Simulation of the near-field focusing and the far-field imaging of microspherical lenses: A review
-
摘要: 微球超分辨显微成像技术能够突破衍射极限并成倍提高传统光学显微镜的成像分辨率。因其具有成像系统简单,可实时成像,无需荧光染料标记,能在白光照明条件下工作,且可与市场上成熟的显微镜产品相兼容等优点,具有重要研究价值与广阔应用前景,发展潜力巨大。该技术发展至今已取得了众多令人瞩目的研究成果,但现阶段的研究主要集中在微球超分辨成像规律、成像质量的提高、微球的操控方法上。而针对微球透镜的超分辨成像机理与模型,目前尚未形成完善统一的认知与可靠一致的解释。在此背景下,文中梳理归纳了微球透镜近场聚焦及远场成像机理、数学模型、仿真技术等方面的研究工作,分析现有工作的意义与所存在的不足,指出该领域需要着重解决的问题,并对微球成像技术未来的发展方向给予展望。Abstract: Microsphere-assisted super-resolution microscopy is an emerging technique which can be used to overcome the diffraction limit of conventional optical microscopes and significantly enhance their resolution. This technique is very promising for various applications because of the simplicity of its operation, its label-free and real-time imaging nature and its ability to be performed under white-light illumination with commercially available optical microscopes. Although there are many impressive results coming out along with the development of this technique, most studies are about the imaging properties, imaging quality improvement and manipulation of microspheres. A comprehensive theory on the super-resolution mechanism is still missing. Within this context, the progress of the microsphere’s imaging theory and the numerical methods in simulating the near-field focusing and far-field imaging phenomenon of microspheres was reported in this paper. The challenges and the future of this technique were also discussed.
-
图 1 (a) CHQ透镜超分辨显微成像[19];(b) SiO2微球超分辨显微成像[20];(c)微球扫描超分辨显微成像[26]; (d) TiO2颗粒自组装超分辨显微成像[30];(e)液体透镜超分辨显微成像[31];(f)表面等离激元增强超分辨显微成像[39]
Figure 1. (a) CHQ microlens-assisted super-resolution microscopy[19]; (b) SiO2 microsphere-assisted super-resolution microscopy[20]; (c) Scanning microsphere super-resolution microscopy[26]; (d) Self-assembled TiO2 particles for super-resolution microscopy[30]; (e) Liquid droplet-assisted super-resolution microscopy[31]; (f) Surface plasmon resonance-enhanced super-resolution microscopy[39]
图 4 (a) 微球成像系统示意图;(b) 基于微球成像系统的二维仿真模型;(c) 微球对离轴单个点光源所成的像;(d) 微球对轴对称分布的两个点光源所成的像;(e) 点光源模式(反相位,同相位,非相干)对微球成像系统分辨率的影响[61]
Figure 4. (a) Schematic drawing of the microsphere imaging system; (b) 2D simulation model based on microsphere imaging system; (c) The images of off-axis single point sources formed by microspheres; (d) The images formed by the microspheres for the two point sources distributed symmetrically along the optical axis; (e) The influence of the mode of the point sources (out of phase, in phase, incoherent) on the resolution of the microsphere imaging system[61]
图 5 (a)~(d) 米氏共振发生时微球对相邻两个点光源所成的像;(e)~(h) 无米氏共振时微球对这两个点光源所成的像[62]
Figure 5. (a)-(d) The images of the two neighboring point sources formed by microspheres when the microspheres are on Mie resonance; (e)-(h) The images of the two neighboring point sources formed by the microspheres when the microspheres are not on Mie resonance[62]
图 6 (a) 通过仿真微透镜对平行光的聚焦现象可得出微透镜的光子纳米射流;(b) 通过仿真微透镜对点光源的成像特性可得出微透镜的点扩散函数[63]
Figure 6. (a) The photonic nanojet of a microlens can be obtained by simulating its focusing performance for plane waves; (b) The point spread function of a microlens can be obtained by simulating its imaging properties for point sources[63]
图 7 (a) 三维成像仿真的步骤:(i) 近场全波仿真,近场-远场耦合算法,远场成像仿真以及 (ii) 虚像仿真;(b)微球对不同间距点光源的仿真成像效果;(c)微球对金属光栅结构成像仿真以及(d)相应的成像结果表明微球可分辨间距 75 nm 的金属线条;(e)微球成像系统对金属样品有更高的分辨率:(i), (iii) 金属微结构,(ii), (iv) 相同尺寸下的非金属微结构[64]
