A practical guide to digital micro-mirror devices (DMDs) for wavefront shaping
Popoff, S. M., R. Gutiérrez-Cuevas, Y. Bromberg, and M. W. Matthés
Journal of Physics: Photonics 6, no. 4, 043001 (2024)
Résumé: Digital micromirror devices have gained popularity in wavefront shaping, offering a high frame rate alternative to liquid crystal spatial light modulators. They are relatively inexpensive, offer high resolution, are easy to operate, and a single device can be used in a broad optical bandwidth. However, some technical drawbacks must be considered to achieve optimal performance. These issues, often undocumented by manufacturers, mostly stem from the device's original design for video projection applications. Herein, we present a guide to characterize and mitigate these effects. Our focus is on providing simple and practical solutions that can be easily incorporated into a typical wavefront shaping setup.
Mots-clés: wavefront shaping; modulation; optics; DMD; modulator; SLM
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Reaching the precision limit with tensor-based wavefront shaping
Gutiérrez-Cuevas, R., D. Bouchet, J. De Rosny, and S. M. Popoff
Nature Communications 15, no. 1 (2024)
Résumé: Perturbations in complex media, due to their own dynamical evolution or to external effects, are often seen as detrimental. Therefore, a common strategy, especially for telecommunication and imaging applications, is to limit the sensitivity to those perturbations in order to avoid them. Here, instead, we consider enhancing the interaction between light and perturbations to produce the largest change in the output intensity distribution. Our work hinges on the use of tensor-based techniques, presently at the forefront of machine learning explorations, to study intensity-based measurements where its quadratic relationship to the field prevents the use of standard matrix methods. With this tensor-based framework, we can identify the maximum-information intensity channel which maximizes the change in its output intensity distribution and the Fisher information encoded in it about a given perturbation. We further demonstrate experimentally its superiority for robust and precise sensing applications. Additionally, we derive the appropriate strategy to reach the precision limit for intensity-based measurements, leading to an increase in Fisher information by more than four orders of magnitude compared to the mean for random wavefronts when measured with the pixels of a camera.
Mots-clés: wavefront shaping, multimode fiber, sensing, information, transmission matrix, optical fibers
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Control of coherent backscattering by breaking optical reciprocity
Bromberg, Y., B. Redding, S. M. Popoff, and H. Cao
Physical Review A 93, no. 2 (2016)
Résumé: Reciprocity is a universal principle that has a profound impact on many areas of physics. A fundamental phenomenon in condensed-matter physics, optical physics, and acoustics, arising from reciprocity, is the constructive interference of quantum or classical waves which propagate along time-reversed paths in disordered media, leading to, for example, weak localization and metal-insulator transition. Previous studies have shown that such coherent effects are suppressed when reciprocity is broken. Here we experimentally show that by tuning a nonreciprocal phase we can coherently control complex coherent phenomena, rather than simply suppress them. In particular, we manipulate coherent backscattering of light, also known as weak localization. By utilizing a magneto-optical effect, we control the interference between time-reversed paths inside a multimode fiber with strong mode mixing, observe the optical analog of weak antilocalization, and realize a continuous transition from weak localization to weak antilocalization. Our results may open new possibilities for coherent control of waves in complex systems.
Mots-clés: wavefront shaping; backscattering; multimode fibers; reciprocity
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Tutorial: How to build and control an all-fiber wavefront modulator using mechanical perturbations
Shekel, R., K. Sulimany, S. Resisi, Z. Finkelstein, O. Lib, S. M. Popoff, and Y. Bromberg
Journal of Physics: Photonics 6, no. 3, 033002 (2024)
Résumé: Multimode optical fibers support the dense, low-loss transmission of many spatial modes, making them attractive for technologies such as communications and imaging. However, information propagating through multimode fibers is scrambled, due to modal dispersion and mode mixing. This is usually rectified using wavefront shaping techniques with devices such as spatial light modulators. Recently, we demonstrated an all-fiber system for controlling light propagation inside multimode fibers using mechanical perturbations, called the fiber piano. In this tutorial we explain the design considerations and experimental methods needed to build a fiber piano, and review applications where fiber pianos have been used.
