  Determining sensor parameters is a prerequisite for quantitative force
measurement. Here we report a direct, high-precision calibration method for
quartz tuning fork(TF) sensors that are popular in the feld of nanomechanical
measurement. In the method, conservative and dissipative forces with controlled
amplitudes are applied to one prong of TF directly to mimic the tip-sample
interaction, and the responses of the sensor are measured at the same time to
extract sensor parameters. The method, for the frst time, allows force gradient
and damping coeffcient which correspond to the conservative and dissipative
interactions to be measured simultaneously. The calibration result shows
surprisingly that, unlike cantilevers, the frequency shift for TFs depends on
both the conservative and dissipative forces, which may be ascribed to the
complex dynamics. The effectiveness of the method is testifed by force spectrum
measurement with a calibrated TF. The method is generic for all kinds of
sensors used for non-contact atomic force microscopy(NC-AFM) and is an
important improvement for quantitative nanomechanical measurement.
