  We report a new method to determine the orientation of individual
nitrogen-vacancy (NV) centers in a bulk diamond and use them to realize a
calibration-free vector magnetometer with nanoscale resolution. Optical vortex
beam is used for optical excitation and scanning the NV center in a
[111]-oriented diamond. The scanning fluorescence patterns of NV center with
different orientations are completely different. Thus, the orientation
information on each NV center in the lattice can be known directly without any
calibration process. Further, we use three differently oriented NV centers to
form a magnetometer and reconstruct the complete vector information on the
magnetic field based on the optically detected magnetic resonance(ODMR)
technique. Compared with previous schemes to realize vector magnetometry using
an NV center, our method is much more efficient and is easily applied in other
NV-based quantum sensing applications.