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Shaping single photons through multimode optical fibers using mechanical perturbations
Shekel, R., O. Lib, R. Gutierrez-Cuevas, S. M. Popoff, A. Ling, and Y. Bromberg
APL Photonics 8, no. 9, 096109 (2023)
Résumé: Multimode optical fibers support low-loss transmission of multiple spatial modes, allowing for the transport of high-dimensional, spatially encoded information. In particular, encoding quantum information in the transverse shape of photons may boost the capacity of quantum channels while using existing infrastructure. However, when photons propagate through a multimode fiber, their transverse shape gets scrambled because of mode mixing and modal interference. This is usually corrected using free-space spatial light modulators, inhibiting a robust all-fiber operation. In this work, we demonstrate an all-fiber approach for controlling the shape of single photons and the spatial correlations between entangled photon pairs, using carefully controlled mechanical perturbations of the fiber. We optimize these perturbations to localize the spatial distribution of a single photon or the spatial correlations of photon pairs in a single spot, enhancing the signal in the optimized spot by over an order of magnitude. Using the same approach, we show a similar enhancement for coupling light from a multimode fiber into a single-mode fiber.
Mots-clés: wavefront shaping; entenglement; quantum optics; multimode fibers
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Restoring and tailoring very high dimensional spatial entanglement of a biphoton state transmitted through a scattering medium
Devaux, F., A. Mosset, S. M. Popoff, and E. Lantz
Journal of Optics 25, no. 5, 055201 (2023)
Résumé: We report experimental results where a momentum entangled biphoton state with a Schmidt number of a few thousand is retrieved and manipulated when only one photon of the pair is transmitted through a thin scattering medium. For this purpose, the transmission matrix of the complex medium is first measured with a phase-shifting interferometry measurement method using a spatial light modulator (SLM) illuminated with a laser source. From this matrix, different phase masks are calculated and addressed on the SLM to spatially control the focusing of the laser through the complex medium. These same masks are used to manipulate the phase of the biphoton wave function transmitted by the thin diffuser in order to restore and control in the same way the momentum correlations between the far-field images of twin beams issued from strongly spatial-multi-mode spontaneous parametric down conversion.
Mots-clés: quantum optics, entenglement, wavefront shaping, scattering media
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Superresolved Imaging Based on Spatiotemporal Wave-Front Shaping
Noetinger, G., S. Métais, G. Lerosey, M. Fink, S. M. Popoff, and F. Lemoult
Physical Review Applied 19, no. 2 (2023)
Résumé: A label-free approach to improving the performances of confocal scanning imaging is proposed. We experimentally demonstrate its feasibility using acoustic waves. It relies on a way to encode spatial information using the temporal dimension. By moving an emitter, used to insonify an object, along a circular path, we create a temporally modulated wavefield. Because of the symmetries of the problem, the spatiotemporal input field can be decomposed into harmonics corresponding to different spatial vortices. Acquiring the back-reflected waves with receivers that are also rotating, multiple images of the same object with different point spread functions are obtained. Not only is the resolution improved compared to a standard confocal configuration, but the accumulation of information also allows the building of images that beat the diffraction limit.
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Roadmap on wavefront shaping and deep imaging in complex media
Gigan, S., O. Katz, H. B. De Aguiar, E. R. Andresen, A. Aubry, J. Bertolotti, E. Bossy, D. Bouchet, J. Brake, S. Brasselet, Y. Bromberg, H. Cao, T. Chaigne, Z. Cheng, W. Choi, T. čižmár, M. Cui, V. R. Curtis, H. Defienne, M. Hofer, R. Horisaki, R. Horstmeyer, N. Ji, A. K. Laviolette, J. Mertz, C. Moser, A. P. Mosk, N. C. Pégard, R. Piestun, S. Popoff, D. B. Phillips, D. Psaltis, B. Rahmani, H. Rigneault, S. Rotter, L. Tian, I. M. Vellekoop, L. Waller, and Wan
Journal of Physics: Photonics 4, no. 4, 042501 (2022)
Résumé: The last decade has seen the development of a wide set of tools, such as wavefront shaping, computational or fundamental methods, that allow us to understand and control light propagation in a complex medium, such as biological tissues or multimode fibers. A vibrant and diverse community is now working in this field, which has revolutionized the prospect of diffraction-limited imaging at depth in tissues. This roadmap highlights several key aspects of this fast developing field, and some of the challenges and opportunities ahead.
