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Variable optical elements for fast focus control

Nature Photonics volume 14, pages 533–542 (2020)Cite this article

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Abstract

In this Review, we survey recent developments in the emerging field of high-speed variable-z-focus optical elements, which are driving important innovations in advanced imaging and materials processing applications. Three-dimensional biomedical imaging, high-throughput industrial inspection, advanced spectroscopies, and other optical characterization and materials modification methods have made great strides forward in recent years due to precise and rapid axial control of light. Three state-of-the-art key optical technologies that enable fast z-focus modulation are reviewed, along with a discussion of the implications of the new developments in variable optical elements and their impact on technologically relevant applications.

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Fig. 1: Performance of varifocal optical systems and the three key technologies enabling higher focal-varying speed.
Fig. 2: Pathways to limit photobleaching and phototoxicity using fast variable optical elements.
Fig. 3: Examples of volumetric imaging using variable optical elements.
Fig. 4: Examples of retrieving enhanced quantitative data and laser micromachining via varifocal optics.

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References

  1. Bawart, M., Jesacher, A., Zelger, P., Bernet, S. & Ritsch-Marte, M. Modified Alvarez lens for high-speed focusing. Opt. Express 25, 29847–29855 (2017).

    ADS  Google Scholar 

  2. Radhakrishnan, H. & Charman, W. N. Optical characteristics of Alvarez variable-power spectacles. Ophthalmic Physiol. Opt. 37, 284–296 (2017).

    Google Scholar 

  3. Zou, Y., Zhang, W., Tian, F., Siong Chau, F. & Zhou, G. Development of miniature tunable multi-element Alvarez lenses. IEEE J. Sel. Top. Quantum Electron. 21, 2–9 (2015).

    Google Scholar 

  4. Bernet, S., Harm, W. & Ritsch-Marte, M. Demonstration of focus-tunable diffractive moiré-lenses. Opt. Express 21, 4317–4322 (2013).

    Google Scholar 

  5. Mishra, K., van den Ende, D. & Mugele, F. Recent developments in optofluidic lens technology. Micromachines 7, 102 (2016).

    Google Scholar 

  6. Choi, J. M., Son, H. M. & Lee, Y. J. Biomimetic variable-focus lens system controlled by winding-type SMA actuator. Opt. Express 17, 8152–8164 (2009).

    ADS  Google Scholar 

  7. Fuh, Y. K., Huang, W. C., Lee, Y. S. & Lee, S. An oscillation-free actuation of fluidic lens for optical beam control. Appl. Phys. Lett. 101, 2010–2013 (2012).

    Google Scholar 

  8. Hasan, N., Kim, H. & Mastrangelo, C. H. Large aperture tunable-focus liquid lens using shape memory alloy spring. Opt. Express 24, 13334–13342 (2016).

    ADS  Google Scholar 

  9. Kim, J., Lee, J. & Won, Y. H. Method to reduce the aberration of a polygonal aperture focus-tunable lens array for high fill factor. Opt. Lett. 44, 2554–2557 (2019).

    ADS  Google Scholar 

  10. Cao, J. et al. Bioinspired zoom compound eyes enable variable-focus imaging. ACS Appl. Mater. Interfaces 12, 10107–10117 (2020).

    Google Scholar 

  11. Ee, H. S. & Agarwal, R. Tunable metasurface and flat optical zoom lens on a stretchable substrate. Nano Lett. 16, 2818–2823 (2016).

    ADS  Google Scholar 

  12. She, A., Zhang, S., Shian, S., Clarke, D. R. & Capasso, F. Adaptive metalenses with simultaneous electrical control of focal length, astigmatism, and shift. Sci. Adv. 4, eaap9957 (2018).

    ADS  Google Scholar 

  13. Aiello, M. D. et al. Achromatic varifocal metalens for the visible spectrum. ACS Photonics 6, 2432–2440 (2019).

    Google Scholar 

  14. Ren, H., Xianyu, H., Xu, S. & Wu, S.-T. Adaptive dielectric liquid lens. Opt. Express 16, 14954–14960 (2008).

    ADS  Google Scholar 

  15. Lu, Y. S., Tu, H., Xu, Y. & Jiang, H. Tunable dielectric liquid lens on flexible substrate. Appl. Phys. Lett. 103, 261113 (2013).

