• Chinese Optics Letters
  • Vol. 21, Issue 4, 041204 (2023)
Yu Zhao1、2、*, Jiawei Li1、2, Menglei Zhang1、2, Yangyang Zhao1、2, Jianglin Zou1、2, and Tao Chen1、2、**
Author Affiliations
  • 1Institute of Advanced Photonic Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China
  • 2Key Laboratory of Trans-scale Laser Manufacturing Technology (Beijing University of Technology), Ministry of Education, Beijing 100124, China
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    DOI: 10.3788/COL202321.041204 Cite this Article Set citation alerts
    Yu Zhao, Jiawei Li, Menglei Zhang, Yangyang Zhao, Jianglin Zou, Tao Chen. Phase-unwrapping algorithm combined with wavelet transform and Hilbert transform in self-mixing interference for individual microscale particle detection[J]. Chinese Optics Letters, 2023, 21(4): 041204 Copy Citation Text show less

    Abstract

    The self-mixing interferometry (SMI) technique is an emerging sensing technology in microscale particle classification. However, due to the nature of the SMI effect raised by a microscattering particle, the signal analysis suffers from many problems compared with a macro target, such as lower signal-to-noise ratio (SNR), short transit time, and time-varying modulation strength. Therefore, the particle sizing measurement resolution is much lower than the one in typical displacement measurements. To solve these problems, in this paper, first, a theoretical model of the phase variation of a single-particle SMI signal burst is demonstrated in detail. The relationship between the phase variation and the particle size is investigated, which predicts that phase observation could be another alternative for particle detection. Second, combined with continuous wavelet transform and Hilbert transform, a novel phase-unwrapping algorithm is proposed. This algorithm can implement not only efficient individual burst extraction from the noisy raw signal, but also precise phase calculation for particle sizing. The measurement shows good accuracy over a range from 100 nm to 6 μm with our algorithm, proving that our algorithm enables a simple and reliable quantitative particle characteristics retrieval and analysis methodology for microscale particle detection in biomedical or laser manufacturing fields.
    P(t)=P0[1+m(t)cosϕ].

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    ϕ0=ϕ+C(cosϕ+arctanα).

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    ϕ(t)=2πfd·t.

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    fd=2V·cosθincλ.

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    P(t)=P0(1+m·cosfd·t)exp[(tt0)22τ2].

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    τ=MVsinθ=K+DVsinθ.

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    Φ=2πfd·τ.

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    Φ=4πλ·cosθsinθ·M=4πλ·cosθsinθ(K+D).

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    D=λ4π·sinθcosθΦK.

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    W(u,s)=1s+Sig(t)ψ(tus)dt,

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    ψ(t)=π1/4eiω0tet2/2.

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    f(t)=ξ(t)+j·Θ(t),

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    Θ(t)=HT[ξ(t)].

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    ϕ(t)=arctanξ(t)Θ(t).

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    Φ=ϕ(t)+2nπ,

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    Yu Zhao, Jiawei Li, Menglei Zhang, Yangyang Zhao, Jianglin Zou, Tao Chen. Phase-unwrapping algorithm combined with wavelet transform and Hilbert transform in self-mixing interference for individual microscale particle detection[J]. Chinese Optics Letters, 2023, 21(4): 041204
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