Due to the common path structure being insensitive to the environmental disturbances, relevant Fabry–Pérot interferometers have been presented for displacement measurement. However, the discontinuous signal distribution exists in the conventional Fabry–Pérot interferometer. Although a polarized Fabry–Pérot interferometer with low finesse was subsequently proposed, the signal processing is complicated, and the nonlinearity error of sub-micrometer order occurs in this signal. Therefore, a differential quadrature Fabry–Pérot interferometer has been proposed for the first time. In this measurement system, the nonlinearity error can be improved effectively, and the DC offset during the measurement procedure can be eliminated. Furthermore, the proposed system also features rapid and convenient replacing the measurement mirrors to meet the inspection requirement in various measuring ranges. In the comparison result between the commercial and self-developed Fabry–Pérot interferometer, it reveals that the maximum standard deviation is less than 0.120 μm in the whole measuring range of 600 mm. According to these results, the developed differential Fabry–Pérot interferometer is feasible for precise displacement measurement.
With the industrial development and the advances in micro-displacement technology, the demands on piezo transducers are increasing. For piezo transducers, the error inspections of the non-linearity and the hysteresis are necessary procedure before piezo transducers utilized. Due to the possible decline or damage during the employment of the transducers, it is important to provide the automatic calibration system. In this investigation, a self-developed automatic calibration system for micro-displacement devices is proposed. The automatic system according to the international specification of ASTM-E2309 has been developed. This system designed for the calibration of piezo transducers is based on the interferometric structure of the common optical path and possesses the resolution of the nanometer order. The experimental verifications demonstrate that the repeatability of the Fabry-Perot interferometer is less than 11 nm. Experimental results of the synchronic measurement with the self-developed interferometer and a commercial interferometer reveal that the differences of the maximum nonlinearity error and maximum hysteresis error are less than 1%. With the proposed correct equations, the maximum nonlinearity error can be minimized to 1% and the maximum hysteresis error will be less than 5.2%.
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