When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: methods relying on optical memory effects, and transmission matrix (TM) approaches. Here we develop a general framework describing the nature of memory effects in structures of arbitrary geometry. We show how this framework, when combined with wavefront shaping driven by feedback from a guide-star, enables estimation of the TM of any such system. This highlights that guide-star assisted imaging is possible regardless of the type of memory effect a scatterer exhibits. We apply this concept to multimode fibres (MMFs) and identify a 'quasi-radial' memory effect. This allows the TM of an MMF to be approximated from only one end - an important step for micro-endoscopy. Our work broadens the applications of memory effects to a range of novel imaging and optical communication scenarios.

Department of Theoretical Physics and Astrophysics Faculty of Science Masaryk University Brno Czech Republic

Institute of Scientific Instruments of CAS Brno Czech Republic

Leibniz Institute of Photonic Technology Jena Germany

Physics and Astronomy University of Exeter Exeter UK

Wuhan National Laboratory for Optoelectronics School of Optical and Electronic Information Huazhong University of Science and Technology Wuhan China

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Vellekoop IM, Mosk AP. Focusing coherent light through opaque strongly scattering media. Opt. Lett. 2007;32:2309–2311. doi: 10.1364/OL.32.002309. PubMed DOI

Yaqoob Z, Psaltis D, Feld MS, Yang C. Optical phase conjugation for turbidity suppression in biological samples. Nat. Photonics. 2008;2:110. doi: 10.1038/nphoton.2007.297. PubMed DOI PMC

Popoff SM, et al. Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. Phys. Rev. Lett. 2010;104:100601. doi: 10.1103/PhysRevLett.104.100601. PubMed DOI

Čižmár T, Mazilu M, Dholakia K. In situ wavefront correction and its application to micromanipulation. Nat. Photonics. 2010;4:388. doi: 10.1038/nphoton.2010.85. DOI

Vellekoop IM, Lagendijk A, Mosk AP. Exploiting disorder for perfect focusing. Nat. Photonics. 2010;4:320. doi: 10.1038/nphoton.2010.3. DOI

Popoff S, Lerosey G, Fink M, Boccara AC, Gigan S. Image transmission through an opaque material. Nat. Commun. 2010;1:81. doi: 10.1038/ncomms1078. PubMed DOI

DiLeonardo R, Bianchi S. Hologram transmission through multi-mode optical fibers. Opt. Express. 2011;19:247–254. doi: 10.1364/OE.19.000247. PubMed DOI

Mosk AP, Lagendijk A, Lerosey G, Fink M. Controlling waves in space and time for imaging and focusing in complex media. Nat. Photonics. 2012;6:283. doi: 10.1038/nphoton.2012.88. DOI

Rotter S, Gigan S. Light fields in complex media: Mesoscopic scattering meets wave control. Rev. Mod. Phys. 2017;89:015005. doi: 10.1103/RevModPhys.89.015005. DOI

Feng S, Kane C, Lee PA, Stone AD. Correlations and fluctuations of coherent wave transmission through disordered media. Phys. Rev. Lett. 1988;61:834. doi: 10.1103/PhysRevLett.61.834. PubMed DOI

Freund I, Rosenbluh M, Feng S. Memory effects in propagation of optical waves through disordered media. Phys. Rev. Lett. 1988;61:2328. doi: 10.1103/PhysRevLett.61.2328. PubMed DOI

Judkewitz B, Horstmeyer R, Vellekoop IM, Papadopoulos IN, Yang C. Translation correlations in anisotropically scattering media. Nat. Phys. 2015;11:684–689. doi: 10.1038/nphys3373. DOI

Yílmaz H, et al. Angular memory effect of transmission eigenchannels. Phys. Rev. Lett. 2019;123:203901. doi: 10.1103/PhysRevLett.123.203901. PubMed DOI

de Boer JF, van Albada MP, Lagendijk A. Transmission and intensity correlations in wave propagation through random media. Phys. Rev. B. 1992;45:658. doi: 10.1103/PhysRevB.45.658. PubMed DOI

Kadobianskyi M, Papadopoulos IN, Chaigne T, Horstmeyer R, Judkewitz B. Scattering correlations of time-gated light. Optica. 2018;5:389–394. doi: 10.1364/OPTICA.5.000389. DOI

Choi Y, et al. Scanner-free and wide-field endoscopic imaging by using a single multimode optical fiber. Phys. Rev. Lett. 2012;109:203901. doi: 10.1103/PhysRevLett.109.203901. PubMed DOI PMC

Čižmár T, Dholakia K. Exploiting multimode waveguides for pure fibre-based imaging. Nat. Commun. 2012;3:1027. doi: 10.1038/ncomms2024. PubMed DOI PMC

Ohayon S, Caravaca-Aguirre A, Piestun R, DiCarlo JJ. Minimally invasive multimode optical fiber microendoscope for deep brain fluorescence imaging. Biomed. Opt. express. 2018;9:1492–1509. doi: 10.1364/BOE.9.001492. PubMed DOI PMC

