# A Novel Fiber Optic Sensor for Microparticle Velocity Measurement Using Multicore Fiber
## 2 Materials and Methods  
A photo of an MCF (Yangtze Optical Fibre and Cable Joint Stock Limited Company (YOFC), Wuhan, Hubei, China) cross-section captured by a fusion splicer (Fujikura, Tokyo, Japan) and the schematic structure of the MCF probe are shown in Figure 2. The MCF has one centric core and six  
Figure 1: Typical structures of optical fiber probes for particle velocity measurement reported by previous researches: blue circles denote light emission fibers; black circles denote light receiving fibers. (**a**) Three-fiber probe; (**b**) five-fiber probe; (**c**) conical lens fiber probe; (**d**) thirty-seven fiber probe; (**e**) fiber bundle probe. side cores. Six side cores are distributed in a regular hexagon around the centric core. The diameter of each core is 8 \(\upmu\)m. The adjacent core-core distance is 41.5 \(\upmu\)m. The diameter of the cladding is 150 \(\upmu\)m. The cores are enclosed by a deep trench so that crosstalk is suppressed. We set a 2D co-ordinate system that has three axes (a-axis, b-axis and c-axis) at the probe end as shown in Figure 3. The angle between adjacent axes is 60 degrees. The seven cores are distributed in the co-ordinate system. When a particle passes through the MCF probe end at the velocity \(V\) in the direction of the a-axis and at the angle \(\alpha\) to the a-axis, \(V_{a}\), \(V_{b}\) and \(V_{c}\) are the velocity components of \(V\) on a-, b- and c-axes of \(V\), respectively. The relation among \(V\), \(V_{a}\), \(V_{b}\) and \(V_{c}\) in Figure 3 is given by:  
\[V_{a}=V\cos(\alpha) \tag{1}\]  
\[V_{b}=V\cos(60^{\lx@math@degree}-\alpha) \tag{2}\]  
\[V_{c}=V\cos(60^{\lx@math@degree}+\alpha) \tag{3}\]  
In principle, the 2D particle velocity \(V\) and its direction \(\alpha\) can be acquired from any two of the three velocity components (\(V_{a}\), \(V_{b}\) and \(V_{c}\)). The measurement technique of velocity components (\(V_{a}\), \(V_{b}\) and \(V_{c}\)) is based on the principle of SFV. SFV is a method of measuring the object velocity by using the spatial filter. A spatial filter consists of a periodic transmittance like a transmission grating or a liquid crystal array. By measuring the central frequency of the output signal of the spatial filter, the velocity can be obtained. Here, we turn the MCF into spatial filters as follows: the 1 st, 2 nd and 5 th cores form the 1 st spatial filter, which is responsible for measuring the velocity component \(V_{a}\) on the a-axis. The 1 st, 3 rd and 6 th cores form  
Figure 3: Schematic illustration of the principle of velocity measurement. Different color circles denote MCF cores; \(V_{a}\) is the velocity component of \(V\) on the a-axis; \(V_{b}\) is the velocity component of \(V\) on the b-axis; and \(V_{c}\) is the velocity component of \(V\) on the c-axis. Figure 2: (**a**) Photo of multicore fiber (MCF) cross-section; (**b**) schematic structure of 7-core fiber probe with a moving particle. the 2 nd spatial filter for measuring the velocity component \(V_{b}\) on the b-axis. The 1 st, 4 th and 7 th cores form the 3 rd spatial filter for measuring the velocity component \(V_{c}\) on the c-axis. The velocity component \(V_{l}\) (\(l\) = \(a\), \(b\), \(c\)) can be expressed as [8]:  
\[V_{l}=\frac{f_{j}p_{j}}{m} \tag{4}\]  
where \(f_{j}\) is the central frequency of the output signal of the j-th spatial filter (\(j\) = 1, 2, 3), \(p_{j}\) is the interval of periodic transmittance of the j-th spatial filter (\(j\) = 1, 2, 3) and \(m\) is the magnification of the image system. Thus by measuring the central frequencies (\(f_{1}\), \(f_{2}\) and \(f_{3}\)) of output signals, the three velocity components (\(V_{a}\), \(V_{b}\) and \(V_{c}\)) can be obtained by Equation (4). According to the cores distribution of MCF, \(p_{1}\) = \(p_{2}\) = \(p_{3}\) = 41.5 \(\upmu\)m. The measurable range of angle is defined as the angle between the first spatial filter and the third spatial filter, which is 0-120\({}^{\circ}\). The particle velocity and its direction can be acquired from two of the three velocity components.