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

Spatiotemporal beam self-cleaning for high-resolution nonlinear fluorescence imaging with multimode fiber

Beam self-cleaning (BSC) in graded-index (GRIN) multimode fibers (MMFs) has been recently reported by different research groups. Driven by the interplay between Kerr effect and beam self-imaging, BSC counteracts random mode coupling, and forces laser beams to recover a quasi-single mode profile at the output of GRIN fibers. Here we show that the associated self-induced spatiotemporal reshaping allows for improving the performances of nonlinear fluorescence (NF) microscopy and endoscopy using multimode optical fibers. We experimentally demonstrate that the beam brightness increase, induced by self-cleaning, enables two and three-photon imaging of biological samples with high spatial resolution. Temporal pulse shortening accompanying spatial beam clean-up enhances the output peak power, hence the efficiency of nonlinear imaging. We also show that spatiotemporal supercontinuum (SC) generation is well-suited for large-band NF imaging in visible and infrared domains. We substantiated our findings by multiphoton fluorescence imaging in both microscopy and endoscopy configurations.

Modeling of iterative time-reversed ultrasonically encoded optical focusing in a reflection mode

Time-reversed ultrasonically-encoded (TRUE) optical focusing is a promising technique to realize deep-tissue optical focusing by employing ultrasonic guide stars. However, the sizes of the ultrasound-induced optical focus are determined by the wavelengths of the ultrasound, which are typically tens of microns. To satisfy the need for high-resolution imaging and manipulation, iterative TRUE (iTRUE) was proposed to break this limit by triggering repeated interactions between light and ultrasound and compressing the optical focus. However, even for the best result reported to date, the resolutions along the ultrasound axial and lateral direction were merely improved by only 2-fold to 3-fold. This observation leads to doubt whether iTRUE can be effective in reducing the size of the optical focus. In this work, we address this issue by developing a physical model to investigate iTRUE in a reflection mode numerically. Our numerical results show that, under the influence of shot noises, iTRUE can reduce the optical focus to a single speckle within a finite number of iterations. This model also allows numerical investigations of iTRUE in detail. Quantitatively, based on the parameters set, we show that the optical focus can be reduced to a size of 1.6 µm and a peak-to-background ratio over 10⁴ can be realized. It is also shown that iTRUE cannot significantly advance the focusing depth. We anticipate that this work can serve as useful guidance for optimizing iTRUE system for future biomedical applications, including deep-tissue optical imaging, laser surgery, and optogenetics.

Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n), with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization.

Experimental generation of perfect optical vortices through strongly scattering media

Perfect optical vortices enable the unprecedented optical multiplexing utilizing orbital angular momentum of light, which, however, suffer from distortion when they propagate in inhomogeneous media. Herein, we report on the experimental demonstration of perfect optical vortice generation through strongly scattering media. The transmission-matrix-based point-spread-function engineering is applied to encode the targeted mask in the Fourier domain before focusing. We experimentally demonstrate the perfect optical vortice generation either through a multimode fiber or a ground glass, where the numerical results agree well with the measured one. Our results might facilitate the manipulation of orbital angular momentum of light through disordered scattering media and shed new light on the optical multiplexing utilizing perfect optical vortices.

Speckle Engineering through Singular Value Decomposition of the Transmission Matrix

Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the singular value decomposition of the transmission matrix. We not only demonstrate control over the speckle grain size and shape but also realize patterns with nonlocal correlations. Moreover, we show that the reach of our method extends also along the axial dimension, allowing volumetric speckle engineering behind scattering layers.

Focusing light into scattering media with ultrasound-induced field perturbation

Focusing light into scattering media, although challenging, is highly desirable in many realms. With the invention of time-reversed ultrasonically encoded (TRUE) optical focusing, acousto-optic modulation was demonstrated as a promising guidestar mechanism for achieving noninvasive and addressable optical focusing into scattering media. Here, we report a new ultrasound-assisted technique, ultrasound-induced field perturbation optical focusing, abbreviated as UFP. Unlike in conventional TRUE optical focusing, where only the weak frequency-shifted first-order diffracted photons due to acousto-optic modulation are useful, here UFP leverages the brighter zeroth-order photons diffracted by an ultrasonic guidestar as information carriers to guide optical focusing. We find that the zeroth-order diffracted photons, although not frequency-shifted, do have a field perturbation caused by the existence of the ultrasonic guidestar. By detecting and time-reversing the differential field of the frequency-unshifted photons when the ultrasound is alternately ON and OFF, we can focus light to the position where the field perturbation occurs inside the scattering medium. We demonstrate here that UFP optical focusing has superior performance to conventional TRUE optical focusing, which benefits from the more intense zeroth-order photons. We further show that UFP optical focusing can be easily and flexibly developed into double-shot realization or even single-shot realization, which is desirable for high-speed wavefront shaping. This new method upsets conventional thinking on the utility of an ultrasonic guidestar and broadens the horizon of light control in scattering media. We hope that it provides a more efficient and flexible mechanism for implementing ultrasound-guided wavefront shaping.

