Memory effects in propagation of optical waves through disordered media

Weight of single and recurrent scattering in the reflection matrix of complex media

In a heterogeneous medium, the wave field can be decomposed as an infinite series known as the Born expansion. Each term of the Born expansion corresponds to a scattering order, it is thus theoretically possible to discriminate single and multiple scattering contribution to the field. Experimentally, what is actually measured is the total field in which all scattering orders interfere. Conventional imaging methods usually rely on the assumption that the multiple scattering contribution can be disregarded. In a back-scattering configuration, this assumption is valid for small depths, and begins to fail for depths larger than the scattering mean-free path ℓ_{s}. It is therefore a key issue to estimate the relative amount of single and multiple scattering in experimental data. To this end, a single-scattering estimator ρ[over ̂] computed from the reflection matrix has been introduced in order to assess the weight of single scattering in the backscattered wave field. In this paper, the meaning of this estimator is investigated and a particular attention is given to recurrent scattering. In a diffraction-limited experiment, a multiple scattering sequence is said to be recurrent if the first and last scattering events occur in the same resolution cell. Recurrent scattering is shown to be responsible for correlations between single scattering and higher scattering orders of the Born expansion, inducing a bias to the estimator ρ[over ̂] that should rather be termed confocal scattering ratio. Interestingly, a more robust estimator is built by projecting the reflection matrix in a focused basis. The argument is sustained by numerical simulations as well as ultrasonic data obtained around 1.5 MHz in a model medium made of nylon rods immersed in water. From a more general perspective, this work raises fundamental questions about the impact of recurrent scattering on wave imaging.

Remote laser-speckle sensing of heart sounds for health assessment and biometric identification

Assessment of heart sounds is the cornerstone of cardiac examination, but it requires a stethoscope, skills and experience, and a direct contact with the patient. We developed a contactless, machine-learning assisted method for heart-sound identification and quantification based on the remote measurement of the reflected laser speckle from the neck skin surface in healthy individuals. We compare the performance of this method to standard digital stethoscope recordings on an example task of heart-beat sound biometric identification. We show that our method outperforms the stethoscope even allowing identification on the test data taken on different days. This method might allow development of devices for remote monitoring of cardiovascular health in different settings.

A boundary migration model for imaging within volumetric scattering media

Effectively imaging within volumetric scattering media is of great importance and challenging especially in macroscopic applications. Recent works have demonstrated the ability to image through scattering media or within the weak volumetric scattering media using spatial distribution or temporal characteristics of the scattered field. Here, we focus on imaging Lambertian objects embedded in highly scattering media, where signal photons are dramatically attenuated during propagation and highly coupled with background photons. We address these challenges by providing a time-to-space boundary migration model (BMM) of the scattered field to convert the scattered measurements in spectral form to the scene information in the temporal domain using all of the optical signals. The experiments are conducted under two typical scattering scenarios: 2D and 3D Lambertian objects embedded in the polyethylene foam and the fog, which demonstrate the effectiveness of the proposed algorithm. It outperforms related works including time gating in terms of reconstruction precision and scattering strength. Even though the proportion of signal photons is only 0.75%, Lambertian objects located at more than 25 transport mean free paths (TMFPs), corresponding to the round-trip scattering length of more than 50 TMFPs, can be reconstructed. Also, the proposed method provides low reconstruction complexity and millisecond-scale runtime, which significantly benefits its application.

Imaging in scattering media is challenging due to signal attenuation and strong coupling of scattered and signal photons. The authors present a boundary migration model of the scattered field, converting scattered measurements in spectral form to scene information in temporal domain, and image Lambertian objects in highly scattering media.

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.

Investigation of image plane for image reconstruction of objects through diffusers via deep learning

SIGNIFICANCE

The imaging of objects hidden in light-scattering media is a vital practical task in a wide range of applications, including biological imaging. Deep-learning-based methods have been used to reconstruct images behind scattering media under complex scattering conditions, but improvements in the quality of the reconstructed images are required.

AIM

To investigate the effect of image plane on the accuracy of reconstructed images.

APPROACH

Light reflected from an object passing through glass diffusers is captured by changing the image plane of an optical imaging system. Images are reconstructed by deep learning, and evaluated in terms of structural similarity index measure, classification accuracy of digital images, and training and testing error curves.