Turtaev S, et al. High-fidelity multimode fibre-based endoscopy for deep brain in vivo imaging. Light.: Sci. Appl. 2018;7:92. doi: 10.1038/s41377-018-0094-x. PubMed DOI PMC

Bertolotti J, et al. Non-invasive imaging through opaque scattering layers. Nature. 2012;491:232. doi: 10.1038/nature11578. PubMed DOI

Fienup JR. Reconstruction of an object from the modulus of its fourier transform. Opt. Lett. 1978;3:27–29. doi: 10.1364/OL.3.000027. PubMed DOI

Fugate RQ, et al. Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star. Nature. 1991;353:144–146. doi: 10.1038/353144a0. DOI

Yoon, S. et al. Deep optical imaging within complex scattering media. Nat. Rev. Phys.2, 1–18, 2020.

Vellekoop IM, Cui M, Yang C. Digital optical phase conjugation of fluorescence in turbid tissue. Appl. Phys. Lett. 2012;101:081108. doi: 10.1063/1.4745775. PubMed DOI PMC

Ruan H, et al. Focusing light inside scattering media with magnetic-particle-guided wavefront shaping. Optica. 2017;4:1337–1343. doi: 10.1364/OPTICA.4.001337. PubMed DOI PMC

Zhou EH, Ruan H, Yang C, Judkewitz B. Focusing on moving targets through scattering samples. Optica. 2014;1:227–232. doi: 10.1364/OPTICA.1.000227. PubMed DOI PMC

Kong F, et al. Photoacoustic-guided convergence of light through optically diffusive media. Opt. Lett. 2011;36:2053–2055. doi: 10.1364/OL.36.002053. PubMed DOI PMC

Judkewitz B, Wang YM, Horstmeyer R, Mathy A, Yang C. Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (trove) Nat. photonics. 2013;7:300. doi: 10.1038/nphoton.2013.31. PubMed DOI PMC

Horstmeyer R, Ruan H, Yang C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nat. Photonics. 2015;9:563. doi: 10.1038/nphoton.2015.140. PubMed DOI PMC

Osnabrugge G, Horstmeyer R, Papadopoulos IN, Judkewitz B, Vellekoop IM. Generalized optical memory effect. Optica. 2017;4:886–892. doi: 10.1364/OPTICA.4.000886. DOI

Papadopoulos IN, Jouhanneau J-S, Poulet JFA, Judkewitz B. Scattering compensation by focus scanning holographic aberration probing (f-sharp) Nat. Photonics. 2016;11:116–123. doi: 10.1038/nphoton.2016.252. DOI

Okamoto, K. Fundamentals of Optical Waveguides. (Academic press, 2006).

Plöschner M, Tyc T, Čižmár T. Seeing through chaos in multimode fibres. Nat. Photonics. 2015;9:529. doi: 10.1038/nphoton.2015.112. DOI

Leach J, Padgett MJ, Barnett SM, Franke-Arnold S, Courtial J. Measuring the orbital angular momentum of a single photon. Phys. Rev. Lett. 2002;88:257901. doi: 10.1103/PhysRevLett.88.257901. PubMed DOI

Amitonova LV, Mosk AP, Pinkse PWH. Rotational memory effect of a multimode fiber. Opt. express. 2015;23:20569–20575. doi: 10.1364/OE.23.020569. PubMed DOI

Shapiro JH. Computational ghost imaging. Phys. Rev. A. 2008;78:061802. doi: 10.1103/PhysRevA.78.061802. DOI

Amitonova LV, De Boer JF. Compressive imaging through a multimode fiber. Opt. Lett. 2018;43:5427–5430. doi: 10.1364/OL.43.005427. PubMed DOI

Turtaev S, et al. Comparison of nematic liquid-crystal and dmd based spatial light modulation in complex photonics. Opt. Express. 2017;25:29874–29884. doi: 10.1364/OE.25.029874. PubMed DOI

Xiong W, et al. Principal modes in multimode fibers: exploring the crossover from weak to strong mode coupling. Opt. Express. 2017;25:2709–2724. doi: 10.1364/OE.25.002709. PubMed DOI

Leite IT, et al. Three-dimensional holographic optical manipulation through a high-numerical-aperture soft-glass multimode fibre. Nat. Photonics. 2018;12:33–39. doi: 10.1038/s41566-017-0053-8. DOI

Zhu L, et al. Chromato-axial memory effect through a forward-scattering slab. Optica. 2020;7:338–345. doi: 10.1364/OPTICA.382209. DOI

Boniface A, Mounaix M, Blochet B, Piestun R, Gigan S. Transmission-matrix-based point-spread-function engineering through a complex medium. Optica. 2017;4:54–59. doi: 10.1364/OPTICA.4.000054. DOI

