Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media

Single-shot hybrid photoacoustic-fluorescent microendoscopy through a multimode fiber with wavefront shaping

We present a minimally-invasive endoscope based on a multimode fiber that combines photoacoustic and fluorescence sensing. From the measurement of a transmission matrix during a prior calibration step, a focused spot is produced and raster-scanned over a sample at the distal tip of the fiber by use of a fast spatial light modulator. An ultra-sensitive fiber-optic ultrasound sensor for photoacoustic detection placed next to the fiber is combined with a photodetector to obtain both fluorescence and photoacoustic images with a distal imaging tip no larger than 250 µm. The high signal-to-noise ratio provided by wavefront shaping based focusing and the ultra-sensitive ultrasound sensor enables imaging with a single laser shot per pixel, demonstrating fast two-dimensional hybrid in vitro imaging of red blood cells and fluorescent beads.

Reciprocity-induced symmetry in the round-trip transmission through complex systems

Reciprocity is a fundamental principle of wave physics and directly relates to the symmetry in the transmission through a system when interchanging the input and output. The coherent transmission matrix (TM) is a convenient method to characterize wave transmission through general media. Here, we demonstrate the optical reciprocal nature of complex media by exploring their TM properties. We measured phase-corrected TMs of forward and round-trip propagation in a single polarization state through a looped 1 m-long step-index optical multimode fiber (MMF) to experimentally verify a transpose relationship between the forward and backward transmission. This symmetry impedes straightforward MMF calibration from proximal measurements of the round-trip TM. Furthermore, we show how focusing through the MMF with digital optical phase conjugation is compromised by system loss since time reversibility relies on power conservation. These insights may inform the development of new imaging techniques through complex media and coherent control of waves in photonic systems.

Self-reference method for measuring the transmission matrices of scattering media

A significant approach for manipulating light propagation through scattering media consists of the measurement of transmission matrices (TMs). Here we propose a TM-measurement method with high stability and universal applicability, which we call the self-reference method. This method uses a new, to the best of our knowledge, way to perform holographic measurement, where the reference light is superimposed directly to the signal light. This method does not pose any restriction on the signal light, so it is applicable to nearly all types of input bases. The effectivity of this method in accurately measuring the TM is verified by experimentally achieving high-quality light focusing through a scattering medium. We believe that the self-reference method provides an ideal way for TM measurement and wavefront shaping, which will be of great significance to imaging and communication technologies in scattering environments.

Fast volumetric fluorescence imaging with multimode fibers

In this Letter, we propose a compact multimode fiber endoscope which employs wavefront shaping with a digital micromirror device (DMD). An automated single calibration step allows us to correct for optical misalignment, and the method achieves accurate focusing at various depths in the sample through rapid switching of holographic patterns by the DMD. The speed of calibration is one or two orders of magnitude faster than existing methods. The method, single calibration multimode fiber imaging (SCMFI), is compared with existing methods, and its performance is validated. We show a near diffraction limited focusing capability at imaging depths up to 110 µm with near constant lateral resolutions of 1.4 µm. Finally, we demonstrate the method for the imaging of small fluorescent beads embedded in a 3D matrix. The results indicate excellent power penetration and focusing performance. Combined with the high speed of SCMFI, this paves the way for volumetric tissue endoscopy at depth.

Disordered Optics: Exploiting Multiple Light Scattering and Wavefront Shaping for Nonconventional Optical Elements

Advances in diverse areas such as inspection, imaging, manufacturing, telecommunications, and information processing have been stimulated by novel optical devices. Conventional material ingredients for these devices are typically made of homogeneous refractive or diffractive materials and require sophisticated design and fabrication, which results in practical limitations related to their form and functional figures of merit. To overcome such limitations, recent developments in the application of disordered materials as novel optical elements have indicated great potential in enabling functionalities that go beyond their conventional counterparts, while the materials exhibit potential advantages with respect to reduced form factors. Combined with wavefront shaping, disordered materials enable dynamic transitions between multiple functionalities in a single active optical device. Recent progress in this field is summarized to gain insight into the physical principles behind disordered optics with regard to their advantages in various applications as well as their limitations compared to conventional optics.

Harnessing a multi-dimensional fibre laser using genetic wavefront shaping

The multi-dimensional laser is a fascinating platform not only for the discovery and understanding of new higher-dimensional coherent lightwaves but also for the frontier study of the complex three-dimensional (3D) nonlinear dynamics and solitary waves widely involved in physics, chemistry, biology and materials science. Systemically controlling coherent lightwave oscillation in multi-dimensional lasers, however, is challenging and has largely been unexplored; yet, it is crucial for both designing 3D coherent light fields and unveiling any underlying nonlinear complexities. Here, for the first time, we genetically harness a multi-dimensional fibre laser using intracavity wavefront shaping technology such that versatile lasing characteristics can be manipulated. We demonstrate that the output power, mode profile, optical spectrum and mode-locking operation can be genetically optimized by appropriately designing the objective function of the genetic algorithm. It is anticipated that this genetic and systematic intracavity control technology for multi-dimensional lasers will be an important step for obtaining high-performance 3D lasing and presents many possibilities for exploring multi-dimensional nonlinear dynamics and solitary waves that may enable new applications.