RESULTS

The reconstruction accuracy was improved for the case in which the diffuser was imaged, compared to the case where the object was imaged. The training and testing error curves show that the loss converged to lower values in fewer epochs when the diffuser was imaged.

CONCLUSIONS

The proposed approach demonstrates an improvement in the accuracy of the reconstruction of objects hidden through glass diffusers by imaging glass diffuser surfaces, and can be applied to objects at unknown locations in a scattering medium.

Explicit-restriction convolutional framework for lensless imaging

Mask-based lensless cameras break the constraints of traditional lens-based cameras, introducing highly flexible imaging systems. However, the inherent restrictions of imaging devices lead to low reconstruction quality. To overcome this challenge, we propose an explicit-restriction convolutional framework for lensless imaging, whose forward model effectively incorporates multiple restrictions by introducing the linear and noise-like nonlinear terms. As examples, numerical and experimental reconstructions based on the limitation of sensor size, pixel pitch, and bit depth are analyzed. By tailoring our framework for specific factors, better perceptual image quality or reconstructions with 4× pixel density can be achieved. This proposed framework can be extended to lensless imaging systems with different masks or structures.

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.

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.

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.

Biocompatible Nanotomography of Tightly Focused Light

Tightly focusing a spatially modulated laser beam lays the foundations for advanced optical techniques, such as a holographic optical tweezer and deterministic super-resolution imaging. Precisely mapping the subwavelength features of those highly confined fields is critical to improving the spatial resolution, especially in highly scattering biotissues. However, current techniques characterizing focal fields are mostly limited to conditions such as under a vacuum and on a glass surface. An optical probe with low cytotoxicity and resistance to autofluorescence is the key to achieving in vivo applications. Here, we use a newly emerging quantum reference beacon, the nitrogen-vacancy (NV) center in the nanodiamond, to characterize the focal field of the near-infrared (NIR) laser focus in Caenorhabditis elegans (C. elegans). This biocompatible background-free focal field mapping technique has the potential to optimize in vivo optical imaging and manipulation.

3D imaging through a highly heterogeneous double-composite random medium by common-path phase-shift digital holography

A method is proposed for 3D imaging through a highly heterogeneous double-composite random medium made of a thick mildly inhomogeneous medium followed by a thin strongly scattering layer. To realize the immunity to the heterogeneous random medium, a system of common-path phase-shift digital holography is designed in such a manner that the wavefront distortion caused by the first inhomogeneous medium is canceled out by the common-path geometry, and the influence of the random phase introduced by the second scattering layer is removed by the intensity-based recording of the digital hologram on the thin scattering layer. The validity of the method was confirmed by experiments.

Image Reconstruction Using Autofocus in Single-Lens System

To reconstruct the wavefront in a single-lens coherent diffraction imaging (CDI) system, we propose a closed-loop cascaded iterative engine (CIE) algorithm based on the known information of the imaging planes. The precision of diffraction distance is an important prerequisite for a perfect reconstruction of samples. For coherent diffraction imaging with a lens, autofocus is investigated to accurately determine the object distance and image distance. For the case of only the object distance being unknown, a diffuser is used to scatter the coherent beam for speckle illumination to improve the performance of autofocus. The optimal object distance is obtained stably and robustly by combing speckle imaging with clarity evaluation functions. SSIM and MSE, using the average pixel value of the reconstructed data set as a reference, are applied on two-unknown-distance autofocus. Simulation and experiment results are presented to prove the feasibility of the CIE and proposed auto-focusing method.

Morphology and statistics of wide-spectrum speckles

Although the theory of scattered speckles was initially established via idealization of treating the incident light as monochromatic, phenomenon and regulations of wide-spectrum speckles are yet urgent to be studied, with immense growing applications of broadband source such as femtosecond laser, light-emitting-diode and sunlight illumination. Here we quantitatively analyze the morphology and statistics of speckles produced by a point-like source with wide-spectrum, using a phase plate model to describe the scattering layer. Due to differences in induced phase related to wavelength, wide-spectrum speckle patterns appear radial divergence in intensity distribution, as well as in visibility of both speckles and that of the second-order coherence. This is significantly different from the translation-invariance of monochromatic speckles. The spatially-varying morphology and statistics of the speckles contain spatial and spectral information of the incidence, thus can be used as an indicator to achieve optical metrology or sensing with a wide-spectrum source in the scattering environment.

