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 interferometers in displacement measurements is fairly well understood, their influence on the calibration of other types of displacement sensors does not seem to be studied as extensively. We have performed a careful analysis of the role of these errors on the calibration of a capacitance displacement sensor, which is integrated into a linear piezoelectric transducer for nanometrology applications over displacement ranges in the sub-micrometer range. Assuming a linear dependence of the output voltage of the capacitance displacement sensor on the displacement, it was found analytically that periodic interferometer errors lead to a decaying oscillation of the sensor sensitivity as the displacement range used in the calibration increases. For use of a double 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 percent for a range of 0.2 micron and 0.029 percent for a range of 1 micron were estimated. The pronounced oscillations of the sensor's sensitivity over very small displacement ranges as predicted by the theoretical description were verified experimentally. (Author)