Lensless light-field imaging through diffuser encoding

Microlens array-based light-field imaging has been one of the most commonly used and effective technologies to record high-dimensional optical signals for developing various potential high-performance applications in many fields. However, the use of a microlens array generally suffers from an intrinsic trade-off between the spatial and angular resolutions. In this paper, we concentrate on exploiting a diffuser to explore a novel modality for light-field imaging. We demonstrate that the diffuser can efficiently angularly couple incident light rays into a detected image without needing any lens. To characterize and analyse this phenomenon, we establish a diffuser-encoding light-field transmission model, in which four-dimensional light fields are mapped into two-dimensional images via a transmission matrix describing the light propagation through the diffuser. Correspondingly, a calibration strategy is designed to flexibly determine the transmission matrix, so that light rays can be computationally decoupled from a detected image with adjustable spatio-angular resolutions, which are unshackled from the resolution limitation of the sensor. The proof-of-concept approach indicates the possibility of using scattering media for lensless four-dimensional light-field recording and processing, not just for two- or three-dimensional imaging.

Seeing through multimode fibers with real-valued intensity transmission matrices

Image transmission through multimode optical fibers has been an area of immense interests driven by the demand for miniature endoscopes in biomedicine and higher speed and capacity in telecommunications. Conventionally, a complex-valued transmission matrix is obtained experimentally to link the input and output light fields of a multimode fiber for image retrieval, which complicates the experimental setup and increases the computational complexity. Here, we report a simple and high-speed method for image retrieval based on our demonstration of a pseudo-linearity between the input and output light intensity distributions of multimode fibers. We studied the impact of several key parameters to image retrieval, including image pixel count, fiber core diameter and numerical aperture. We further demonstrated with experiments and numerical simulations that a wide variety of input binary and gray scale images could be faithfully retrieved from the corresponding output speckle patterns. Thus, it promises to be useful for highly miniaturized endoscopy in biomedicine and spatial-mode-division multiplexing in telecommunications.

Increasing the enhancement factor for DMD-based wavefront shaping

Focusing through scattering media is a subject of great interest due to its direct impact in the field of biomedical optics. However, the greatest barrier currently limiting direct applications is the fact that most scattering media that we wish to deliver light through are dynamic. To focus or deliver light through dynamic scattering media, using a digital micromirror device (DMD) has been demonstrated to be a potential solution, as it enables fast modulation speeds. However, since a DMD is a binary amplitude modulator, the large number of controlled modes needed to acquire adequate focus enhancement has limited optimal usage. Here we demonstrate a novel (to the best of our knowledge) scheme to use the "thrown-away" components of light to effectively use a binary amplitude DMD as a binary phase modulator, thereby increasing the correction efficiency by a factor of two. Our concept can be applied to any iterative optimization algorithm and can speed up the iterative optimization process by increasing the enhancement factor, rather than the measurement or modulation speeds.

Distortion matrix concept for deep optical imaging in scattering media

In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. On the basis of a dynamic correction of the incident and/or reflected wavefronts, adaptive optics has been used to compensate for those aberrations. However, it only applies to spatially invariant aberrations or to thin aberrating layers. Here, we propose a global and noninvasive approach based on the distortion matrix concept. This matrix basically connects any focusing point of the image with the distorted part of its wavefront in reflection. A singular value decomposition of the distortion matrix allows to correct for high-order aberrations and forward multiple scattering over multiple isoplanatic modes. Proof-of-concept experiments are performed through biological tissues including a turbid cornea. We demonstrate a Strehl ratio enhancement up to 2500 and recover a diffraction-limited resolution until a depth of 10 scattering mean free paths.

Imaging through opacity using a near-infrared low-spatial-coherence fiber light source

Memory-effect-based speckle correlation is one of the most practical techniques for imaging through scattering opaque media, where a light source with low spatial coherence and moderate bandwidth plays a pivotal role. Usually, a rapidly rotating diffuser is applied to make the light source spatially decoherent. Here, an all-fiber-based low-spatial-coherence light source is proposed and demonstrated for such speckle-correlated imaging. The illumination structure is greatly simplified, the lightening efficiency is enhanced, and the wavelength is extended to the near-infrared band, which is favorable for a larger memory effect range and deeper penetrating depth through opacity. Moreover, the proposed local illumination method can identify the orientation of the object, which has not been revealed by former methods. This work would facilitate the research in optical biomedical imaging and broaden the applications of multimode random fiber lasers.

Distortion matrix approach for ultrasound imaging of random scattering media

Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wave fronts and degrade image quality. Adaptive focusing can compensate for such aberration but is only effective over a restricted field of view. Here, we introduce a full-field approach to wave imaging based on the concept of the distortion matrix. This operator essentially connects any focal point inside the medium with the distortion that a wave front, emitted from that point, experiences due to heterogeneities. A time-reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing a full-field image of the medium with diffraction-limited resolution. Importantly, this process is particularly efficient in random scattering media, where traditional approaches such as adaptive focusing fail. Here, we first present an experimental proof of concept on a tissue-mimicking phantom and then, apply the method to in vivo imaging of human soft tissues. While introduced here in the context of acoustics, this approach can also be extended to optical microscopy, radar, or seismic imaging.

