Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle

All-optical phase conjugation using diffractive wavefront processing

Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with applications ranging from imaging to beam focusing. Here, we present a diffractive wavefront processor to approximate all-optical phase conjugation. Leveraging deep learning, a set of diffractive layers was optimized to all-optically process an arbitrary phase-aberrated input field, producing an output field with a phase distribution that is the conjugate of the input wave. We experimentally validated this wavefront processor by 3D-fabricating diffractive layers and performing OPC on phase distortions never seen during training. Employing terahertz radiation, our diffractive processor successfully performed OPC through a shallow volume that axially spans tens of wavelengths. We also created a diffractive phase-conjugate mirror by combining deep learning-optimized diffractive layers with a standard mirror. Given its compact, passive and multi-wavelength nature, this diffractive wavefront processor can be used for various applications, e.g., turbidity suppression and aberration correction across different spectral bands.

Single-pixel transmission matrix recovery via two-photon fluorescence

Imaging at depth in opaque materials has long been a challenge. Recently, wavefront shaping has enabled notable advance for deep imaging. Nevertheless, most noninvasive wavefront-shaping methods require cameras, lack the sensitivity for deep imaging under weak optical signals, or can only focus on a single "guidestar." Here, we retrieve the transmission matrix (TM) noninvasively using two-photon fluorescence exploiting a single-pixel detection combined with a computational framework, allowing to achieve single-target focus on multiple guidestars spread beyond the memory effect range. In addition, if we assume that memory effect correlations exist in the TM, we are able to substantially reduce the number of measurements needed.

Spatial pilot-aided fast-adapted framework for stable image transmission over long multi-mode fiber

Multi-mode fiber (MMF) has emerged as a promising platform for spatial information transmission attributed to its high capacity. However, the scattering characteristic and time-varying nature of MMF pose challenges for long-term stable transmission. In this study, we propose a spatial pilot-aided learning framework for MMF image transmission, which effectively addresses these challenges and maintains accurate performance in practical applications. By inserting a few reference image frames into the transmitting image sequence and leveraging a fast-adapt network training scheme, our framework adaptively accommodates to the physical channel variations and enables online model update for continuous transmission. Experimented on 100 m length unstable MMFs, we demonstrate transmission accuracy exceeding 92% over hours, with pilot frame overhead around 2%. Our fast-adapt learning scheme requires training of less than 2% of network parameters and reduces the computation time by 70% compared to conventional tuning approaches. Additionally, we propose two pilot-insertion strategies and elaborately compare their applicability to a wide range of scenarios including continuous transmission, burst transmission and transmission after fiber re-plugging. The proposed spatial pilot-aided fast-adapt framework opens up the possibility for MMF spatial transmission in practical complicated applications.

Extrapolated speckle-correlation imaging with an untrained deep neural network

We present a method for speckle-correlation imaging with an extended field of view to observe spatially non-sparse objects. In speckle-correlation imaging, an object is recovered from a non-invasively captured image through a scattering medium by assuming shift-invariance of the optical process called the memory effect. The field of view of speckle-correlation imaging is limited by the size of the memory effect, and it can be extended by extrapolating the speckle correlation in the reconstruction process. However, spatially sparse objects are assumed in the inversion process because of its severe ill-posedness. To address this issue, we introduce a deep image prior, which regularizes the image statistics by using the structure of an untrained convolutional neural network, to speckle-correlation imaging. We experimentally demonstrated the proposed method and showed the possibility of extending the method to imaging through scattering media.

Functional imaging through scattering medium via fluorescence speckle demixing and localization

Recently, fluorescence-based optical techniques have emerged as a powerful tool to probe information in the mammalian brain. However, tissue heterogeneities prevent clear imaging of deep neuron bodies due to light scattering. While several up-to-date approaches based on ballistic light allow to retrieve information at shallow depths inside the brain, non-invasive localization and functional imaging at depth still remains a challenge. It was recently shown that functional signals from time-varying fluorescent emitters located behind scattering samples could be retrieved by using a matrix factorization algorithm. Here we show that the seemingly information-less, low-contrast fluorescent speckle patterns recovered by the algorithm can be used to locate each individual emitter, even in the presence of background fluorescence. We test our approach by imaging the temporal activity of large groups of fluorescent sources behind different scattering phantoms mimicking biological tissues, and through a brain slice with a thickness of ∼200 µm.

