## 3 Experimental Study  
### Experimental Setup  
The experimental measurement setup is illustrated in Figure 4, which consists of three parts: the laser diode based SMI sensor, the microfluidic platform, and the signal processing algorithm. The SMI sensor was based on a commercial distributed feedback laser diode (DFB) working at a wavelength of 690 nm (Thorlabs, Newton, US), and the laser operated at a constant voltage through a DC voltage-stabilized source (Rigol, Beijing, CN). The incident angle \(\theta\) between the laser emission axis and perpendicular to the plane of the channel chip was set to \(4^{\circ}\), weighing a satisfying trade-off that allows us to maintain a good signal-to-noise ratio and a sufficient Doppler shift frequency that fitted our acquisition devices. For the laser beam shaping, we used two spherical lenses in the same mode (Thorlabs, Newton, USA) with an 8 mm focal length. The DFB laser and the lens pair were assembled within a cage system (Thorlabs, Newton, USA). Subsequently, the entire optical arrangement was mounted on a 3D translation stage that allowed the adjustment of the focus location. The DFB sensor and the optical arrangement were mounted on a home-made printed circuit band (PCB); by monitoring the embedded photodiode inside the package, the output power fluctuation of the laser diode in the presence of feedback modulation was retrieved. A home-made transimpedance amplifier was employed here to enhance the signal by transforming the photodiode current to voltage. Finally, the signal was acquired using a National Instrument acquisition card (NI-6361 USB) driven by a customized LabVIEW algorithm. The time domain signal was processed by a home-made MATLAB script for burst certification and particle sizing. In the experimental setup, we applied the single particle sizing measurements using five different diameters polystyrene sphere (PS) aqueous dispersions (Zhongkeleiming, Beijing, CN). The dimension coefficients of variation (CV) values of the particle dimension were better than 3% for each sample. Since the mass density of PS is 1.05 g/cm\({}^{3}\), similar to that of water, the particles can suspend uniformly in water after being mixed well with an ultrasonic cleaner. As shown in Figure 5, a customized hydrodynamic focusing polydimethylsiloxane (PDMS) microfluidic channel of 100 \(\upmu\)m thickness was employed as the particle sequence generator chamber and sensing reactor. The dispersions were injected into the channel from the central inlet. Meanwhile, two deionized water fluids were injected using another pump through the other inlets on the left and right side as the sheath flow. Compressed by the double sheath fluids, the particle solution was confined within the center of the channel in the horizontal direction, so the particle group was transformed to a one-by-one sequence after well particle suspension dilution [23]. This allowed for an individual particle to be characterized as they passed through the SMI sensing region at a constant velocity. Figure 4: Schematic experimental setup. The system consists of a laser diode, doublet lenses optical arrangement, and microchannel. In the present work, a home-made data processing algorithm was also proposed. Hilbert transform (HT) is a useful signal processing tool for the description of the complex envelope of a carrier signal. Such a method could represent a signal in its analytical form by performing a \(90^{\circ}\) phase shift of the original signal over the orthogonal plane without modifying the amplitude, and the phase information is independent of the signal amplitude variations [24]. So far, HT has presented a good performance on SMI signals, as proven in many reports [25; 26; 27]. Herein, we employed the HT to unwrap the simultaneous external phase \(\phi\)(t) and extract the fringe number correctly. The transform \(HT(u(t))\) was calculated as the convolution of function \(u(t)\) with an impulse response function \(h(t)=1/\pi t\).