Abstract
Wavefront shaping systems enable deep tissue imaging by correcting scattering aberrations, but estimating optimal modulation correction is challenging, since it depends on the unknown tissue structures. Most current methods use slow coordinate descent algorithms, which sequentially scan all modulation parameters and query them independently, thus their complexity scales prohibitively with the number of parameters. We introduce a rapid wavefront shaping system, replacing coordinate descent with gradient descent optimization. To this end, our system acquires a gradient vector, which allows simultaneous update of all modulation parameters. We start with a non-invasive, guide-star-free score function to assess modulation quality and analytically derive its gradient with respect to all modulation parameters. Although the gradient depends on unknown tissue structure, we show it can be inferred from optical measurements. This enables fast, high-resolution wavefront correction with complexity independent of parameter count. We demonstrate the system’s effectiveness in correcting aberrations in a coherent confocal microscope.
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Data availability
The data that support the findings of this study is available in ref. 68.
Code availability
The code used for acquiring and processing the data is available at ref. 68.
References
Elliott, A. D. Confocal microscopy: principles and modern practices. Curr. Protoc. Cytom. 92, 68 (2020).
Koustenis, A. Jr. et al. Optical coherence tomography angiography: an overview of the technology and an assessment of applications for clinical research. Br. J. Ophthalmol. 101, 16–20 (2016).
Choi, W. et al. Tomographic phase microscopy. Nat. Methods 4, 717–719 (2007).
Choi, Y. et al. Overcoming the diffraction limit using multiple light scattering in a highly disordered medium. Phys. Rev. Lett. 107, 023902 (2011).
Kang, S. et al. Imaging deep within a scattering medium using collective accumulation of single-scattered waves. Nat. Photonics 9, 253–258 (2015).
Badon, A. et al. Distortion matrix concept for deep optical imaging in scattering media. Science Advances, 6, eaay7170 (2020).
Kwon, Y. et al. Computational conjugate adaptive optics microscopy for longitudinal through-skull imaging of cortical myelin. Nat. Commun. 14, 105 (2023).
Kang, S. et al. Tracing multiple scattering trajectories for deep optical imaging in scattering media. Nat. Commun. 14, 6871 (2023).
Zhang, Y. et al. Deep imaging inside scattering media through virtual spatiotemporal wavefront shaping. Preprint at https://arxiv.org/abs/2306.08793 (2024).
Lee, Y., Kim, D., Jo, Y., Kim, M. & Choi, W. Exploiting volumetric wave correlation for enhanced depth imaging in scattering medium. Nat. Commun. 14, 1878 (2023).
Feng, B. Y. et al. Neuws: neural wavefront shaping for guidestar-free imaging through static and dynamic scattering media. Sci. Adv. 9, 4671 (2023).
Yeminy, T. & Katz, O. Guidestar-free image-guided wavefront shaping. Sci. Adv. 7, 5364 (2021).
Haim, O., Boger-Lombard, J., Katz, O. Image-guided computational holographic wavefront shaping. Nat. Photonics 19, 44–53 (2025).
Balondrade, P. et al. Multi-spectral reflection matrix for ultrafast 3d label-free microscopy. Nat. Photonics 18, 1097–1104 (2024).
Kang, S. et al. High-resolution adaptive optical imaging within thick scattering media using closed-loop accumulation of single scattering. Nat. Commun. 8, 2157 (2017).
Najar, U. et al. Harnessing forward multiple scattering for optical imaging deep inside an opaque medium. Nat. Commun. 15, 7349 (2024).
Zhu, L. et al. Large field-of-view non-invasive imaging through scattering layers using fluctuating random illumination. Nat. Commun. 13, 1447 (2022).
Baek, Y., Aguiar, H. B. & Gigan, S. Phase conjugation with spatially incoherent light in complex media. Nat. Photonics 17, 1114–1119 (2023).
Jeong, S. et al. Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering. Nat. Photonics 12, 277–283 (2018).
Weinberg, G., Sunray, E. & Katz, O. Noninvasive megapixel fluorescence microscopy through scattering layers by a virtual incoherent reflection matrix. Sci. Adv. 10, 5218 (2024).
Jo, Y. et al. Through-skull brain imaging in vivo at visible wavelengths via dimensionality reduction adaptive-optical microscopy. Sci. Adv. 8, 4366 (2022).