Compressive Sensing Imaging Based on Modulation of Atmospheric Scattering Medium

Long-distance imaging in time-varying scattering media, such as atmosphere, is a significant challenge. Light is often heavily diffused while propagating through scattering media, because of which the clear imaging of objects concealed by media becomes difficult. In this study, instead of suppressing diffusion by multiple scattering, we used natural randomness of wave propagation through atmospheric scattering media as an optimal and instantaneous compressive imaging mechanism. A mathematical model of compressive imaging based on the modulation of atmospheric scattering media was established. By using the Monte Carlo method, the atmospheric modulation matrix was obtained, and the numerical simulation of modulation imaging of atmospheric scattering media was performed. Comparative experiments show that the atmospheric matrix can achieve the same modulation effect as the Hadamard and Gaussian random matrices. The effectiveness of the proposed optical imaging approach was demonstrated experimentally by loading the atmospheric measurement matrix onto a digital micromirror device to perform single pixel compressive sensing measurements. Our work provides a new direction to ongoing research in the field of imaging through scattering media.

Delivering targeted color light through a multimode fiber by field synthesis

Recent developments of wavefront shaping make the multimode fiber (MMF) as a promising tool to deliver images in endoscopy. However, previous studies using the MMF were limited to monochromatic light or polychromatic light with narrow bandwidth. The desires for colored imaging stimulate us to deliver multi-wavelength light that covers the entire visible spectrum through the MMF. In this work, we demonstrated delivering targeted color light through the MMF by mixing three primary colors (red, green, and blue) with a single spatial light modulator. The optimum phase map that considers all three colors was generated through field synthesis (FS), which requires every pixel of the SLM to partially account for all colors. With both theoretical and numerical approaches, we showed that FS exhibited much better performance than the previously developed spatial segmentation method that employs different pixels to represent different colors. Moreover, by computationally adjusting the compositions of the weight for each color, the colors of the delivered focus can be switched at video framerate. We anticipate that our work paves a way for future applications of delivering color images through the MMF in endoscopy.

Full-polarization wavefront shaping for imaging through scattering media

The scattering effect occurring when light passes through inhomogeneous-refractive-index media such as atmosphere or biological tissues will scramble the light wavefront into speckles and impede optical imaging. Wavefront shaping is an emerging technique for imaging through scattering media that works by addressing correction of the disturbed wavefront. In addition to the phase and amplitude, the polarization of the output scattered light will also become spatially randomized in some cases. The recovered image quality and fidelity benefit from correcting as much distortion of the scattered light as possible. Liquid-crystal spatial light modulators (LC-SLMs) are widely used in the wavefront shaping technique, since they can provide a great number of controlled modes and thereby high-precision wavefront correction. However, due to the working principle of LC-SLMs, the wavefront correction is restricted to only one certain linear polarization state, resulting in retrieved image information in only the right polarization, while the information in the orthogonal polarization is lost. In this paper, we describe a full-polarization wavefront correction system for shaping the scattered light wavefront in two orthogonal polarizations with a single LC-SLM. The light speckles in both polarizations are corrected for retrieval of the full polarization information and faithful images of objects. As demonstrated in the experiments, the focusing intensity can be increased by full-polarization wavefront correction, images of objects in arbitrary polarization states can be retrieved, and the polarization state of the object's light can also be recognized.

Effect of image artefacts on phase conjugation with spectral domain optical coherence tomography

Recently the acquisition of the time-resolved reflection matrix was demonstrated based on spectral domain optical coherence tomography. In principle, the matrix describes the linear dependence of the OCT signal received from different depths on the field which is incident to the scattering sample. Knowledge of the matrix, hence, enables beam shaping to selectively enhance the received signal, for example to increase the penetration depth when imaging turbid media. We investigate the impact of image artefacts on the approach. Phase conjugation is shown to enhance the OCT signal, but not autocorrelation and mirror artefacts. Imaging applications are demonstrated indicating the potential for future in-vivo studies on biotissues.

Speckle-Correlation Scattering Matrix Approaches for Imaging and Sensing through Turbidity

The development of optical and computational techniques has enabled imaging without the need for traditional optical imaging systems. Modern lensless imaging techniques overcome several restrictions imposed by lenses, while preserving or even surpassing the capability of lens-based imaging. However, existing lensless methods often rely on a priori information about objects or imaging conditions. Thus, they are not ideal for general imaging purposes. The recent development of the speckle-correlation scattering matrix (SSM) techniques facilitates new opportunities for lensless imaging and sensing. In this review, we present the fundamentals of SSM methods and highlight recent implementations for holographic imaging, microscopy, optical mode demultiplexing, and quantification of the degree of the coherence of light. We conclude with a discussion of the potential of SSM and future research directions.