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Fourier transform acousto-optic imaging with off-axis holographic detection
Dutheil, L., M. Bocoum, M. Fink, S. M. Popoff, F. Ramaz, and J. M. Tualle
Applied Optics 60, no. 24, 7107-7112 (2021)
Résumé: Acousto-optic (AO) imaging is an in-depth optical imaging technique of highly scattering media. One challenging end-application for this technique is to perform imaging of living biological tissues. Indeed, because it relies on coherent illumination, AO imaging is sensitive to speckle decorrelation occurring on the millisecond time scale. Camera-based detections are well suited for in vivo imaging provided their integration time is lower than those decorrelation time scales. We present Fourier transform acousto-optic imaging combined with off-axis holography, which relies on plane waves and long-duration pulses. We demonstrate, for the first time to the best of our knowledge, a two-dimensional imaging system fully compatible with in vivo imaging prerequisites. The method is validated experimentally by performing in-depth imaging inside a multiple scattering sample.
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Image Transmission Through a Dynamically Perturbed Multimode Fiber by Deep Learning
Resisi, S., S. M. Popoff, and Y. Bromberg
Laser & Photonics Reviews, 2000553 (2021)
Résumé: When multimode optical fibers are perturbed, the data that is transmitted through them is scrambled. This presents a major difficulty for many possible applications, such as multimode fiber based telecommunication and endoscopy. To overcome this challenge, a deep learning approach that generalizes over mechanical perturbations is presented. Using this approach, successful reconstruction of the input images from intensity-only measurements of speckle patterns at the output of a 1.5 m-long randomly perturbed multimode fiber is demonstrated. The model's success is explained by hidden correlations in the speckle of random fiber conformations.
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Learning and Avoiding Disorder in Multimode Fibers
Matthès, M. W., Y. Bromberg, J. De Rosny, and S. M. Popoff
Physical Review X 11, no. 2 (2021)
Résumé: Multimode optical fibers (MMFs) have gained renewed interest in the past decade, emerging as a way to boost optical communication data rates in the context of an expected saturation of current single-mode fiber-based networks. They are also attractive for endoscopic applications, offering the possibility to achieve a similar information content as multicore fibers, but with a much smaller footprint, thus reducing the invasiveness of endoscopic procedures. However, these advances are hindered by the unavoidable presence of disorder that affects the propagation of light in MMFs and limits their practical applications. We introduce here a general framework to study and avoid the effect of disorder in wave-based systems and demonstrate its application for multimode fibers. We experimentally find an almost complete set of optical channels that are resilient to disorder induced by strong deformations. These deformation principal modes are obtained by only exploiting measurements for weak perturbations harnessing the generalized Wigner-Smith operator. We explain this effect by demonstrating that, even for a high level of disorder, the propagation of light in MMFs can be characterized by just a few key properties. These results are made possible thanks to a precise and fast estimation of the modal transmission matrix of the fiber which relies on a model-based optimization using deep learning frameworks.
Mots-clés: multimode fiber; wavefront shaping; disorder; Wigner-Smith; telecommunications; transmission matrix
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Contrôle spatio-temporel de la lumière en milieux complexes
Popoff, S.