Beam Formation and Vernier Steering Off of a Rough Surface

Wavefront shaping can refocus light after it reflects from an optically rough surface. One proposed use case of this effect is in indirect imaging; if any rough surface could be turned into an illumination source, objects out of the direct line of sight could be illuminated. In this paper, we demonstrate the superior performance of a genetic algorithm compared to other iterative feedback-based wavefront shaping algorithms in achieving reflective inverse diffusion for a focal plane system. Next, the ability to control the pointing direction of the refocused beam with high precision over a narrow angular range is demonstrated, though the challenge of increasing the overall scanning range of the refocused beam remains. The method of beam steering demonstrated in this paper could act as a vernier adjustment to a coarse adjustment offered by another method.

Anti-scattering light focusing by fast wavefront shaping based on multi-pixel encoded digital-micromirror device

Speed and enhancement are the two most important metrics for anti-scattering light focusing by wavefront shaping (WS), which requires a spatial light modulator with a large number of modulation modes and a fast speed of response. Among the commercial modulators, the digital-micromirror device (DMD) is the sole solution providing millions of modulation modes and a pattern rate higher than 20 kHz. Thus, it has the potential to accelerate the process of anti-scattering light focusing with a high enhancement. Nevertheless, modulating light in a binary mode by the DMD restricts both the speed and enhancement seriously. Here, we propose a multi-pixel encoded DMD-based WS method by combining multiple micromirrors into a single modulation unit to overcome the drawbacks of binary modulation. In addition, to efficiently optimize the wavefront, we adopted separable natural evolution strategies (SNES), which could carry out a global search against a noisy environment. Compared with the state-of-the-art DMD-based WS method, the proposed method increased the speed of optimization and enhancement of focus by a factor of 179 and 16, respectively. In our demonstration, we achieved 10 foci with homogeneous brightness at a high speed and formed W- and S-shape patterns against the scattering medium. The experimental results suggest that the proposed method will pave a new avenue for WS in the applications of biomedical imaging, photon therapy, optogenetics, dynamic holographic display, etc.

Side-view holographic endomicroscopy via a custom-terminated multimode fibre

Microendoscopes based on optical fibres have recently come to the fore as promising candidates allowing in-vivo observations of otherwise inaccessible biological structures in animal models. Despite being still in its infancy, imaging can now be performed at the tip of a single multimode fibre, by relying on powerful holographic methods for light control. Fibre based endoscopy is commonly performed en face, resulting in possible damage of the specimen owing to the direct contact between the distal end of the probe and target. On this ground, we designed an all-fibre probe with an engineered termination that reduces compression and damage to the tissue under investigation upon probe insertion. The geometry of the termination brings the field of view to a plane parallel to the fibre's longitudinal direction, conveying the probe with off-axis imaging capabilities. We show that its focusing ability also benefits from a higher numerical aperture, resulting in imaging with increased spatial resolution. The effect of probe insertion was investigated inside a tissue phantom comprising fluorescent particles suspended in agarose gel, and a comparison was established between the novel side-view probe and the standard en face fibre probe. This new concept paves the way to significantly less invasive deep-tissue imaging.

Genetic-algorithm-assisted coherent enhancement absorption in scattering media by exploiting transmission and reflection matrices

The investigations on coherent enhancement absorption (CEA) inside scattering media are critically important in biophotonics. CEA can deliver light to the targeted position, thus enabling deep-tissue optical imaging by improving signal strength and imaging resolution. In this work, we develop a numerical framework that employs the method of finite-difference time-domain. Both the transmission and reflection matrices of scattering media with open boundaries are constructed, allowing the studies on the eigenvalues and eigenchannels. To realize CEA for scattering media with local absorption, we develop a genetic-algorithm-assisted numerical model. By minimizing the total transmittance and reflectance simultaneously, different realizations of CEA are observed and, without setting internal monitors, can be differentiated with cases of light leaked from sides. By modulating the incident wavefront at only one side of the scattering medium, it is shown that for a 5-μm-diameter absorber buried inside a scattering medium of 15 μm × 12 μm, more than half of the incident light can be delivered and absorbed at the target position. The enhancement in absorption is more than four times higher than that with random input. This value can be even higher for smaller absorption regions. We also quantify the effectiveness of the method and show that it is inversely proportional to the openness of the scattering medium. This result is potentially useful for targeted light delivery inside scattering media with local absorption.

