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

Wavefront shaping: A versatile tool to conquer multiple scattering in multidisciplinary fields

Optical techniques offer a wide variety of applications as light-matter interactions provide extremely sensitive mechanisms to probe or treat target media. Most of these implementations rely on the usage of ballistic or quasi-ballistic photons to achieve high spatial resolution. However, the inherent scattering nature of light in biological tissues or tissue-like scattering media constitutes a critical obstacle that has restricted the penetration depth of non-scattered photons and hence limited the implementation of most optical techniques for wider applications. In addition, the components of an optical system are usually designed and manufactured for a fixed function or performance. Recent advances in wavefront shaping have demonstrated that scattering- or component-induced phase distortions can be compensated by optimizing the wavefront of the input light pattern through iteration or by conjugating the transmission matrix of the scattering medium. This offers unprecedented opportunities in many applications to achieve controllable optical delivery or detection at depths or dynamically configurable functionalities by using scattering media to substitute conventional optical components. In this article, the recent progress of wavefront shaping in multidisciplinary fields is reviewed, from optical focusing and imaging with scattering media, functionalized devices, modulation of mode coupling, and nonlinearity in multimode fiber to multimode fiber-based applications. Apart from insights into the underlying principles and recent advances in wavefront shaping implementations, practical limitations and roadmap for future development are discussed in depth. Looking back and looking forward, it is believed that wavefront shaping holds a bright future that will open new avenues for noninvasive or minimally invasive optical interactions and arbitrary control inside deep tissues. The high degree of freedom with multiple scattering will also provide unprecedented opportunities to develop novel optical devices based on a single scattering medium (generic or customized) that can outperform traditional optical components.

Imaging Complex Targets through a Scattering Medium Based on Adaptive Encoding

The scattering of light after passing through a complex medium poses challenges in many fields. Any point in the collected speckle will contain information from the entire target plane because of the randomness of scattering. The detailed information of complex targets is submerged in the aliased signal caused by random scattering, and the aliased signal causes the quality of the recovered target to be degraded. In this paper, a new neural network named Adaptive Encoding Scattering Imaging ConvNet (AESINet) is constructed by analyzing the physical prior of speckle image redundancy to recover complex targets hidden behind the opaque medium. AESINet reduces the redundancy of speckle through adaptive encoding which effectively improves the separability of data; the encoded speckle makes it easier for the network to extract features, and helps restore the detailed information of the target. The necessity for adaptive encoding is analyzed, and the ability of this method to reconstruct complex targets is tested. The peak signal-to-noise ratio (PSNR) of the reconstructed target after adaptive encoding can be improved by 1.8 dB. This paper provides an effective reference for neural networks combined with other physical priors in scattering processes.

Incoherent optical phase conjugation

Optical phase conjugation is a known technique for optically reproducing an object behind a scattering medium. Here we present digital optical phase conjugation through scattering media with spatially and temporally incoherent light. This enables us to eliminate the inevitable light coherence and the need for interferometric measurement for optical phase conjugation. Moreover, we show a method for suppressing background noise, which is critical in incoherent optical phase conjugation. We numerically and experimentally demonstrate the proposed method with background suppression.

Beamshaping for infrared hyperspectral imaging: a sequential optimization for infrared source coupling

Focal plane array (FPA) detectors have escalated Fourier transform infrared (FTIR) microspectroscopy to a potent hyperspectral imaging method. Yet, despite the instrumental multiplex/multichannel advantages, the fidelity of the hyperspectral images relies on the throughput as the total flux of the source is divided among each FPA pixel. Additionally, maintaining the spectral resolution requires a certain level of collimation of the beam which adversely affect the flux of high étendue source. To this end, we propose an implementation of two deformable mirror (DM) sensorless adaptive optics system for infrared (IR) source coupling. The deflection shape of each DM membrane is optimized individually to deal with the beam intensity and the rays' direction in a separate manner, while preserving the spectral quality across the entire mid-IR range. This paper contemplates the choice of metrics in sequential optimization in conjunction with two variations of stochastic parallel gradient descent optimization algorithm. We discuss this approach with respect to a state-of-the-art FTIR microscope.

Multiplexed spatially-focused localization of light in adipose biological tissues

Last decades the effects of localization and focusing of light in turbid randomly inhomogeneous tissue-like scattering medium have been attracting a particular attention. Weak localization of light in disordered and weakly ordered biological tissue, polarization memory effect, correlations in transmission matrices, focusing light by wavefronts shaping have been widely exploited. Here, we represent an experimentally observed and theoretically confirmed new type of spatial localization of light within biological tissues. General description of the observed phenomenon based on Monte Carlo ray tracing model is provided. We find that innate body arrangements of individual adipocytes can act as a cascade of quasi-ordered microscale lenses confining propagation of light within adipose tissues similar to lens lightguides. The observed spatially-resolved longitudinal multi-focusing of light within disordered adipose biological tissues can naturally lead greater spatial control and enhance light-tissue interactions.

