Microscopic imaging in three dimensions enables numerous biological and clinical applications. However, high-resolution optical imaging preserved in a relatively large depth range is hampered by the rapid spread of tightly confined light due to diffraction. Here, we show that a particular disposition of light illumination and collection paths liberates optical imaging from the restrictions imposed by diffraction. This arrangement, realized by metasurfaces, decouples lateral resolution from the depth of focus by establishing a one-to-one correspondence (bijection) along a focal line between the incident and collected light. Implementing this approach in optical coherence tomography, we demonstrate tissue imaging at a wavelength of 1.3 µm with ~3.2 µm lateral resolution, maintained nearly intact over a 1.25 mm depth of focus, with no additional acquisition or computational burden. This method, termed bijective illumination collection imaging, is general and might be adapted across various existing imaging modalities.
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All data generated and analysed are included in the paper and its supplementary information. The imaging data presented in Fig. 6 are available at https://figshare.com/articles/figure/Fig_6e_TIF/17124062.
All custom codes or algorithms used to generate results that are reported in this manuscript are available from the corresponding authors upon reasonable request.
Stephens, D. J. & Allan, V. J. Light microscopy techniques for live cell imaging. Science 300, 82–86 (2003).
Denk, W., Strickler, J. H. & Webb, W. W. Two-photon laser scanning fluorescence microscopy. Science 248, 73–76 (1990).
Beaulieu, D. R., Davison, I. G., Kılıç, K., Bifano, T. G. & Mertz, J. Simultaneous multiplane imaging with reverberation two-photon microscopy. Nat. Methods 17, 283–286 (2020).
Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nat. Methods 2, 932–940 (2005).
Huang, D. et al. Optical coherence tomography. Science 254, 1178–1181 (1991).
Fujimoto, J. G. et al. Optical biopsy and imaging using optical coherence tomography. Nat. Med. 1, 970–972 (1995).
Tearney, G. J. et al. In vivo endoscopic optical biopsy with optical coherence tomography. Science 276, 2037–2039 (1997).
Fujimoto, J. G. Optical coherence tomography for ultrahigh resolution in vivo imaging. Nat. Biotechnol. 21, 1361–1367 (2003).
Vakoc, B. J., Fukumura, D., Jain, R. K. & Bouma, B. E. Cancer imaging by optical coherence tomography: preclinical progress and clinical potential. Nat. Rev. Cancer 12, 363–368 (2012).
Zhou, K. C., Qian, R., Degan, S., Farsiu, S. & Izatt, J. A. Optical coherence refraction tomography. Nat. Photonics 13, 794–802 (2019).
Curatolo, A. et al. Quantifying the influence of Bessel beams on image quality in optical coherence tomography. Sci. Rep. 6, 23483 (2016).
Zhang, M., Ren, Z. & Yu, P. Improve depth of field of optical coherence tomography using finite energy Airy beam. Opt. Lett. 44, 3158–3161 (2019).
Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).
Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298–302 (2014).
Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).
Khorasaninejad, M. et al. Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging. Science 352, 1190–1194 (2016).
Khorasaninejad, M. & Capasso, F. Metalenses: versatile multifunctional photonic components. Science 358, eaam8100 (2017).
Durnin, J., Miceli, J. J. & Eberly, J. H. Diffraction-free beams. Phys. Rev. Lett. 58, 1499–1501 (1987).
Berry, M. V. & Balazs, N. L. Nonspreading wave packets. Am. J. Phys. 47, 264–267 (1979).
Gutierrez-Vega, J. C., Iturbe-Castillo, M. D. & Chavez-Cerda, S. Alternative formulation for invariant optical fields: Mathieu beams. Opt. Lett. 25, 1493–1495 (2000).
Bandres, M. A., Gutierrez-Vega, J. C. & Chavez-Cerda, S. Parabolic nondiffracting optical wave fields. Opt. Lett. 29, 44–46 (2004).
Lopez-Mariscal, C., Bandres, M. A., Gutierrez-Vega, J. C. & Chavez-Cerda, S. Observation of parabolic nondiffracting optical fields. Opt. Express 13, 2364–2369 (2005).
Fahrbach, F. O., Simon, P. & Rohrbach, A. Microscopy with self-reconstructing beams. Nat. Photonics 4, 780–785 (2010).
Webb, R. H. Confocal optical microscopy. Rep. Prog. Phys. 59, 427–471 (1996).
Stelzer, E. H. K. & Steffen, L. Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy. Opt. Commun. 111, 536–547 (1994).
Born, M. & Wolf, E. Principles of Optics (Pergamon, 1970)
Blatter, C. et al. Extended focus high-speed swept source OCT with self-reconstructive illumination. Opt. Express 19, 12141–12155 (2011).
Lorenser, D., Christian Singe, C., Curatolo, A. & Sampson, D. D. Energy-efficient low-Fresnel-number Bessel beams and their application in optical coherence tomography. Opt. Lett. 39, 548–551 (2014).
Fattal, D., Li, J., Peng, Z., Fiorentino, M. & Beausoleil, R. G. Flat dielectric grating reflectors with focusing abilities. Nat. Photonics 4, 466–470 (2010).
Khorasaninejad, M. & Crozier, K. B. Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter. Nat. Commun. 5, 5386 (2014).
Arbabi, A., Horie, Y., Ball, A. J., Bagheri, M. & Faraon, A. Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays. Nat. Commun. 6, 7069 (2015).