Memory effect assisted imaging through multimode optical fibres

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

Generalization of Wigner time delay to subunitary scattering systems

We introduce a complex generalization of the Wigner time delay τ for subunitary scattering systems. Theoretical expressions for complex time delays as a function of excitation energy, uniform and nonuniform loss, and coupling are given. We find very good agreement between theory and experimental data taken on microwave graphs containing an electronically variable lumped-loss element. We find that the time delay and the determinant of the scattering matrix share a common feature in that the resonant behavior in Re[τ] and Im[τ] serves as a reliable indicator of the condition for coherent perfect absorption (CPA). By reinforcing the concept of time delays in lossy systems this work provides a means to identify the poles and zeros of the scattering matrix from experimental data. The results also enable an approach to achieving CPA at an arbitrary frequency in complex scattering systems.

Dynamic mutation enhanced particle swarm optimization for optical wavefront shaping

Particle swarm optimization (PSO) is a well-known iterative algorithm commonly adopted in wavefront shaping for focusing light through or inside scattering media. The performance is, however, limited by premature convergence in an unstable environment. Therefore, we aim to solve this problem and enhance the focusing performance by adding a dynamic mutation operation into the plain PSO. With dynamic mutation, the "particles," or the optimized masks, are mutated with quantifiable discrepancy between the current and theoretical optimal solution, i.e., the "error rate." Gauged by that, the diversity of the "particles" is effectively expanded, and the adaptability of the algorithm to noise and instability is significantly promoted, yielding optimization approaching the theoretical optimum. The simulation and experimental results show that PSO with dynamic mutation demonstrates considerably better performance than PSO without mutation or with a constant mutation, especially under a noisy environment.

Noninvasive imaging of two isolated objects through a thin scattering medium beyond the 3D optical memory effect

A speckle image formed by scattering lights can be decoded by recently invented techniques, owing to the optical memory effect, thereby enabling the observation of a hidden object behind a thin scattering medium. However, the range of three-dimensional OME is typically small; therefore, both the field of view and depth of field are limited. We propose a method that can significantly and simultaneously improve both values for a specific scenario, where one object moves around the other position-fixed object. The effectiveness of the proposed scheme is demonstrated through a set of experiments.

Optical computation of a spin glass dynamics with tunable complexity

Spin glasses (SGs) are paradigmatic models for physical, computer science, biological, and social systems. The problem of studying the dynamics for SG models is nondetermistic polynomial-time (NP) hard; that is, no algorithm solves it in polynomial time. Here we implement the optical simulation of an SG, exploiting the N segments of a wavefront-shaping device to play the role of the spin variables, combining the interference downstream of a scattering material to implement the random couplings between the spins (the [Formula: see text] matrix) and measuring the light intensity on a number P of targets to retrieve the energy of the system. By implementing a plain Metropolis algorithm, we are able to simulate the spin model dynamics, while the degree of complexity of the potential energy landscape and the region of phase diagram explored are user defined, acting on the ratio [Formula: see text] We study experimentally, numerically, and analytically this Hopfield-like system displaying a paramagnetic, ferromagnetic, and SG phase, and we demonstrate that the transition temperature [Formula: see text] to the glassy phase from the paramagnetic phase grows with α. We demonstrate the computational advantage of the optical SG where interaction terms are realized simultaneously when the independent light rays interfere on the detector's surface. This inherently parallel measurement of the energy provides a speedup with respect to purely in silico simulations scaling with N.

Noise-tolerant wavefront shaping in a Hadamard basis

Light scattering is the main limitation for optical imaging. However, light can be focused through or inside turbid media by spatially shaping the incident wavefront. Wavefront shaping is ultimately limited by the available photon budget. We developed a new 'dual reference' wavefront shaping algorithm that optimally uses the available light. Our method allows for multi-target wavefront shaping, making it suitable for transmission matrix measurements or transmitting images. We experimentally confirmed the improvement of the focus intensity compared to existing methods.

Computational Method for Wavefront Sensing Based on Transport-of-Intensity Equation

Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.

Coherent Wave Control in Complex Media with Arbitrary Wavefronts

Wavefront shaping (WFS) has emerged as a powerful tool to control the propagation of diverse wave phenomena (light, sound, microwaves, etc.) in disordered matter for applications including imaging, communication, energy transfer, micromanipulation, and scattering anomalies. Nonetheless, in practice the necessary coherent control of multiple input channels remains a vexing problem. Here, we overcome this difficulty by doping the disordered medium with programmable meta-atoms in order to adapt it to an imposed arbitrary incoming wavefront. Besides lifting the need for carefully shaped incident wavefronts, our approach also unlocks new opportunities such as sequentially achieving different functionalities with the same arbitrary wavefront. We demonstrate our concept experimentally for electromagnetic waves using programmable metasurfaces in a chaotic cavity, with applications to focusing with the generalized Wigner-Smith operator as well as coherent perfect absorption. We expect our fundamentally new perspective on coherent wave control to facilitate the transition of intricate WFS protocols into real applications for various wave phenomena.

