## 4 Results and Discussion
### Single Particle Sizing Measurement  
Hundreds of monodispersed signal bursts in different particle sizes were captured and processed by our system as mentioned in the previous section. The sampling frequency and acquisition data number were 500 kHz and 217, respectively. The data processing results of an 8 \(\upmu\)m diameter PS particle are shown in Figure 8. In Figure 8a, the blue and red curves represent the raw SMI signal and the filtered signal in the time domain, respectively. It can be observed that the band-pass filter effectively eliminated the electronic noise, and the impulse waveform evoked from the flowing particle was  
Figure 6: Flow chart drawing of the data acquisition and processing algorithm. Figure 7: Photographs of the dye fluid in the focusing chamber with sheath-sample-sheath flow rate: (a) 15 \(\upmu\)L/min–20 \(\upmu\)L/min–15 \(\upmu\)L/min; (b) 20 \(\upmu\)L/min–10 \(\upmu\)L/min–20 \(\upmu\)L/min; (c) 20 \(\upmu\)L/min–5 \(\upmu\)L/min–20 \(\upmu\)L/min; (d) 32 \(\upmu\)L/min–4 \(\upmu\)L/min–32 \(\upmu\)L/min. distinguished easily. Though the fringes could be observed, there was still some signal perturbation ambiguity in the waveform edge. Thus, after the filter, the phase characterization via Hilbert transform was also employed to extract the fringe number precisely, as shown in Figure 8b, and the fringe number ambiguity was further improved. We processed 30 signals in the range of 5 \(\upmu\)m and 10 \(\upmu\)m particle diameters. The distribution of the fringe numbers of the PS particle is shown in Figure 9. It should be emphasized that though the particles were spatially restricted in a small area (20 \(\upmu\)m width) inside the hydrodynamic focusing channel center, Doppler frequency shift deviations still existed from 3 kHz to 4.8 kHz. However, according to a given size particle, the fringe number did not vary dramatically at different Doppler frequencies. The fringe number was the eventual characteristic of the given particle. The filtered SMI signal waveforms of different sizes PS samples are illustrated in Figure 10. Well-defined fringe patterns were observed from each particle size, and the waveform performance reassembled that of the hypothesis above-mentioned in Equation (9) and Figure 3. It was noted that although the 200 nm PS particle was smaller than half of the laser wavelength (350 nm), one integrated waveform could still be presented in the time domain in Figure 10a. Another point worth highlighting is that the signal frequency was not constant during the passage period, and the up-chirp phenomena were observed in the signal bursts, particularly in the bigger particles as shown in Figure 10d. The intervals of the fringes were reduced due to the increase in the frequency. This phenomenon can be explained by the fact that due to the incident angle between the particle flowing direction and the laser axis, the scattering light direction and the Doppler frequency changed during acquisition. Figure 8: Data processing on the SMI signal from a polystyrene sphere particle of 8 \(\upmu\)m diameter. (**a**) Raw SMI signal (blue) and filtered SMI signal by a home-made band-pass filter (red). (**b**) Instantaneous phase visualization via Hilbert transform to interfere with fringe number retrieving (in the frame). Figure 9: Fringe number trend with SMI signal Doppler frequency of PS particles in different diameters. The blue circles denote 5 \(\upmu\)m and the red squares denote 10 \(\upmu\)m.  
The particle characterization of each particle size was repeated around 100 times, the fringe number trend as a function of the PS particle diameter is depicted in Figure 11. This particle diameter range corresponds to typical human cell dimensions in capillaries. It was observed that the results were in good agreement with the theoretical results calculated by Equation (7), increasing linearly with the particle diameter.