## 3 Sensing Characteristics and Demodulation
### Analysis of Sensing Characteristics
\tag{5}\]  
where \(C_{\text{fec}}=1.178\times 10^{-5}/^{\circ}\)C is the thermal expansion coefficient of the optical fiber, \(C_{\text{foc}}=5.5\times 10^{-7}/^{\circ}\)C is the thermo-optic coefficient of the optical fiber [23], and \(L1\), \(L2\) are the lengths of the two arms of the interferometer. Figure 4b shows a partial detail of the output interference with temperature increasing and the OMCI arm difference is 1 mm. It can be seen from the result that the interference peak spacing does not change significantly, but only the peak value changes when the ambient temperature changing. Under the small arm difference, the phase change of the interferometer caused by changing temperature is very limited. Therefore, waist region of OMC plays a leading role in the sensing function of OMCI. It should be noted that higher precision temperature sensing can be achieved by monitoring the intensity change of the interference peak. This can provide means and data analysis ideas for accurate self-calibration of temperature sensing. The temperature sensitivity of the intensity change in Figure 4b (at wavelength of 1582.3 nm) is about \(-0.45\) dB/\({}^{\circ}\)C.  
Because of the little value of thermo-optic coefficient and thermal expansion coefficient on conventional SMF. While the OMCI with large initial arm difference can improve the temperature response capability of the interferometer. When the initial arm difference \(la=20\) mm, by monitoring the interference peak spacing d, the temperature response sensitivity of the sensor is about S\({}_{\text{T-Ad}}=0.1\) pm/\({}^{\circ}\)C.  
It is worth noting that the interference peaks will be very dense when the initial arm difference \(la\) of OMCI is large. In practical applications, higher precision spectral demodulation equipment is required to ensure that the signal is not distorted. In addition, the large interferometer arm difference will also bring some problems such as the vibration noise, and increase the burden on the sensor package design. When the initial arm difference of OMCI is relatively small (less than 3 mm), the interference peaks in the envelope will become sparse (as shown in Figure 4a). In this case, tracking the envelope dip drift for temperature sensing will produce a large test error. Therefore, in the application of OMCI in temperature sensing, it is more appropriate to choose equal arm or control the arm difference within the range of 5-20 mm, which is easier to implement in the actual production of OMCI. For using the interferometer unit in temperature sensing, a special optical fiber with a larger thermal-optical coefficient and a larger thermal expansion coefficient can be selected to manufacture the interferometer. For example, by improving the sensor structure, the arm of interferometer \(L2\) was replaced with plastic optical fiber (\(C_{\text{foc}}=1.3\times 10^{-4}/^{\circ}\)C, \(C_{\text{fec}}=8\times 10^{-5}/^{\circ}\)C [24]), then the temperature response of the interferometer can be greatly increased. When conventional SMF and plastic optical fiber are respectively applied to the two arms of OMCI, and set \(L1=20\) m, \(L2=20.02\) m, the temperature response sensitivity of the interferometer is about S\({}_{\text{T-Ad}}=7\) pm/\({}^{\circ}\)C, the simulation result is shown in Figure 5.  
In summary, if the OMCI interferometer is selected as the sensing unit, a certain temperature sensitization method needs to be adopted. For example, when the initial arm difference is appropriately increased, utilizing a special optical fiber with high thermal expansion coefficient and thermal optical coefficient. Furthermore, we can also refer to the structure of the interference type optical fiber hydrophone, an object with a high thermal expansion coefficient is wrapped by one arm of the interferometer to improve the temperature sensitivity.