Ji, N. Adaptive optical fluorescence microscopy. Nat. Methods 14, 374–380 (2017).
Hampson, K. et al. Adaptive optics for high-resolution imaging. Nat. Rev. Methods Prim. 1, 68 (2021).
Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nat. Photonics 9, 563–571 (2015).
Yu, H. et al. Recent advances in wavefront shaping techniques for biomedical applications. Curr. Appl. Phys. 15, 632–641 (2015).
Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. J. Phys.: Photonics 4, 042501 (2022).
Cui, M., Kahraman, S. S. & Wang, L. V. Optical focusing into scattering media via iterative time reversal guided by absorption nonlinearity. Nat. Commun. 16, 7807 (2025).
Prada, C., Thomas, J.-L. & Fink, M. The iterative time reversal process: analysis of the convergence. J. Acoust. Soc. Am. 97, 62–71 (1995).
Jang, J. et al. Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography. Opt. Express 21, 2890–2902 (2013).
Boniface, A., Blochet, B., Dong, J. & Gigan, S. Noninvasive light focusing in scattering media using speckle variance optimization. Optica 6, 1381–1385 (2019).
Aizik, D., Gkioulekas, I. & Levin, A. Fluorescent wavefront shaping using incoherent iterative phase conjugation. Optica 9, 746–754 (2022).
Aizik, D. & Levin, A. Non-invasive and noise-robust light focusing using confocal wavefront shaping. Nat. Commun. 15, 5575 (2024).
Stern, G. & Katz, O. Noninvasive focusing through scattering layers using speckle correlations. Opt. Lett. 44, 143 (2018).
Katz, O., Small, E., Guan, Y. & Silberberg, Y. Noninvasive nonlinear focusing and imaging through strongly scattering turbid layers. Optica 1, 170–174 (2014).
Vellekoop, I. M. & Mosk, A. P. Focusing coherent light through opaque strongly scattering media. Opt. Lett. 32, 2309–2311 (2007).
Conkey, D. B., Brown, A. N., Caravaca-Aguirre, A. M. & Piestun, R. Genetic algorithm optimization for focusing through turbid media in noisy environments. Opt. Express 20, 4840 (2012).
Popoff, S. M. et al. Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. Phys. Rev. Lett. 104, 100601 (2010).
Vellekoop, I. M., Lagendijk, A. & Mosk, A. P. Exploiting disorder for perfect focusing. Nat. Photonics 4, 320–322 (2010).
Yaqoob, Z., Psaltis, D., Feld, M. S. & Yang, C. Optical phase conjugation for turbidity suppression in biological samples. Nat. Photonics 2, 110–115 (2008).
Chen, Y., Sharma, M. K., Sabharwal, A., Veeraraghavan, A. & Sankaranarayanan, A. C. 3PointTM: faster measurement of high-dimensional transmission matrices. In Computer Vision – ECCV 2020 (eds. Vedaldi, A., Bischof, H., Brox, T. & Frahm, J.-M.) 153–169 (Springer International Publishing, 2020).
Tang, J., Germain, R. N. & Cui, M. Superpenetration optical microscopy by iterative multiphoton adaptive compensation technique. Proc. Natl. Acad. Sci. USA 109, 8434–8439 (2012).
Wang, C. et al. Multiplexed aberration measurement for deep tissue imaging in vivo. Nat. Methods 11, 1037–1040 (2014).
Liu, T. L. et al. Observing the cell in its native state: imaging subcellular dynamics in multicellular organisms. Science 360, 1392 (2018).
Fiolka, R., Si, K. & Cui, M. Complex wavefront corrections for deep tissue focusing using low coherence backscattered light. Opt. Express 20, 16532–16543 (2012).
Xu, X., Liu, H. & Wang, L. V. Time-reversed ultrasonically encoded optical focusing into scattering media. Nat. Photonics 5, 154–157 (2011).
Wang, Y. M., Judkewitz, B., DiMarzio, C. A. & Yang, C. Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light. Nat. Commun. 3, 928 (2012).
Kong, F. et al. Photoacoustic-guided convergence of light through optically diffusive media. Opt. Lett. 36, 2053–2055 (2011).
Vellekoop, I. M., Cui, M. & Yang, C. Digital optical phase conjugation of fluorescence in turbid tissue. Appl. Phys. Lett. 101, 081108 (2012).
