• Photonics Research
  • Vol. 9, Issue 8, 1455 (2021)
Chuankang Li1、†, Yuzhu Li1、†, Zhengyi Zhan1, Yuhang Li1, Xin Liu1, Yong Liu2、5、*, Xiang Hao1, Cuifang Kuang1、3、4、6、*, and Xu Liu1、3
Author Affiliations
  • 1State Key Laboratory of Modern Optical Instrumentation, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
  • 2College of Electronics and Information Engineering, Shanghai University of Electric Power, Shanghai 200090, China
  • 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
  • 4Research Center for Intelligent Sensing, Zhejiang Lab, Hangzhou 311100, China
  • 5e-mail: liuyongdx@shiep.edu.cn
  • 6e-mail: cfkuang@zju.edu.cn
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    DOI: 10.1364/PRJ.429933 Cite this Article Set citation alerts
    Chuankang Li, Yuzhu Li, Zhengyi Zhan, Yuhang Li, Xin Liu, Yong Liu, Xiang Hao, Cuifang Kuang, Xu Liu. Sub-diffraction dark spot localization microscopy[J]. Photonics Research, 2021, 9(8): 1455 Copy Citation Text show less

    Abstract

    Single molecular localization microscopy (SMLM) is a useful tool in biological observation with sub-10-nm resolution. However, SMLM is incapable of discerning two molecules within the diffraction-limited region unless with the help of a stochastic on–off switching scheme which yet entails time-consuming processes. Here, we produce a novel kind of focal spot pattern, called sub-diffraction dark spot (SDS), to localize molecules within the sub-diffraction region of interest. In our proposed technique nominated as sub-diffracted dark spot localization microscopy (SDLM), multiple molecules within the diffraction-limited region could be distinguished without the requirement of stochastic fluorescent switches. We have numerically investigated some related impacts of SDLM, such as detection circle diameter, collected photon number, background noise, and SDS size. Simulative localization framework has been implemented on randomly distributed and specifically structured samples. In either two- or three-dimensional case, SDLM is evidenced to have 2 nm localization accuracy.
    η(r)=exp[ln(2)Idep(r)/Is],

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    Is=kfhc/(σλ),

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    PSFhexc/dep(r)=A04eln(2)r2FWHM2e4ln(2)r2FWHM2,

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    PSFSDS(r)=PSFhexc(r)·η(r).

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    pi(0)=μij=0k1μjwith  j[0,,k1].

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    pi=SBRSBR+1pi(0)+1k(SBR+1).

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    μi=PSFhexc(r¯mr¯i)·η(r)=PSFhexc(r¯mr¯i)exp[ln(2)PSFdep(r¯mr¯i)kfhc/(σλ)].

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    L(p¯,n¯)=N!Πi=0k1nk!Πi=0k1pini.

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    Fp¯=E[2pipjlnL(p¯,n¯)]with  i,j[0,,k1].

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    Fp¯=N(1pk1+δij1pi),

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    Fr¯=Ni=0k11pi((piri)2pir1pirdpirdpir1(pird)2).

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    σCRB_xy=12Ni=0k11pi[(pix)2+(piy)2][i=0k11pi(pix)2][i=0k11pi(piy)2][i=0k11pipixpiy]2.

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    σCRB_z=1Ni=0k11pi(piz)2.

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    Chuankang Li, Yuzhu Li, Zhengyi Zhan, Yuhang Li, Xin Liu, Yong Liu, Xiang Hao, Cuifang Kuang, Xu Liu. Sub-diffraction dark spot localization microscopy[J]. Photonics Research, 2021, 9(8): 1455
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