# Self-Mixing Interferometry-Based Micro Flow Cytometry System for Label-Free Cells Classification
## 4 Results and Discussion
### Size Classification Calibration  
In order to evaluate the size sensitivity of the device, the PS suspensions with different diameters (500 nm, 2 \(\upmu\)m, 5 \(\upmu\)m and 10 \(\upmu\)m) were prepared and employed as the micro targets here for calibration purposes. All the particle suspensions were diluted with deionized water in order to obtain the same particle number concentration of \(\sim\)10\({}^{6}\) per milliliter. Each particle population was injected into the channel chip, and the resulting signal bursts were acquired subsequently. Figure 5 showed the SMI signal bursts induced by the flowing PS particles of 2 \(\upmu\)m diameter (Figure 5a) and 5 \(\upmu\)m (Figure 5b). It was noted that the bursts show several well-resolved interferometric fringes, and the fringe number \(N\) presented an obvious particle size dependence: the larger particles (5 \(\upmu\)m diameter) induced 8 interferometric fringes, more than the smaller 2 \(\upmu\)m PS particle, which produced 3 fringes. Another point of interest from Figure 5 is that for 5 \(\upmu\)m particles provided more than 2500 mV signal amplitude is observed which is higher than the one of 2 \(\upmu\)m particles. This aspect can be explained by the particle size also determining the particle scattering cross-section, so larger particle scatters more light feeding back into the laser cavity and resulting in a bigger modulation index \(m\) value and higher SMI signal amplitude level [33]. The fringe counting method's feasibility for PS spherical particle sizing has been proved [31]. However, this technique really depends on the target geometry and surface properties, according to the practical nonspherical living cells, the fringe series might be irregular and fringe counting difficult  
Figure 4: Particle concentration classification measurement results. (**a**) Time-domain self-mixing interferometry (SMI) signal trace. The red arrows denote the individual detection events and the black dashed lines denote the noise floor level. (**b**) The detection rate profile as a function of particle concentration. The dashed line denotes the linear fitting results. Figure 5: The SMI signal bursts polystyrene sphere (PS) particles in (**a**) 2 \(\upmu\)m diameter (**b**) 5 \(\upmu\)m diameter. to achieve. Here, we propose a novel alternative to characterize the particle or cell dimension. The scattering target dimension passing through the laser beam can be calculated in first approximation as the product of the passage duration \(w\) and the velocity \(V\). \[S=w\cdot V \tag{5}\]  
From Equation (3), the Doppler frequency is proportional to the flow velocity. We introduce a non-dimensional parameter \(K\) which value is proportional to the cell or particle dimension, and the value can be expressed from the passage duration \(w\) and Doppler frequency \(f_{D}\). \[K=w\cdot f_{D} \tag{6}\]  
In this work, fast Fourier transform (FFT) was computed as shown in Figure 6a. The sharp peak locus denotes the value of Doppler frequency shift \(f_{D}\). In Figure 5 there were some ambiguities in the burst edge, the \(w\) value was difficult to measure directly. In order to extract \(w\) more precisely, we used the Hilbert transform (HT) thus retrieving the instantaneous phase information [31; 38; 39]. Figure 6b illustrated two \(2\pi\) phase periods, clearly implying the beginning and ending time points of the individual particle-induced burst, of 0.76 ms duration (\(w\)) were measured from the phase oscillation. We correlated the size parameter \(K\) and the signal amplitude for size discrimination, and the plots of around 1600 detections were shown in Figure 7, where each dot denotes a detected PS particle. In this figure the dots were grouped into four clusters, corresponding to each particle dimension (red: 500 nm, blue: 2 \(\upmu\)m, pink: 5 \(\upmu\)m, green: 10 \(\upmu\)m). The dot groups induced by 500 nm and 2 \(\upmu\)m overlapped significantly and could not be distinguished easily.