2026-08-12 –, Room 4
Magnetic fields are vital in numerous applications, including the medical imaging modality magnetic particle imaging, where field-related artifacts affect image quality. A good approximation of these fields is essential and can be done via spherical harmonic expansions derived from calibration measurements. The Julia package SphericalHarmonicExpansions.jl facilitates representation, transformations, and fast numerical evaluation, providing efficient tools for accurate magnetic field analysis.
The Julia package SphericalHarmonicExpansions.jl provides a flexible and efficient framework for working with spherical harmonics and their expansions. By expanding general solutions to Laplace’s equation inside a sphere into spherical harmonics, the package enables a broad range of applications. It offers easy manipulation of the coefficients, including coordinate transformations such as translation, rotation, and point reflection, as well as fast numerical evaluations of the expansion.
The focus of the talk is the application of the package to magnetic fields, which play a crucial role in medical imaging techniques such as magnetic particle imaging (MPI). In MPI, static and dynamic fields excite iron-oxide nanoparticles to achieve spatial encoding. Field-related imperfections can cause artifacts that degrade image quality, making precise knowledge and characterization of these fields essential. Spherical harmonic expansions offer a compact and robust representation of the magnetic fields within a spherical region, which can be obtained by calibration measurements on a spherical surface.
While the package itself is application-independent, it serves as the core component to handle magnetic fields using spherical harmonics in Julia. Example code demonstrating its application to magnetic field representation and evaluation is available in the SphericalHarmonicExpansionOfMagneticFields repository. Complementary, in-development packages like MPISphericalHarmonics.jl, which provides interfaces tailored to magnetic field handling in MPI, and MPIUI.jl, with an interactive GUI for visualization, extend this foundation with practical tools for research and application.
The focus of this talk will be
* Structure and functionality of SphericalHarmonicExpansions.jl
* Application to magnetic fields
* Usage example in MPI
Marija Boberg is a doctoral candidate associated with the University Medical Center Hamburg-Eppendorf and the Hamburg University of Technology (Germany). Her academic background is in mathematics, and her research is focused on magnetic fields and image reconstruction in magnetic particle imaging.