## 1 Introduction  
With the rapid developments in micro-nano technology, a large number of innovative micro- or nanoscale particles have been synthesized that are known to play a crucial role in the biomedical domain such as drug carriers or imaging agents in living tissues. Thus, the characterization of the particle size and other properties remains an extremely fundamental aspect. As a low-cost, self-aligned, nonintrusive, compact, and reliable sensing approach, self-mixing interferometry (SMI) technology-based microfluidic sensing has gained much attention during the last several decades [1; 2; 3; 4; 5]. In such schemes, the laser output amplitude and frequency are modulated when a small fraction of the laser emission is scattered backward by a small particle in the microchannel coupled into the laser cavity. The characteristics of the particle can be extracted from the properties of the SMI modulated signal in both the time-domain and frequency domain. To date, a great deal of effort has been made in the measurement of the frequency domain. The dynamic scattering (DS) method, as a typical tool for the characterization of the Brownian motion of small particles, can provide a promising assay in SMI-based particle sizing experiments. By measuring the Doppler power frequency spectrum of scattered light from a particle group, the average particle size can be retrieved. [PERSON] et al. presented for the first time a theoretical model to describe the frequency-shifted signal power spectrum of a laser source subjected to dynamic scattering light from the particles based on the DS method [6; 7]. They demonstrated the possibility of measuring particle sizes ranging from 20 nm to 200 nm. [PERSON] et al. also successfully implemented particle sizing measurement using the DS method, where the particle dimension and concentration were quantitatively characterized using the Lorentz fitting of the power spectrum of the SMI signal from polystyrene particles of diameters ranging from 20 nm to 500 nm [8; 9]. They also reported a forward experimental work by means of an acoustic-optical modulated self-mixing laser metrology for the accurate measurement of diffusion constants [10; 11; 12; 13]. More recently, [PERSON] et al. reported a fast and economic home-made signal processing algorithm for nanoparticle size measurement. With a 16 channel analog circuit, the self-mixing AC signal was transformed into DC signals, thus retrieving the size of the nanoparticles [14; 15]. However, particle size evaluation techniques in the frequency domain like the DS method are often employed on particle sizes from several to hundreds of nanometers, which are smaller than the laser spot size for a longer autocorrelation time. Moreover, these techniques can only estimate the average particle size of the sample suspension in a high particle number density and low target velocities. For low density particles in the probe volume, the detection was not qualified enough due to a low backscattering efficiency. Single particle detection using the SMI technique still remains challenging, and there are very few reports on single particle detection in a SMI setup [16; 17; 18]. [PERSON] et al. presented a particle size characterization study of single polystyrene spheres with a diameter in several tens of microns in the time domain [17]. They employed a novel SMI scheme with edge-filter enhanced self-mixing interferometry (ESMI), yielding around two orders of magnitude a higher signal-to-noise ratio (SNR) in a lower feedback region even at a 10 m operation distance. [PERSON] et al. facilitated a robust and real time single particle detection system based on the SMI technique [19]. However, none of the works above-mentioned could measure the particle size with a considerable applied resolution of 1 \(\upmu\)m. The existing system still cannot satisfy high throughout real time particle size analysis. In the present work, we presented a simple and capable SMI-based single particle size characterization method by analyzing the time domain.