Enhancing spatiotemporal focusing of light deep inside scattering media with Time-Gated Reflection Matrix

Time-gated reflection matrix (RM) has been successfully used for optical imaging deep inside scattering media. Recently, this method was extended to enhance the spatiotemporal focusing of light ultra-deep inside scattering media. This is achieved by calibrating the decomposition of the RM with the Tikhonov regularization parameter to convert multiply scattered photons that share the same time of flight with the singly scattered photons into singly scattered photons. Such a capability suggests a reshaping to the interaction mechanism between light and scattering media, which may benefit or inspire wide optical applications that desire enhanced spatiotemporal focusing of light at depths inside scattering media.

Light-field focusing and modulation through scattering media based on dual-polarization-encoded digital optical phase conjugation

Digital optical phase conjugation (DOPC) can be applied for light-field focusing and imaging through or within scattering media. Traditional DOPC only recovers the phase but loses the polarization information of the original incident beam. In this Letter, we propose a dual-polarization-encoded DOPC to recover the full information (both phase and polarization) of the incident beam. The phase distributions of two orthogonal polarization components of the speckle field coming from a multimode fiber are first measured by using digital holography. Then, the phase distributions are separately modulated on two beams and their conjugations are superposed to recover the incident beam through the fiber. By changing the phase difference or amplitude ratio between the two conjugate beams, light fields with complex polarization distribution can also be generated. This method will broaden the application scope of DOPC in imaging through scattering media.

cGAN-assisted imaging through stationary scattering media

Analyzing images taken through scattering media is challenging, owing to speckle decorrelations from perturbations in the media. For in-line imaging modalities, which are appealing because they are compact, require no moving parts, and are robust, negating the effects of such scattering becomes particularly challenging. Here we explore the use of conditional generative adversarial networks (cGANs) to mitigate the effects of the additional scatterers in in-line geometries, including digital holographic microscopy. Using light scattering simulations and experiments on objects of interest with and without additional scatterers, we find that cGANs can be quickly trained with minuscule datasets and can also efficiently learn the one-to-one statistical mapping between the cross-domain input-output image pairs. Importantly, the output images are faithful enough to enable quantitative feature extraction. We also show that with rapid training using only 20 image pairs, it is possible to negate this undesired scattering to accurately localize diffraction-limited impulses with high spatial accuracy, therefore transforming a shift variant system to a linear shift invariant (LSI) system.

Robust correction of interferometer phase drift in transmission matrix measurements

A complex-valued transmission matrix describing a scattering medium can be constructed from a sequence of many interferometric measurements. A major challenge in such experiments is to correct for rapid phase drift of the optical system during the data acquisition process, especially when the phase drifts significantly between consecutive measurements. Therefore, a new method is presented where the exact phase drift between two measurements is characterized and corrected using a single additional measurement. This approach removes the need to continuously track the phase and significantly relaxes the phase stability requirements of the interferometer, allowing transmission matrices to be constructed in the presence of fast and erratic phase drift.

Focus quality in raster-scan imaging via a multimode fiber

A multimode fiber (MMF) is a minimally invasive imaging probe. The most popular approach of MMF-based microscopy is raster-scan imaging, where the sample is illuminated by foci optimized on the fiber output facet by wavefront shaping (WFS). Imaging quality can be quantified by characteristic parameters of the optimized spots. We investigate the influence of the input light position on WFS through a round-core MMF with partial mode control, a situation often encountered in real life. We further demonstrate a trade-off between the shape and contrast of the foci generated on the output facet: the center input position is beneficial for high-contrast imaging, while the edge input position helps to reduce focus aberrations. These results are important for high field-of-view raster-scan imaging via an MMF.

Prior-free imaging unknown target through unknown scattering medium

Imaging through scattering medium based on deep learning has been extensively studied. However, existing methods mainly utilize paired data-prior and lack physical-process fusion, and it is difficult to reconstruct hidden targets without the trained networks. This paper proposes an unsupervised neural network that integrates the universal physical process. The reconstruction process of the network is irrelevant to the system and only requires one frame speckle pattern and unpaired targets. The proposed network enables online optimization by using physical process instead of fitting data. Thus, large-scale paired data no longer need to be obtained to train the network in advance, and the proposed method does not need prior information. The optimization of the network is a physical-based process rather than a data mapping process, and the proposed method also increases the insufficient generalization ability of the learning-based method in scattering medium and targets. The universal applicability of the proposed method to different optical systems increases the likelihood that the method will be used in practice.

Non-invasive chemically selective energy delivery and focusing inside a scattering medium guided by Raman scattering

Raman scattering is a chemically selective probing mechanism with diverse applications in industry and clinical settings. Yet, most samples are optically opaque limiting the applicability of Raman probing at depth. Here, we demonstrate chemically selective energy deposition behind a scattering medium by combining prior information on the chemical's spectrum with the measurement of a spectrally resolved Raman speckle as a feedback mechanism for wavefront shaping. We demonstrate unprecedented sixfold signal enhancement in an epi-geometry, realizing targeted energy deposition and focusing on individual Raman active particles.