Near-field transmission matrix microscopy for mapping high-order eigenmodes of subwavelength nanostructures

As nanoscale photonic devices are densely integrated, multiple near-field optical eigenmodes take part in their functionalization. Inevitably, these eigenmodes are highly multiplexed in their spectra and superposed in their spatial distributions, making it extremely difficult for conventional near-field scanning optical microscopy (NSOM) to address individual eigenmodes. Here, we develop a near-field transmission matrix microscopy for mapping the high-order eigenmodes of nanostructures, which are invisible with conventional NSOM. At an excitation wavelength where multiple modes are superposed, we measure the near-field amplitude and phase maps for various far-field illumination angles, from which we construct a fully phase-referenced far- to near-field transmission matrix. By performing the singular value decomposition, we extract orthogonal near-field eigenmodes such as anti-symmetric mode and quadruple mode of multiple nano-slits whose gap size (50 nm) is smaller than the probe aperture (150 nm). Analytic model and numerical mode analysis validated the experimentally observed modes.

Nanoscale integrated photonic devices have complicated combinations of optical eigenmodes. Here, the authors develop a far- to near-field transmission matrix microscopy that enables measuring higher-order modes of nanostructures beyond the capabilities of conventional near-field microscopy.

Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces

We demonstrate the local optimization of nonlinear luminescence from disordered gold metasurfaces by shaping the phase of femtosecond excitation. This process is enabled by the far-field wavefront control of plasmonic modes delocalized over the sample surface, leading to a coherent enhancement of subwavelength electric fields. In practice, the increase in nonlinear luminescence is strongly sensitive to both the nanometer-scale morphology and the level of structural complexity of the gold metasurface. We typically observe a 2 orders of magnitude enhancement of the luminescence signal for an optimized excitation wavefront compared to a random one. These results demonstrate how disordered metasurfaces made of randomly coupled plasmonic resonators, together with wavefront shaping, provide numerous degrees of freedom to program locally optimized nonlinear responses and optical hotspots.

OAM-basis transmission matrix in optics: a novel approach to manipulate light propagation through scattering media

Transmission matrix (TM) is an ideal theoretical model describing light propagation through scattering media. Until now, most of the present TMs utilize the eigenstates of spatial position as input and output bases. Thus, they describe the relationship between the spatial distributions of two light fields. Here, we demonstrate that wider relationships between the light fields could be described by a TM. As a significant example, we propose a generalized TM with the eigenstates of OAM as input bases - OAM-basis TM. With the measured OAM-basis TM, we achieved single-spot and multiple-spot focusing, verifying its availability in light propagation manipulation. The distinct eigenchannels property was also discussed. The OAM-basis TM has broadened the definition of TM. Meanwhile, it will open new perspectives for OAM-based communication, as well as the applications of wavefront shaping technology in biomedical photonics and optical communication.

Averaging speckle patterns to improve the robustness of compressive multimode fiber imaging against fiber bend

Fiber bend is a major challenge of multimode fiber (MMF) imaging. More robustness against fiber bend is demonstrated in compressive MMF imaging using mean speckle patterns captured at multiple potential bending configurations beforehand, rather than sticking to single patterns at initial configuration. Experiments demonstrate an overall quality improvement on recovered images than previous work, which is important for robust endoscopic application.

Imaging through highly scattering environments using ballistic and quasi-ballistic light in a common-path Sagnac interferometer

The survival of time-reversal symmetry in the presence of strong multiple scattering lies at the heart of some of the most robust interference effects of light in complex media. Here, the use of time-reversed light paths for imaging in highly scattering environments is investigated. A common-path Sagnac interferometer is constructed that is able to detect objects behind a layer of strongly scattering material at up to 14 mean free paths of total attenuation length. A spatial offset between the two light paths is used to suppress non-specific scattering contributions, limiting the signal to the volume of overlap. Scaling of the specific signal intensity indicates a transition from ballistic to quasi-ballistic contributions as the scattering thickness is increased. The characteristic frequency dependence for the coherent modulation signal provides a path length dependent signature, while the spatial overlap requirement allows for short-range 3D imaging. The technique of common-path, bistatic interferometry offers a conceptually novel approach that could open new applications in diverse areas such as medical imaging, machine vision, sensors, and lidar.

Retrieving the optical transmission matrix of a multimode fiber using the extended Kalman filter

Characterizing the transmission matrix (TM) of a multimode fiber (MMF) benefits many fiber-based applications and allows in-depth studies on the physical properties. For example, by modulating the incident field, the knowledge of the TM allows one to synthesize any optical field at the distill end of the MMF. However, the extraction of optical fields usually requires holographic measurements with interferometry, which complicates the system design and introduces additional noise. In this work, we developed an efficient method to retrieve the TM of the MMF in a referenceless optical system. With pure intensity measurements, this method uses the extended Kalman filter (EKF) to recursively search for the optimum solution. To facilitate the computational process, a modified speckle-correlation scatter matrix (MSSM) is constructed as a low-fidelity initial estimation. This method, termed EKF-MSSM, only requires 4N intensity measurements to precisely solve for N unknown complex variables in the TM. Experimentally, we successfully retrieved the TM of the MMF with high precision, which allows optical focusing with the enhancement (>70%) close to the theoretical value. We anticipate that this method will serve as a useful tool for studying physical properties of the MMFs and potentially open new possibilities in a variety of applications in fiber optics.