Hybrid optimization algorithm based on neural networks and its application in wavefront shaping

The scattering effect of turbid media can lead to optical wavefront distortion. Focusing light through turbid media can be achieved using wavefront shaping techniques. Intelligent optimization algorithms and neural network algorithms are two powerful types of algorithms in the field of wavefront shaping but have their advantages and disadvantages. In this paper, we propose a new hybrid algorithm that combines the particle swarm optimization algorithm (PSO) and single-layer neural network (SLNN) to achieve the complementary advantages of both. A small number of training sets are used to train the SLNN to obtain preliminary focusing results, after which the PSO continues to optimize to the global optimum. The hybrid algorithm achieves faster convergence and higher enhancement than the PSO, while reducing the size of training samples required for SLNN training. SLNN trained with 1700 training sets can speed up the convergence of the PSO by about 50% and boost the final enhancement by about 24%. This hybrid algorithm will be of great significance in fields such as biomedicine and particle manipulation.

Focusing light through multimode fibres using a digital micromirror device: a comparison study of non-holographic approaches

Focusing light through a multimode fibre (MMF) has attracted significant research interest, mainly driven by the need for miniature endoscopes in biomedicine. In recent years, digital micromirror devices (DMD) have become increasingly popular as a high-speed alternative to liquid-crystal spatial light modulators for light focusing via wavefront shaping based on binary amplitude modulations. To exploit the potentials and limitations of the state-of-the-art DMD-based wavefront shaping methods, in this study, for the first time, we compared four representative, non-holographic and DMD-based methods that are reported so far in literature with the same experimental and simulation conditions, including a real-valued intensity transmission matrix (RVITM)-based algorithm, a complex-valued transmission matrix (TM)-based algorithm, a conditional probability algorithm and a genetic algorithm. We investigated the maximum achievable peak-to-background ratio (PBR) in comparison to theoretical expectations, and further improved the performance of the RVITM-based method. With both numerical simulations and experiments, we found that the genetic algorithm offered the highest PBR but suffered from the lowest focusing speed, while the RVITM-based algorithm provided a comparable PBR to that of the genetic algorithm, and the highest focusing speed.

Tunable mode control through myriad-mode fibers

Multimode fibers are attractive for imaging, communication, computation, and energy delivery. Unfortunately, intermodal and polarization coupling precludes direct control of the delivered mode composition. We present a technique to tailor the mode composition at the output of a multimode fiber with thousands of modes, which we refer to as myriad-mode fiber, using its experimentally measured transmission matrix. While precise mode control has been demonstrated in typical multimode fibers with up to 210 modes, the method proposed here is particularly useful for high mode number fibers, such as when the number of modes is comparable to the number of modes of the wavefront shaping spatial light modulator. To illustrate the technique, we select different subsets of modes to create focal spots at the output of a fiber with 7140 modes. Importantly, we define efficiency and fidelity metrics to evaluate the mode control and demonstrate the relationship between efficiency, fidelity, and the spatial location of the spots across the distal fiber cross-section.

Optical information transmission through complex scattering media with optical-channel-based intensity streaming

For the past decade, optical wavefront shaping has been the standard technique to control light through scattering media. Implicit in this dominance is the assumption that manipulating optical interference is a necessity for optical control through scattering media. In this paper, we challenge this assumption by reporting on an alternate approach for light control through a disordered scattering medium - optical-channel-based intensity streaming (OCIS). Instead of actively tuning the interference between the optical paths via wavefront shaping, OCIS controls light and transmits information through scattering media through linear intensity operations. We demonstrate a set of OCIS experiments that connect to some wavefront shaping implementations, i.e. iterative wavefront optimization, digital optical phase conjugation, image transmission through transmission matrix, and direct imaging through scattering media. We experimentally created focus patterns through scattering media on a sub-millisecond timescale. We also demonstrate that OCIS enables a scattering medium mediated secure optical communication application.

Compressively sampling the optical transmission matrix of a multimode fibre

The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.