Adaptive Wave-Front Shaping and Beam Focusing through Fiber Bundles for High-Resolution Bioimaging

We demonstrate an adaptive wave-front shaping of optical beams transmitted through fiber bundles as a powerful resource for multisite, high-resolution bioimaging. With the phases of all the beamlets delivered through up to 6000 different fibers within the fiber bundle controlled individually, by means of a high-definition spatial light modulator, the overall beam transmitted through the fiber bundle can be focused into a beam waist with a diameter less than 1 μm within a targeted area in a biotissue, providing a diffraction-limited spatial resolution adequate for single-cell or even subcellular bioimaging. The field intensity in the adaptively-focused continuous-wave laser beam in our fiber-bundle-imaging setting is more than two orders of magnitude higher than the intensity of the speckle background. Once robust beam focusing was achieved with a suitable phase profile across the input face of the fiber bundle, the beam focus can be scanned over a targeted area with no need for a further adaptive search, by applying a physically intuitive, wave-front-tilting phase mask on the field of input beamlets. This method of beam-focus scanning promises imaging speeds compatible with the requirements of in vivo calcium imaging.

Noninvasive imaging of two isolated objects through a thin scattering medium beyond the 3D optical memory effect by speckle-based difference strategy

The shape of two objects hidden behind a thin scattering medium is retrieved by the presented method. One of the two objects keeps stationary, while the other one is supposed to be gradually moving, and the Euclidean distance between them is always beyond the range of the 3D optical memory effect. We capture two speckle patterns to image the two isolated objects by using a developed speckle-differential-based strategy and the traditional speckle autocorrelation technique. The feasibility of our method is demonstrated by theoretical analysis and a set of experiments.

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.

Non-line-of-sight imaging under white-light illumination: a two-step deep learning approach

Non-line-of-sight (NLOS) imaging has received considerable attentions for its ability to recover occluded objects from an indirect view. Various NLOS imaging techniques have been demonstrated recently. Here, we propose a white-light NLOS imaging method that is equipped only with an ordinary camera, and not necessary to operate under active coherent illumination as in other existing NLOS systems. The central idea is to incorporate speckle correlation-based model into a deep neural network (DNN), and form a two-step DNN strategy that endeavors to learn the optimization of the scattered pattern autocorrelation and object image reconstruction, respectively. Optical experiments are carried out to demonstrate the proposed method.

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.

Cryptographic analysis on an optical random-phase-encoding cryptosystem for complex targets based on physics-informed learning

Optical cryptanalysis based on deep learning (DL) has grabbed more and more attention. However, most DL methods are purely data-driven methods, lacking relevant physical priors, resulting in generalization capabilities restrained and limiting practical applications. In this paper, we demonstrate that the double-random phase encoding (DRPE)-based optical cryptosystems are susceptible to preprocessing ciphertext-only attack (pCOA) based on DL strategies, which can achieve high prediction fidelity for complex targets by using only one random phase mask (RPM) for training. After preprocessing the ciphertext information to procure substantial intrinsic information, the physical knowledge DL method based on physical priors is exploited to further learn the statistical invariants in different ciphertexts. As a result, the generalization ability has been significantly improved by increasing the number of training RPMs. This method also breaks the image size limitation of the traditional COA method. Optical experiments demonstrate the feasibility and the effectiveness of the proposed learning-based pCOA method.

Polarization-based intensity correlation of a depolarized speckle pattern

A different kind of intensity correlation, denoted as polarization-based intensity correlation (PBIC), is proposed and demonstrated to investigate the correlation between different polarizations of a depolarized speckle pattern (DSP), which has non-uniform spatial polarization distribution. It is shown both theoretically and experimentally that the range of the PBIC for any polarization of the DSP depends on the spatial average intensity of the speckles corresponding to that particular polarization. The experimentally determined nature of the change of the range of the PBIC for different polarization components, due to the variation in the average intensity, is found to be matching well with the theoretical prediction. The existence of non-zero correlation between two orthogonally polarized speckle patterns, filtered from a partially DSP, is also observed. This study may be useful in exploiting the PBIC for different applications such as speckle cryptography.

