# Measurement of Structural Loads Using a Novel MEMS Extrinsic Fabry-Perot Strain Sensor
## 3 Sensor Fabrication
Then, substituting Equation (9) into Equation (5), the wavelength shift due to strain change is given by  
\[\Delta\lambda=\frac{4\Delta d}{2m+1}=\frac{4\cdot L\varepsilon}{2m+1}. \tag{10}\]  
Figure 3: Manufacturing process of the extrinsic fiber Fabry–Perot probe. (**a**) Lithography. (**b**) Deep reactive ion etching (DRIE) etching of silicon-on-insulator (SOI) silicon wafer. (**c**) Etching intermediate oxide layer. (**d**) Deposition of reflective film \(\mathbb{S}_{2}\). (**e**) Deposition of reflective film \(\mathbb{S}_{1}\). (**f**) Anodic bonding. (**g**) Anti-reflection film. (**h**) Passivation layer. Under different positive and negative strain conditions, the simulated reflection spectrum of the EFFP sensor is shown in Figure 4.  
The sensor measurement range and measurement accuracy can be designed by adjusting the thickness of the MEMS optical reflective micromirrors (silicon) diaphragm. The cavity length of the FP is 31.2 um, and the reflectivity fringe finesse \(F_{R}=10\). Considering that the bandwidth of the light source in the signal demodulation device is limited to 80 nm (the wavelength range of a flattened broadband source is usually C + L, while the bandwidth in the experiment is 1510-1590 nm), at least one interference level can be found to satisfy the strain detection requirement (the strain corresponding to the load of the tested structure); that is, the wavelength variation range is within the detection band. Thus, using Equations (8) and (10), it is well known that the integer \(m\) should satisfy the following formula:  
\[\frac{\lambda}{2m+1}+\frac{4\cdot L\cdot\varepsilon_{\text{max}}}{2m+1}\leq 80 \text{nm}\left(1510\text{nm}\sim 1590\,\text{nm}\right) \tag{11}\]  
In fact, since the sensor is connected to the structure through the welding layer, the stretching or compression of the tested structure results in the transfer of strain from the structure to the sensor. Therefore, there is a strain transfer coefficient between the strain measured by the sensor and the actual strain of the tested structure, which is determined by the welding layer. After the sensor is bonded to the tested structure, the strain transfer coefficient is constant, and it can be defined by the following formula [32]:  
\[\eta=\frac{\varepsilon}{\varepsilon_{s}} \tag{12}\]  
where \(\varepsilon_{s}\) represents the strain of the tested structure. The area and elastic modulus of the structure are \(A\) and \(E_{s}\), respectively. With the basic small deformation assumption of material mechanics [31], the relationship between the strain of sensor and applied load of the tested structure is  
\[\varepsilon_{s}=\frac{F}{E_{s}A}. \tag{13}\]  
For a fiber Bragg grating (FBG) sensor, the elastic deformation with axial force and the photoelastic effect of the optical fiber are the main factors for its strain sensitivity. Meanwhile, for temperature sensitivity, both the thermo-optical effect and the thermal expansion effect of the material have to be considered. Its wavelength shift with strain and temperature changes can be written as Equation (14) [33]. The interference fringes of the EFFP sensor also shift with strain and temperature  
Figure 3.0 Reflection spectrum of the extrinsic fiber Fabry–Perot (EFFP) sensor with different strains. variation. Due to the thermal expansion effect of the cavity material, a linear relationship between the optical path difference and temperature variation can be obtained. The equation can be written as  
Figure 3.1 Figure 3.2  
where \(K_{11}\) and \(K_{12}\) represent the temperature and strain sensitivity coefficients of FBG, respectively; and \(K_{21}\) and \(K_{22}\) are expressed as the sensitivity coefficients of temperature and strain for the EFFP sensor, respectively. The influences of temperature and strain on the fiber Bragg grating and the EFFP sensor are independent. Assuming that the FBG is only affected by temperature, the temperature coefficient is 10.3 pm/\({}^{\circ}\)C, with the wavelength of the FBG being 1539.97 nm.