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Single molecule localization microscopy (SMLM) detects and locates sparsely luminous single fluorescent molecules to achieve super-resolution imaging at nanoscale spatial resolution. In order to improve the temporal resolution, it is necessary to increase the density of the simultaneously emitting molecules. However, with the increase of the density, the point spread function (PSF) of different molecules will overlap severely on the detector, resulting in reduced spatial resolution, especially for three-dimensional (3D) SMLM. To solve this problem, a high density 3D-SMLM imaging method based on orthogonal astigmatism is proposed. Analysis and numerical simulation study for the method are carried out and presented. The main idea of the proposed orthogonal astigmatic method is to split the collected fluorescence in a SMLM microscope into two beams, each of which passes through a separate channel with a cylindrical lens and arrives at a specific region on the same detector. The two cylindrical lenses have the same optical parameters, but their orientations are set to be orthogonal to each other. They are used to obtain both positive and negative astigmatic PSF images of the same fluorescent molecule. Then, a linear projection model of the imaging process is established, and the 3D localization of the fluorescent molecules is realized by using a compression sensing algorithm. The results show that the two orthogonal cylindrical lenses produce a pair of astigmatic PSFs for one single molecule so that different PSF pairs between different molecules have lower mutual correlation, and thus the 3D localization accuracy for high density imaging can be significantly improved as compared with traditional astigmatic method, in which one single cylindrical lens is used. The larger the defocusing degree, the greater the shape difference between the two astigmatic PSFs is, and the more obvious this advantage.
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Keywords:
- single molecule localization microscopy /
- orthogonal astigmatism /
- three-dimensional single molecule localization /
- high-density imaging
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图 1 正交像散单分子定位成像光路和原理示意图 (a)成像光路示意图; (b)正交像散PSF图像对; (c)正交像散校准曲线. OL, 物镜; DM, 二向色镜; EF, 发射滤光片; BS, 分束器; A, 光阑; CL, 柱透镜; L, 透镜; M, 平面镜; EMCCD, 电子倍增电荷耦合器件
Figure 1. Schematic diagram of the optical path and principle of single molecule localization imaging based on orthogonal astigmatism: (a) Optical path; (b) orthogonal astigmatic PSFs; (c) calibration curves. OL, objective lens; DM, dichroic mirror; EF, emission filter; BS, beam splitter; A, aperture; CL, cylindrical lens; L, lens; M, mirror; EMCCD, electron-multiplying charge-coupled device.
图 2 PSF相关系数 (a)传统像散法; (b)正交像散法
Figure 2. Mutual correlation values between PSFs: (a) Traditional astigmatic method; (b) orthogonal astigmatic method
图 3 单帧双通道图像及定位结果 (a)单帧双通道图像; (b)正交像散法定位结果; (c)传统像散法定位结果
Figure 3. Single frame image and localization results: (a) Single frame of two-channel image; (b) localization results using orthogonal astigmatic method; (c) localization results using traditional astigmatic method.
图 4 不同轴向深度分子定位准确性、召回率和错误率比较
Figure 4. Comparison of localization accuracy, recall rate and error rate of molecules with different axial depths.
图 5 不同密度分子的定位准确性、召回率和错误率比较
Figure 5. Comparison of localization accuracy, recall rate and error rate of molecules with different densities.
图 6 螺旋线的模拟成像结果 (a)正交像散法; (b)传统像散法
Figure 6. Simulated imaging results of a helix structure: (a) Orthogonal astigmatic method; (b) traditional astigmatic method.
图 7 平行线的模拟成像结果 (a), (c), (e)正交像散法; (b), (d), (f)传统像散法; (c)—(f)间距最小(50 nm)平行线的放大图; (g)图(c)和(d)的绿色方框区域的强度分布曲线; (h)图(e)和(f)的黄色方框区域的强度分布曲线. 标尺大小: (a), (b) 500 nm; (c)—(f) 200 nm
Figure 7. Simulated imaging results of parallel line structures: (a), (c), (e) Orthogonal astigmatic method; (b), (d), (f) traditional astigmatic method; (c)–(f) zoomed-in view of the minimum spacing (50 nm) lines; (g) cross-sectional profiles of the green boxes in panel (c) and (d); (h) cross-sectional profiles of the yellow boxes in panel (e) and (f). Scale bars: (a), (b) 500 nm; (c)–(f) 200 nm.
图 8 双通道图像偏差的影响和有无图像偏差及配准的模拟成像结果比较 (a)定位准确性随横向偏移量、旋转角度和缩放倍率的变化; (b)有偏差双通道图像配准后的模拟成像结果; (c)无偏差双通道图像的模拟成像结果. 标尺大小: 500 nm
Figure 8. Influence of deviation between two channel images, and comparison of simulated imaging results with and without image deviation and registration: (a) Localization accuracy versus lateral offset, rotation angle and scaling ratio; (b) simulated image obtained after registration of biased dual channel images; (c) simulated image of unbiased dual channel images. Scale bars: 500 nm.
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[1] Rust M J, Bates M, Zhuang X W 2006 Nat. Methods 3 793
Google Scholar
[2] Bates M, Jones S A, Zhuang X 2013 Cold Spring Harbor Protoc. 2013 498
Google Scholar
[3] Huang B, Wang W, Bates M, Zhuang X 2008 Science 319 810
Google Scholar
[4] Huang B, Jones S A, Brandenburg B, Zhuang X W 2008 Nat. Methods 5 1047
Google Scholar
[5] Betzig E, Patterson G H, Sougrat R, Lindwasser O W, Olenych S, Bonifacino J S, Davidson M W, Lippincott-Schwartz J, Hess H F 2006 Science 313 1642
Google Scholar
[6] Holden S J, Uphoff S, Kapanidis A N 2011 Nat. Methods 8 279
Google Scholar
[7] Zhu L, Zhang W, Elnatan D, Huang B 2012 Nat. Methods 9 721
Google Scholar
[8] Babcock H, Sigal Y M, Zhuang X 2012 Opt. Nanoscopy 1 6
Google Scholar
[9] Gu L, Sheng Y, Chen Y, Chang H, Zhang Y, Lv P, Ji W, Xu T 2014 Biophys. J. 106 2443
Google Scholar
[10] Min J, Holden S J, Carlini L, Unser M, Manley S, Ye J C 2014 Biomedical Optics Express 5 3935
Google Scholar
[11] Huang J Q, Sun M Z, Gumpper K, Chi Y J, Ma J J 2015 Biomed. Opt. Express 6 902
Google Scholar
[12] Huang J Q, Sun M Z, Ma J J, Chi Y J 2017 IEEE Transa. Comput. Imaging 3 763
Google Scholar
[13] Von Middendorff C, Egner A, Geisler C, Hell S, Schonle A 2008 Opt. Express 16 20774
Google Scholar
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