The role of periodic interferometer errors in the calibration of capacitance displacement sensors for nanometrology applications

Although the role of the periodic errors of optical heterodyne interferomet ers; in displacement measurements is fairly well understood, their influenc e on the calibration of other types of displacement sensor does not seem to be studied as extensively. We have performed a careful analysis of the rol e of these errors on the calibration of a capacitance displacement sensor, which is integrated into a linear piezoelectric transducer for nanometrolog y applications over displacement ranges in the sub-micrometre range. Assumi ng a linear dependence of the output voltage of the capacitance displacemen t sensor on the displacement it was found analytically that periodic interf erometer errors lead to a decaying oscillation of the sensor sensitivity as the displacement range used in the calibration increases. For use of a dou ble path interferometer with a polarization mixing amplitude of 0.5 nm and a polarization mixing wavelength of 79 nm, deviations of sensor sensitivity of 0.3% for a range of 0.2 mum and 0.029% for a range of 1 mum were estima ted. The pronounced oscillations of the sensor's sensitivity over very smal l displacement ranges as predicted by the theoretical description were veri fied experimentally.