BPM-Matlab: an open-source optical propagation simulation tool in MATLAB

We present the use of the Douglas-Gunn Alternating Direction Implicit finite difference method for computationally efficient simulation of the electric field propagation through a wide variety of optical fiber geometries. The method can accommodate refractive index profiles of arbitrary shape and is implemented in a tool called BPM-Matlab. We validate BPM-Matlab by comparing it to published experimental, numerical, and theoretical data and to commercially available state-of-the-art software. It is user-friendly, fast, and is available open-source. BPM-Matlab has a broad scope of applications in modeling a variety of optical fibers for diverse fields such as imaging, communication, material processing, and remote sensing.

Scattering-lens based quantum imaging beyond shot noise

The scheme of optical imaging using scattering lens can provide a resolution beyond the classical optical diffraction limit with a coherent-state input. Nevertheless, due to the shot noise of the coherent state, the corresponding signal-to-noise ratio and resolution are both still shot-noise-limited. In order to circumvent this problem, we theoretically propose an alternative scheme where the squeezed state (with a sub-shot noise) is considered as input and the quantum noise is then suppressed below the shot-noise level. Consequently, when comparing with the previous imaging scheme (using combination of coherent state and scattering lens), our proposal is able to achieve an enhanced signal-to-noise ratio for a given scattering lens. Meanwhile, it is demonstrated that the resolution is also improved. We believe that this method may afford a new way of using squeezed states and enable a higher performance than that of using coherent state and scattering lens.

Large-scale, high-contrast glare suppression with low-transmittance eigenchannels of aperture-target transmission matrices

Glare suppression with wavefront shaping is a significant technique in terms of actively controlling the speckle light field. A novel glare suppression method based on transmission matrix (TM) measurement is demonstrated in this Letter. An aperture-target TM model is proposed, and its low-transmittance eigenchannel is utilized to minimize the speckle intensity inside a given target area. We verified the availability of this method by experimentally realizing high-contrast glare suppression in areas of various sizes and shapes. For a large-scale area containing 100 speckle grains, the average intensity was suppressed to 6.3% of the background intensity. We believe our method provides an ideal method for glare suppression, and it holds interesting prospects for areas such as speckle optical tweezers and imaging under scattering conditions.

Gradient-assisted focusing light through scattering media

Focusing light through a scattering medium is a longstanding challenge in biomedical optics, to which wavefront shaping is a powerful solution. The state-of-the-art feedback-based approach is the widely used genetic algorithm method. However, it can only achieve relatively low enhancement of the focus, and the genetic algorithm is known to be time-consuming. To tackle those issues, we propose a gradient-assisted strategy for wavefront shaping. The proposed method conducts optimization in the function distribution space. Specifically, when optimizing the parameters along each iteration, the consequent function distribution changes within a distance as measured by the Kullback-Leibler divergence. Taking advantage of the gradient information, the proposed method is over 60× faster to obtain the same peak-to-background ratio (PBR) level. Compared with the genetic algorithm that is able to optimize a number of 64×64 phase segments, the proposed gradient strategy is able to optimize 256×256 phase segments, and gives 20× higher focus enhancement as quantified by the PBR.

Spectrally resolved point-spread-function engineering using a complex medium

Propagation of an ultrashort pulse of light through strongly scattering media generates an intricate spatio-spectral speckle that can be described by means of the multi-spectral transmission matrix (MSTM). In conjunction with a spatial light modulator, the MSTM enables the manipulation of the pulse leaving the medium; in particular focusing it at any desired spatial position and/or time. Here, we demonstrate how to engineer the point-spread-function of the focused beam both spatially and spectrally, from the measured MSTM. It consists of numerically filtering the spatial content at each wavelength of the matrix prior to focusing. We experimentally report on the versatility of the technique through several examples, in particular as an alternative to simultaneous spatial and temporal focusing, with potential applications in multiphoton microscopy.

Spectral speckle-correlation imaging

We present a method for single-shot spectrally resolved imaging through scattering media by using the spectral memory effect of speckles. In our method, a single speckle pattern from a multi-colored object is captured through scattering media with a monochrome image sensor. The color object is recovered by correlation of the captured speckle and a three-dimensional phase retrieval process. The proposed method was experimentally demonstrated by using point sources with different emission spectra located between diffusers. This study paves the way for non-invasive and low-cost spectral imaging through scattering media.

