Simultaneous determination of local magnetic fields and sensor orientation with nitrogen-vacancy centers in nanodiamond

Nitrogen-vacancy (NV) centers in nanodiamonds have emerged as a promising quantum sensing platform for biomedical imaging applications. However, the random distribution of nanodiamond crystal orientations in biological samples presents significant challenges in calibrating particle-to-particle variations. In this study, we propose a novel approach to simultaneously detect the crystal orientations of various nanodiamond particles alongside their associated local vector magnetic fields. We demonstrate that a minimum of three different bias magnetic fields is required to accurately determine the local magnetic field. We develop several experimental configurations tailored for optimizing either imaging speed or accuracy and flexibility, depending on the experimental context. Finally, we validate our methods experimentally using NV centers in two scenarios: (1) a widefield microscope on bulk diamond crystals to assess accuracy, and (2) a confocal fluorescence microscope on various single nanodiamonds to simulate real-world applications.