  Optically levitated nanoparticles offer enormous potential for precision
sensing. However, as for any other metrology device, the absolute measurement
performance of a levitated-particle sensor is limited by the accuracy of the
calibration relating the measured signal to an absolute displacement of the
particle. Here, we suggest and demonstrate calibration protocols for
levitated-nanoparticle sensors. Our calibration procedures include the
treatment of anharmonicities in the trapping potential, as well as a protocol
using a harmonic driving force, which is applicable if the sensor is coupled to
a heat bath of unknown temperature. Finally, using the calibration, we
determine the center-of-mass temperature of an optically levitated particle in
thermal equilibrium from its motion, and discuss the optimal measurement time
required to determine said temperature.