Manuscrit de thèse (2011)
Résumé: L'objectif des travaux présentés dans cette thèse est d'associer les outils et le formalisme développés en acoustique aux techniques propres à l'optique. Ces études ont été rendues possibles grâce aux avancées technologiques récentes qui autorisent le contrôle et la mesure, spatialement et temporellement, des ondes optiques. En nous appuyant sur un système permettant de contrôler et de mesurer spatialement le champ complexe optique, nous avons enregistré la matrice de transmission d'un milieu diffusant. Nous exploitons cette matrice pour focaliser la lumière et détecter des images à travers le milieu ainsi que pour l'étude de ses propriétés physiques. En utilisant un montage et un modèle similaire, nous mesurons ensuite à travers un milieu aberrateur la matrice de réflexion d'un milieu contenant quelques diffuseurs efficaces. Nous exploitons la décomposition en valeurs singulières de cette matrice pour détecter les diffuseurs et focaliser la lumière sélectivement sur plusieurs d'entre eux, en compensant les aberrations du milieu de propagation. Une autre approche présentée est l'exploitation de l'analyse de la matrice de réflexion pour l'étude des modes de rayonnement d'une particule unique. La dernière étude réalisée concerne l'application du retournement sur modulation en optique. Cette technique consiste à apprendre les réponses d'un milieu diffusant ou réverbérant à une modulation et à exploiter ces réponses pour focaliser la lumière au sein du milieu. Nous prouvons l'efficacité de cette technique pour la focalisation temporelle dans une cavité et tentons de l'étendre pour une focalisation à la fois spatiale et temporelle.
Mots-clés: Optics; Scattering; Phase conjugation; Time reversal; Focusing; Imaging; Optique; Diffusion; Conjugaison de phase; Retournement temporel; Focalisation; Imagerie
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Wavefront shaping in multimode fibers by transmission matrix engineering
Resisi, S., Y. Viernik, S. M. Popoff, and Y. Bromberg
APL Photonics 5, no. 3, 036103 (2020)
Résumé: © 2020 Author(s). We present a new approach for shaping light at the output of a multimode fiber by modulating the transmission matrix of the system rather than the incident light. We apply computer-controlled mechanical perturbations to the fiber and obtain a desired intensity pattern at its output resulting from the changes to its transmission matrix. Using an all-fiber apparatus, we demonstrate focusing light at the distal end of the fiber and dynamic conversion between fiber modes in the few-mode regime. Since in this approach the number of available degrees of control scales with the number of spectral channels and can thus be larger than the number of fiber modes, it potentially opens the door to simultaneous control over multiple inputs and at multiple wavelengths.
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Optimizing Light Storage in Scattering Media with the Dwell-Time Operator
Durand, M., S. M. Popoff, R. Carminati, and A. Goetschy
Physical Review Letters 123, no. 24 (2019)
Résumé: © 2019 American Physical Society. We prove that optimal control of light energy storage in disordered media can be reached by wave front shaping. For this purpose, we build an operator for dwell times from the scattering matrix and characterize its full eigenvalue distribution both numerically and analytically in the diffusive regime, where the thickness L of the medium is much larger than the mean free path â.,". We show that the distribution has a finite support with a maximal dwell time larger than the most likely value by a factor (L/â.,")2≫1. This reveals that the highest dwell-time eigenstates deposit more energy than the open channels of the medium. Finally, we show that the dwell-time operator can be used to store energy in resonant targets buried in complex media, without any need for guide stars.
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WE2.3-performing linear operations using optical complex media (Invited)
Matthes, M., P. Del Hougne, J. De Rosny, G. Lerosey, and S. Popoff
IEEE Photonics Society Summer Topical Meeting Series 2019, SUM 2019 (2019)
Résumé: © 2019 IEEE. We propose using complex media as platforms to build any linear operator using wavefront shaping. We demonstrate that system composed of multimode fiber and spatial light modulator can act like any linear operator and can be reconfigured at will. We experimentally performed several 16×16-single-shot operations.