Separating single- and multiple-scattering components in laser speckle contrast imaging of tissue blood flow

Random matrix theory provides new insights into multiple scattering in random media. In a recent study, we demonstrated the statistical separation of single- and multiple-scattering components based on a Wishart random matrix. The first- and second-order moments were estimated with a Wishart random matrix constructed using dynamically backscattered speckle images. In this study, this new strategy was applied to laser speckle contrast imaging (LSCI) of in vivo blood flow. The random matrix-based method was adopted and parameterized using electric field Monte Carlo simulations and in vitro blood flow phantom experiments. The new method was further applied to in vivo experiments, demonstrating the benefits of separating the single- and multiple-scattering components, and the method was compared with the traditional temporal laser speckle contrast analysis (LASCA) method. More specifically, the new method separates the stimulus-induced functional changes in blood flow and tissue perfusion in the superficial (<2l _t , l _t is the transport mean free path) and deep layers (1l _t  ∼ 7l _t ), extending LSCI to the evaluation of functional and pathological changes.

Focusing of a Laser Beam Passed through a Moderately Scattering Medium Using Phase-Only Spatial Light Modulator

The rarely considered case of laser beam propagation and focusaing through the moderately scattering medium was researched. A phase-only spatial light modulator (SLM) with 1920×1080 pixel resolution was used to increase the efficiency of focusing of laser radiation propagated through the 5 mm layer of the scattering suspension of 1 µm polystyrene microbeads in distilled water with the concentration values ranging from 105 to 106 mm−3. A CCD camera with micro-objective was used to estimate the intensity distribution of the far-field focal spot. A Shack-Hartmann sensor was used to measure wavefront distortions. The conducted experimental research demonstrated the 8% increase in integral intensity and 16% decrease in diameter of the far-field focal spot due to the use of the SLM for laser beam focusing.

Enhance the delivery of light energy ultra-deep into turbid medium by controlling multiple scattering photons to travel in open channels

Multiple light scattering is considered as the major limitation for deep imaging and focusing in turbid media. In this paper, we present an innovative method to overcome this limitation and enhance the delivery of light energy ultra-deep into turbid media with significant improvement in focusing. Our method is based on a wide-field reflection matrix optical coherence tomography (RM-OCT). The time-reversal decomposition of the RM is calibrated with the Tikhonov regularization parameter in order to get more accurate reversal results deep inside the scattering sample. We propose a concept named model energy matrix, which provides a direct mapping of light energy distribution inside the scattering sample. To the best of our knowledge, it is the first time that a method to measure and quantify the distribution of beam intensity inside a scattering sample is demonstrated. By employing the inversion of RM to find the matched wavefront and shaping with a phase-only spatial light modulator, we succeeded in both focusing a beam deep (~9.6 times of scattering mean free path, SMFP) inside the sample and increasing the delivery of light energy by an order of magnitude at an ultra-deep (~14.4 SMFP) position. This technique provides a powerful tool to understand the propagation of photon in a scattering medium and opens a new way to focus light inside biological tissues.

Optical reciprocity induced wavefront shaping for axial and lateral shifting of focus through a scattering medium

Light propagating along a reversed path experiences the same transmission coefficient as in the forward direction, independent of the path complexity. This is called the optical reciprocity of light, which is valid for not too intense scattering media as well. Hence, by utilizing the reciprocity principle, the proposed novel technique can achieve axially and laterally tunable focus, non-invasively, through a scattering media without a priori knowledge or modeling of its scattering properties. Moreover, the uniqueness of the proposed technique lies in the fact that the illumination and detection are on the same side of the scattering media.

Complex amplitude field reconstruction in atmospheric turbulence based on deep learning

In this paper, we use deep neural networks (DNNs) to simultaneously reconstruct the amplitude and phase information of the complex light field transmitted in atmospheric turbulence based on deep learning. The results of amplitude and phase reconstruction by four different training methods are compared comprehensively. The obtained results indicate that the training method that can more accurately reconstruct the complex amplitude field is to input the amplitude and phase pattern pairs into the neural network as two channels to train the model.

On-Demand Phase Control of a 7-Fiber Amplifiers Array with Neural Network and Quasi-Reinforcement Learning

We report a coherent beam combining technique using a specific quasi-reinforcement learning scheme. A neural network learned by this method enables the tailoring and locking of a tiled beam array on any phase map. We present the experimental implementation of on-demand phase control by a neural network in a seven-fiber laser array. This servo loop needs only six phase corrections to converge to the desired phase set at any profile, with a bandwidth higher than 1 kHz. Moreover, we demonstrate the dynamical feature of adaptive phase control, performing sequences of controlled phase sets. It is the first time, to the best of our knowledge, that an actual array of seven-fiber amplifiers has been successfully phase-locked and controlled by machine learning.