Figure 7. (a) The steps for the three-dimensional imaging simulation: (i) The near-field full-wave simulation, the near-to-far-field transformation, the far-field imaging simulation and (ii) the simulation for the formation of virtual images; (b) The simulated microsphere’s imaging performance for the two point sources with various gaps between them; (c) The simulation of microsphere’s imaging for metallic grating structures and (d) the corresponding simulation results show that the metallic lines with 75 nm separation can be resolved by the microsphere; (e) Microsphere imaging system has a higher resolution for metallic samples: (i), (iii) Metallic microstructures; (ii), (iv) Non-metallic microstructures with the same dimension[64]
-
[1] Abbe E. Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung [J]. Archiv für Mikroskopische Anatomie, 1873, 9: 413-418. [2] Shimomura O, Johnson F H, Saiga Y. Extraction, purification and properties of aequorin, a bioluminescent protein from the luminous hydromedusan, Aequorea [J]. Journal of Cellular Physiology, 1962, 59: 223-239. doi: 10.1002/jcp.1030590302 [3] Giloh H, Sedat J W. Fluorescence microscopy: Reduced photobleaching of rhodamine and fluorescein protein conjugates by n-propyl gallate [J]. Science, 1982, 217(4566): 1252-1255. doi: 10.1126/science.7112126 [4] Webb R H. Confocal optical microscopy [J]. Reports on Progress in Physics, 1996, 59: 427. doi: 10.1088/0034-4885/59/3/003 [5] Axelrod D. Total internal reflection fluorescence microscopy in cell biology [J]. Traffic, 2001, 2: 764-774. doi: 10.1034/j.1600-0854.2001.21104.x [6] Diaspro A. Confocal and Two-Photon Microscopy: Foundations, Applications and Advances[M]. Hoboken: Wiley-Liss, 2001. [7] Zipfel W R, Williams R M, Webb W W. Nonlinear magic: multiphoton microscopy in the biosciences [J]. Nature Biotechnology, 2003, 21: 1369-1377. doi: 10.1038/nbt899 [8] Huisken J, Swoger J, Bene F D, et al. Optical sectioning deep inside live embryos by selective plane illumination microscopy [J]. Science, 2004, 305(5686): 1007-1009. doi: 10.1126/science.1100035 [9] Olarte O E, Andilla J, Gualda E J, et al. Light-sheet microscopy: A tutorial [J]. Advances in Optics and Photonics, 2018, 10(1): 111-179. doi: 10.1364/AOP.10.000111 [10] Hell S W, Wichmann J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy [J]. Optics Letters, 1994, 19: 780-782. doi: 10.1364/OL.19.000780 [11] Betzig E, Patterson G H, Sougrat R, et al. Imaging intracellular fluorescent proteins at nanometer resolution [J]. Science, 2006, 313(1642): 1642-1645. [12] Rust M J, Bates M, Zhuang X. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM) [J]. Nature Methods, 2006, 3: 793-796. doi: 10.1038/nmeth929 [13] Stephens D J, Allan V J. Light microscopy techniques for live cell imaging [J]. Science, 2003, 300: 82-86. doi: 10.1126/science.1082160 [14] Evanko D. Label-free microscopy [J]. Nature Methods, 2010, 7: 36. [15] Zangle T A, Teitell M A. Live-cell mass profiling: An emerging approach in quantitative biophysics [J]. Nature Methods, 2014, 11: 1221-1228. doi: 10.1038/nmeth.3175 [16] Zernike F. Phase contrast, a new method for the microscopic observation of transparent objects [J]. Physica, 1942, 9: 686-698. doi: 