Li, S. et al. Compressively sampling the optical transmission matrix of a multimode fibre. Light.: Sci. Appl.10, 1–15 (2021). PubMed PMC

Sivankutty S, et al. Ultra-thin rigid endoscope: two-photon imaging through a graded-index multi-mode fiber. Opt. express. 2016;24:825–841. doi: 10.1364/OE.24.000825. PubMed DOI

Conkey DB, Caravaca-Aguirre AM, Piestun R. High-speed scattering medium characterization with application to focusing light through turbid media. Opt. express. 2012;20:1733–1740. doi: 10.1364/OE.20.001733. PubMed DOI

Matthès, M. W., Bromberg, Y., de Rosny, J., & Popoff, S. M. Learning and avoiding disorder in multimode fibers. Preprint at: https://arxiv.org/abs/2010.14813 (2020).

Boniface A, Blochet B, Dong J, Gigan S. Noninvasive light focusing in scattering media using speckle variance optimization. Optica. 2019;6:1381–1385. doi: 10.1364/OPTICA.6.001381. DOI

Boniface A, Dong J, Gigan S. Non-invasive focusing and imaging in scattering media with a fluorescence-based transmission matrix. Nat. Commun. 2020;11:6154. doi: 10.1038/s41467-020-19696-8. PubMed DOI PMC

Kamaljith V, et al. Ultrafast-laser-ablation-assisted spatially selective attachment of fluorescent sensors onto optical fibers. Opt. Lett. 2020;45:2716–2719. doi: 10.1364/OL.381018. PubMed DOI

Gu RY, Mahalati RN, Kahn JM. Design of flexible multi-mode fiber endoscope. Opt. express. 2015;23:26905–26918. doi: 10.1364/OE.23.026905. PubMed DOI

Gu, R. Y., Chou, E., Rewcastle, C., Levi, O., and Kahn, J. M. Improved spot formation for flexible multi-mode fiber endoscope using partial reflector. Preprint at: https://arxiv.org/abs/1805.07553 (2018).

Gordon GSD, et al. Characterizing optical fiber transmission matrices using metasurface reflector stacks for lensless imaging without distal access. Phys. Rev. X. 2019;9:041050.

Chen H, Fontaine NK, Ryf R, Neilson DT, Winzer P. Remote spatio-temporal focusing over multimode fiber enabled by single-ended channel estimation. IEEE J. Sel. Top. Quantum Electron. 2020;26:1–9.

Rosen, S., Gilboa, D., Katz, O. & Silberberg, Y. Focusing and scanning through flexible multimode fibers without access to the distal end. Preprint at: https://arxiv.org/abs/1506.08586 (2015).

Xiong W, Hsu CW, Cao H. Long-range spatio-temporal correlations in multimode fibers for pulse delivery. Nat. Commun. 2019;10:1–7. doi: 10.1038/s41467-018-07882-8. PubMed DOI PMC

Mounaix M, Carpenter J. Control of the temporal and polarization response of a multimode fiber. Nat. Commun. 2019;10:1–8. doi: 10.1038/s41467-019-13059-8. PubMed DOI PMC

Carpenter J, Eggleton BJ, Schröder J. 110 × 110 optical mode transfer matrix inversion. Opt. express. 2014;22:96–101. doi: 10.1364/OE.22.000096. PubMed DOI

Flaes DEB, et al. Robustness of light-transport processes to bending deformations in graded-index multimode waveguides. Phys. Rev. Lett. 2018;120:233901. doi: 10.1103/PhysRevLett.120.233901. PubMed DOI

Mekis A, et al. High transmission through sharp bends in photonic crystal waveguides. Phys. Rev. Lett. 1996;77:3787. doi: 10.1103/PhysRevLett.77.3787. PubMed DOI

Kuschmierz R, Scharf E, Koukourakis N, Czarske JW. Self-calibration of lensless holographic endoscope using programmable guide stars. Opt. Lett. 2018;43:2997–3000. doi: 10.1364/OL.43.002997. PubMed DOI

Choudhury D, et al. Computational optical imaging with a photonic lantern. Nat. Commun. 2020;11:1–9. doi: 10.1038/s41467-020-18818-6. PubMed DOI PMC

Katz O, Heidmann P, Fink M, Gigan S. Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations. Nat. photonics. 2014;8:784. doi: 10.1038/nphoton.2014.189. DOI

Brown BR, Lohmann AW. Complex spatial filtering with binary masks. Appl. Opt. 1966;5:967–969. doi: 10.1364/AO.5.000967. PubMed DOI

Lee W-H. Binary computer-generated holograms. Appl. Opt. 1979;18:3661–3669. doi: 10.1364/AO.18.003661. PubMed DOI

"There's plenty of room at the bottom": deep brain imaging with holographic endo-microscopy

110 μm thin endo-microscope for deep-brain in vivo observations of neuronal connectivity, activity and blood flow dynamics