The nitrogen-vacancy (NV) center in diamond has become a widely used platform for quantum sensing. The four NV axes in mono-crystalline diamond specifically allow for vector magnetometry, with magnetic-field sensitivities reaching down to fT/Hz. The current literature primarily focuses on improving the precision of NV-based magnetometers. Here, we study the experimental accuracy of determining the magnetic field from measured spin-resonance frequencies via solving the NV Hamiltonian. We derive exact, analytical, and fast-to-compute formulas for calculating resonance frequencies from a known magnetic-field vector, and vice versa, formulas for calculating the magnetic-field vector from measured resonance frequencies. Additionally, the accuracy of often-used approximations is assessed. Finally, we promote using the Voigt profile as a fit model to determine the linewidth of measured resonances accurately. An open-source Python package accompanies our analysis.
@article{arxiv.2504.20750,
title = {Limits of absolute vector magnetometry with NV centers in diamond},
author = {Dennis Lönard and Isabel Cardoso Barbosa and Stefan Johansson and Jonas Gutsche and Artur Widera},
journal= {arXiv preprint arXiv:2504.20750},
year = {2025}
}