## 4 Conclusions  
In summary, an OD-PDH system was built in this study. Based on this system, a method used to analyze the complicated resonances in MBR was presented. This method is repeatable, simple, sensitive, and accurate. The OD-PDH system can eliminate the phase difference between the local oscillation and detection signal, and generate a stable IQ curve. The IQ curve relates to the optical field rather than the light intensity, and contains both the amplitude and the phase information of the complex transmitted spectrum. The OD-PDH system transforms the sharp imaginary information of the resonance and the slope information of the resonance into the IQ curve. Any tiny change of resonance will influence the IQ curves significantly. Thus, the IQ curves can be used to analyze the complicated resonances that the transmitted spectrum cannot be used to analyze. We used the IQ curve to analyze the asymmetrical resonance caused by overlapping and weak-coupling resonances, which cannot be discriminated by the transmitted spectrum. Moreover, we analyzed the strong-coupling resonance, which may be mistakenly treated as an overlapping resonance. The resonance parameters were obtained accurately by fitting the  
Figure 4: (**a**) Experimental spectrum (blue scattered line), its IQ curve (black scattered line), IQ fitting, replotted spectrum (red solid line), resonance fitting, and replotted IQ curve (yellow dashed line). The pressure is 0.229 bar. (**b**) The experimental spectrum shift as the MBR internal pressure (0.229, 0.327, 0.424, and 0.522 bar) increases.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Fitting Object** & \(\mathbf{q_{1}}\) & \(\mathbf{q_{2}}\) & \(\Delta\mathbf{A_{d}}\)/pm & \(\mathbf{g}\)/GHz & \(\mathbf{x_{\text{T}}}\)/MHz & \(\mathbf{\text{FCOD}^{3}}\) & \(\mathbf{\text{RCOD}^{4}}\) \\ \hline Figure 4a Res. 1 (0.229 bar) & \(1.03\times 10^{6}\) & \(1.67\times 10^{6}\) & 1.41 & 1.43 & 208 & 0.996 & 0.933 \\ Figure 4a IQ. 2 & \(9.00\times 10^{5}\) & \(1.64\times 10^{6}\) & 1.41 & 1.34 & 279 & 0.985 & 0.983 \\ Figure 4b Res. (0.327 bar) & \(9.69\times 10^{5}\) & \(1.71\times 10^{6}\) & 1.24 & 1.37 & 249 & 0.997 & - \\ Figure 4b Res. (0.424 bar) & \(9.71\times 10^{6}\) & \(1.79\times 10^{6}\) & 1.23 & 1.31 & 263 & 0.998 & - \\ Figure 4b Res. (0.522 bar) & \(9.71\times 10^{6}\) & \(1.87\times 10^{6}\) & 1.15 & 1.25 & 276 & 0.998 & - \\ \hline \hline \end{tabular}  
* Res., Resonance. 2 IQ, IQ curve. 3 FCOD, Fitting Coefficient of determination (Fitting R-Square). 4 RCOD, Replotted Coefficient of determination (Replotted R-Square).  
\end{table}
Table 3: Strongly coupled resonance fitting results.  
IQ curve and validated by replotting the spectrum. This method can increase the measurement range in differential resonance sensing, thus allowing the differential sensing of overlapped resonances.  
Conceptualization, J.H. and L.X.; data curation, S.L. and B.L.; formal analysis, J.H., B.L. and L.X.; funding acquisition, L.L. and L.X.; investigation, J.H., B.L. and L.X.; methodology, J.H., L.L. and L.X.; project administration, L.L. and L.X.; resources, L.L. and X.W.; software, J.H.; supervision, L.L.; validation, S.L. and Z.G.; visualization, J.H. and Z.G.; writing--original draft, J.H.; writing--review and editing, L.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (NSFC), grant number 11874122, 11474070, 61327008 and 11074051 and the Doctoral Program of Higher Education, grant number 20130071130004.  
The authors declare no conflict of interest.