Popoff, S. M. et al. Exploiting the time-reversal operator for adaptive optics, selective focusing, and scattering pattern analysis. Phys. Rev. Lett. 107, 263901 (2011).
Mertz, J., Paudel, H. & Bifano, T. G. Field of view advantage of conjugate adaptive optics in microscopy applications. Appl. Opt. 54, 3498–3506 (2015).
Alterman, M., Bar, C., Gkioulekas, I. & Levin, A. Imaging with local speckle intensity correlations: theory and practice. ACM TOG 40, 22 (2021).
Osnabrugge, G., Horstmeyer, R., Papadopoulos, I. N., Judkewitz, B. & Vellekoop, I. M. Generalized optical memory effect. Optica 4, 886–892 (2017).
Dean, B. H. & Bowers, C. W. Diversity selection for phase-diverse phase retrieval. J. Opt. Soc. Am. A 20, 1490–1504 (2003).
Gonsalves, R. A. Phase retrieval and diversity in adaptive optics. Opt. Eng. 21, 215829 (1982).
Candes, E. J., Li, X. & Soltanolkotabi, M. Phase retrieval via Wirtinger flow: theory and algorithms. IEEE Trans. Inf. Theory 61, 1985–2007 (2015).
Smartt, R. N. & Steel, W. H. Theory and application of point-diffraction interferometers. Jpn. J. Appl. Phys. 14, 351 (1975).
Akondi, V., Jewel, A. & Vohnsen, B. Digital phase-shifting point diffraction interferometer. Opt. Lett. 39, 1641–4 (2014).
Song, H. C., Kuperman, W. A., Hodgkiss, W. S., Akal, T. & Ferla, C. Iterative time reversal in the ocean. J. Acoust. Soc. Am. 105, 3176–3184 (1999).
Ruan, H., Jang, M., Judkewitz, B. & Yang, C. Iterative time-reversed ultrasonically encoded light focusing in backscattering mode. Sci. Rep. 4, 7156 (2014).
Si, K., Fiolka, R. & Cui, M. Breaking the spatial resolution barrier via iterative sound-light interaction in deep tissue microscopy. Sci. Rep. 2, 748 (2012).
Papadopoulos, I., Jouhanneau, J.-S., Poulet, J. & Judkewitz, B. Scattering compensation by focus scanning holographic aberration probing (f-sharp). Nat. Photonics 11, 116–123 (2016).
Mididoddi, C. K. et al. Threading light through dynamic complex media. Nat. Photonics 19, 123–134 (2025).
Boniface, A., Dong, J. & Gigan, S. Non-invasive focusing and imaging in scattering media with a fluorescence-based transmission matrix. Nat. Commun. 11, 6154 (2020).
Wang, W. & Li, C. Measurement of the light absorption and scattering properties of onion skin and flesh at 633nm. Postharvest Biol. Technol. 86, 494–501 (2013).
Chen, W.-Y., O’Toole, M., Sankaranarayanan, A. C. & Levin, A. Enhancing speckle statistics for imaging inside scattering media. Optica 9, 1408–1416 (2022).
Chen, W.-Y., Sankaranarayanan, A. C., Levin, A. & O’Toole, M. Coherence as texture - passive textureless 3d reconstruction by self-interference. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (eds. Roth, S., Torralba, A. & Wu, J.) 25058–25066 (IEEE/CVF, 2024).
Baek, Y., de Aguiar, H.B. & Gigan, S. Three-dimensional holographic imaging of incoherent objects through scattering media. Nat. Commun. 16, 11653 (2025).
Monin, S. Rapid-wavefront-shaping-code. figshare. https://doi.org/10.6084/m9.figshare.29245634.v1 (2025).
Acknowledgements
This research was funded by ERC SpeckleCorr-101043471, ISF 563/24.
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S.M. designed and constructed the system. S.M. and M.A. performed the experiments. S.M. analyzed the data. A.L. conceived and supervised the project. All authors contributed to writing of the manuscript.
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Monin, S., Alterman, M. & Levin, A. Rapid wavefront shaping using an optical gradient acquisition. Nat Commun (2026). https://doi.org/10.1038/s41467-025-68259-2
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DOI: https://doi.org/10.1038/s41467-025-68259-2
