## 1 Introduction
The analysis method of the mean normalization is adopted to evaluate the amplitude and DC offset of the orthogonal signal in this study. Theoretically, if the signal amplitude is uniform change and there is no DC offset existing, the center (offset) of the orthogonal signal will  
Figure 1: Optical arrangement of Fabry–Perot interferometer: (**a**) Conventional structure, and (**b**) quadrature phase-shifted fiber-optic structure. be at the zero points, and it will become a circle shape after the mean normalization processing. Interferometric signals (I\({}_{\rm s}\), I\({}_{\rm p}\)) can be processed by the mean normalization (I\({}_{\rm s-nom}\), I\({}_{\rm p-nom}\)) individually represented in Equations (3) and (4). Then, the normalized orthogonal signal illustrated in Figure 3b can be obtained, where I\({}_{\rm max}\), I\({}_{\rm min}\), and \(\mu\) are the maximum, minimum, and average intensity. \[{\rm I}_{\rm s}=\frac{\frac{1}{2}{\rm A}_{0}{}^{2}\times{\rm T}^{2}\times{\rm T }}{1+{\rm R}^{2}\times{\rm T}^{\prime^{2}}-2\times{\rm T}\times{\rm R}\times \cos\!\left(\delta-\frac{\pi}{4}\right)} \tag{1}\]  
\[{\rm I}_{\rm p}=\frac{\frac{1}{2}{\rm A}_{0}{}^{2}\times{\rm T}^{2}\times{\rm T }}{1+{\rm R}^{2}\times{\rm T}^{\prime^{2}}-2\times{\rm T}\times{\rm R}\times \cos\!\left(\delta+\frac{\pi}{4}\right)} \tag{2}\]  
\[{\rm I}_{\rm s-nom}=\frac{{\rm I}_{\rm s}-\mu}{{\rm I}_{\rm s,max}-{\rm I}_{ \rm s,min}} \tag{3}\]  
\[{\rm I}_{\rm p-nom}=\frac{{\rm I}_{\rm p}-\mu}{{\rm I}_{\rm p,max}-{\rm I}_{ \rm p,min}} \tag{4}\]  
In this structure, there are two critical issues, including the existing large nonlinearity error in the signal and involving the complex signal processing for the elimination of the direct current (DC) offset. The nonlinearity error is caused by the DC offset, unequal alternating current (AC) amplitudes, and quadrature phase errors that occur in the orthogonal signal. In the simulation results in Figure 3, the orthogonal signal after the mean normalization processing reveals that the signal possesses the DC offset and unequal AC amplitudes, which will lead to the nonlinearity error. Therefore, the measurement accuracy of this measurement structure will be affected by the nonlinearity  
Figure 3: Orthogonal signal of polarized Fabry–Pérot interferometer. (**a**) Original signal; (**b**) signal with mean normalization processing. Figure 2: The optical arrangement of polarized Fabry–Pérot interferometer. PBS, polarizing beam splitter; PD, photodiode. error during the measurement. The formula for the analysis of the nonlinearity error is revealed in Equation (5), where \(\mathrm{I_{x}}\) and \(\mathrm{I_{y}}\) are the interferometric signals, \(\psi\) represents the ideal phase, and \(\mathrm{m}\) is a constant [13; 14; 15]. \[\mathrm{Nonlinearity\ error}=\arctan\left(\mathrm{I_{y}}/\mathrm{I_{x}}\right)- \psi+\mathrm{m}\pi \tag{5}\]  
In accordance with the measurement structure of the polarized Fabry-Perot interferometer, the analysis of the nonlinearity error is based on the simulated orthogonal signal, shown in Figure 3. The simulation result (Figure 4) reveals that the nonlinearity error is ranging from \(-48\) to \(131\) nm in the polarized Fabry-Perot interferometer. For subsequent signal subdivision, significant interpolation error will occur. Furthermore, the conventional correction method of nonlinearity error is also difficult to implement in this signal [16; 17]. Subsequently, a look-up table method was provided to carry out the signal subdivision with the resolution of \(0.1\) nm in the polarized Fabry-Perot interferometer [18]. Still, this method can only be processed for a single Lissajous signal under specific measurement conditions, e.g., measuring speed and range, etc. If the measurement signal changes, this method will not be able to carry out. In the correlated study, the Lissajous signal of the start-point and the endpoint in the whole measuring range of \(500\) mm is different, which means that the signal phase and amplitude are changing [11].