    ADS  Google Scholar 

  16. Jin, B., Ren, H. & Choi, W.-K. Dielectric liquid lens with chevron-patterned electrode. Opt. Express 25, 32411–32419 (2017).

    ADS  Google Scholar 

  17. Miccio, L., Paturzo, M., Grilli, S., Vespini, V. & Ferraro, P. Hemicylindrical and toroidal liquid microlens formed by pyro-electro-wetting. Opt. Lett. 34, 1075–1077 (2009).

    ADS  Google Scholar 

  18. Hao, C. et al. Electrowetting on liquid-infused film (EWOLF): complete reversibility and controlled droplet oscillation suppression for fast optical imaging. Sci. Rep. 4, 6846 (2014).

    Google Scholar 

  19. Li, L., Wang, J.-H., Wang, Q.-H. & Wu, S.-T. Displaceable and focus-tunable electrowetting optofluidic lens. Opt. Express 26, 25839–25848 (2018).

    ADS  Google Scholar 

  20. Lee, J., Park, Y. & Chung, S. K. Multifunctional liquid lens for variable focus and aperture. Sensors Actuators A 287, 177–184 (2019).

    Google Scholar 

  21. Shin, D., Kim, C., Koo, G. & Won, Y. Depth plane adaptive integral imaging system using a vari-focal liquid lens array for realizing augmented reality. Opt. Express 28, 5602–5616 (2020).

    ADS  Google Scholar 

  22. Xiao, W. & Hardt, S. An adaptive liquid microlens driven by a ferrofluidic transducer. J. Micromech. Microeng. 20, 055032 (2010).

    ADS  Google Scholar 

  23. Cheng, H. C., Xu, S., Liu, Y., Levi, S. & Wu, S. T. Adaptive mechanical-wetting lens actuated by ferrofluids. Opt. Commun. 284, 2118–2121 (2011).

    ADS  Google Scholar 

  24. Oku, H. & Ishikawa, M. High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error. Appl. Phys. Lett. 94, 2–5 (2009).

    Google Scholar 

  25. Patra, R., Agarwal, S., Kondaraju, S. & Bahga, S. S. Membrane-less variable focus liquid lens with manual actuation. Opt. Commun. 389, 74–78 (2017).

    ADS  Google Scholar 

  26. Dong, L., Agarwal, A. K., Beebe, D. J. & Jiang, H. Adaptive liquid microlenses activated by stimuli-responsive hydrogels. Nature 442, 551–554 (2006).

    ADS  Google Scholar 

  27. Kim, J., Kim, J., Na, J.-H., Lee, B. & Lee, S.-D. Liquid crystal-based square lens array with tunable focal length. Opt. Express 22, 3316–3324 (2014).

    ADS  Google Scholar 

  28. Zhou, Z., Li, X. & Ren, H. Liquid crystal lens with a concave polyimide layer. Opt. Eng. 56, 077102 (2017).

    ADS  Google Scholar 

  29. Kim, S. U., Na, J. H., Kim, C. & Lee, S. D. Design and fabrication of liquid crystal-based lenses. Liq. Cryst. 44, 2121–2132 (2017).

    Google Scholar 

  30. Ma, Y. et al. Fast switching ferroelectric liquid crystal Pancharatnam–Berry lens. Opt. Express 27, 10079–10086 (2019).

    ADS  Google Scholar 

  31. Chen, H. et al. A large bistable negative lens by integrating a polarization switch with a passively anisotropic focusing element. Opt. Express 22, 13138–13145 (2014).

    ADS  Google Scholar 

  32. Bharath, M. et al. Compact vari-focal augmented reality display based on ultrathin, polarization-insensitive, and adaptive liquid crystal lens. Opt. Lasers Eng. 128, 26–32 (2020).

