• Chinese Optics Letters
  • Vol. 22, Issue 3, 031103 (2024)
Yongzhuang Zhou1,2,*, Hongshuo Zhang1,2, Yong Shen1,2, Andrew R. Harvey3, and Hongxin Zou1,2
Author Affiliations
  • 1Institute for Quantum Science and Technology, College of Science, National University of Defense Technology, Changsha 410073, China
  • 2Hunan Key Laboratory of Mechanism and Technology of Quantum Information, Changsha 410073, China
  • 3School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK
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    DOI: 10.3788/COL202422.031103 Cite this Article Set citation alerts
    Yongzhuang Zhou, Hongshuo Zhang, Yong Shen, Andrew R. Harvey, Hongxin Zou, "Geometric phase helical PSF for simultaneous orientation and 3D localization microscopy," Chin. Opt. Lett. 22, 031103 (2024) Copy Citation Text show less

    Abstract

    The 3D location and dipole orientation of light emitters provide essential information in many biological, chemical, and physical systems. Simultaneous acquisition of both information types typically requires pupil engineering for 3D localization and dual-channel polarization splitting for orientation deduction. Here we report a geometric phase helical point spread function for simultaneously estimating the 3D position and dipole orientation of point emitters. It has a compact and simpler optical configuration compared to polarization-splitting techniques and yields achromatic phase modulation in contrast to pupil engineering based on dynamic phase, showing great potential for single-molecule orientation and localization microscopy.
    PSF|F{A(r,ϕ)e2πi[ΔΦ(r,ϕ)+D(r,z)]}|2,

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    Eout=cosΓ2Ein+isinΓ2e±i2αχ.

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    ΔΦ(r,ϕ)=(2l1)ϕ,(l1L)ϵ<r<(lL)ϵ,l=1,,L,

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    α=12ΦPSFeng+Φshift.

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    M14λR(θ)Lx=(100i)(cosθsinθsinθcosθ)(10)=(cosθisinθ)=cL2(1i)+cR2(1i).

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    cL=12(cosθsinθ),cR=12(cosθ+sinθ),

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    Ii,j=k=1K1µX,k+β(lnµX,kXi)T(lnµX,kXj),

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    σ(θ)=σ[NL(θ)]2+σ[NR(θ)]2N2[NL(θ)NR(θ)]2=NL(θ)+NR(θ)N2[NL(θ)NR(θ)]2.

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    Yongzhuang Zhou, Hongshuo Zhang, Yong Shen, Andrew R. Harvey, Hongxin Zou, "Geometric phase helical PSF for simultaneous orientation and 3D localization microscopy," Chin. Opt. Lett. 22, 031103 (2024)
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