Single-shot noninvasive imaging through scattering medium under white-light illumination

We experimentally investigate image reconstruction through a scattering medium under white-light illumination. To solve the inverse problem of noninvasive scattering imaging, a modified iterative algorithm is employed with an interpretable constraint on the optical transfer function (OTF). As a result, a sparse and real object can be retrieved whether it is illuminated with a narrowband or broadband light. Compared with the well-known speckle correlation technique (SCT), the proposed method requires no restrictions on the speckle autocorrelation and shows a potential advantage in scattering imaging.

High-performance imaging with an advanced non-imaging lens based on full-path optical diffraction calculation in two-dimensional space

High-performance image-forming systems often require high system complexity due to the overdetermined nature of optical aberration correction. What we present here is a novel computational imaging modality which can achieve high-performance imaging using a simple non-image-forming optical system. The presented optical system contains an aspherical non-imaging lens which is designed with the optimal transfer of light radiation between an object and a detector. All spatial frequencies of the object collected by the non-imaging lens are delivered to the detector. No image is formed on the detector, and a full-path optical diffraction calculation method is developed to recover a high-quality image of the object from multiple intensity measurements. The effectiveness and high performance of the proposed imaging modality is verified by the examples.

Near perfect focusing through multimode fibres

Holographic, multimode fibre (MMF) based endoscopes envision high-quality in-vivo imaging inside previously inaccessible structures of living organisms, amongst other perspective applications. Within these instruments, a digital micro-mirror device (DMD) is deployed in order to holographically synthesise light fields which, after traversing the multimode fibre, form foci at desired positions behind the distal fibre facet. When applied in various imaging modalities, the purity and sharpness of the achieved foci are determinant for the imaging performance. Here we present diffraction-limited foci, which contain in excess of 96% of optical power delivered by the fibre which, to the best of our knowledge, represents the highest value reported to date. Further, we quantitatively study the impact of various conditions of the experimental procedure including input polarisation settings, influence of ghost diffraction orders, light modulation regimes, bias of the calibration camera and the influence of noise.

Dual-compressed photoacoustic single-pixel imaging

Photoacoustic imaging, an acoustic imaging modality with potentially optical resolution in an optical turbid medium, has attracted great attention. However, the convergence of wavefront optimization and raster scanning in computational photoacoustic imaging leads to the challenge of fast mapping, especially for a spatial resolution approaching the acoustic deep-subwavelength regime. As a sparse sampling paradigm, compressive sensing has been applied in numerous fields to accelerate data acquisition without significant quality losses. In this work, we propose a dual-compressed approach for photoacoustic surface tomography that enables high-efficiency imaging with 3D spatial resolution unlimited by the acoustics in a turbid environment. The dual-compressed photoacoustic imaging with single-pixel detection, enabled by spatially optical modulation with synchronized temporally photoacoustic coding, allows decoding of the fine optical information from the modulated acoustic signal even when the variance of original photoacoustic signals is weak. We perform a proof-of-principle numerical demonstration of dual-compressed photoacoustic imaging, that resolves acoustic sub-acoustic-wavelength details with a significantly reduced number of measurements, revealing the potential for dynamic imaging. The dual-compressed concept, which transforms unobtrusive spatial difference into spatio-temporal detectable information, can be generalized to other imaging modalities to realize efficient, high-spatial-resolution imaging.

Wavefront shaping with a Hadamard basis for scattering soil imaging

Soil is a scattering medium that inhibits imaging of plant-microbial-mineral interactions that are essential to plant health and soil carbon sequestration. However, optical imaging in the complex medium of soil has been stymied by the seemingly intractable problems of scattering and contrast. Here, we develop a wavefront shaping method based on adaptive stochastic parallel gradient descent optimization with a Hadamard basis to focus light through soil mineral samples. Our approach allows a sparse representation of the wavefront with reduced dimensionality for the optimization. We further divide the used Hadamard basis set into subsets and optimize a certain subset at once. Simulation and experimental optimization results demonstrate our method has an approximately seven times higher convergence rate and overall better performance compared to that with optimizing all pixels at once. The proposed method can benefit other high-dimensional optimization problems in adaptive optics and wavefront shaping.

Large field-of-view non-invasive imaging through scattering layers using fluctuating random illumination

Non-invasive optical imaging techniques are essential diagnostic tools in many fields. Although various recent methods have been proposed to utilize and control light in multiple scattering media, non-invasive optical imaging through and inside scattering layers across a large field of view remains elusive due to the physical limits set by the optical memory effect, especially without wavefront shaping techniques. Here, we demonstrate an approach that enables non-invasive fluorescence imaging behind scattering layers with field-of-views extending well beyond the optical memory effect. The method consists in demixing the speckle patterns emitted by a fluorescent object under variable unknown random illumination, using matrix factorization and a novel fingerprint-based reconstruction. Experimental validation shows the efficiency and robustness of the method with various fluorescent samples, covering a field of view up to three times the optical memory effect range. Our non-invasive imaging technique is simple, neither requires a spatial light modulator nor a guide star, and can be generalized to a wide range of incoherent contrast mechanisms and illumination schemes.

