnetic particle imaging (MPI) | solid harmonic expansions | spherical harmonicsTechnology::610: Medicine, HealthNatural Sciences and Mathematics::510: MathematicsJournal Articlehttps://doi.org/10.15480/882.1496910.1017/S095679252400088310.15480/882.14969Journal Article