Optical memory effect in square multimode fibers

We demonstrate experimentally the existence of a translational optical memory effect in square-core multimode fibers. We found that symmetry properties of square-core waveguides lead to speckle patterns shifting along four directions at the fiber output for any given shift direction at the input. A simple theoretical model based on a perfectly reflective square waveguide is introduced to predict and interpret this phenomenon. We report experimental results obtained with 532-nm coherent light propagating through a square-core step-index multimode fiber, demonstrating that this translational memory effect can be observed for shift distances up to typically 10 µm after propagation through several centimeters of fiber.

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.

Imaging through dynamical scattering media by two-photon absorption detectors

Imaging through a dynamical opaque scattering medium is an almost impossible task, where strong multiple light scattering from moving scatters dynamically prevents imaging formations even with state-of-art techniques like correlation imaging or adaptive optics. Meanwhile, a small number of ballistic photons can still penetrate through but require demanding detection in terms of a ultrashort time gate and high sensitivity. However, visible light is strongly scattered for most of scattering media. Here we experimentally demonstrate a non-invasive coherent imaging scheme based on two-photon absorption capable of imaging through dynamical scattering media with a length equivalent to 28 times mean free paths for single photon transport, where two-photon absorption in a conventional semiconductor photodetector when phase matching is not required works over a wide bandwidth so it can support a fast time gate down to femtosecond level, short enough to distinguish ballistic photons from scattering background, and allows accessing longer wavelengths for deeper penetration. This technique combined with successful optical coherence tomography may pave a new way for imaging through fog, storm, and rain as well as biomedical imaging applications.

Simultaneously improving multiple imaging parameters with scattering media

Traditional optical imaging systems can provide high-quality imaging with a complicated and expensive optical design by eliminating aberrations. With the help of an optical memory effect, rather than independently improving a single imaging parameter, the simultaneous improvement of several imaging parameters by adding scattering media to the imaging systems is, to the best of our knowledge, demonstrated for the first time. As an example, in a simple single lens imaging system, in addition to the depth of field being greatly improved, spherical aberration, coma aberration, and chromatic aberration are simultaneously eliminated by placing a scattering medium between the lens and the camera. The results indicate the potential applications of scattering media in many fields such as optical imaging, optical measurements, and biomedical applications.

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.

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.

Non-invasive super-resolution imaging through dynamic scattering media

Super-resolution imaging has been revolutionizing technical analysis in various fields from biological to physical sciences. However, many objects are hidden by strongly scattering media such as biological tissues that scramble light paths, create speckle patterns and hinder object’s visualization, let alone super-resolution imaging. Here, we demonstrate non-invasive super-resolution imaging through scattering media based on a stochastic optical scattering localization imaging (SOSLI) technique. After capturing multiple speckle patterns of photo-switchable point sources, our computational approach utilizes the speckle correlation property of scattering media to retrieve an image with a 100-nm resolution, an eight-fold enhancement compared to the diffraction limit. More importantly, we demonstrate our SOSLI to do non-invasive super-resolution imaging through not only static scattering media, but also dynamic scattering media with strong decorrelation such as biological tissues. Our approach paves the way to non-invasively visualize various samples behind scattering media at nanometer levels of detail.

The authors introduce stochastic optical scattering localization imaging (SOSLI) for non-invasive super-resolution imaging through scattering media. They capture multiple speckle patterns of photo-switchable point sources and use the speckle correlation to retrieve images with 100 nm resolution.

Single-pixel scatter-plate microscopy

Based on the optical memory effect of scattered light, we developed a new single-pixel camera concept. The retrieved images contain both 3D and spectral information about the sample. A spatial light modulator (SLM) generates a random intensity modulation. The signal recorded by the single-pixel detector is cross correlated by the calculated point spread function (PSF) signals of the SLM to retrieve the image. In this publication, both simulations and experimental results are presented.

Guidestar-free image-guided wavefront shaping

Optical imaging through scattering media is a fundamental challenge in many applications. Recently, breakthroughs such as imaging through biological tissues and looking around corners have been obtained via wavefront-shaping approaches. However, these require an implanted guidestar for determining the wavefront correction, controlled coherent illumination, and most often raster scanning of the shaped focus. Alternative novel computational approaches that exploit speckle correlations avoid guidestars and wavefront control but are limited to small two-dimensional objects contained within the "memory-effect" correlation range. Here, we present a new concept, image-guided wavefront shaping, allowing widefield noninvasive, guidestar-free, incoherent imaging through highly scattering layers, without illumination control. The wavefront correction is found even for objects that are larger than the memory-effect range, by blindly optimizing image quality metrics. We demonstrate imaging of extended objects through highly scattering layers and multicore fibers, paving the way for noninvasive imaging in various applications, from microscopy to endoscopy.

