  Diamond-based magnetic field sensors have attracted great interest in recent
years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV)
centers in diamond has been previously demonstrated in condensed matter,
biological, and paleomagnetic applications. Vector magnetic imaging with NV
ensembles typically requires an applied field (>10 G) to separate the
contributions from four crystallographic orientations, hindering studies of
magnetic samples that require measurement in low or independently specified
bias fields. Here we decompose the NV ensemble magnetic resonance spectrum
without such a bias field by modulating the collected light at the microscope's
Fourier plane. In addition to enabling vector magnetic imaging at arbitrarily
low fields, our method can be used to extend the dynamic range at a given bias
field. As demonstrated here, optically-detected diamond magnetometry stands to
benefit from Fourier optical approaches, which have already found widespread
utility in other branches of photonics.