Optical focusing inside scattering media with iterative time-reversed ultrasonically encoded near-infrared light

Focusing light inside scattering media is a long-sought goal in optics. Time-reversed ultrasonically encoded (TRUE) focusing, which combines the advantages of biological transparency of the ultrasound and the high efficiency of digital optical phase conjugation (DOPC) based wavefront shaping, has been proposed to tackle this problem. By invoking repeated acousto-optic interactions, iterative TRUE (iTRUE) focusing can further break the resolution barrier imposed by the acoustic diffraction limit, showing great potential for deep-tissue biomedical applications. However, stringent requirements on system alignment prohibit the practical use of iTRUE focusing, especially for biomedical applications at the near-infrared spectral window. In this work, we fill this blank by developing an alignment protocol that is suitable for iTRUE focusing with a near-infrared light source. This protocol mainly contains three steps, including rough alignment with manual adjustment, fine-tuning with a high-precision motorized stage, and digital compensation through Zernike polynomials. Using this protocol, an optical focus with a peak-to-background ratio (PBR) of up to 70% of the theoretical value can be achieved. By using a 5-MHz ultrasonic transducer, we demonstrated the first iTRUE focusing using near-infrared light at 1053 nm, enabling the formation of an optical focus inside a scattering medium composed of stacked scattering films and a mirror. Quantitatively, the size of the focus decreased from roughly 1 mm to 160 µm within a few consecutive iterations and a PBR up to 70 was finally achieved. We anticipate that the capability of focusing near-infrared light inside scattering media, along with the reported alignment protocol, can be beneficial to a variety of applications in biomedical optics.

Light scattering control with the two-step focusing method based on neural networks and multi-pixel coding

Focusing light through scattering media is essential for high-resolution optical imaging and deep penetration. Here, a two-step focusing method based on neural networks (NNs) and multi-pixel coding is proposed to achieve high-quality focusing with theoretical maximum enhancement. In the first step, a single-layer neural network (SLNN) is used to obtain the initial mask, which can be used to focus with a moderate enhancement. In the second step, we use multi-pixel coding to encode the initial mask. The coded masks and their corresponding speckle patterns are used to train another SLNN to get the final mask and achieve high-quality focusing. In this experiment, for a mask of 16 × 16 modulation units, in the case of using 8 pixels in a modulation unit, focus with the enhancement of 40.3 (only 0.44 less than the theoretical value) has been achieved with 3000 pictures (1000 pictures in the first step and 2000 pictures in the second step). Compared with the case of employing only the initial mask and the direct multi-pixel encoded mask, the enhancement is increased by 220% and 24%. The proposed method provides a new idea for improving the focusing effect through the scattering media using NNs.

Speedy light focusing through scattering media by a cooperatively FPGA-parameterized genetic algorithm

We developed an accelerated Genetic Algorithm (GA) system based on the cooperation of a field-programmable gate array (FPGA) and the optimized parameters that enables fast light focusing through scattering media. Starting at the searching space, which influences the convergence of the optimization algorithms, we manipulated the mutation rate that defines the number of mutated pixels on the spatial light modulator to accelerate the GA process. We found that the enhanced decay ratio of the mutation rate leads to a much faster convergence of the GA. A convergence-efficiency function was defined to gauge the tradeoff between the processing time and the enhancement of the focal spot. This function allowed us to adopt the shorter iteration number of the GA that still achieves applicable light focusing. Furthermore, the accelerated GA configuration was programmed in FPGA to boost processing speed at the hardware level. It shows the ability to focus light through scattering media within a few seconds, 150 times faster than the PC-based GA. The processing cycle could be further promoted to a millisecond-level with the advanced FPGA processor chips. This study makes the evolution-based optimization approach adaptable in dynamic scattering media, showing the capability to tackle wavefront shaping in biological material.

Photonic Assemblies of Randomly Oriented Nanocrystals for Engineered Nonlinear and Electro-Optic Effects

Nonlinear crystals that have a noncentrosymmetric crystalline structure, such as lithium niobate (LiNbO₃) and barium titanate (BaTiO₃) exhibit nonzero second-order tensor susceptibilities (χ⁽²⁾) and linear electro-optic coefficients (r _ij ). The constraints associated with top-down nanofabrication methods have led to bottom up approaches to harness the strong nonlinearities and electro-optical properties. Here, we present an overview of photonic assemblies made of randomly oriented noncentrosymmetric nanocrystals via bottom-up fabrication methods. In this configuration, nanocrystals can form objects with tunable dimensions, increased complexity, and a great span of symmetry level, ranging from thin layers to spheres. At the same time, according to their shape, photonic assemblies may support optical modes, that is, Mie or guided, which can tailor linear optical properties and enhance nonlinear and electro-optic responses. As a result, assemblies of noncentrosymmetric nanocrystals can form a disruptive platform to realize photonic integrated devices free of etching process and over large surface areas. Last, we foresee potential applications of noncentrosymmetric nanocrystals in various fields of nano-optics and sensing.