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.

Lensless inference camera: incoherent object recognition through a thin mask with LBP map generation

We propose a preliminary lensless inference camera (LLI camera) specialized for object recognition. The LLI camera performs computationally efficient data preprocessing on the optically encoded pattern through the mask, rather than performing computationally expensive image reconstruction before inference. Therefore, the LLI camera avoids expensive computation and achieves real-time inference. This work proposes a new data preprocessing approach, named local binary patterns map generation, dedicated for optically encoded pattern through the mask. This preprocessing approach greatly improves encoded pattern's robustness to local disturbances in the scene, making the LLI camera's practical application possible. The performance of the LLI camera is analyzed through optical experiments on handwritten digit recognition and gender estimation under conditions with changing illumination and a moving target.

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.

Three-dimensional broadband light beam manipulation in forward scattering samples

Focusing light into highly disordered biological tissue is a major challenge in optical microscopy and biomedical imaging due to scattering. However, correlations in the scattering matrix, known as "memory effects", can be used to improve imaging capabilities. Here we discuss theoretically and numerically the possibility to achieve three-dimensional ultrashort laser focusing and scanning inside forward scattering media, beyond the scattering mean free path, by simultaneously taking advantage of the angular and the chromato-axial memory effects. The numerical model is presented in details, is validated within the state of the art theoretical and experimental framework and is finally used to propose a scheme for focusing ultra-short laser pulses in depth through forward scattering media.

Preventing forgery attacks in computational ghost imaging or disabling ghost imaging in a "spatiotemporal" scattering medium with weighted multiplicative signals

The ghost imaging (GI) approach is an intriguing and promising image acquisition technique that can transmit high-quality image information in a scattering environment. In this paper, we focus on two concerns recently emerged in the GI modality: one is the vulnerability to forgery attacks in GI-based optical encryption [Opt. Lett.45, 3917 (2020)OPLEDP0146-959210.1364/OL.392424], and the other is the potential threat of GI to personal privacy regarding non-invasive imaging [Opt. Express28, 17232 (2020)OPEXFF1094-408710.1364/OE.391788]. The core idea is to recommend introducing weighted multiplicative signals [Opt. Express27, 36505 (2019)OPEXFF1094-408710.1364/OE.27.036505] into the computational GI system, whether on the transmitting end or the receiving end. At the transmitting end, the random multiplicative signal can be used as an additional key that can reduce the possibility of forgery attacks, thereby increasing image transmission security. On the receiving end, the introduction of a random multiplicative signal to a spatial scattering medium makes it a "spatiotemporal" scattering medium, whose transmittance changes with time. Further, the spatiotemporal scattering medium can disable direct imaging and GI at the same time with low cost, thereby having great potential in privacy protection in daily lives.

Scatter-plate microscopy with spatially coherent illumination and temporal scatter modulation

Scatter-plate microscopy (SPM) is a lensless imaging technique for high-resolution imaging through scattering media. So far, the method was demonstrated for spatially incoherent illumination and static scattering media. In this publication, we demonstrate that these restrictions are not necessary. We realized imaging with spatially coherent and spatially incoherent illumination. We further demonstrate that SPM is still a valid imaging method for scatter-plates, which change their scattering behaviour (i.e. the phase-shift) at each position on the plate continuously but independently from other positions. Especially we realized imaging through rotating ground glass diffusers.

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.

In situ measurement of the isoplanatic patch for imaging through intact bone

Wavefront-shaping (WS) enables imaging through scattering tissues like bone, which is important for neuroscience and bone-regeneration research. WS corrects for the optical aberrations at a given depth and field-of-view (FOV) within the sample; the extent of the validity of which is limited to a region known as the isoplanatic patch (IP). Knowing this parameter helps to estimate the number of corrections needed for WS imaging over a given FOV. In this paper, we first present direct transmissive measurement of murine skull IP using digital optical phase conjugation based focusing. Second, we extend our previously reported phase accumulation ray tracing (PART) method to provide in-situ in-silico estimation of IP, called correlative PART (cPART). Our results show an IP range of 1 to 3 μm for mice within an age range of 8 to 14 days old and 1.00 ± 0.25 μm in a 12-week old adult skull. Consistency between the two measurement approaches indicates that cPART can be used to approximate the IP before a WS experiment, which can be used to calculate the number of corrections required within a given field of view.