Khorasaninejad, M. & Capasso, F. Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters. Nano Lett. 15, 6709–6715 (2015).
Khorasaninejad, M. et al. Achromatic metasurface lens at telecommunication wavelengths. Nano Lett. 15, 5358–5362 (2015).
Khorasaninejad, M., Chen, W. T., Oh, J. & Capasso, F. Super-dispersive off-axis meta-lenses for compact high resolution spectroscopy. Nano Lett. 16, 3732–3737 (2016).
Khorasaninejad, M. et al. Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion. Nano Lett. 17, 1819–1824 (2017).
Arbabi, E., Arbabi, A., Kamali, S. M., Horie, Y. & Faraon, A. Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces. Optica 4, 625–632 (2017).
Chen, W. T. et al. A broadband achromatic metalens for focusing and imaging in the visible. Nat. Nanotechnol. 13, 220–226 (2018).
Yun, S. H., Tearney, G. J., de Boer, J. F. & Bouma, B. E. Removing the depth-degeneracy in optical frequency domain imaging with frequency shifting. Opt. Express 12, 4822–4828 (2004).
Yun, S. H. et al. Comprehensive volumetric optical microscopy in vivo. Nat. Med. 12, 1429–1433 (2006).
Huang, L., Whitehead, J., Colburn, S. & Majumdar, A. Design and analysis of extended depth of focus metalenses for achromatic computational imaging. Photonics Res. 8, 1613–1623 (2020).
Bayati, E. et al. Inverse designed metalenses with extended depth of focus. ACS Photonics 7, 873–878 (2020).
Colburn, S. & Majumdar, A. Simultaneous achromatic and varifocal imaging with quartic metasurfaces in the visible. ACS Photonics 7, 120–127 (2020).
Colburn, S., Zhan, A. & Majumdar, A. Metasurface optics for full-color computational imaging. Sci. Adv. 4, 2114 (2018).
Ralston, T. S., Marks, D. L., Carney, P. S. & Boppart, S. A. Interferometric synthetic aperture microscopy. Nat. Phys. 3, 129–134 (2007).
Liu, L. et al. Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography. Nat. Med. 17, 1010–1014 (2011).
Yuan, W., Brown, R., Mitzner, W., Yarmus, L. & Li, X. Super-achromatic monolithic microprobe for ultrahigh-resolution endoscopic optical coherence tomography at 800 nm. Nat. Commun. 8, 1531 (2017).
Desjardins, A. E. et al. Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction. Opt. Express 15, 6200–6209 (2007).
Klein, T., Raphael, A., Wolfgang, W., Tom, P. & Huber, R. Joint aperture detection for speckle reduction and increased collection efficiency in ophthalmic MHz OCT. Biomed. Opt. Express 4, 619–634 (2013).
Zhao, Y. et al. Dual-axis optical coherence tomography for deep tissue imaging. Opt. Lett. 42, 2302–2305 (2017).
Cheng, X. et al. Comparing the fundamental imaging depth limit of two-photon, three-photon, and non-degenerate two-photon microscopy. Opt. Lett. 45, 2934–2937 (2020).
Wang, C., Qiao, L., Mao, Z., Cheng, Y. & Xu, Z. Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation. J. Opt. Soc. Am. B 25, 976–982 (2008).
Kobat, D., Zhu, G. & Xu, C. Background reduction with two-color two-beam multiphoton excitation. In Proc. Biomedical Optics paper BMF6 (Optical Society of America, 2008); https://doi.org/10.1364/biomed.2008.bmf6
Liu, J. T. C. et al. Dual-axes confocal reflectance microscope for distinguishing colonic neoplasia. J. Biomed. Opt. 11, 054019 (2006).
Hell, S. & Stelzer, E. H. K. Properties of a 4Pi confocal fluorescence microscope. J. Opt. Soc. Am. A 9, 2159–2166 (1992).
Power, R. M. & Huisken, J. A guide to light-sheet fluorescence microscopy for multiscale imaging. Nat. Methods 14, 360–373 (2017).
Gao, P. F., Lei, G. & Huang, C. Z. Dark-field microscopy: recent advances in accurate analysis and emerging applications. Anal. Chem. 93, 4707–4726 (2021).
Schmitt, J. M., Xiang, S. H. & Yung, K. M. Speckle in optical coherence tomography. J. Biomed. Opt. 4, 95–105 (1999).
Pahlevaninezhad, H. et al. Nano-optic endoscope for high-resolution optical coherence tomography in vivo. Nat. Photonics 12, 540–547 (2018).
Gissibl, T., Thiele, S., Herkommer, A. & Giessen, H. Two-photon direct laser writing of ultracompact multi-lens objectives. Nat. Photonics 10, 554–560 (2016).
This project was supported by funding from the Department of Defense under grant no. W81XWH2010300 awarded to H.P., the Natural Sciences and Engineering Research Council of Canada under grant no. 392075 awarded to M. Pahlevani and the National Institutes of Health under grant no. 5R01HL133664 and grant no. 1R01CA255326 awarded to M.J.S. This work was performed in part at Harvard’s Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure (NNCI), supported by the National Science Foundation (NSF) under NSF award no. 1541959.
The authors declare no competing interests.
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Pahlevaninezhad, M., Huang, YW., Pahlevani, M. et al. Metasurface-based bijective illumination collection imaging provides high-resolution tomography in three dimensions. Nat. Photon. 16, 203–211 (2022). https://doi.org/10.1038/s41566-022-00956-6
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