Calibration of subnanometer motion with picometer accuracy

We have developed a method for calibrating subnanometer movements of a piezoelectric actuator with picometer accuracy and for a wide range of frequencies. This range make this calibration useful for scanning probe microscopes, particularly for an apertureless scanning near-field optical microscope in which the tip is dithered to modulate the optical signal. The setup consists of a Michelson interferometer that has a mobile arm capable of moving more than one fringe. The piezoelectric actuator to be calibrated vibrates at the desired frequency in the other arm. Net displacement can be calculated by simultaneous measurement of an interferometric signal and its derivative. Hysteresis of the system can be also measured. It will be shown that the actuator response is linear only for the low-frequency region (in our case as much as approximately 10 kHz). Above that frequency range, higher harmonics appear and cannot be neglected to obtain real displacement. Finally, it will be shown that the use of higher harmonics in calibration or detection schemes (that rely on the linearity of the response) must be validated, and this technique has proved adequate for that purpose.