Deconvolved Image Restoration From Auto-Correlations

The recovery of a real signal from its auto-correlation is a wide-spread problem in computational imaging, and it is equivalent to retrieve the phase linked to a given Fourier modulus. Image-deconvolution, on the other hand, is a funda- mental aspect to take into account when we aim at increasing the resolution of blurred signals. These problems are addressed separately in a large number of experimental situations, ranging from adaptive astronomy to optical microscopy. Here, instead, we tackle both at the same time, performing auto-correlation inversion while deconvolving the current object estimation. To this end, we propose a method based on I -divergence optimization, turning our formalism into an iterative scheme inspired by Bayesian-based approaches. We demonstrate the method by recovering sharp signals from blurred auto-correlations, regardless of whether the blurring acts in auto-correlation, object, or Fourier domain.

Pump-shaping of non-collinear and non-degenerate entangled photons

Free-space quantum key distribution is gaining increasing interest as a leading platform for long range quantum communication. However, the sensitivity of quantum correlations to scattering induced by turbulent atmospheric links limits the performance of such systems. Recently, a method for compensating for the scattering of entangled photons was demonstrated, allowing for real-time optimization of their quantum correlations. In this Letter, we demonstrate the use of wavefront shaping for compensating for the scattering of non-collinear and non-degenerate entangled photons. These results demonstrate the applicability of wavefront shaping schemes for protocols utilizing the large bandwidth and emission angle of the entangled photons.

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.

Particle-Based Reconfigurable Scattering Masks for Lensless Imaging

Light scattering is typically undesired in optical systems as it often introduces defects or otherwise negatively impacts device performance. However, rather than being a hindrance, scattering can also be exploited to achieve lensless imaging using a scattering mask instead of lenses to enable devices with low-cost, compact construction, and yet a large field of view. Lensless imaging can benefit greatly from the ability to dynamically tune the scattering pattern produced by the mask; however, this often results in increased complexity and cost. Herein, we propose and demonstrate particle-based reconfigurable scattering masks to dynamically tune light scattering for lensless imaging, enabling multishot image reconstruction. Disordered particle populations are tuned by rational application of electric fields without requiring bulky or expensive components. Several assembly motifs are explored and studied for optimal performance; in particular, gold nanowires chained between planar electrodes yield the best reconstruction quality and are the main focus in this study. The distinct gold nanowire based scattering masks achieve a complex wavelet structural similarity as low as 0.36. By leveraging the submicrometer thickness of particles and the resultant large optical memory effect, an angular field of view of ±45° is demonstrated. The reconfigurable nature of the particle arrays enables multishot reconstruction which results in enhanced image quality and improved signal-to-noise ratios by up to 10-fold. These results suggest that reconfigurable particle masks could be a broadly applicable means of achieving dynamically tunable light scattering with potential applications in lensless microscopy or high-resolution imaging.

Quantitative analysis of hidden particles diffusing behind a scattering layer using speckle correlation

Speckle-correlation imaging is a family of methods that makes use of the "memory effect" to image objects hidden behind visually opaque layers. Here, we show that a correlation analysis can be applied to quantitative imaging of an ensemble of dynamic fluorescent beads diffusing on a 2D surface. We use an epi-fluorescence microscope where both the illumination and detection light patterns are speckled, due to light scattering by a thin disordered layer. The spatio-temporal cross-correlation of the detection speckle pattern is calculated as a function of lag time and spatial shift and is used to determine the diffusion constant and number of fluorescent particles in the sample without requiring any phase retrieval procedure. It is worth to note that the "memory effect" range is not required to extend beyond a distance of few speckle grains, thus making our method potentially useful for nearly arbitrary values of the thickness of the scattering layer.

100,000 frames-per-second compressive imaging with a conventional rolling-shutter camera by random point-spread-function engineering

We demonstrate an approach that allows taking videos at very high frame-rates of over 100,000 frames per second by exploiting the fast sampling rate of the standard rolling-shutter readout mechanism, common to most conventional sensors, and a compressive-sampling acquisition scheme. Our approach is directly applied to a conventional imaging system by the simple addition of a diffuser to the pupil plane that randomly encodes the entire field-of-view to each camera row, while maintaining diffraction-limited resolution. A short video is reconstructed from a single camera frame via a compressed-sensing reconstruction algorithm, exploiting the inherent sparsity of the imaged scene.