Recurrent neural network reveals transparent objects through scattering media

Scattering generally worsens the condition of inverse problems, with the severity depending on the statistics of the refractive index gradient and contrast. Removing scattering artifacts from images has attracted much work in the literature, including recently the use of static neural networks. S. Li et al. [Optica5(7), 803 (2018)10.1364/OPTICA.5.000803] trained a convolutional neural network to reveal amplitude objects hidden by a specific diffuser; whereas Y. Li et al. [Optica5(10), 1181 (2018)10.1364/OPTICA.5.001181] were able to deal with arbitrary diffusers, as long as certain statistical criteria were met. Here, we propose a novel dynamical machine learning approach for the case of imaging phase objects through arbitrary diffusers. The motivation is to strengthen the correlation among the patterns during the training and to reveal phase objects through scattering media. We utilize the on-axis rotation of a diffuser to impart dynamics and utilize multiple speckle measurements from different angles to form a sequence of images for training. Recurrent neural networks (RNN) embedded with the dynamics filter out useful information and discard the redundancies, thus quantitative phase information in presence of strong scattering. In other words, the RNN effectively averages out the effect of the dynamic random scattering media and learns more about the static pattern. The dynamical approach reveals transparent images behind the scattering media out of speckle correlation among adjacent measurements in a sequence. This method is also applicable to other imaging applications that involve any other spatiotemporal dynamics.

Displacement-agnostic coherent imaging through scatter with an interpretable deep neural network

Coherent imaging through scatter is a challenging task. Both model-based and data-driven approaches have been explored to solve the inverse scattering problem. In our previous work, we have shown that a deep learning approach can make high-quality and highly generalizable predictions through unseen diffusers. Here, we propose a new deep neural network model that is agnostic to a broader class of perturbations including scatterer change, displacements, and system defocus up to 10× depth of field. In addition, we develop a new analysis framework for interpreting the mechanism of our deep learning model and visualizing its generalizability based on an unsupervised dimension reduction technique. We show that our model can unmix the scattering-specific information and extract the object-specific information and achieve generalization under different scattering conditions. Our work paves the way to a robust and interpretable deep learning approach to imaging through scattering media.

Image reconstruction through a multimode fiber with a simple neural network architecture

Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups have recently shown that convolutional neural networks (CNNs) can be trained to perform high-fidelity MMF image reconstruction. We find that a considerably simpler neural network architecture, the single hidden layer dense neural network, performs at least as well as previously-used CNNs in terms of image reconstruction fidelity, and is superior in terms of training time and computing resources required. The trained networks can accurately reconstruct MMF images collected over a week after the cessation of the training set, with the dense network performing as well as the CNN over the entire period.

Resampling the transmission matrix in an aberration-corrected Bessel mode basis

The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is measured. While conventional experimental methods suffer from sampling effects and optical aberrations, we use a basis of Bessel modes of the first kind to faithfully recover the singular values, eigenvalues and eigenmodes of light propagation through a finite thickness of air.

Spatiotemporal focusing through a multimode fiber via time-domain wavefront shaping

We shape fs optical pulses and deliver them in a single spatial mode to the input of a multimode fiber. The pulse is shaped in time such that at the output of the multimode fiber an ultrashort pulse appears at a predefined focus. Our result shows how to raster scan an ultrashort pulse at the output of a stiff piece of square-core step-index multimode fiber and in this way show the potential for making a nonlinear fluorescent image of the scene behind the fiber, while the connection to the multimode fiber can be established via a thin and flexible single-mode fiber. The experimental results match our numerical simulation well.

Non-invasive optical imaging using the extension of the Fourier-domain shower-curtain effect

Optical imaging for non-self-luminous objects surrounded by complex scattering environments is scientifically challenging and technologically important. We propose a non-invasive imaging method by externally sending the illuminating light through the scattering medium and by detecting and analyzing the speckle patterns. The imaging of the object is recovered by extending the application scope of the Fourier-domain shower-curtain effect. It is found that the imaging depth is substantially extended and that faster imaging restoration is realized with the improved illumination scheme assisted with optical lenses, hence making it possible to apply the non-invasive optical imaging technique for practical applications.

Locating and Imaging through Scattering Medium in a Large Depth

Scattering medium brings great difficulties to locate and reconstruct objects especially when the objects are distributed in different positions. In this paper, a novel physics and learning-heuristic method is presented to locate and image the object through a strong scattering medium. A novel physics-informed framework, named DINet, is constructed to predict the depth and the image of the hidden object from the captured speckle pattern. With the phase-space constraint and the efficient network structure, the proposed method enables to locate the object with a depth mean error less than 0.05 mm, and image the object with an average peak signal-to-noise ratio (PSNR) above 24 dB, ranging from 350 mm to 1150 mm. The constructed DINet firstly solves the problem of quantitative locating and imaging via a single speckle pattern in a large depth. Comparing with the traditional methods, it paves the way to the practical applications requiring multi-physics through scattering media.

