Micro Particle Sizing Using Hilbert Transform Time Domain Signal Analysis Method in Self-Mixing Interferometry

Abstract

The present work envisages the development of a novel and low-cost self-mixing interferometry (SMI) technology-based single particle sensing system in a microchannel chip for real time single micro-scale particle sizing. We proposed a novel theoretical framework to describe the impulse SMI signal expression in the time domain induced by a flowing particle. Using Hilbert transform, the interferometric fringe number of the impulse SMI signal was retrieved precisely for particle size discrimination. For the ease of particle sensing, a hydrodynamic focusing microfluidic channel was employed by varying the flow rate ratio between the sample stream and the sheath liquid, and the particle stream of a controllable width was formed very easily. The experimental results presented good agreement with the theoretical values, providing a 300 nm resolution for the particle sizing measurement.

Self-Mixing Interferometry-Based Micro Flow Cytometry System for Label-Free Cells Classification

“…More recently, Herbert et al have developed a numerical simulation model for an SMI-based particle-sensing technique [30]. In 2019, we employed Hilbert transform in SMI detection to measure the micro particle size, by counting the interferometric fringe number, where we observed that a 300 nm resolution can be approached [31]. So far, no relevant work has been reported in actual human living cells for clinical diagnosis or detection.…”

“…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 to achieve.…”

“…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 2π 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.…”

“…Figure 6b illustrated two 2π 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. 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 to achieve.…”

Phase-unwrapping algorithm combined with wavelet transform and Hilbert transform in self-mixing interference for individual microscale particle detection

“…They developed a novel SMI scheme with edge-filter-enhanced self-mixing interferometry (ESMI) [16] , and they approached around 2 orders of magnitude, even at a 10 m operating distance. Zhao et al presented a fringe counting method for single-microparticle sizing based on the Hilbert transform (HT) [17] ; the resolution was still a half wavelength. Unlike the continuous SMI signal from a bulk translating target, particle-induced signals represent a discrete waveform burst.…”