Non-invasive single-shot recovery of a point-spread function of a memory effect based scattering imaging system

Accessing the point-spread function (PSF) of a complex optical system is important for a variety of imaging applications. However, placing an invasive point source is often impractical, and estimating it blindly with multiple frames is slow and requires a complex nonlinear optimization. Here, we introduce a simple single-shot method to noninvasively recover the accurate PSF of an isoplanatic imaging system, in the context of multiple light scattering. Our approach is based on the reconstruction of any unknown sparse hidden object using the autocorrelation imaging technique, followed by a deconvolution with a blur kernel derived from the statistics of a speckle pattern. A deconvolution on the camera image then retrieves the accurate PSF of the system, enabling further imaging applications. We demonstrate numerically and experimentally the effectiveness of this approach compared to previous deconvolution techniques.

Real-time shaping of entangled photons by classical control and feedback

Quantum technologies hold great promise for revolutionizing photonic applications such as cryptography. Yet, their implementation in real-world scenarios is challenging, mostly because of sensitivity of quantum correlations to scattering. Recent developments in optimizing the shape of single photons introduce new ways to control entangled photons. Nevertheless, shaping single photons in real time remains a challenge due to the weak associated signals, which are too noisy for optimization processes. Here, we overcome this challenge and control scattering of entangled photons by shaping the classical laser beam that stimulates their creation. We discover that because the classical beam and the entangled photons follow the same path, the strong classical signal can be used for optimizing the weak quantum signal. We show that this approach can increase the length of free-space turbulent quantum links by up to two orders of magnitude, opening the door for using wavefront shaping for quantum communications.

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

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

Optical flow optical coherence tomography for determining accurate velocity fields

Determining micron-scale fluid flow velocities using optical coherence tomography (OCT) is important in both biomedical research and clinical diagnosis. Numerous methods have been explored to quantify the flow information, which can be divided into either phase-based or amplitude-based methods. However, phase-based methods, such as Doppler methods, are less sensitive to transverse velocity components and suffer from wrapped phase and phase instability problems for axial velocity components. On the other hand, amplitude-based methods, such as speckle variance OCT, correlation mapping OCT and split-spectrum amplitude-decorrelation angiography, focus more on segmenting flow areas than quantifying flow velocities. In this paper, we propose optical flow OCT (OFOCT) to quantify accurate velocity fields. The equivalence between optical flow and real velocity fields is validated in OCT imaging. The sensitivity fall-off of a Fourier-domain OCT (FDOCT) system is considered in the modified optical flow continuity constraint. Spatial-temporal smoothness constraints are used to make the optical flow problem well-posed and reduce noises in the velocity fields. An iteration solution to the optical flow problem is implemented in a graphics processing unit (GPU) for real-time processing. The accuracy of the velocity fields is verified through phantom flow experiments by using a diluted milk powder solution as a scattering medium. Velocity fields are then used to detect flow turbulence and reconstruct flow trajectory. The results show that OFOCT is accurate in determining velocity fields and applicable to research concerning fluid dynamics.

PhlatCam: Designed Phase-Mask Based Thin Lensless Camera

We demonstrate a versatile thin lensless camera with a designed phase-mask placed at sub-2 mm from an imaging CMOS sensor. Using wave optics and phase retrieval methods, we present a general-purpose framework to create phase-masks that achieve desired sharp point-spread-functions (PSFs) for desired camera thicknesses. From a single 2D encoded measurement, we show the reconstruction of high-resolution 2D images, computational refocusing, and 3D imaging. This ability is made possible by our proposed high-performance contour-based PSF. The heuristic contour-based PSF is designed using concepts in signal processing to achieve maximal information transfer to a bit-depth limited sensor. Due to the efficient coding, we can use fast linear methods for high-quality image reconstructions and switch to iterative nonlinear methods for higher fidelity reconstructions and 3D imaging.

Distortion matrix approach for ultrasound imaging of random scattering media

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

Compressive Sensing Imaging Based on Modulation of Atmospheric Scattering Medium

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