Volumetric two-photon fluorescence imaging of live neurons using a multimode optical fiber

Multimode optical fibers (MMFs), combined with wavefront control methods, have achieved minimally invasive in vivo imaging of neurons in deep-brain regions with diffraction-limited spatial resolution. Here, we report a method for volumetric two-photon fluorescence imaging with a MMF-based system requiring a single transmission matrix measurement. Central to this method is the use of a laser source able to generate both continuous wave light and femtosecond pulses. The chromatic dispersion of pulses generated an axially elongated excitation focus, which we used to demonstrate volumetric imaging of neurons and their dendrites in live rat brain slices through a 60 µm core MMF.

Visual data detection through side-scattering in a multimode optical fiber

Light propagation in optical fibers is accompanied by random omnidirectional scattering. The small fraction of coherent guided light that escapes outside the cladding of the fiber forms a speckle pattern. Here, visual information imaged into the input facet of a multimode fiber with a transparent buffer is retrieved, using a convolutional neural network, from the side-scattered light at several locations along the fiber. This demonstration can promote the development of distributed optical imaging systems and optical links interfaced via the sides of the fiber.

Wavefront Shaping Concepts for Application in Optical Coherence Tomography-A Review

Optical coherence tomography (OCT) enables three-dimensional imaging with resolution on the micrometer scale. The technique relies on the time-of-flight gated detection of light scattered from a sample and has received enormous interest in applications as versatile as non-destructive testing, metrology and non-invasive medical diagnostics. However, in strongly scattering media such as biological tissue, the penetration depth and imaging resolution are limited. Combining OCT imaging with wavefront shaping approaches significantly leverages the capabilities of the technique by controlling the scattered light field through manipulation of the field incident on the sample. This article reviews the main concepts developed so far in the field and discusses the latest results achieved with a focus on signal enhancement and imaging.

Laser beam focusing through a moderately scattering medium using a bimorph mirror

The rarely considered case when the optical radiation passes through the weakly scattering medium, e.g. mid-density atmospheric fog with the number of scattering events up to 10 was investigated in this paper. We demonstrated an improvement of focusing of a laser beam (λ=0.65 µm) passed through the 5 mm-thick layer of scattering suspension of 1 µm polystyrene microbeads diluted in a distilled water. For the first time the low-order aberration corrector - wide aperture bimorph deformable mirror with 48 electrodes configured in 6 rings was used to optimize a far-field focal spot. We compared efficiencies of the algorithm that optimized the positions of the focal spots on Shack-Hartmann type sensor and the algorithm that optimized the peak brightness and the diameter of the far-field focal spot registered with a CCD. We experimentally demonstrated the increase of the peak brightness of the far-field focal spot by up to 60% due to the use of the bimorph deformable mirror for beam focusing through the scattering medium with concentration values of scatterers ranged from 10⁵ to 10⁶ mm^-3.

Non-invasive focusing and imaging in scattering media with a fluorescence-based transmission matrix

In biological microscopy, light scattering represents the main limitation to image at depth. Recently, a set of wavefront shaping techniques has been developed in order to manipulate coherent light in strongly disordered materials. The Transmission Matrix approach has shown its capability to inverse the effect of scattering and efficiently focus light. In practice, the matrix is usually measured using an invasive detector or low-resolution acoustic guide stars. Here, we introduce a non-invasive and all-optical strategy based on linear fluorescence to reconstruct the transmission matrices, to and from a fluorescent object placed inside a scattering medium. It consists in demixing the incoherent patterns emitted by the object using low-rank factorizations and phase retrieval algorithms. We experimentally demonstrate the efficiency of this method through robust and selective focusing. Additionally, from the same measurements, it is possible to exploit memory effect correlations to image and reconstruct extended objects. This approach opens up a new route towards imaging in scattering media with linear or non-linear contrast mechanisms.

Light scattering represents the main limitation to image at depth in biological microscopy. The authors present a strategy to characterize light propagation in and out of a scattering medium based on linear fluorescence feedback and from the same measurements exploit memory effect correlations to image and reconstruct extended objects.

Optical Tweezers Exploring Neuroscience

Over the past decade, optical tweezers (OT) have been increasingly used in neuroscience for studies of molecules and neuronal dynamics, as well as for the study of model organisms as a whole. Compared to other areas of biology, it has taken much longer for OT to become an established tool in neuroscience. This is, in part, due to the complexity of the brain and the inherent difficulties in trapping individual molecules or manipulating cells located deep within biological tissue. Recent advances in OT, as well as parallel developments in imaging and adaptive optics, have significantly extended the capabilities of OT. In this review, we describe how OT became an established tool in neuroscience and we elaborate on possible future directions for the field. Rather than covering all applications of OT to neurons or related proteins and molecules, we focus our discussions on studies that provide crucial information to neuroscience, such as neuron dynamics, growth, and communication, as these studies have revealed meaningful information and provide direction for the field into the future.