Sub-acoustic resolution optical focusing through scattering using photoacoustic fluctuation guided wavefront shaping

Focusing light through turbid media using wavefront shaping generally requires a noninvasive guide star to provide feedback on the focusing process. Here we report a photoacoustic guide star mechanism suitable for wavefront shaping through a scattering wall that is based on the fluctuations in the photoacoustic signals generated in a micro-vessel filled with flowing absorbers. The standard deviation of photoacoustic signals generated from random distributions of particles is dependent on the illumination volume and increases nonlinearly as the illumination volume is decreased. We harness this effect to guide wavefront shaping using the standard deviation of the photoacoustic response as the feedback signal. We further demonstrate sub-acoustic resolution optical focusing through a diffuser with a genetic algorithm optimization routine.

Fighting against fast speckle decorrelation for light focusing inside live tissue by photon frequency shifting

Focusing light inside live tissue by digital optical phase conjugation (DOPC) has been intensively investigated due to its potential biomedical applications in deep-tissue imaging, optogenetics, microsurgery, and phototherapy. However, fast physiological motions in a live animal, such as blood flow and respiratory motions, produce undesired photon perturbation and thus inevitably deteriorate the performance of light focusing. Here, we develop a photon-frequency-shifting DOPC method to fight against fast physiological motions by switching the states of a guide star at a distinctive frequency. Therefore, the photons tagged by the guide star are well detected at the specific frequency, separating them from the photons perturbed by fast motions. Light focusing was demonstrated in both phantoms in vitro and mice in vivo with substantially improved focusing contrast. This work puts a new perspective on light focusing inside live tissue and promises wide biomedical applications.

Velocity measurements with structured light transmitted through a multimode optical fiber using digital optical phase conjugation

Lensless fiber microendoscopes enable optical diagnostics and therapy with minimal invasiveness. Because of their small diameters, multimode fibers are ideal candidates, but mode scrambling hinders the transmission of structured light fields. We present the generation of a localized fringe system at variable distances from the distal fiber end by exploiting digital optical phase conjugation. The replayed fringe system was used for quantitative metrology. Velocity measurements of a microchannel flow in the immediate proximity of the fiber end without the use of any imaging lenses are shown. Lensless multimode fiber systems are of interest especially for biomedical imaging and stimulation as well as technical inspection and flow measurements.

Manipulating cold atoms through a high-resolution compact system based on a multimode fiber

We show that a standard multimode optical fiber can act as a high-resolution ultra-compact tool to manipulate cold atoms in setups with limited optical access. Spatial light modulators allow us to generate control beams at the in-vacuum fiber end by digital optical phase conjugation. With no additional in-vacuum optics, this system reaches a $ \sim 1\;{\unicode{x00B5}{\rm m}} $∼1µm resolution for a transverse size of only 225 µm. As a demonstration, we use it to optically transport cold atoms towards the in-vacuum fiber end, to load them in optical microtraps, and to re-cool them in optical molasses. This work shows that the rapid progress of optics in complex media opens new, to the best of our knowledge, perspectives for spatially constrained quantum technology platforms combining cold atoms with other optical, electronic, or opto-mechanical systems.

Time-gated iterative phase conjugation for efficient light energy delivery in scattering media

Light waves propagating through complex biological tissues are spatially spread by multiple light scattering, and this spread limits the working depth in optical bioimaging, phototherapy, and optogenetics. Here, we propose the iterative phase conjugation of time-gated backscattered waves for enhancing the light energy delivered to a target object embedded in a scattering medium. We demonstrate the enhancement of light energy delivered to a target object hidden behind a 200-µm-thick mouse skull by more than ten times in comparison with the initial random input. The maximum enhancement was reached in only 10 iterations, more than a hundred times smaller than existing methods based on either a time-gated reflection matrix or iterative feedback optimization of the time-gated reflection intensity. Consequently, the proposed method is less sensitive to sample perturbations. Furthermore, the number of images required for optimization remained almost unchanged with an increase in the illumination area, unlike existing methods, where the convergence time scales with the illumination area. The proposed method provides high operation speed over a wide illumination area, which can facilitate the use of wavefront shaping in practical applications.

Physical Layer Security in Multimode Fiber Optical Networks

The light propagation through a multimode fiber is used to increase information security during data transmission without the need for cryptographic approaches. The use of an inverse precoding method in a multimode fiber-optic communication network is based on mode-dependent losses on the physical layer. This leads to an asymmetry between legitimate (Bob) and illegitimate (Eve) recipients of messages, resulting in significant SNR advantage for Bob. In combination with dynamic mode channel changes, there are defined hurdles for Eve to reconstruct a sent message even in a worst-case scenario in which she knows the channel completely. This is the first time that physical layer security has been investigated in a fiber optical network based on measured transmission matrices. The results show that messages can be sent securely using traditional communication techniques. The technology introduced is a step towards the development of cyber physical systems with increased security.

Realistic phase screen model for forward multiple-scattering media

Existing random phase screen (RPS) models for forward multiple-scattering media fail to incorporate ballistic light. In this Letter, we redesign the angular spectrum of the screen by means of Monte Carlo simulation based on an assumption that a single screen should represent all the scattering events a photon experiences between two adjacent screens. Three examples demonstrate that the proposed model exhibits more realistic optical properties than conventional RPS models in terms of attenuation of ballistic light, evolution of beam profile, and angular memory effect. The proposed model also provides the flexibility to balance the computing accuracy, speed, and memory usage by tuning the screen spacing.