Surveillance of few-mode fiber-communication channels with a single hidden layer neural network

Multi- and few-mode fibers (FMFs) promise to enhance the capacity of optical communication networks by orders of magnitude. The key for this evolution was the strong advancement of computational approaches that allowed inherent complex light transmission to be surpassed, learned, or controlled, reined in by modal crosstalk and mode-dependent losses. However, complex light transmission through FMFs can be learned by a single hidden layer neural network (NN). The emerging developments in NNs additionally allow the implementation of novel concepts for security enhancements in optical communication. Once the transmission characteristics of FMFs are learned, it is possible to survey the incoming and outgoing light fields via monitoring channels during data transmission. If an eavesdropper tries to gain unauthorized access to the FMF, its transmission properties are impaired through sensitive modal crosstalk. This process is registered by the NN and thus the eavesdropper is revealed. With our solution, the security of optical communication can be improved.

Time-reversal focusing of ultrashort pulses through thin scattering media

When ultrashort pulses propagate through a disordered medium, scattering occurs and the intensity of the ballistic component decreases drastically. This limits the applicability of time-resolved nonlinear optical spectroscopy and microscopy. The wavefront shaping technique makes it possible to focus light through the scattering medium; however, complete time-reversal of the ultrashort pulses (as short as 10 fs) is still a very challenging problem. This is due to the in-depth characterization and precise control needed for such pulses in the time domain in order to compress down the Fourier-transform limit. In this work, we develop new spatiotemporal wavefront shaping techniques to focus ultrashort pulses at the target position through a thin scattering medium. Compared to other studies, one significant advantage of this method is that most of the characterization of the spectrally-resolved transmission matrix and temporal profile of the ultrashort pulses can be done using single-beam geometry. An interferometer with external reference is necessary to measure the difference of the phase profile between the focused and reference pulses. Furthermore, the number of controllable phase components in the spectral domain is not limited by the spectral correlations of the speckle patterns because we used a pulse shaper in the time domain to optimize the temporal properties of the ultrashort focused pulse. Our new method provides increased flexibility and precise control for manipulating extremely ultrashort pulses through thin scattering media in order to achieve time-reversal focusing at the target position.

Efficient sorting for an orbital angular momentum multiplexing communication link based on a digital micromirror device and a diffuser

Efficient sorting multiple orbital angular momentum (OAM) spatial modes is a significant step in OAM multiplexing communications. Recently, wavefront shaping (WS) techniques have been implemented to manipulate light scattering through a diffuser. We reported a novel scheme for sorting multiplexed OAM modes faster and more accurately, using the complex amplitude WS based on a digital micromirror device (DMD) through a diffuser to shape the full field (phase and amplitude) of the OAM modes. In this study, we simulate this complex sorter for demultiplexing multiple modes and make a performance comparison with the previous sorter using the phase-only WS. Our results showed that for arbitrary two multiplexed modes, the sorter could achieve a high detection probability of more than 0.99. As the number of the multiplexed modes increases, the detection probability decreases to ∼0.82 when sorting seven modes, which contrasts the ∼0.71 of the phase-only sorters. We also experimentally verified the feasibility, that for arbitrary two modes, the sorter could reach a high detection probability of more than 0.99, and the complex sorter is capable of higher detection probability than the phase-only sorter under the same conditions. Hence, we anticipate that this sorter may potentially be demultiplexing multiple OAM spatial modes efficiently and quickly.

Calibration-free speckle matrix imaging

Unknown speckle patterns can be used to image targets embedded in complex scattering media 100 times faster than previous techniques based on carefully calibrated illuminations.

Repeated imaging through a multimode optical fiber using adaptive optics

Multimode optical fibers (MMF) have shown considerable potential for minimally invasive diffraction-limited fluorescence imaging of deep brain regions owing to their small size. They also look to be suitable for imaging across long time periods, with repeated measurements performed within the same brain region, which is useful to assess the role of synapses in normal brain function and neurological disease. However, the approach is not without challenge. Prior to imaging, light propagation through a MMF must be characterized in a calibration procedure. Manual repositioning, as required for repeated imaging, renders this calibration invalid. In this study, we provide a two-step solution to the problem consisting of (1) a custom headplate enabling precise reinsertion of the MMF implant achieving low-quality focusing and (2) sensorless adaptive optics to correct translational shifts in the MMF position enabling generation of high-quality imaging foci. We show that this approach achieves fluorescence imaging after repeated removal and reinsertion of a MMF.

