Precise 3D field measurements of large, complex magnet geometries are time-consuming and error-susceptible. For large magnets, it is common to record Hall probe data on a sparse grid, then use an interpolation algorithm to estimate field values at the remaining points. For common magnet geometries, such as quadrupoles and dipoles, linear interpolation often provides accurate results. However, for complex magnet geometries, this method can yield lower accuracy. In this paper, we present a method based on a locally Maxwell-consistent algorithm for sparse Hall probe measurements. Through the k-nearest neighbors algorithm, we locally fit the magnetic field with Tikhonov regularization. We test this method on a novel Compton spectrometer, capable of measuring single-shot, double-differential, energy-angle gamma spectra, ranging from 180 keV to 28 MeV. Using held-out validation, we demonstrate that we can reconstruct its magnetic fields with higher accuracy than linear interpolation and radial basis function (RBF) interpolation with cubic, thin plate spline, and quintic kernels. We also analyze the dependence of point sparsity on accuracy.

Precise 3D field measurements of large, complex magnet geometries are time-consuming and error-susceptible. For large magnets, it is common to record Hall probe data on a sparse grid, then use an interpolation algorithm to estimate field values at the remaining points. For common magnet geometries, such as quadrupoles and dipoles, linear interpolation often provides accurate results. However, for complex magnet geometries, this method can yield lower accuracy. In this paper, we present a method based on a locally Maxwell-consistent algorithm for sparse Hall probe measurements. Through the k-nearest neighbors algorithm, we locally fit the magnetic field with Tikhonov regularization. We test this method on a novel Compton spectrometer, capable of measuring single-shot, double-differential, energy-angle gamma spectra, ranging from 180 keV to 28 MeV. Using held-out validation, we demonstrate that we can reconstruct its magnetic fields with higher accuracy than linear interpolation and radial basis function (RBF) interpolation with cubic, thin plate spline, and quintic kernels. We also analyze the dependence of point sparsity on accuracy.