# Reviews on Corrugated Diaphrags in Miniature Fiber-Optic Pressure Sensors
## 2 With initial stress
### Influences on the Performance of the Sensor  
As the core part of diaphragm-based fiber-optic pressure sensor, the sensitive diaphragm greatly determines the performance of the sensor. In the following, the influence of the mechanical properties of the diaphragm on the sensor overall performance, such as sensitivity, measurement range and stability, will be discussed. 1. Sensitivity  
The overall sensitivity of the sensor can be expressed as [16]  
\[S_{sensor}=S_{m}|H_{sensor}|, \tag{17}\]  
where S\({}_{m}\) is the mechanical sensitivity of the diaphragm and \(|H_{sensor}|\) is the transfer function of the sensor, which depends on the overall structure of the sensor. Detailed discussion on the transfer function is difficult and beyond the scope of this manuscript. But according to (17), one can see that S\({}_{m}\) has a great impact on the overall sensitivity of the sensor. It has been proved theoretically and experimentally that the sensor's overall sensitivity will increase with the diaphragm's mechanical sensitivity to some extent [16]. Therefore, the introduction of the corrugated structure in the diaphragm with initial stress will do good to improve the overall sensitivity of the sensor. Detailed discussion will be given in our future work. 2. Measurement range (Dynamic range)  
The measurement range of the fiber-optic pressure sensor represents the range in which the output signal has a linear relationship with the input pressure. For static pressure sensors, the minimum is usually set to be zero and the maximum is the input pressure when the output remains linear. For dynamic pressure sensors, the measurement range usually is referred to as the dynamic range, where the minimum is determined by the minimum detectable pressure (MDP), and the maximum depends on the total harmonic distortion in the output signal caused by the nonlinearity. Typically, the output response of the sensor is considered linear when the total harmonic distortion is less than \(-\)30 dB [16]. The MDP can be expressed as [47]  
\[P_{MDP}=U/M_{V}, \tag{18}\]  
where \(P_{MDP}\) is the minimum detectable pressure of the sensor (Pa/Hz\({}^{1/2}\)), \(U\) is the measured overall noise spectrum of the sensor (V/Hz\({}^{1/2}\)), \(M_{V}\) is the measured voltage sensitivity of the sensor (V/Pa). For fiber-optic pressure sensors, the overall noise is usually dominated by the environmental noise, which varies little for different sensors. Therefore, the MDP depends on the voltage sensitivity of the sensor. As the voltage sensitivity can be rewritten as \(M_{v}=kS_{m}\) (\(k\) is a constant in the measurement range), the MDP will decrease with the increase in the sensor's mechanical sensitivity. For the case of \"with initial stress\", the corrugated structure can effectively improve the overall sensitivity of the sensor, thus reducing the MDP of the sensor. Meanwhile, as the cubic item (or the nonlinear item) in Equation (10) is reduced with the help of corrugations, the maximum linear deform range of the diaphragm (or the upper limits of the measurement range) will increase. Both lead to the extension of the sensor's measurement range, for static and dynamic pressure sensor simultaneously. But things will change in the case of \"without initial stress\". For the static pressure sensor, the measurement range will increase due to the reduction of the cubic item in Equation (5). For the dynamic pressure sensor, the corrugated structure will reduce the overall sensitivity of the sensor, thus increasing the MDP of the sensor. So, the estimation of change of the sensor's measurement range is difficult. The measurement range of the sensor in this case should be determined by experiment. 3. Stability  
As discussed in Equations (10) and (16), the diaphragm's internal stress, no matter how it is generated, will be released more or less by the corrugation. It has been calculated that the corrugated zone in a diaphragm can easily reduce the stress by more than 1000 times [48].