Optimized number of the primary singular values for image reconstruction in reflection matrix based optical coherence tomography

A reflection matrix based optical coherence tomography (OCT) is recently proposed and expected to extend the imaging-depth limit twice. However, the imaging depth and hence the image quality heavily depend on the number of primary singular values considered for image reconstruction. To this regard, we propose a method based on correlation between image pairs reconstructed from different number of singular values and corresponding remainders. The obtained correlation curve and another feature curve fetched from the former are then fed to a long short-term memory (LSTM) network classifier to identify the optimized number of primary singular values for image reconstruction. Simulated targets with different combinations of filling fraction and signal-to-noise ratio (SNR) are reconstructed by the developed method as well as two current adopted methods for comparison. The results demonstrate that the proposed method is robust to recover the image with satisfactory similarity close to the reference one. To our knowledge, this is the first comprehensive study on the optimized number of the primary singular values considered for image reconstruction in reflection matrix based OCT.

Direct construction of an optical linear transform and its application on optical complex data generation

Optical computing technique has emerged as a promising platform for highly parallel data processing. In most optical computing architectures, optical linear transform is the basic composition, which is commonly designed by the established deep learning-based methods or general-purpose optimizers. There still lacks in-depth study to construct a solver targeted at optical linear transform applications. In this work, we propose a new algorithm that solves the transformation matrix of a linear optical system consisting of cascaded phase masks directly and show that its efficiency is significantly higher than those common solvers. As a direct application of this method, we can create target array of optical beams even with a single layer of phase mask in the experiment. The amplitude and phase of each beam in the array can be controlled independently without affecting each other. The optical system requires only one light source and one programmable phase mask. This setup can be readily incorporated into most current optical computing configurations. Our method may find broad applications in classic and quantum optical information processing.

Wavefront shaping for reconfigurable beam steering in lithium niobate multimode waveguide

Reconfigurable photonic devices are important constituents for future optical integrated circuits, where electro-optic manipulation of the light field in a lithium niobate (LN) waveguide is one of the promising solutions. Herein, we demonstrate a paradigm shift of the beam steering mechanism where reconfigurable beam steering is enabled by the wavefront shaping technology. Furthermore, this strategy is fully compatible with the electro-optic tuning mechanism of the LN multimode waveguide, where microstructured serrated array electrodes are employed to fine tune the output beam upon its reconfigurable output position. Our results provide new, to the best of our knowledge, insight for molding the flow of light in multimode waveguides and shed new light on beam steering photonic devices.

High-throughput volumetric adaptive optical imaging using compressed time-reversal matrix

Deep-tissue optical imaging suffers from the reduction of resolving power due to tissue-induced optical aberrations and multiple scattering noise. Reflection matrix approaches recording the maps of backscattered waves for all the possible orthogonal input channels have provided formidable solutions for removing severe aberrations and recovering the ideal diffraction-limited spatial resolution without relying on fluorescence labeling and guide stars. However, measuring the full input-output response of the tissue specimen is time-consuming, making the real-time image acquisition difficult. Here, we present the use of a time-reversal matrix, instead of the reflection matrix, for fast high-resolution volumetric imaging of a mouse brain. The time-reversal matrix reduces two-way problem to one-way problem, which effectively relieves the requirement for the coverage of input channels. Using a newly developed aberration correction algorithm designed for the time-reversal matrix, we demonstrated the correction of complex aberrations using as small as 2% of the complete basis while maintaining the image reconstruction fidelity comparable to the fully sampled reflection matrix. Due to nearly 100-fold reduction in the matrix recording time, we could achieve real-time aberration-correction imaging for a field of view of 40 × 40 µm2 (176 × 176 pixels) at a frame rate of 80 Hz. Furthermore, we demonstrated high-throughput volumetric adaptive optical imaging of a mouse brain by recording a volume of 128 × 128 × 125 µm3 (568 × 568 × 125 voxels) in 3.58 s, correcting tissue aberrations at each and every 1 µm depth section, and visualizing myelinated axons with a lateral resolution of 0.45 µm and an axial resolution of 2 µm.

Endoscopic Imaging Using a Multimode Optical Fibre Calibrated with Multiple Internal References

The interferometric acquisition of the transmission matrix (TM) of a multimode optical fibre (MMF), which is at the heart of multimode fibre-based endoscopic imaging methods, requires using a reference beam. Attempts to use an internal reference, that is to provide the reference in a common pathway geometry through the MMF itself, lead to a speckled reference intensity and consequential occurrence of “blind spots”—locations where insufficient optical power in the reference wave inflicts strong measurement errors. Here we show that combining a relatively small number of TMs, which are measured using different internal references, facilitates a complete elimination of blind spots, and thereby a significant enhancement of the imaging quality.

Neurophotonic tools for microscopic measurements and manipulation: status report

Neurophotonics was launched in 2014 coinciding with the launch of the BRAIN Initiative focused on development of technologies for advancement of neuroscience. For the last seven years, Neurophotonics' agenda has been well aligned with this focus on neurotechnologies featuring new optical methods and tools applicable to brain studies. While the BRAIN Initiative 2.0 is pivoting towards applications of these novel tools in the quest to understand the brain, this status report reviews an extensive and diverse toolkit of novel methods to explore brain function that have emerged from the BRAIN Initiative and related large-scale efforts for measurement and manipulation of brain structure and function. Here, we focus on neurophotonic tools mostly applicable to animal studies. A companion report, scheduled to appear later this year, will cover diffuse optical imaging methods applicable to noninvasive human studies. For each domain, we outline the current state-of-the-art of the respective technologies, identify the areas where innovation is needed, and provide an outlook for the future directions.

