# A Novel Fiber Optic Sensor for Microparticle Velocity Measurement Using Multicore Fiber
## 2 Materials and Methods
In practice, which two signals will be chosen for velocity calculation is up to the signal quality. Taking the components \(V_{a}\) and \(V_{b}\) as an example, the power spectrums of the \(V_{a}\) signal and the \(V_{b}\) signal are obtained by fast Fourier transform (FFT), which gives two frequency spectra. The central frequency value (\(f_{1}\), \(f_{2}\)) of each spectrum is used to calculate the particle velocities \(V_{a}\) and \(V_{b}\) by using Equation (4). Further, taking the component \(V_{a}\) as an example, after calculating the central frequency \(f_{1}\) of the output signal of the 1 st spatial filter, \(V_{a}\) is obtained by \(V_{a}\) = \(f_{1}\)\(p_{1}\)/\(m\), where \(p_{1}\) is the adjacent core-core distance, which is 41.5 \(\upmu\)m, and \(m\) is the magnification of the image system. The calculation of other speed components is the same as \(V_{a}\). The experimental setup for 2D particle velocity measurement by using MCF is shown in Figure 4. A broadband light source of an amplified spontaneous emission (ASE) with an output power of 2.3 mW and a central wavelength of 1550 nm is connected to a beam collimator, which provides the parallel illumination. The MCF is divided into seven separate cores by the MCF FIFO (fan in fan out) module. The 1 st core is connected to an erbium doped fiber amplifier (EDFA) and a 1 \(\times\) 3 splitter. The splitter divides the output of the EDFA into three paths, each path connecting to a different photo detector (PD). The 1 st, 2 nd and 5 th cores are connected to PD\({}_{\text{a}}\). The 1 st, 3 rd and 6 th cores are connected to PD\({}_{\text{b}}\). The 1 st, 4 th and 7 th cores are connected to PD\({}_{\text{c}}\). The above connection method among different cores and PDs turns the MCF into three spatial filters for velocity components measurement as described in Figure 1:0  
A natural non-spherical sand particle (the widest part of the particle is 100 \(\upmu\)m, and the narrowest part is 70 \(\upmu\)m; its main mineral component is SiO\({}_{2}\)) moves with velocity \(V\) between the sensor probe and the beam collimator. The particle is stuck to a needle, which is adhered to a rotating disk driven by an electric motor. Since the particle blocks the light when it passes through the fiber end, the sensor probe will receive a shadow image signal of the particle. Note that the parallel illumination is projected to the moving particle; this shadow image is as big as the particle, which means the image magnification \(m\) equals 1. That signal is divided by the MCF FIFO module and transmitted into seven cores. The output signals of the 1 st core are shared by the three spatial filters. The power amplification in each filter is utilized to compensate the power loss during the splitting. After that, the light signals in different cores  
Figure 1:1 Experimental setup for two-dimensional particle velocity measurement by using MCF. MCF FIFO: MCF fan in fan out; EDFA: erbium doped fiber amplifiers; PD: photo detector. are received by PDa, PDb and PDc as shown in Figure 1:2 The photo of the major part of experimental setup is shown in Figure 1:3