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.

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.

Characterization of the spectral memory effect of scattering media

The optical memory effect is an interesting phenomenon exploited for deep-tissue optical imaging. Besides the widely studied memory effects in the spatial domain to accelerate point scanning speed, the spectral memory effect is also important in multispectral wavefront shaping. Although being theoretically analyzed for decades, quantitative studies of spectral memory effect on a variety of scattering media including biological tissue were rarely reported. In practice, quantifying the range of the spectral memory effect is essential in efficiently shaping broadband light, as it determines the optimum spectral resolution in realizing spatiotemporal focus through scattering media. In this work, we analyze the spectral memory effect based on a diffusion model. An explicit analytical expression involves the illumination wavelength, the diffusion constant, and the sample thickness is derived, which is consistent with the one in the literature. We experimentally quantified the range of spectral correlation for two types of biological tissue, tissue-mimicking phantoms with different concentrations, and diffusers. Specifically, for tissue-mimicking phantoms with calibrated scattering parameters, we show that a correction factor of more than 20 should be inserted, indicating that the range of spectral correlation is much larger than one would expect. This finding is particularly beneficial to multispectral wavefront shaping, as stringent requirements on the spectral resolution could be alleviated by at least one order of magnitude.

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.

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

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

Sound Out the Deep Colors: Photoacoustic Molecular Imaging at New Depths

Photoacoustic tomography (PAT) has become increasingly popular for molecular imaging due to its unique optical absorption contrast, high spatial resolution, deep imaging depth, and high imaging speed. Yet, the strong optical attenuation of biological tissues has traditionally prevented PAT from penetrating more than a few centimeters and limited its application for studying deeply seated targets. A variety of PAT technologies have been developed to extend the imaging depth, including employing deep-penetrating microwaves and X-ray photons as excitation sources, delivering the light to the inside of the organ, reshaping the light wavefront to better focus into scattering medium, as well as improving the sensitivity of ultrasonic transducers. At the same time, novel optical fluence mapping algorithms and image reconstruction methods have been developed to improve the quantitative accuracy of PAT, which is crucial to recover weak molecular signals at larger depths. The development of highly-absorbing near-infrared PA molecular probes has also flourished to provide high sensitivity and specificity in studying cellular processes. This review aims to introduce the recent developments in deep PA molecular imaging, including novel imaging systems, image processing methods and molecular probes, as well as their representative biomedical applications. Existing challenges and future directions are also discussed.

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

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

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

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

Full-polarization wavefront shaping for imaging through scattering media

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

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

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

Dynamic conjugate F-SHARP microscopy

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

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

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

Spatial light modulator aided noninvasive imaging through scattering layers

We propose and demonstrate a new imaging technique to noninvasively see through scattering layers with the aid of a spatial light modulator (SLM). A relay system projects the incoherent light pattern emitting from the scattering layer onto the SLM. Two coded phase masks are displayed, one after another, on the SLM to modulate the projected scattered field and the two corresponding intensity patterns are recorded by a digital camera. The above procedure helps to achieve two goals. Firstly, since the coded phase masks are digitally synthesized, the point spread function of the imaging system can be engineered such that the image retrieval becomes more reliable. Secondly, the two recorded intensity patterns are subtracted one from the other and by that the background noise of the recovered image is minimized. The above two advantages along with a modified phase retrieval algorithm enable a relatively easier and accurate convergence to the image of the covered object.

Imaging hair cells through laser-ablated cochlear bone

We report an innovative technique for the visualization of cells through an overlying scattering medium by combining femtosecond laser bone ablation and two-photon excitation fluorescence (TPEF) microscopy. We demonstrate the technique by imaging hair cells in an intact mouse cochlea ex vivo. Intracochlear imaging is important for the assessment of hearing disorders. However, the small size of the cochlea and its encasement in the densest bone in the body present challenging obstacles, preventing the visualization of the intracochlear microanatomy using standard clinical imaging modalities. The controlled laser ablation reduces the optical scattering of the cochlear bone while the TPEF allows visualization of individual cells behind the bone. We implemented optical coherence tomography (OCT) simultaneously with the laser ablation to enhance the precision of the ablation and prevent inadvertent damage to the cells behind the bone.