    Google Scholar 

  33. Yin, S. et al. Nanosecond KTN varifocal lens without electric field induced phase transition. Photonic Fiber Cryst. Devices Adv. Mater. Innov. Device Appl. XI https://doi.org/10.1117/12.2276511 (2017).

  34. Kawamura, S., Tadayuki, I., Miyazu, J., Sakamoto, T. & Kobayashi, J. 2.5-fold increase in lens power of a KTN varifocal lens by employing an octagonal structure. Appl. Opt. 54, 4197–4201 (2015).

    ADS  Google Scholar 

  35. Inagaki, T., Imai, T., Miyazu, J. & Kobayashi, J. Polarization independent varifocal lens using KTN crystals. Opt. Lett. 38, 2673–2675 (2013).

    ADS  Google Scholar 

  36. Shibaguchi, T. & Funato, H. Lead–lanthanum zirconate–titanate (PLZT) electrooptic variable focal-length lens with stripe electrodes. Jpn. J. Appl. Phys. 31, 3196–3200 (1992).

    ADS  Google Scholar 

  37. Mermillod-Blondin, A., McLeod, E. & Arnold, C. B. Acoustic gradient index of refraction lens. Opt. Lett. 33, 2146–2148 (2008).

    ADS  Google Scholar 

  38. Koyama, D., Isago, R. & Nakamura, K. Three-dimensional focus scanning by an acoustic variable-focus optical liquid lens. AIP Conf. Proc. 1474, 355–358 (2012).

    ADS  Google Scholar 

  39. Koyama, D., Isago, R. & Nakamura, K. Ultrasonic variable-focus optical lens using viscoelastic material. Appl. Phys. Lett. 100, 091102 (2012).

    ADS  Google Scholar 

  40. Kaplan, A., Friedman, N. & Davidson, N. Acousto-optic lens with very fast focus scanning. Opt. Lett. 26, 1078–1080 (2001).

    ADS  Google Scholar 

  41. Reddy, G. D. & Saggau, P. Fast three-dimensional laser scanning scheme using acousto-optic deflectors. J. Biomed. Opt. 10, 064038 (2005).

    ADS  Google Scholar 

  42. Boucher, P., Barré, N., Pinel, O., Labroille, G. & Treps, N. Continuous axial scanning of a Gaussian beam via beam steering. Opt. Express 25, 23060–23069 (2017).

    ADS  Google Scholar 

  43. Shain, W. J., Vickers, N. A., Goldberg, B. B., Bifano, T. & Mertz, J. Extended depth-of-field microscopy with a high-speed deformable mirror. Opt. Lett. 42, 995–998 (2017).

    ADS  Google Scholar 

  44. Žurauskas, M., Barnstedt, O., Frade-Rodriguez, M., Waddell, S. & Booth, M. J. Rapid adaptive remote focusing microscope for sensing of volumetric neural activity. Biomed. Opt. Express 8, 4369–4379 (2017).

    Google Scholar 

  45. Salter, P. S., Iqbal, Z. & Booth, M. J. Analysis of the three-dimensional focal positioning capability of adaptive optic elements. Int. J. Optomechatronics 7, 1–14 (2013).

    ADS  Google Scholar 

  46. Duocastella, M. & Arnold, C. B. Transient response in ultra-high speed liquid lenses. J. Phys. D 46, 075102 (2013).

    ADS  Google Scholar 

  47. Sato, S. Applications of liquid crystals to variable-focusing lenses. Opt. Rev. 6, 471–485 (1999).

    Google Scholar 

  48. Lin, Y., Wang, Y. & Reshetnyak, V. Liquid crystal lenses with tunable focal length. Liq. Cryst. Rev. 5, 111–143 (2017).

    Google Scholar 

  49. Rahman, A., Said, S. M. & Balamurugan, S. Blue phase liquid crystal: strategies for phase stabilization and device development. Sci. Technol. Adv. Mater. 16, 033501 (2015).

