- Letter
- Open Access
Statistical dependencies beyond linear correlations in light scattered by disordered media
Phys. Rev. Research 4, L022033 – Published 11 May, 2022
DOI: https://doi.org/10.1103/PhysRevResearch.4.L022033
Abstract
Imaging through scattering and random media is an outstanding problem that, to date, has been tackled by either measuring the medium transmission matrix or exploiting linear correlations in the transmitted speckle patterns. However, transmission matrix techniques require interferometric stability and linear correlations, such as the memory effect, can be exploited only in thin scattering media. Here we show the existence of a statistical dependency in strongly scattered optical fields in a case where first-order correlations are not expected. We also show that this statistical dependence and the related information transport is directly linked to artificial neural network imaging in strongly scattering, dynamic media. These nontrivial dependencies provide a key to imaging through dynamic and thick scattering media with applications for deep-tissue imaging or imaging through smoke or fog.
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References (36)
- J. Goodman, Speckle Phenomena in Optics: Theory and a Applications (Roberts & Co, Englewood, CO, 2007).
- R. Berkovits and S. Feng, Correlations in coherent multiple scattering, Phys. Rep. 238, 135 (1994).
- S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media, Phys. Rev. Lett. 61, 834 (1988).
- I. Freund, M. Rosenbluh, and S. Feng, Memory Effects in Propagation of Optical Waves through Disordered Media, Phys. Rev. Lett. 61, 2328 (1988).
- I. Freund, Looking through walls and around corners, Physica A 168, 49 (1990).
- J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, Non-invasive imaging through opaque scattering layers, Nature (London) 491, 232 (2012).
- O. Katz, P. Heidmann, M. Fink, and S. Gigan, Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations, Nat. Photon. 8, 784 (2014).
- I. Starshynov, A. M. Paniagua-Diaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, Non-Gaussian Correlations between Reflected and Transmitted Intensity Patterns Emerging from Opaque Disordered Media, Phys. Rev. X 8, 021041 (2018).
- A. M. Paniagua-Diaz, I. Starshynov, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti, Blind ghost imaging, Optica 6, 460 (2019).
- T. W. Anderson, An Introduction to Multivariate Statistical Analysis (Wiley-Interscience, Hoboken, NJ, 2003).
- G. J. Foschini and M. J. Gans, On limits of wireless communications in a fading environment when using multiple antennas, Wireless Pers. Commun. 6, 311 (1998).
- A. L. Moustakas, H. U. Baranger, L. Balents, A. M. Sengupta, and S. H. Simon, Communication through a diffusive medium: Coherence and capacity, Science 287, 287 (2000).
- S. H. Simon, A. L. Moustakas, M. Stoytchev, and H. Safar, Communication in a disordered world, Phys. Today 54, 38 (2001).
- J. Stäring, A. Eriksson, and B. Mehlig, Fluctuations of the shannon capacity in a rayleigh model of wireless communication, Physica Status Ssolidi (b) 241, 2136 (2004).
- N. Byrnes and M. R. Foreman, Universal bounds for imaging in scattering media, New J. Phys. 22, 083023 (2020).
- C. W. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys. 69, 731 (1997).
- S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, 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).
- E. G. van Putten and A. P. Mosk, The information age in optics: Measuring the transmission matrix, Physics 3, 22 (2010).
- S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, Image transmission through an opaque material, Nat. Commun. 1, 81 (2010).
- M. Plöschner, T. Tyc, and T. Čižmár, Seeing through chaos in multimode fibres, Nat. Photon. 9, 529 (2015).
- A. Albertazzi, Jr., M. Viotti, F. Silva, C. Veiga, E. Barrera, M. Benedet, A. Fantin, and D. Willemann, Speckle interferometry in harsh environments: Design considerations and successful examples, in Optical Micro-and Nanometrology VII (SPIE, Bellingham, WA, 2018), Vol. 10678, p. 1067802.
- T. Ando, R. Horisaki, and J. Tanida, Speckle-learning-based object recognition through scattering media, Opt. Express 23, 33902 (2015).
- G. Satat, M. Tancik, O. Gupta, B. Heshmat, and R. Raskar, Object classification through scattering media with deep learning on time resolved measurement, Opt. Express 25, 17466 (2017).
- A. Turpin, I. Vishniakou, and J. Seelig, Light scattering control in transmission and reflection with neural networks, Opt. Express 26, 30911 (2018).
- S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, Imaging through glass diffusers using densely connected convolutional networks, Optica 5, 803 (2018).
- G. Barbastathis, A. Ozcan, and G. Situ, On the use of deep learning for computational imaging, Optica 6, 921 (2019).
- O. Ronneberger, P. Fischer, and T. Brox, U-net: Convolutional networks for biomedical image segmentation, in Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015, edited by N. Navab, J. Hornegger, W. M. Wells, and A. F. Frangi (Springer International Publishing, Cham, Switzerland, 2015), pp. 234–241.
- Y. Li, Y. Xue, and L. Tian, Deep speckle correlation: A deep learning approach toward scalable imaging through scattering media, Optica 5, 1181 (2018).
- S. Resisi, S. M. Popoff, and Y. Bromberg, Image transmission through a dynamically perturbed multimode fiber by deep learning, Laser Photon. Rev. 15, 2000553 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L022033 for additional details on the numerical model and mutual information calculations..
- L. Paninski, Estimation of entropy and mutual information, Neural Comput. 15, 1191 (2003).
- MNIST image database: http://yann.lecun.com/exdb/mnist/.
- Y. Li, S. Cheng, Y. Xue, and L. Tian, Displacement-agnostic coherent imaging through scatter with an interpretable deep neural network, Opt. Express 29, 2244 (2021).
- R. Uppu, T. A. Wolterink, S. A. Goorden, B. Chen, B. Škorić, A. P. Mosk, and P. W. Pinkse, Asymmetric cryptography with physical unclonable keys, Quantum Sci. Technol. 4, 045011 (2019).
- A. Fratalocchi, A. Fleming, C. Conti, and A. D. Falco, NIST-certified secure key generation via deep learning of physical unclonable functions in silica aerogels, Nanophotonics 10, 20200368 (2020).
- Dataset for the paper Statistical Dependencies Beyond Linear Correlations in Light Scattered by Disordered Media, http://doi.org/10.5525/gla.researchdata.1089.