Extended imaging depth of en-face optical coherence tomography based on fast measurement of a reflection matrix by wide-field heterodyne detection

Multiple light scattering in biomedical tissue limits the penetration depth of optical imaging systems such as optical coherence tomography. To increase the imaging depth in scattering media, a computational method based on coherent reflection matrix measurement has been developed using low coherence interferometry. The complex reflection matrix is obtained via point-by-point scanning followed by a phase-shifting method; then singular value decomposition is used to retrieve the singly back-scattered light. However, the in vivo application of the current reported method is limited due to the slow acquisition speed of the matrix. In this Letter, a wide-field heterodyne-detection method is adopted to speed up the complex matrix measurement at a deep tissue layer. Compared to the phase-shifting method, the heterodyne-detection scheme retrieves depth-resolved complex amplitudes faster and is more stable without mechanical movement of the reference mirror. As a result, the matrix measurement speed is increased by more than one order of magnitude.

Real-time frequency-encoded spatiotemporal focusing through scattering media using a programmable 2D ultrafine optical frequency comb

Optical wavefront shaping is a powerful tool for controlling photons in strongly scattering media. Its speed, however, has been the bottleneck for in vivo applications. Moreover, unlike spatial focusing, temporal focusing from a continuous-wave source has rarely been exploited yet is highly desired for nonlinear photonics. Here, we present a novel real-time frequency-encoded spatiotemporal (FEST) focusing technology. FEST focusing uses a novel programmable two-dimensional optical frequency comb with an ultrafine linewidth to perform single-shot wavefront measurements, with a fast single-pixel detector. This technique enables simultaneous spatial and temporal focusing at microsecond scales through thick dynamic scattering media. This technology also enabled us to discover the large-scale temporal shift, a new phenomenon that, with the conventional spatial memory effect, establishes a space-time duality. FEST focusing opens a new avenue for high-speed wavefront shaping in the field of photonics.

Implementation of an Off-Axis Digital Optical Phase Conjugation System for Turbidity Suppression on Scattering Medium

Due to the light scattering effect, it is difficult to directly achieve optical focusing and imaging in turbid media, such as milk and biological tissue. The turbidity suppression of a scattering medium and control of light through the scattering medium are important for imaging on biological tissue or biophotonics. Optical phase conjugation is a novel technology on turbidity suppression by directly creating phase conjugation light waves to form time-reversed light. In this work, we report a digital optical phase conjugation system based on off-axis holography. Compared with traditional digital optical phase conjugation methods, the off-axis holography acquires the conjugation phase using only one interference image, obviously saving photo acquisition time. Furthermore, we tested the optical phase conjugate reduction performance of this system and also achieved optical focusing through the diffuser. We also proved that the reversing of random scattering in turbid media is achievable by phase conjugation.

Structured light beams created through a multimode fiber via virtual Fourier filtering based on digital optical phase conjugation

Digital optical phase conjugation (DOPC) is a newly developed technique in wavefront shaping to control light propagation through complex media. Currently, DOPC has been demonstrated for the reconstruction of two- and three-dimensional targets and enabled important applications in many areas. Nevertheless, the reconstruction results are only phase conjugated to the original input targets. Herein, we demonstrate that DOPC could be further developed for creating structured light beams through a multimode fiber (MMF). By applying annular filtering in the virtual Fourier domain of the acquired speckle field, we realize the creation of the quasi-Bessel and donut beams through the MMF. In principle, arbitrary amplitude and/or phase circular symmetry filtering could be performed in the Fourier domain, thus generating the corresponding point spread functions. We expect that the reported technique can be useful for super-resolution endoscopic imaging and optical manipulation through MMFs.

Intelligently optimized digital optical phase conjugation with particle swarm optimization

Wavefront shaping (WFS) based on digital optical phase conjugation (DOPC) has gained major interest in focusing light through or inside scattering media. However, the quality of DOPC is greatly limited by imperfections of the system in a complicated and coupled way. In this Letter, we incorporate the concept of global optimization to solve this problem comprehensively for the first time, to the best of our knowledge. An automatic and intelligent optimization framework for DOPC techniques is proposed, leveraging the global optimization ability of particle swarm optimization (PSO). We demonstrate the general and powerful ability of the proposed approach in a series of DOPC-related experiments for focusing through and inside scattering media. This novel work can improve the OPC quality greatly and simplify the development of a high-performance DOPC system, which may open up a new avenue for the general scientific community to benefit from DOPC-based WFS in their potential applications.

A compact single channel interferometer to study vortex beam propagation through scattering layers

We propose and demonstrate a single channel interferometer that can be used to study how vortex beams propagate through a scatterer. The interferometer consists of a multifunctional diffractive optical element (MDOE) synthesized by the spatial random multiplexing of a Fresnel zone plate and a spiral Fresnel zone plate with different focal lengths. The MDOE generates two co-propagating beams, such that only the beam carrying orbital angular momentum is modulated by an annular stack of thin scatterers located at the focal plane of the Fresnel zone plate, while the other beam passes through the centre of the annulus without any modulation. The interference pattern is recorded at the focal plane of the spiral Fresnel zone plate. The scattering of vortex beams through stacks consisting of different number of thin scatterers was studied using the proposed optical setup. Conflicting results have been reported earlier on whether higher or lower charge beams suffer more deterioration. The proposed interferometer provides a relatively simple and compact means of experimentally studying propagation of vortex beams through scattering medium.