    Google Scholar 

  50. Xu, S. et al. Fast-response liquid crystal microlens. Micromachines 5, 300–324 (2014).

    Google Scholar 

  51. Guo, Q., Zhao, X., Zhao, H. & Chigrinov, V. G. Reverse bistable effect in ferroelectric liquid crystal devices with ultra-fast switching at low driving voltage. Opt. Lett. 40, 2413–2416 (2015).

    ADS  Google Scholar 

  52. Sreenilayam, S. P. et al. Spontaneous helix formation in non-chiral bent-core liquid crystals with fast linear electro-optic effect. Nat. Commun. 7, 11369 (2016).

    ADS  Google Scholar 

  53. Basu, R. Effects of graphene on electro-optic switching and spontaneous polarization of a ferroelectric liquid crystal. Appl. Phys. Lett. 105, 112905 (2014).

    ADS  Google Scholar 

  54. Shukla, R. K. et al. Electro-optic and dielectric properties of a ferroelectric liquid crystal doped with chemically and thermally stable emissive carbon dots. RSC Adv. 5, 34491–34496 (2015).

    Google Scholar 

  55. Chang, C., Lin, Y., Srivastava, A. K. & Chigrinov, V. G. An optical system via liquid crystal photonic devices for photobiomodulation. Sci. Rep. 8, 4251 (2018).

    ADS  Google Scholar 

  56. Zhang, Z., You, Z. & Chu, D. Fundamentals of phase-only liquid crystal on silicon (LCOS) devices. Light Sci. Appl. 3, e213 (2014).

    ADS  Google Scholar 

  57. Karagyozov, D., Mihovilovic Skanata, M., Lesar, A. & Gershow, M. Recording neural activity in unrestrained animals with 3D tracking two photon microscopy. Cell Rep. 25, 1371–1383 (2018).

    Google Scholar 

  58. Kong, L. et al. Continuous volumetric imaging via an optical phase-locked ultrasound lens. Nat. Methods 12, 759–762 (2015).

    Google Scholar 

  59. Zong, W. et al. Large-field high-resolution two-photon digital scanned light-sheet microscopy. Cell Res. 25, 254–257 (2015).

    Google Scholar 

  60. Grulkowski, I., Szulzycki, K. & Wojtkowski, M. Microscopic OCT imaging with focus extension by ultrahigh-speed acousto-optic tunable lens and stroboscopic illumination. Opt. Express 22, 31746–31760 (2014).

    ADS  Google Scholar 

  61. Wei, M. T. et al. Phase behaviour of disordered proteins underlying low density and high permeability of liquid organelles. Nat. Chem. 9, 1118–1125 (2017).

    Google Scholar 

  62. Kang, S., Dotsenko, E., Amrhein, D., Theriault, C. & Arnold, C. B. Ultra-high-speed variable focus optics for novel applications in advanced imaging. Proc. SPIE 10539, https://doi.org/10.1117/12.2294487 (2018).

  63. Duocastella, M. & Arnold, C. B. Enhanced depth of field laser processing using an ultra-high-speed axial scanner. Appl. Phys. Lett. 102, 061113 (2013).

    ADS  Google Scholar 

  64. Chen, T., Fardel, R. & Arnold, C. B. Ultrafast z-scanning for high-efficiency micro-machining. Light Sci. Appl. 7, 17181 (2018).

    ADS  Google Scholar 

  65. Lopez, C. A. & Hirsa, A. H. Fast focusing using a pinned-contact oscillating liquid lens. Nat. Photon. 2, 610–613 (2008).

    Google Scholar 

  66. Murade, C. U., Van Der Ende, D. & Mugele, F. High speed adaptive liquid microlens array. Opt. Express 20, 18180–18187 (2012).

    ADS  Google Scholar 

  67. Laissue, P. P., Alghamdi, R. A., Tomancak, P., Reynaud, E. G. & Shroff, H. Assessing phototoxicity in live fluorescence imaging. Nat. Methods 14, 657–661 (2017).