Optimal Control of Coherent Light Scattering for Binary Decision Problems

Because of quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general framework to calculate and minimize this bound using coherent probe fields with tailored spatial distributions. As an example, we experimentally study a target located in between two disordered scattering media. We first show that the optimal field distribution can be directly identified using a general approach based on scattering matrix measurements. We then demonstrate that this optimal light field successfully probes the presence of the target with a number of photons that is reduced by more than 2 orders of magnitude as compared to unoptimized fields.

Time-of-flight 3D imaging through multimode optical fibers

[Figure: see text].

Optical analog-signal transmission and retrieval through turbid water

In this paper, we propose a new, to the best of our knowledge, and robust method to optically transmit analog signals in free space through turbid water. In the proposed method, each pixel of original signal is sequentially encoded into random amplitude-only patterns as information carrier. A single-pixel detector is utilized to collect light intensity at the receiving end. To verify feasibility and effectiveness of the proposed method, a number of optical experiments are carried out in different kinds of water conditions, e.g., clean water, water mixed with milk, water with salt, and water with salt and milk. In addition, real seawater samples are also tested. Experimental results demonstrate that the proposed method shows high robustness against different propagation distances through turbid water and resists the effect of various turbulence factors. The proposed method is applicable to transmit information with high fidelity and high robustness against light wave diffusion in free space through complex environment. Furthermore, the proposed method is easy to operate and is cost-effective, which could open up a novel insight into optical signal transmission in free space through turbid water.

Efficient color imaging through unknown opaque scattering layers via physics-aware learning

Color imaging with scattered light is crucial to many practical applications and becomes one of the focuses in optical imaging fields. More physics theories have been introduced in the deep learning (DL) approach for the optical tasks and improve the imaging capability a lot. Here, an efficient color imaging method is proposed in reconstructing complex objects hidden behind unknown opaque scattering layers, which can obtain high reconstruction fidelity in spatial structure and accurate restoration in color information by training with only one diffuser. More information is excavated by utilizing the scattering redundancy and promotes the physics-aware DL approach to reconstruct the color objects hidden behind unknown opaque scattering layers with robust generalization capability by an efficient means. This approach gives impetus to color imaging through dynamic scattering media and provides an enlightening reference for solving complex inverse problems based on physics-aware DL methods.

Fast non-line-of-sight imaging with high-resolution and wide field of view using synthetic wavelength holography

The presence of a scattering medium in the imaging path between an object and an observer is known to severely limit the visual acuity of the imaging system. We present an approach to circumvent the deleterious effects of scattering, by exploiting spectral correlations in scattered wavefronts. Our Synthetic Wavelength Holography (SWH) method is able to recover a holographic representation of hidden targets with sub-mm resolution over a nearly hemispheric angular field of view. The complete object field is recorded within 46 ms, by monitoring the scattered light return in a probe area smaller than 6 cm × 6 cm. This unique combination of attributes opens up a plethora of new Non-Line-of-Sight imaging applications ranging from medical imaging and forensics, to early-warning navigation systems and reconnaissance. Adapting the findings of this work to other wave phenomena will help unlock a wider gamut of applications beyond those envisioned in this paper.

Feedback-assisted transmission matrix measurement of a multimode fiber in a referenceless system

Recent development in wavefront shaping shows the promise to employ multimode fibers (MMFs) to deliver images in endoscopy. In these applications, retrieving the transmission matrix (TM) of the MMF is especially important. Among existing non-holographic approaches, feedback-based wavefront shaping requires a large number of measurements, while directly measuring the TM can be easily trapped into local optimums if the constraints are insufficient. To reduce the required number of measurements, we combine the concepts of these two approaches and develop a scheme termed feedback-assisted TM measurements. We show that under such a hybrid scheme, less than 3N intensity measurements are sufficient to accurately retrieve one row of the TM that contains N unknown complex elements. As a proof of concept, we experimentally demonstrated retrieving multiple rows of the TM of an MMF using the proposed scheme with high fidelity. In particular, a single focus and dual foci through the MMF with enhancements larger than 75% of the theoretical values were reported.

Unscrambling OAM mode using digital phase-shifting in the Stokes fluctuations correlation

In this Letter, we propose and experimentally demonstrate a new, to the best of our knowledge, non-interferometric and highly stable technique to unscramble the incident orbital angular momentum (OAM) state and quantitatively measure the phase structure from the non-imaged random light. A new theoretical basis is developed and also verified by numerical simulation and experimental demonstration. We also quantitatively investigate the OAM modes of the incident light using orthogonal projection.

