## 2 Sensor Principle
### Response of Multiple Fiber Optic Sensor Probes  
Two sensor probes are multiplexed through on optical fiber line as shown in Figure 4. Two pairs of sensing and reference connectors are connected and the fiber bending effects studied. The fiber bending loss between these two connectors is investigated by winding the fiber one-turn on a cylindrical mandrel having several diameters. As shown in Figure 9, the bending losses at the location of two probes are almost same and the differences are less than 1 dB in the bending diameter range of 12-24 mm. However the bending losses are gradually increased according to the decrease of the bending diameter. In Figure 9, the curves show the bending loss effect due to the bending diameter. The bending loss is generally directly related to the radius of curvature and the arc length [17]. The output power of the sensor probe considering bending loss, \(P_{out}\), will be as follows:  
\[P_{out}=C_{1}P_{in}\exp(-C_{2}\gamma s) \tag{5}\]  
where C\({}_{1}\) and C\({}_{2}\) are constants that depend on the dimensions of the waveguide, and on the shape of the optical mode. \(P_{in}\) is an input power, \(\gamma\) is the radius of curvature, \(s\) is an arc length. By employing an arc angle, we can evaluate the radius of curvature. In order to investigate the radius and arc angle of our sensor probe, we measure the vertical location of the optical fiber and use trigonometric relations to determine the bending radius, as shown in Figure 10.  
To confirm the evaluated diameter and measured bending loss, we utilize a cylindrical mandrel with various diameters. These diameters shown in Figure 10 are matched with the measured diameters in Figure 9. In order to evaluate the diameter of the cylindrical mandrel case in Figure 9, the coefficient considering the arc angle should be multiplied by the diameters in Figure 10. The coefficient can be easily obtained from Equation (5). In the 3.0 dB bending loss case, the diameter in the cylindrical mandrel case will be about 20. 4 mm (=4.2 mm \(\times\) 360 degree/74 degree) since the bending loss in Figure 9 is measured under winding an optical fiber onto the cylindrical mandrel once. Figure 8: Absorbed state and received signal of a sensor probe. After studying the bending losses, the vessels with WCS are designed to ensure the sensor probe responses by having bending diameters of less than 24 mm according to the water absorption. Then, three sensor probes, A, B and C-type, are prepared to study the size effect of the probe shown in Figure 6. An amount of water (12 mL) is injected in the vessel by an injector at regular time intervals, about 5 minutes. The sensor outputs of these probes are investigated according to the amount of water absorption as shown in Figure 11. In the figure, the injected water ratio, \(\gamma\), is defined as the volume of water normalized with respect to the volume of its own vessel. When more and more water is injected in the vessel, B-type probe shows the fastest response to water injection. A and B-type probes are starting to be responsive at the injected water ratio of 0.5. However, C-type probe is responsive from the injected water ratio of 0.7. Also, the B and C-type probes show some small declines in the sensor outputs after the injected water ratios of 0.7 and 1.1, respectively. These can be explained by the fact that the B-type probe is responsive to water injection. Figure 10: Bending loss according to bending diameters and arc angles of an optical fiber (SMF-28). Figure 9: Bending loss according to winding one turn of an optical fiber, SMF-28, on a mandrel with various diameters. that the WCS material becomes jellylike after absorbing water. Therefore, it can be concluded that WCS material can't bend the optical fiber any even though more water is injected into the vessel. A-type probe might also show the same signal decline if some more water were provided.