10.1016/S0031-8914(42)80035-X [17] Zhou R, Wu M, Shen F, et al. Super-resolution microscopic effect of microsphere based on the near-field optics [J]. Acta Physica Sinca, 2017, 66: 140702. (in Chinese) doi: 10.7498/aps.66.140702 [18] Vobornik D, Vobornik S. Scanning near-field optical microscopy [J]. Bosnian Journal of Basic Medical Sciences, 2008, 8: 63-71. doi: 10.17305/bjbms.2008.3000 [19] Lee J Y, Hong B H, Kim W Y, et al. Near-field focusing and magnification through self-assembled nanoscale spherical lenses [J]. Nature, 2009, 460: 498-501. doi: 10.1038/nature08173 [20] Wang Z, Guo W, Li L, et al. Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope [J]. Nature Communications, 2011, 2: 218. doi: 10.1038/ncomms1211 [21] Hao X, Kuang C, Liu X, et al. Microsphere based microscope with optical super-resolution capability [J]. Applied Physics Letters, 2011, 99: 20310. [22] Darafsheh A, Walsh G F, Negro L D, et al. Optical super-resolution by high-index liquid-immersed microspheres [J]. Applied Physics Letters, 2012, 101: 141128. doi: 10.1063/1.4757600 [23] Vlad A, Huynen I, Melinte S. Wavelength-scale lens microscopy via thermal reshaping of colloidal particles [J]. Nanotechnology, 2012, 23(28): 285708. doi: 10.1088/0957-4484/23/28/285708 [24] Lee S, Li L. Rapid super-resolution imaging of sub-surface nanostructures beyond diffraction limit by high refractive index microsphere optical nanoscopy [J]. Optics Communications, 2015, 334: 253-257. doi: 10.1016/j.optcom.2014.08.048 [25] Yan Y, Li L, Feng C, et al. Microsphere-coupled scanning laser confocal nanoscope for sub-diffraction-limited imaging at 25 nm lateral resolution in the visible spectrum [J]. ACS Nano, 2014, 8: 1809-1816. doi: 10.1021/nn406201q [26] Wang F, Liu L, Yu H, et al. Scanning superlens microscopy for non-invasive large field-of-view visible light nanoscale imaging [J]. Nature Communications, 2016, 7: 13748. doi: 10.1038/ncomms13748 [27] Jin G, Bachman H, Naquin T D, et al. Acoustofluidic scanning nanoscope with high resolution and large field of view [J]. ACS Nano, 2020, 14: 8624-8633. doi: 10.1021/acsnano.0c03009 [28] Zhang T, Yu H, Li P, et al. Microsphere-based super-resolution imaging for visualized nanomanipulation [J]. ACS Applied Materials & Interfaces, 2020, 12(42): 48093-48100. doi: 10.1021/acsami.0c12126 [29] Luo H, Yu H, Wen Y, et al. Enhanced high-quality super-resolution imaging in air using microsphere lens group [J]. Optics Letters, 2020, 45: 2981-2984. doi: 10.1364/OL.393041 [30] Fan W, Yan B, Wang Z, et al. Three-dimensional all-dielectric metamaterial solid immersion lens for subwavelength imaging at visible frequencies [J]. Science Advances, 2016, 2: e1600901. doi: 10.1126/sciadv.1600901 [31] Chen X, Wu T, Gong Z, et al. Subwavelength imaging and detection using adjustable and movable droplet microlenses [J]. Photonics Research, 2020, 8: 225-234. doi: 10.1364/PRJ.377795 [32] Ye R, Ye Y-H, Ma H F, et al. Experimental far-field imaging properties of a ~5-µm diameter spherical lens [J]. Optics Letters, 2013, 38: 1829-1831. doi: 10.1364/OL.38.001829 [33] Ye R, Ye Y-H, Ma H F, et al. Experimental imaging properties of immersion microscale spherical lenses [J]. Scientific Reports, 2014, 4: 3769. [34] Guo M, Ye Y-H, Hou J, et al. Experimental far-field imaging properties of high refractive