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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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The quality of processed workpieces is affected directly by the precision of the linear stage. Therefore, the linear displacement calibration of machine tools must be implemented before delivery and after employment for a period of time. How to perform a precise calibration with high inspection efficiency is a critical issue in the precision mechanical engineering industry. In this study, the self-developed system integrated by the measurement module based on the common path Fabry–Pérot interferometer for linear displacement and the auto-alignment module for optical axes was proposed to realize the automatic linear displacement calibration of the linear stages. The measurement performance of the developed structure was verified experimentally. With the auto-alignment module, the cosine error was reduced to 0.36 nm and the entire procedure accomplished within 75 s without the limitation of the perceived resolution of the human eye, operational experience, and the risk of misalignment and broken cable. According to the comparison of experimental results for the linear displacement, the repeatability of the proposed measurement module was less than 0.171 μm. After the compensation procedure according to the linear displacement calibration, the systematic positional deviation, repeatability, and accuracy of the linear axis could be improved to 4 μm, 1 μm, and 5 μm respectively. Hence, the calibration efficiency can be improved by 80% with the proposed compact system, which is beneficial for the linear displacement calibration of machine tools in the precision mechanical engineering industry.

Laser interferometers have been widely implemented for the displacement sensing and positioning calibration of the precision mechanical industry, due to their excellent measuring features and direct traceability to the dimensional definition. Currently some kinds of modified Fabry-Perot interferometers with a planar mirror or a corner cube prism as the measurement mirror have been proposed. Each optical structure of both models has the individual particularity and performance for measuring applications. In this investigation, a multi-interferometric displacement system has been proposed whose measurement mirror can be quickly and conveniently altered with a planar mirror or a corner cube reflector depending on the measuring demand. Some experimental results and analyses about the interpolation error and displacement measurements with both reflectors have been demonstrated. According to the results, suggestions about the choice of a measuring reflector and interpolation model have been presented. With the measuring verifications, the developed system with a maximum standard deviation less than 0.2081 μm in measuring range of 300 mm would be a compact and robust tool for sensing or calibrating the linear displacement of mechanical equipment.

The construction of Fabry-Perot interferometer is very simple and it has been already utilized in different measurement systems. The result of displacement measurement is obviously influenced by the tilt angles of measurement mirror, if a Fabry-Perot interferometer is utilized for displacement measurement. Hence, the measuring range of current systems is rather small (less than 1 mm). The goal of this investigation is to develop a Fabry-Perot interferometer for large travelling range (till 60 mm) by aid of compensation of tilt angles with an angular sensor, piezo translators, control mechanism and self-designed software. To verify the measuring characteristic of the self-developed Fabry-Perot interferometer, some comparison measurements have been performed. A commercial laser interferometer serves as reference standard and the differences between Fabry-Perot interferometer and the commercial Laser interferometer are measured. Through experimental tests, the differences are less than 0.3 m in the full measurement range. The results show that the Fabry-Perot interferometer can meet the measuring requirement with high accuracy of sub-micrometer order and large measurement range.

A new optical encoder system is presented for displacement measurement by the curve fitting method. In this paper, another pondering model is based on the previous development. That is the new measurement method using a homemade periodical gray level code, which can be used to replace the traditional doublet grating. A high precision is achieved by a fitting method with one single-frequency harmonic function. The experiment result shows that the concept is feasible.