Mots-clés: Multimode Fiber; Optical Linear Operations; Wavefront Shaping
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Optical complex media as universal reconfigurable linear operators
Matthès, M. W., P. Del Hougne, J. De Rosny, G. Lerosey, and S. M. Popoff
Optica 6, no. 4, 465-472 (2019)
Résumé: © 2019 Optical Society of America. Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunications to optical analog computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies, reconfigurability, and scalability. We propose a way to perform linear operations using complex optical media such as multimode fibers or scattering media as a computational platform driven by wavefront shaping. Given a large random transmission matrix representing light propagation in such a medium, we can extract any desired smaller linear operator by finding suitable input and output projectors. We demonstrate this concept by finding input wavefronts using a spatial light modulator that cause the complex medium to act as a desired complex-valued linear operator on the optical field. We experimentally build several 16 × 16 operators and discuss the fundamental limits of the scalability of our approach. It offers the prospect of reconfigurable, robust, and easy-to-fabricate linear optical analog computation units.
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Remote key establishment by random mode mixing in multimode fibers and optical reciprocity
Bromberg, Y., B. Redding, S. M. Popoff, N. Zhao, G. Li, and H. Cao
Optical Engineering 58, no. 1 (2019)
Résumé: © 2019 The Authors. Disorder and scattering in photonic systems have long been considered a nuisance that should be circumvented. Recently, disorder has been harnessed for a rapidly growing number of applications, including imaging, sensing, and spectroscopy. The chaotic dynamics and extreme sensitivity to external perturbations make random media particularly well-suited for optical cryptography. However, using random media for distribution of secret keys between remote users still remains challenging since it requires the users have access to the same scattering sample. Here, we utilize random mode mixing in long multimode fibers to generate and distribute keys simultaneously. Fast fluctuations in fiber mode mixing provide the source of randomness for key generation, and optical reciprocity guarantees that the keys at the two ends of the fiber are identical. We experimentally demonstrate the scheme using classical light and off-the-shelf components, opening the door for a practically secure key establishment at the physical layer of fiber-optic networks.
Mots-clés: fiber optics; key distribution; optical communications; optical cryptography; random media; reciprocity
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Coherent Control of Photocurrent in a Strongly Scattering Photoelectrochemical System
Liew, S. F., S. M. Popoff, S. W. Sheehan, A. Goetschy, C. A. Schmuttenmaer, A. D. Stone, and H. Cao
Acs Photonics 3, no. 3, 449-455 (2016)
Mots-clés: photoelectrochemical; dye-sensitized solar cells; wavefront shaping; multiple scattering; multimode interference
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Coherent perfect absorption and coherent enhancement of absorption
Douglas Stone, A., H. Cao, Y. D. Chong, L. Ge, S. Popoff, and A. Goetschy
CLEO: QELS - Fundamental Science, CLEO_QELS 2015, 1551p (2015)
Résumé: Coherent illumination and wave-front shaping can be used to make a weakly absorbing cavity perfectly absorbing and to enhance strongly the absorption of a multiple scattering medium. © 2015 Optical Society of America.
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Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix.
Andreoli, D., G. Volpe, S. Popoff, O. Katz, S. Gresillon, and S. Gigan
Scientific reports 5, 10347 (2015)
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Image transmission through a scattering medium: Inverse problem and sparsity-based imaging
Gigan, S., S. M. Popoff, A. Liutkus, D. Martina, O. Katz, G. Chardon, R. Carminati, G. Lerosey, M. A. Fink., A. C. Boccara, I. Carron, and L. Daudet
2014 13th Workshop on Information Optics, WIO 2014 (2014)
Résumé: © 2014 IEEE. We demonstrate how to measure accurately the transmission matrix of a complex medium. With this information, we show how to focus light, recover an image, and even perform efficient reconstruction of a sparse object.
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Imaging with nature: compressive imaging using a multiply scattering medium.
Liutkus, A., D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron
Scientific reports 4, 5552 (2014)
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Exploiting the time-reversal operator for adaptive optics, selective focusing and scattering pattern analysis
Popoff, S. M., A. Aubry, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan
2012 Conference on Lasers and Electro-Optics, CLEO 2012 (2012)
Résumé: We report on the optical measurement of the backscattering matrix in a weakly scattering medium. A decomposition of the time reversal operator allows selective and efficient focusing on individual scatterers, even through an aberrating layer. © 2012 OSA.