Arbitrary optical wave evolution with Fourier transforms and phase masks

A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)10.1103/PhysRevLett.73.58], it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a deterministic algorithm that can find an exact and efficient implementation of any unitary transformation, using only Fourier transforms and phase masks. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from some of the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.

Computational image enhancement of multimode fibre-based holographic endo-microscopy: harnessing the muddy modes

In imaging geometries, which employ wavefront-shaping to control the light transport through a multi-mode optical fibre (MMF), this terminal hair-thin optical component acts as a minimally invasive objective lens, enabling high resolution laser-scanning fluorescence microscopy inside living tissues at depths hardly accessible by any other light-based technique. Even in the most advanced systems, the diffraction-limited foci scanning the object across the focal plane are contaminated by a stray optical signal carrying typically few tens of % of the total optical power. The stray illumination takes the shape of a randomised but reproducible speckle, and is unique for each position of the focus. We experimentally demonstrate that the performance of imaging a fluorescent object can be significantly improved, when resulting images are computationally post-processed, utilising records of intensities of all speckle-contaminated foci used in the imaging procedure. We present two algorithms based on a regularised iterative inversion and regularised direct pseudo-inversion respectively which lead to enhancement of the image contrast and resolution.

Analysis of Milk from Different Sources Based on Light Propagation and Random Laser Properties

Milk is a valuable contributor to a healthy diet as it contains nutritional components such as fats, proteins, carbohydrates, calcium, phosphorous and vitamins. This research aimed to differentiate milk from animal, plant and human sources based on light propagation and random-laser properties. Experimental, statistical and theoretical analyses were used. Light propagation in different types of milk such as almond milk, oat milk, soy milk, fresh milk, goat milk and human breast milk was measured using the spectrometry method. Near-IR and visible light transmission through the diluted milk samples were compared. Soy milk and fresh milk have the highest absorbance and fluorescence of light, respectively, due to a high content of fat, protein and carbohydrates. Principal component analysis was used to determine the accuracy of the experimental results. The research method is comprehensive as it covers light propagation from 350 nm to 1650 nm of wavelength range and non-intrusive as it does not affect the sample. Meanwhile, analysis of milk was also conducted based on random-laser properties such as multiple emission peaks and lasing threshold. Higher fat content in milk produces a lower random lasing threshold. Thus, we found that milk from animals, plants and humans can be analyzed using light absorption, fluorescence and random lasers. The research method might be useful for future study of milk contaminants that change the properties of milk.

Time-resolved detection of early-arriving ballistic waves in a quasi-diffusive regime

Ballistic waves directly carry image information in imaging through a scattering medium, but they are often obscured by much intense multiple-scattered waves. Detecting early arriving photons has been an effective method to extract ballistic waves in the transmission-mode imaging. However, it has been difficult to identify the temporal distribution of ballistic waves relative to the multiple scattering waves in the quasi-diffusive regime. Here, we present a method to separately quantify ballistic and multiple-scattered waves at their corresponding flight times even when multiple scattering is much stronger than the ballistic waves. This is realized by measuring the transmission matrix of an object embedded within scattering medium and comparing the coherent accumulation of ballistic waves with their incoherent addition. To further elucidate the temporal behavior of ballistic waves in quasi-diffusive regime, we analyze the flight time difference between ballistic and multiple-scattered waves and the effect of coherence gating on their relative intensities for the scattering medium of different thicknesses. The presented method to distinctively detect the temporal behavior of ballistic and multiple-scattered waves will lay a foundation to exploit multiple-scattered waves for deep-tissue imaging.

Compressive endoscopic imaging with complementary light modulation

We propose an effective endoscopic imaging method utilizing compressive sensing (CS) theory on the basis of complementary light modulation of a spatial light modulator. Both the simulated and the experimental results show that complementary compressive sensing (CCS) always needs less time to obtain better work than conventional CS with normal modulation at the same sampling rate. First, the speed of CCS is at least twice as fast as CS. Second, in comparison with CS, CCS can improve the signal-to-noise ratio of the reconstructed image by 49.7%, which indicates that this method is of great significance to endoscopic applications in terms of image fidelity and denoising performance.

Single-shot imaging through scattering media under strong ambient light interference

Speckle correlation imaging (SCI) has found tremendous versatility compared with other scattering imaging approaches due to its single-shot data acquisition strategy, relatively simple optical setup, and high-fidelity reconstruction performance. However, this simplicity requires SCI experiments to be performed strictly in a darkroom condition. As background noise increases, the speckle contrast rapidly decreases, making precise interpretation of the data extremely difficult. Here, we demonstrate a method by refining the speckle in the autocorrelation domain to achieve high-performance single-shot imaging. Experiment results prove that our method is adapted to estimate objects in a low signal-to-background ratio (SBR) circumstance even if the SBR is about -23dB. Laboratory and outdoor SCI experiments are performed.

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.