## 1 Introduction  
From the comparison between the resolution and measuring range of different measurement devices, high resolution and contactless measurement can be realized by the laser interferometer in various measuring ranges. Hence, the industrial application, including the calibration of the linear axis for the machine tool, the positioning of the microelectromechanical equipment, and the wafer dicing, must rely on it to ensure the quality of production and the high-precision inspection requirement [1; 2; 3; 4]. Currently, the Michelson interferometer is the primary tool for displacement measurement in a large dynamic range. In the optical structure, the laser beam is divided into a reference beam and a measurement beam by a non-polarizing beam splitter (BS), and corresponding mirrors reflect each beam and then form the interferometric signal. The phase of this signal depends on the optical path difference between the reference beam and the measurement beam. Because the reference path is separate from the measurement path, this kind of interferometer is susceptible to relative environmental changes. In contrast, the Fabry-Perot interferometer is based on the common path structure. For this reason, laser beams propagate in the same optical path, and this interferometer possesses high resistance of environmental disturbances that contain thermal expansion, micro-flow gradient, and the tiny vibration [5; 6; 7]. The optical arrangement of the conventional Fabry-Perot interferometer, which contains a laser light source, a detector, and an optical cavity composed of two plane mirrors (PMs) had been proposed by [PERSON] and [PERSON] in 1897 (illustrated in Figure 1a) [8]. The laser light source is incident into the optical cavity in a nearly vertical direction, and the laser beam is divided into numerous transmitted beams from the cavity reciprocally. Then the interferometric signal can be acquired by the detector. Because the optical cavity of the conventional Fabry-Perot interferometer is composed of two PMs with a high reflectance, which results in the discontinuous signal distribution with high finesse. Furthermore, displacement or vibration can only be realized by the fringe counting method, and it is rarely utilized in large-scale dynamic displacement measurements. According to the development of the optical encoder and the interferometer system, to improve the measurement accuracy, correlated technologies, including orthogonal signal processing and signal subdivision, have been proposed. Therefore, the quadrature phase-shifted fiber-optic Fabry-Perot interferometer demonstrated in Figure 1b had been presented by [PERSON] et al. in 1999 [9]. This structure is based on the spatial phase-shifted method to form the orthogonal signal, which will be obtained by two detectors (D\({}_{1}\), D\({}_{2}\)). The phase shift is mainly decided by the position and angle of the probe and the measured surface. For this reason, the measuring range is limited by the performance of the optical-mechanical alignment. In the recent study, polarized Fabry-Perot interferometer with low finesse, shown in Figure 2, had been proposed by [PERSON] et al. in 2013 [10; 11]. The octadic-wave plate is placed in the optical cavity, and its polarization axis must be the same as that of the polarizing beam splitter (PBS) to introduce the orthogonal phase shift between two interferometric signals. By reducing the reflectance of the plane mirror, continuous signal distribution can be acquired, and the interferometric signals (I\({}_{\text{s}}\), I\({}_{\text{p}}\)) can be detected by the photodiodes (PD\({}_{1}\), PD\({}_{2}\)). The orthogonal interferometric signal, shown in Figure 3a, can be expressed by Equations (1) and (2) [12], where A\({}_{0}\) is the amplitude of the incident beam, R and T are the reflectance and transmittance of the coated plane mirror, T' is the transmittance of the optical cavity, and \(\delta\) is the phase difference. In the simulation, optical parameters of R, T, and T' are 0.25, 0.75, and 0.86, respectively.