A physical unclonable neutron sensor for nuclear arms control inspections

Classical sensor security relies on cryptographic algorithms executed on trusted hardware. This approach has significant shortcomings, however. Hardware can be manipulated, including below transistor level, and cryptographic keys are at risk of extraction attacks. A further weakness is that sensor media themselves are assumed to be trusted, and any authentication and encryption is done ex situ and a posteriori. Here we propose and demonstrate a different approach to sensor security that does not rely on classical cryptography and trusted electronics. We designed passive sensor media that inherently produce secure and trustworthy data, and whose honest and non-malicious nature can be easily established. As a proof-of-concept, we manufactured and characterized the properties of non-electronic, physical unclonable, optically complex media sensitive to neutrons for use in a high-security scenario: the inspection of a military facility to confirm the absence or presence of nuclear weapons and fissile materials.

Time reversed optical waves by arbitrary vector spatiotemporal field generation

Lossless linear wave propagation is symmetric in time, a principle which can be used to create time reversed waves. Such waves are special “pre-scattered” spatiotemporal fields, which propagate through a complex medium as if observing a scattering process in reverse, entering the medium as a complicated spatiotemporal field and arriving after propagation as a desired target field, such as a spatiotemporal focus. Time reversed waves have previously been demonstrated for relatively low frequency phenomena such as acoustics, water waves and microwaves. Many attempts have been made to extend these techniques into optics. However, the much higher frequencies of optics make for very different requirements. A fully time reversed wave is a volumetric field with arbitrary amplitude, phase and polarisation at every point in space and time. The creation of such fields has not previously been possible in optics. We demonstrate time reversed optical waves with a device capable of independently controlling all of light’s classical degrees of freedom simultaneously. Such a class of ultrafast wavefront shaper is capable of generating a sequence of arbitrary 2D spatial/polarisation wavefronts at a bandwidth limited rate of 4.4 THz. This ability to manipulate the full field of an optical beam could be used to control both linear and nonlinear optical phenomena.

Truly arbitrary spatiotemporal wavefront shaping has many potential applications in optics. Here the authors develop a system capable of arbitrary waveshaping to the extent of full time reversal of spatiotemporal optical beams.

High-fidelity off-axis digital optical phase conjugation with transmission matrix assisted calibration

The spatial information carried by light is scrambled when it propagates through a scattering medium, such as frosted glass, biological tissue, turbulent air, or multimode optical fibres. Digital optical phase conjugation (DOPC) is a technique that 'pre-aberrates' an illuminating wavefront to compensate for scatterer induced distortion. DOPC systems act as phase-conjugate mirrors: they require a camera to holographically record a distorted wavefront emanating from the scatterer and a spatial light modulator (SLM) to synthesize a phase conjugate of the measured wavefront, which is sent back through the scatterer thus creating a time-reversed copy of the original optical field. High-fidelity DOPC can be technically challenging to achieve as it typically requires pixel-perfect alignment between the camera and SLM. Here we describe a DOPC system in which the normally stringent alignment criteria are relaxed. In our system the SLM and camera are placed in-line in the same optical path from the sample, and the SLM is used in an off-axis configuration. This means high-precision alignment can be achieved by measurement of the transmission matrix (TM) mapping optical fields from the SLM to the camera and vice-versa, irrespective of their relative position. The TM also absorbs and removes other aberrations in the optical system, such as the curvature of the SLM and camera chips. Using our system we demonstrate high-fidelity focussing of light through two ground glass diffusers with a peak-intensity to mean-background ratio of ∼700. We provide a step-by-step guide detailing how to align this system and discuss the trade-offs with alternative configurations. We also describe how our setup can be used as a 'single-pixel camera' based DOPC system, offering potential for DOPC at wavelengths in which cameras are not available or are prohibitively expensive.

Single-shot time-reversed optical focusing into and through scattering media

Optical time reversal can focus light through or into scattering media, which raises a new possibility for conquering optical diffusion. Because optical time reversal must be completed within the correlation time of speckles, enhancing the speed of time-reversed optical focusing is important for practical applications. Although employing faster digital devices for time-reversal helps, more efficient methodologies are also desired. Here, we report a single-shot time-reversed optical focusing method to minimize the wavefront measurement time. In our approach, all information requisite for optical time reversal is extracted from a single-shot hologram, and hence no other preconditions or measurements are required. In particular, we demonstrate the first realization of single-shot time-reversed ultrasonically encoded (TRUE) optical focusing into scattering media. By using the minimum amount of measurement, this work breaks the fundamental speed limit of digitally based time reversal for focusing into and through scattering media, and constitutes an important step toward high-speed wavefront shaping applications.

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.