On the Formulation of the Magnetic Particle Imaging System Function in Fourier Space

Several publications on magnetic particle imaging (MPI)are based on the Langevin theory of paramagnetism todescribe the imaging process [1-4]. However, althoughsome reconstruction methods require the Fouriertransform of the Langevin function and its derivative, inpractice, due to the lack of a closed-form expression, theyare approximated either numerically or via the Lorentzianfunction, which works quite well in practice.Nevertheless, we here give a closed-form solutionfor theFourier transform of the Langevin function and derive thetemporal and spatial Fourier transformed versions of thesystem function according to the Langevin model.