Halbach permanent magnet array characterization

The Halbach permanent magnet array (HPMA) is a convenient and cost-effective way to generate strong magnetic fields in low-field magnetic resonance imaging (MRI). Our group developed an HPMA that can switch on and off dynamically during imaging to enhance the signal-to-noise ratio. However, manufacturing imperfections and temperature fluctuations can change magnetization direction and/or strength from their specified values after switching, leading to dynamic variations in the magnetic fields. These variations can be compensated for during post-processing if the changes are known. In this paper, we report a multiple linear regression algorithm for estimating magnetization orientation errors and magnetization strength deviations from magnetic field measurements. The results can be used to improve the accuracy of HPMA-produced magnetic fields and reduce image distortions as a post-processing step. We validated the algorithm using computer simulations in COMSOL Multiphysics and experimental measurements on the ultra-low-field MRI (ULF-MRI) system developed at the University of Queensland. The computer simulations confirmed that the algorithm can accurately estimate errors in permanent magnet parameters, even with 5% errors in the magnetic field measurements. The prediction error is negligible for noiseless measurements and 0.1° in magnetization orientation and is 0.1% in magnetization change if the magnetic field measurements contain 1% error. Experimental measurements on the ULF-MRI system yield an accuracy of 1 μT at the center of the HPMA. Although designed for an ultra-low-field MRI system, the algorithm may also potentially be applied to estimate magnetic fields or examine magnets in other HPMA applications.