    Google Scholar 

  68. Icha, J., Weber, M., Waters, J. C. & Norden, C. Phototoxicity in live fluorescence microscopy, and how to avoid it. BioEssays 39, https://doi.org/10.1002/bies.201700003 (2017).

  69. Power, R. M. & Huisken, J. Adaptable, illumination patterning light sheet microscopy. Sci. Rep. 8, 9615 (2018).

    ADS  Google Scholar 

  70. Donnert, G., Eggeling, C. & Hell, S. W. Major signal increase in fluorescence microscopy through dark-state relaxation. Nat. Methods 4, 81–86 (2007).

    Google Scholar 

  71. Duocastella, M., Vicidomini, G. & Diaspro, A. Simultaneous multiplane confocal microscopy using acoustic tunable lenses. Opt. Express 22, 19293–19301 (2014).

    ADS  Google Scholar 

  72. Fahrbach, F. O., Voigt, F. F., Schmid, B., Helmchen, F. & Huisken, J. Rapid 3D light-sheet microscopy with a tunable lens. Opt. Express 21, 21010–21026 (2013).

    ADS  Google Scholar 

  73. Zuo, C., Chen, Q., Qu, W. & Asundi, A. High-speed transport-of-intensity phase microscopy with an electrically tunable lens. Opt. Express 21, 24060–24075 (2013).

    ADS  Google Scholar 

  74. Jiang, J. et al. Fast 3-D temporal focusing microscopy using an electrically tunable lens. Opt. Express 23, 24362–24368 (2015).

    ADS  Google Scholar 

  75. Lu, R. et al. Video-rate volumetric functional imaging of the brain at synaptic resolution. Nat. Neurosci. 20, 620–628 (2017).

    Google Scholar 

  76. Colomb, T. et al. Extended depth-of-focus by digital holographic microscopy. Opt. Lett. 35, 1840–1842 (2010).

    ADS  Google Scholar 

  77. Liu, S. & Hua, H. Extended depth-of-field microscopic imaging with a variable focus microscope objective. Opt. Express 19, 353–362 (2011).

    ADS  Google Scholar 

  78. Piazza, S., Bianchini, P., Sheppard, C., Diaspro, A. & Duocastella, M. Enhanced volumetric imaging in 2-photon microscopy via acoustic lens beam shaping. J. Biophotonics 11, e201700050 (2018).

    Google Scholar 

  79. Zheng, J., Zuo, C., Gao, P. & Nienhaus, G. U. Dual-mode phase and fluorescence imaging with a confocal laser scanning microscope. Opt. Lett. 43, 5689–5692 (2018).

    ADS  Google Scholar 

  80. Lu, S.-H. & Hua, H. Imaging properties of extended depth of field microscopy through single-shot focus scanning. Opt. Express 23, 10714–10731 (2015).

    ADS  Google Scholar 

  81. Prevedel, R. et al. Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy. Nat. Methods 11, 727–730 (2014).

    Google Scholar 

  82. Martínez-Corral, M. & Javidi, B. Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems. Adv. Opt. Photonics 10, 512–566 (2018).

    ADS  Google Scholar 

  83. Grewe, B. F., Voigt, F. F., van ’t Hoff, M. & Helmchen, F. Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens. Biomed. Opt. Express 2, 2035–2046 (2011).

    Google Scholar 

  84. Sheffield, M. E. J. & Dombeck, D. A. Calcium transient prevalence across the dendritic arbour predicts place field properties. Nature 517, 200–204 (2015).

    ADS  Google Scholar 

  85. Szulzycki, K., Savaryn, V. & Grulkowski, I. Rapid acousto-optic focus tuning for improvement of imaging performance in confocal microscopy. Appl. Opt. 57, C14–C18 (2018).

    ADS  Google Scholar 

  86. Kong, L., Tang, J. & Cui, M. In vivo volumetric imaging of biological dynamics in deep tissue via wavefront engineering. Opt. Express 24, 1214–1221 (2016).