Mots-clés: Backscattering matrix; Decomposition of the time reversal operator; Optical measurement; Scattering medium; Scattering pattern; Time-reversal operator; Lasers; Optical data processing; Scattering
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Exploiting the time-reversal operator for adaptive optics, selective focusing, and scattering pattern analysis
Popoff, S. M., A. Aubry, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan
Physical Review Letters 107, no. 26 (2011)
Résumé: We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the time-reversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles. © 2011 American Physical Society.
Mots-clés: Backscattering matrix; Experimental measurements; matrix; Nanobeads; Optical imaging; Scattering medium; Scattering pattern; Selective excitations; Single nanoparticle; Time-reversal operator; Nanoparticles; Scattering
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Controlling light through optical disordered media: Transmission matrix approach
Popoff, S. M., G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan
New Journal of Physics 13 (2011)
Résumé: We experimentally measure the monochromatic transmission matrix (TM) of an optical multiple scattering medium using a spatial light modulator together with a phase-shifting interferometry measurement method. The TM contains all the information needed to shape the scattered output field at will or to detect an image through the medium. We confront theory and experiment for these applications and study the effect of noise on the reconstruction method. We also extracted from the TM information about the statistical properties of the medium and the light transport within it. In particular, we are able to isolate the contributions of the memory effect and measure its attenuation length. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Mots-clés: Attenuation lengths; Disordered media; Light transport; Memory effects; Multiple-scattering medium; Phase shifting Interferometry; Reconstruction method; Spatial light modulators; Statistical properties; Transmission matrix; Light modulators; Light transmission
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Transmission matrix in optics: Taking advantage of transmission channels for image transmission in disordered materials
Popoff, S. M., G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan
2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011)
Résumé: Recently, a method has been proposed by I. Vellekoop et al. [1] to focus light through a multiple scattering material, using a spatial light modulator as a tool to shape the incoming beam to obtain a maximal interference on a speckle spot of the output speckle pattern. The result is a bright, diffraction limited, spot which can be several hundred times brighter than the rest of the speckle. © 2011 IEEE.
Mots-clés: Diffraction limited; Disordered materials; Spatial light modulators; Speckle patterns; Transmission channels; Transmission matrix; Electron optics; Light modulators; Optics; Quantum electronics; Speckle; Light
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Image transmission through an opaque material
Popoff, S., G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan
Nature Communications 1, no. 6 (2010)
Résumé: Optical imaging relies on the ability to illuminate an object, collect and analyse the light it scatters or transmits. Propagation through complex media such as biological tissues was so far believed to degrade the attainable depth, as well as the resolution for imaging, because of multiple scattering. This is why such media are usually considered opaque. Recently, we demonstrated that it is possible to measure the complex mesoscopic optical transmission channels that allow light to traverse through such an opaque medium. Here, we show that we can optimally exploit those channels to coherently transmit and recover an arbitrary image with a high fidelity, independently of the complexity of the propagation. © 2010 Macmillan Publishers Limited. All rights reserved.
Mots-clés: article; imaging system; laser diffraction; light scattering; optical tomography; visual system
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Measuring and exploiting the transmission matrix in optics
Popoff, S. M., G. Lerosey, R. Carminati, M. Fink, A. C. Boceara, and S. Gigan
Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference: 2010 Laser Science to Photonic Applications, CLEO/QELS 2010 (2010)
Résumé: We introduce a method to measure the transmission matrix of a complex medium. This matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. ©2010 IEEE.
Mots-clés: Complex medium; Light focusing; matrix; Random matrix theory; Random medium; Statistical properties; Transmission matrix
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Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media
Popoff, S. M., G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan
Physical Review Letters 104, no. 10 (2010)
Résumé: We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a full-field interferometric measurement on a camera. We determine the transmission matrix of a thick random scattering sample. We show that this matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. This method might give important insight into the mesoscopic properties of a complex medium. © 2010 The American Physical Society.
Mots-clés: Complex medium; Disordered media; Full-field; Interferometric measurement; matrix; Mesoscopic properties; Random matrix theory; Random medium; Random scattering; Spatial phase modulator; Statistical properties; Transmission matrix; Light; Light propagation; Light transmission
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