• Chinese Optics Letters
  • Vol. 17, Issue 12, 121103 (2019)
Zhiyuan Gu, Xianghui Wang*, Jianxin Wang, Fei Fan, and Shengjiang Chang
Author Affiliations
  • Institute of Modern Optics, Tianjin Key Laboratory of Optoelectronic Sensor and Sensing Network Technology, Nankai University, Tianjin 300350, China
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    DOI: 10.3788/COL201917.121103 Cite this Article Set citation alerts
    Zhiyuan Gu, Xianghui Wang, Jianxin Wang, Fei Fan, Shengjiang Chang. Sidelobe suppression and axial resolution enhancement in 4pi microscopy with higher-order radially polarized Laguerre–Gaussian beams using subtractive imaging[J]. Chinese Optics Letters, 2019, 17(12): 121103 Copy Citation Text show less

    Abstract

    Subtractive imaging is used to suppress the axial sidelobes and improve the axial resolution of 4pi microscopy with a higher-order radially polarized (RP) Laguerre–Gaussian (LG) beam. A solid-shaped point spread function (PSF) and a doughnut-shaped PSF with a dark spot along the optical axis are generated by tightly focusing a higher-order RP-LG beam and a modulated circularly polarized beam, respectively. By subtracting the two images obtained with those two different PSFs, the axial sidelobes of the subtracted PSF are reduced from 37% to about 10% of the main lobe, and the axial resolution is increased from 0.21λ to 0.15λ.
    PSF4pi-c=PSFill·PSFdet,(1)

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    PSFill(r,z)=|E1,ill(r,z)+E2,ill(r,z)|2,(2)

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    PSFdet(εr,εz)=|E1,det(εr,εz)+E2,det(εr,εz)|2,(3)

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    E(r,φp,z)=iCΩA(θ)sinθcosθT(θ,φ)exp[iΔ(θ)]exp{ikn[zcosθ+rsinθcos(φφp)]}dθdφ,(4)

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    A(θ)=β02sinθsin2αexp(β02sin2θsin2α)Lp1(2β02sin2θsin2α),(5)

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    T(θ,φ)=[cosθsinφcosθcosφsinθ],(6)

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    A(θ)=exp(β02sin2θsin2α),(7)

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    T(θ,φ)=12[1+(cosθ1)(cos2φ+icosφsinφ)i+(cosθ1)(isin2φ+cosφsinφ)sinθ(cosφ+isinφ)].(8)

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    Δ(θ)={0(αθ)π(0θα).(9)

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    I(x,y)=Ibright(x,y)-γIdark(x,y)PSFsub(x,y)Ob(x,y),(10)

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    PSFsub=PSFbrightγ·PSFdark.(11)

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    OTF(fx,fy,fz)=PSF(x,y,z)exp[2πi(xfx+yfy+zfz)]dxdydz.(12)

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    Zhiyuan Gu, Xianghui Wang, Jianxin Wang, Fei Fan, Shengjiang Chang. Sidelobe suppression and axial resolution enhancement in 4pi microscopy with higher-order radially polarized Laguerre–Gaussian beams using subtractive imaging[J]. Chinese Optics Letters, 2019, 17(12): 121103
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