Dynamic conjugate F-SHARP microscopy

Optical microscopy is an indispensable tool in biomedical sciences, but its reach in deep tissues is limited due to aberrations and scattering. This problem can be overcome by wavefront-shaping techniques, albeit at limited fields of view (FOVs). Inspired by astronomical imaging, conjugate wavefront shaping can lead to an increased field of view in microscopy, but this correction is limited to a set depth and cannot be dynamically adapted. Here, we present a conjugate wavefront-shaping scheme based on focus scanning holographic aberration probing (F-SHARP). We combine it with a compact implementation that can be readily adapted to a variety of commercial and home-built two-photon microscopes. We demonstrate the power of the method by imaging with high resolution over extended FOV (>80 µm) deeper than 400 μm inside a mouse brain through a thinned skull.

Multimode fibre probe calibration

Multimode fibres (MMF) used in endoscopy have advantage of small diameter and flexibility, thus causing less damage to living animals. However, the imaging requires wavefront shaping techniques to obtain a sharp image despite the mode dispersion in the waveguide. We suggest version of transmission matrix calibration which uses internal modes of the waveguide and, thus, lessens requirements on the endoscopy apparatus removing the external reference path.

Fast 3D movement of a laser focusing spot behind scattering media by utilizing optical memory effect and optical conjugate planes

Controlling light propagation intentionally through turbid media such as ground glass or biological tissue has been demonstrated for many useful applications. Due to random scattering effect, one of the important goals is to draw a desired shape behind turbid media with a swift and precise method. Feedback wavefront shaping method which is known as a very effective approach to focus the light, is restricted by slow optimization process for obtaining multiple spots. Here we propose a technique to implement feedback wavefront shaping with optical memory effect and optical 4f system to speedy move focus spot and form shapes in 3D space behind scattering media. Starting with only one optimization process to achieve a focusing spot, the advantages of the optical configuration and full digital control allow us to move the focus spot with high quality at the speed of SLM frame rate. Multiple focusing spots can be achieved simultaneously by combining multiple phase patterns on a single SLM. By inheriting the phase patterns in the initial focusing process, we can enhance the intensity of the focusing spot at the edge of memory effect in with 50% reduction in optimization time. With a new focusing spot, we have two partially overlapped memory effect regions, expanding our 3D scanning range. With fast wavefront shaping devices, our proposed technique could potentially find appealing applications with biological tissues.

Optimizing Light Storage in Scattering Media with the Dwell-Time Operator

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 ℓ. We show that the distribution has a finite support with a maximal dwell time larger than the most likely value by a factor (L/ℓ)^{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.

Multi-objective optimization genetic algorithm for multi-point light focusing in wavefront shaping

We introduce a new multi-objective genetic algorithm for wavefront shaping and realize controllable multi-point light focusing through scattering medium. Different from previous single-objective optimization genetic algorithms, our algorithm named Non-dominated Sorting Genetic Algorithm II based on hybrid optimization scheme (NSGA2-H) can make all focus points have uniform intensity while ensuring that their enhancement is as high as possible. We demonstrate the characteristics of NSGA2-H through simulations and experiments in amplitude optimization, analyze its optimization mechanisms and show its powerful optical control capability in uniform intensity focusing and even in customizable intensity focusing. This research will be expected to further promote future practical applications based on multi-point focusing of wavefront shaping, especially in optical trapping and optogenetics.

Quantitative phase and polarization imaging through an optical fiber applied to detection of early esophageal tumorigenesis

Phase and polarization of coherent light are highly perturbed by interaction with microstructural changes in premalignant tissue, holding promise for label-free detection of early tumors in endoscopically accessible tissues such as the gastrointestinal tract. Flexible optical multicore fiber (MCF) bundles used in conventional diagnostic endoscopy and endomicroscopy scramble phase and polarization, restricting clinicians instead to low-contrast amplitude-only imaging. We apply a transmission matrix characterization approach to produce full-field en-face images of amplitude, quantitative phase, and resolved polarimetric properties through an MCF. We first demonstrate imaging and quantification of biologically relevant amounts of optical scattering and birefringence in tissue-mimicking phantoms. We present an entropy metric that enables imaging of phase heterogeneity, indicative of disordered tissue microstructure associated with early tumors. Finally, we demonstrate that the spatial distribution of phase and polarization information enables label-free visualization of early tumors in esophageal mouse tissues, which are not identifiable using conventional amplitude-only information.