    ADS  Google Scholar 

  87. Kong, L., Tang, J. & Cui, M. Multicolor multiphoton in vivo imaging flow cytometry. Opt. Express 24, 6126–6135 (2016).

    ADS  Google Scholar 

  88. Har-gil, H. et al. PySight: plug and play photon counting for fast intravital microscopy. Optica 5, 29–37 (2018).

    Google Scholar 

  89. Yamato, K., Yamashita, T., Chiba, H. & Oku, H. Fast volumetric feedback under microscope by temporally coded exposure camera. Sensors 19, 1606 (2019).

    Google Scholar 

  90. Deschout, H. et al. Precisely and accurately localizing single emitters in fluorescence microscopy. Nat. Methods 11, 253–266 (2014).

    Google Scholar 

  91. Manzo, C. & Garcia-Parajo, M. F. A review of progress in single particle tracking: from methods to biophysical insights. Rep. Prog. Phys. 78, 124601 (2015).

    ADS  Google Scholar 

  92. Elson, E. L. Fluorescence correlation spectroscopy: past, present, future. Biophys. J. 101, 2855–2870 (2011).

    ADS  Google Scholar 

  93. Duocastella, M., Theriault, C. & Arnold, C. B. Three-dimensional particle tracking via tunable color-encoded multiplexing. Opt. Lett. 41, 863–866 (2016).

    ADS  Google Scholar 

  94. Sancataldo, G. et al. Three-dimensional multiple-particle tracking with nanometric precision over tunable axial ranges. Optica 4, 367–373 (2017).

    ADS  Google Scholar 

  95. Hou, S., Lang, X. & Welsher, K. Robust real-time 3D single-particle tracking using a dynamically moving laser spot. Opt. Lett. 42, 2390–2393 (2017).

    ADS  Google Scholar 

  96. Dertinger, T., Colyer, R., Iyer, G., Weiss, S. & Enderlein, J. Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Proc. Natl Acad. Sci. USA 106, 22287–22292 (2009).

    ADS  Google Scholar 

  97. Agarwal, K. & Macha, R. Multiple signal classification algorithm for super-resolution fluorescence microscopy. Nat. Commun. 7, 13752 (2016).

    ADS  Google Scholar 

  98. Ashdown, G., Owen, D. M., Pereira, P. M., Gustafsson, N. & Henriques, R. Fast live-cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuation. Nat. Commun. 7, 12471 (2016).

    ADS  Google Scholar 

  99. Hausotte, T., Gröschl, A. & Schaude, J. High-speed focal-distance-modulated fiber-coupled confocal sensor for coordinate measuring systems. Appl. Opt. 57, 3907–3914 (2018).

    ADS  Google Scholar 

  100. Yang, X., Song, X., Jiang, B. & Luo, Q. Multifocus optical-resolution photoacoustic microscope using ultrafast axial scanning of single laser pulse. Opt. Express 25, 28192–28200 (2017).

    ADS  Google Scholar 

  101. Duocastella, M. et al. Fast inertia-free volumetric light-sheet microscope. ACS Photonics 4, 1797–1804 (2017).

    Google Scholar 

  102. Sheppard, C. J. R. Limitations of the paraxial Debye approximation. Opt. Lett. 38, 1074–1076 (2013).

    ADS  Google Scholar 

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Acknowledgements

We acknowledge financial support from Princeton University. M.D. is a Serra Hunter Fellow. M.D. acknowledges Compagnia di San Paolo, ROL 34704.

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  1. SeungYeon Kang

    Present address: Mechanical Engineering, University of Connecticut, Storrs, CT, USA

  2. Martí Duocastella

    Present address: Department of Applied Physics, Universitat de Barcelona, Barcelona, Spain

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ, USA

    SeungYeon Kang & Craig B. Arnold

  2. Nanophysics, Isituto Italiano di Tecnologia, Genova, Italy

    Martí Duocastella

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Kang, S., Duocastella, M. & Arnold, C.B. Variable optical elements for fast focus control. Nat. Photonics 14, 533–542 (2020). https://doi.org/10.1038/s41566-020-0684-z

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