index microsphere lens [J]. Photonics Research, 2015, 3: 339-342. doi: 10.1364/PRJ.3.000339 [35] Yang S, Wang F, Ye Y-H, et al. Influence of the photonic nanojet of microspheres on microsphere imaging [J]. Optics Express, 2017, 25: 27551-27558. doi: 10.1364/OE.25.027551 [36] Wang F, Yang S, Ma H, et al. Microsphere-assisted super-resolution imaging with enlarged numerical aperture by semi-immersion [J]. Applied Physics Letters, 2018, 112: 023101. doi: 10.1063/1.5011067 [37] Yang S, Wang X, Wang J, et al. Reduced distortion in high-index microsphere imaging by partial immersion [J]. Applied Optics, 2018, 57: 7818-7822. doi: 10.1364/AO.57.007818 [38] Yang S, Cao Y, Shi Q, et al. Label-free super-resolution imaging of transparent dielectric objects assembled on silver film by a microsphere-assisted microscope [J]. Journal of Physical Chemistry C, 2019, 123: 28353-28358. doi: 10.1021/acs.jpcc.9b07285 [39] Cao Y, Yang S, Wang J, et al. Surface plasmon enhancement for microsphere-assisted super-resolution imaging of metallodielectric nanostructures [J]. Journal of Applied Physics, 2020, 127: 233103. doi: 10.1063/1.5144944 [40] Yang S, Ye Y-H, Shi Q, et al. Converting evanescent waves into propagating waves: The super-resolution mechanism in microsphere-assisted microscopy [J]. Journal of Physical Chemistry C, 2020, 124: 25951-25956. doi: 10.1021/acs.jpcc.0c07067 [41] Wang Y, Guo S, Wang D, et al. Resolution enhancement phase-contrast imaging by microsphere digital holography [J]. Optics Communications, 2016, 366: 81-87. doi: 10.1016/j.optcom.2015.12.031 [42] Leong-Hoi A, Hairaye C, Perrin S, et al. High resolution microsphere-assisted interference microscopy for 3 D characterization of nanomaterials [J]. Physica Status Solidi A, 2018, 215: 1700858. doi: 10.1002/pssa.201700858 [43] Xie Z, Hu S, Tang Y, et al. 3 D super-resolution reconstruction using microsphere-assisted structured illumination microscopy [J]. IEEE Photonics Technology Letters, 2019, 31: 1783-1786. doi: 10.1109/LPT.2019.2946793 [44] Chen L, Zhou Y, Li Y, et al. Microsphere enhanced optical imaging and patterning: From physics to applications [J]. Applied Physics Reviews, 2019, 6: 021304. doi: 10.1063/1.5082215 [45] Duan Y, Barbastathis G, Zhang B. Classical imaging theory of a microlens with super-resolution [J]. Optics Letters, 2013, 38: 2988-2990. doi: 10.1364/OL.38.002988 [46] Hoang T X, Duan Y, Chen X, et al. Focusing and imaging in microsphere-based microscopy [J]. Optics Express, 2015, 23: 12337-12353. doi: 10.1364/OE.23.012337 [47] Shang Q, Tang F, Yu L, et al. Super-resolution imaging with patchy microspheres [J]. Photonics, 2021, 8: 513. doi: 10.3390/photonics8110513 [48] Luk’Yanchuk B S, Paniagua-Domínguez R, Minin I V, et al. Refractive index less than two: Photonic nanojets yesterday, today and tomorrow [J]. Optical Materials Express, 2017, 7(6): 1820-1847. doi: 10.1364/OME.7.001820 [49] Yang H, Trouillon R, Huszka G, et al. Super-resolution imaging of a dielectric microsphere is governed by the waist of its photonic nanojet [J]. Nano Letters, 2016, 16: 4862-4870. doi: 10.1021/acs.nanolett.6b01255 [50] Darafsheh A. Influence of the background medium on imaging performance of microsphere-assisted super-resolution microscopy [J]. Optics Letters, 2017, 42: 735. doi: 10.1364/OL.42.000735 [51] Chen X, Wu