Focusing light inside live tissue using reversibly switchable bacterial phytochrome as a genetically encoded photochromic guide star

Focusing light deep by engineering wavefronts toward guide stars inside scattering media has potential biomedical applications in imaging, manipulation, stimulation, and therapy. However, the lack of endogenous guide stars in biological tissue hinders its translations to in vivo applications. Here, we use a reversibly switchable bacterial phytochrome protein as a genetically encoded photochromic guide star (GePGS) in living tissue to tag photons at targeted locations, achieving light focusing inside the tissue by wavefront shaping. As bacterial phytochrome-based GePGS absorbs light differently upon far-red and near-infrared illumination, a large dynamic absorption contrast can be created to tag photons inside tissue. By modulating the GePGS at a distinctive frequency, we suppressed the competition between GePGS and tissue motions and formed tight foci inside mouse tumors in vivo and acute mouse brain tissue, thus improving light delivery efficiency and specificity. Spectral multiplexing of GePGS proteins with different colors is an attractive possibility.

Angular Memory Effect of Transmission Eigenchannels

The optical memory effect has emerged as a powerful tool for imaging through multiple-scattering media; however, the finite angular range of the memory effect limits the field of view. Here, we demonstrate experimentally that selective coupling of incident light into a high-transmission channel increases the angular memory-effect range. This enhancement is attributed to the robustness of the high-transmission channels against perturbations such as sample tilt or wave front tilt. Our work shows that the high-transmission channels provide an enhanced field of view for memory-effect-based imaging through diffusive media.

Photon-limited imaging through scattering medium based on deep learning

Imaging under ultra-weak light conditions is affected by Poisson noise heavily. The problem becomes worse if a scattering media is present in the optical path. Speckle patterns detected under ultra-weak light condition carry very little information which makes it difficult to reconstruct the image. Off-the-shelf methods are no longer available in this condition. In this paper, we experimentally demonstrate the use of a deep learning network to reconstruct images through scattering media under ultra-weak light illumination. The weak light limitation of this method is analyzed. The random Poisson detection under weak light condition obtains partial information of the object. Based on this property, we demonstrated better performance of our method by enlarging the training dataset with multiple detections of the speckle patterns. Our results demonstrate that our approach can reconstruct images through scattering media from close to 1 detected signal photon per pixel (PPP) per image.

Control of the temporal and polarization response of a multimode fiber

Control of the spatial and temporal properties of light propagating in disordered media have been demonstrated over the last decade using spatial light modulators. Most of the previous studies demonstrated spatial focusing to the speckle grain size, and manipulation of the temporal properties of the achieved focus. In this work, we demonstrate an approach to control the total temporal impulse response, not only at a single speckle grain but over all spatial degrees of freedom (spatial and polarization modes) at any arbitrary delay time through a multimode fiber. Global enhancement or suppression of the total light intensity exiting a multimode fibre is shown for arbitrary delays and polarization states. This work could benefit to applications that require pulse delivery in disordered media.

Scanning a focus through scattering media without using the optical memory effect

Wavefront shaping makes it possible to form a focus through opaque scattering materials. In some cases, this focus may be scanned over a small distance using the optical memory effect. However, in many cases of interest, the optical memory effect has a limited range or is even too small to be measured. In such cases, one often resorts to measuring the full transmission matrix (TM) of the sample to completely control the light transmission. However, this process is time-consuming and may not always be possible. We introduce a new method, to the best of our knowledge, for focusing and scanning the focus at any arbitrary position behind the medium by measuring only a subset of the TM, called sparse field focusing (SFF). With SFF, the scan range is not limited to the memory effect, and there is no need to measure the full TM. Our experimental results agree well with our theoretical model. We expect that this method will find applications in imaging through scattering media, especially when the optical memory effect range is small.

Shaping of amplified beam from a highly multimode Yb-doped fiber using transmission matrix

The transmission matrix of an ytterbium doped multimode fiber with gain was measured. It was shown to vary owing to the pump power level. Amplified beam focusing, beam steering and shaping were demonstrated using the measured matrix for input wavefront shaping, with an efficiency similar to the case of a passive fiber. The impact of weak gain saturation was lastly investigated.

Attenuation-free non-diffracting Bessel beams

We report on a versatile method to compensate the linear attenuation in a medium, independently of its microscopic origin. The method exploits diffraction-limited Bessel beams and tailored on-axis intensity profiles, which are generated using a phase-only spatial light modulator. This technique for compensating one of the most fundamental limiting processes in linear optics is shown to be efficient for a wide range of experimental conditions (modifying the refractive index and the attenuation coefficient). Finally, we explain how this method can be advantageously exploited in applications ranging from bio-imaging light sheet microscopy to quantum memories for future quantum communication networks.

Double Interferometer Design for Independent Wavefront Manipulation in Spectral Domain Optical Coherence Tomography

Spectral domain optical coherence tomography (SD-OCT) is a highly versatile method which allows for three dimensional optical imaging in scattering media. A number of recent publications demonstrated the technique to benefit from structured illumination and beam shaping approaches, e.g. to enhance the signal-to-noise ratio or the penetration depth with samples such as biological tissue. We present a compact and easy to implement design for independent wavefront manipulation and beam shaping at the reference and sample arm of the interferometric OCT device. The design requires a single spatial light modulator and can be integrated to existing free space SD-OCT systems by modifying the source arm only. We provide analytical and numerical discussion of the presented design as well as experimental data confirming the theoretical analysis. The system is highly versatile and lends itself for applications where independent phase or wavefront control is required. We demonstrate the system to be used for wavefront sensorless adaptive optics as well as for iterative optical wavefront shaping for OCT signal enhancement in strongly scattering media.