T, Gong Z, et al. Lipid droplets as endogenous intracellular microlenses[J]. Light: Science & Applications, 2021, 10: 242. [52] Yue L, Minin O V, Wang Z, et al. Photonic hook: A new curved light beam [J]. Optics Letters, 2018, 43: 771-774. doi: 10.1364/OL.43.000771 [53] Minin I V, Minin O V, Latyba G M, et al. Experimental observation of a photonic hook [J]. Applied Physics Letters, 2019, 114: 031105. doi: 10.1063/1.5065899 [54] Liu C Y, Chung H J, E H P. Reflective photonic hook achieved by a dielectric-coated concave hemicylindrical mirror [J]. Journal of the Optical Society of America B, 2020, 37: 2528-2533. doi: 10.1364/JOSAB.399434 [55] Minin I V, Minin O V, Liu C Y, et al. Experimental demonstration of a tunable photonic hook by a partially illuminated dielectric microcylinder [J]. Optics Letters, 2020, 45: 4899-4902. doi: 10.1364/OL.402248 [56] Gu G, Zhang P, Chen S, et al. Inflection point: A perspective on photonic nanojets [J]. Photonics Research, 2021, 9: 1157-1171. doi: 10.1364/PRJ.419106 [57] Geints Y E, Minin I V, Minin O V. Tailoring “photonic hook” from Janus dielectric microbar [J]. Journal of Optics, 2020, 22: 065606. doi: 10.1088/2040-8986/ab8e9e [58] Gu G, Shao L, Song J, et al. Photonic hooks from Janus microcylinders [J]. Optics Express, 2019, 27: 37771-37780. doi: 10.1364/OE.27.037771 [59] Shen X, Gu G, Shao L, et al. Twin photonic hooks generated by twin-ellipse microcylinder [J]. IEEE Photonics Journal, 2020, 12(3): 1-9. doi: 10.1109/JPHOT.2020.2966782 [60] Tang F, Shang Q, Yang S, et al. Generation of photonic hooks from patchy microcylinders [J]. Photonics, 2021, 8: 466. doi: 10.3390/photonics8110466 [61] Maslov A V, Astratov V N. Imaging of sub-wavelength structures radiating coherently near microspheres [J]. Applied Physics Letters, 2016, 108: 051104. doi: 10.1063/1.4941030 [62] Maslov A V, Astratov V N. Optical nanoscopy with contact Mie-particles: Resolution analysis [J]. Applied Physics Letters, 2017, 110: 261107. doi: 10.1063/1.4989687 [63] Maslov A V, Astratov V N. Resolution and reciprocity in microspherical nanoscopy: Point-spread function versus photonic nanojets [J]. Physical Review Applied, 2019, 11: 064004. doi: 10.1103/PhysRevApplied.11.064004 [64] Yu L Y, Cyue Z R, Su G D J. Three-stage full-wave simulation architecture for in-depth analysis of microspheres in microscopy [J]. Optics Express, 2020, 28(6): 8862-8877. doi: 10.1364/OE.381526 [65] Hopkins H H. On the diffraction theory of optical images[C]//Proceedings of the Royal Society of London Series A, 1953, 217(1130): 408–432. [66] Astratov V. Label-Free Super-Resolution Microscopy[M]. Berlin: Springer, 2019. [67] Kim M K. Principles and techniques of digital holographic microscopy [J]. SPIE Reviews, 2010, 1: 018005. doi: 10.1117/6.0000006 [68] Zuo C, Li J, Sun J, et al. Transport of intensity equation: A tutorial [J]. Optics and Lasers in Engineering, 2020, 135: 106187. doi: 10.1016/j.optlaseng.2020.106187 [69] Fan Y, Li J, Lu L, et al. Smart computational light microscopes (SCLMs) of smart computational imaging laboratory (SCILab) [J]. PhotoniX, 2021, 2: 19. doi: 10.1186/s43074-021-00040-2 [70] Wu Y, Shroff H. Faster, sharper, and deeper: structured illumination microscopy for biological imaging [J]. Nature Methods, 2018, 15(12): 1011-1019. doi: 10.1038/s41592-018-0211-z