Light focusing through scattering media via linear fluorescence variance maximization, and its application for fluorescence imaging

We demonstrate focusing and imaging through a scattering medium without access to the fluorescent object by using wavefront shaping. Our concept is based on utilizing the spatial fluorescence contrast which naturally exists in the hidden target object. By scanning the angle of incidence of the illuminating laser beam and maximizing the variation of the detected fluorescence signal from the object, as measured by a bucket detector at the front of the scattering medium, we are able to generate a tightly focused excitation spot. Thereafter, an image is obtained by scanning the focus over the object within the memory effect range. The requirements for applicability of the method and the comparison with speckle-correlation based focusing methods are discussed.

Speckle rotation decorrelation based single-shot video through scattering media

Optical imaging and tracking moving objects through scattering media is a challenge with important applications. However, previous works suffer from time-consuming recovery process, object complexity limit, or object information lost. Here we present a method based on the speckle rotation decorrelation property. The rotational speckles detected at short intervals are uncorrelated and multiplexed in a single-shot camera image. Object frames of the video are recovered by cross-correlation deconvolution of the camera image with a computationally rotated point spread function. The near real-time recovery provides sharp object image frames with accurate object relative positions, exact movement velocity, and continuous motion trails. This multiplexing technique has important implications for a wide range of real-world imaging scenarios.

Evaluation of the Returned Electromagnetic Signal from Retro-reflectors in Turbid Media

We provide first-principle theoretical and numerical simulations using the coherent Transfer Matrix Approach (TMA) to describe the behavior of the three main class of the optical beacons namely phase conjugators, reflectors, and retroreflectors within a turbid medium. Our theory describes the extraordinary enhancement (about 5 dB) offered by retroreflectors compared to reflectors in our detailed experiments and shows that they effectively act as local optical phase conjugators. Moreover, the performance of retroreflectors shows little degradation for increased light incident angles in turbid media, while the performance of reflectors degrades drastically. These results may find applications for detection of the echoes of electromagnetic radiation in turbid media.

Rapid wide-field imaging through scattering media by digital holographic wavefront correction

Imaging through scattering media has been a long standing challenge in many disciplines. One of the promising solutions to address the challenge is the wavefront shaping technique, in which the phase distortion due to a scattering medium is corrected by a phase modulation device such as a spatial light modulator (SLM). However, the wide-field imaging speed is limited either by the feedback-based optimization to search the correction phase or by the update rate of SLMs. In this report, we introduce a new method called digital holographic wavefront correction, in which the correction phase is determined by a single-shot off-axis holography. The correction phase establishes the so-called "scattering lens", which allows any objects to be imaged through scattering media; in our case, the "scattering lens" is a digital one established through computational methods. As no SLM is involved in the imaging process, the imaging speed is significantly improved. We have demonstrated that moving objects behind scattering media can be recorded at the speed of 2.8 fps with each frame corrected by the updated correction phase while the image contrast is maintained as high as 0.9. The image speed can potentially reach the video rate if the computing power is sufficiently high. We have also demonstrated that the digital wavefront correction method also works when the light intensity is low, which implicates its potential usefulness in imaging dynamic processes in biological tissues.

Controlling 1550-nm light through a multimode fiber using a Hadamard encoding algorithm

To meet the demand for higher capacity fiber-optic communication, multimode fibers have gradually attracted attention, but they introduce spatial distortions. To overcome this limitation, wavefront shaping technology promises to control scattered light after it is transmitted through multimode fibers. In this work, we introduce a Hadamard encoding algorithm (HEA) to control 1550-nm light that has passed through a multimode fiber. A series of Hadamard bases is iteratively added to the current optimum phase map, and the coefficient of each order is determined through a simple four-step phase-shifting mechanism. Using a laser source at 1550-nm wavelength, we experimentally achieved an optical focus through a 2-meter-long multimode fiber. With 1024 orders, the experimental enhancement reached 690, which is 86% of the theoretical value. As far as we know, this is the best result ever reported in focusing 1550-nm light through a multimode fiber. Moreover, we note that the HEA can also be used to reduce the intensity of the targeted light, suggesting broad applications in glare suppression. These results demonstrate superior performance in controlling targeted light transport through a multimode fiber at a telecommunication wavelength. We anticipate that this work will open new possibilities in a variety of applications in fiber optics.

Single-shot coherent power-spectrum imaging of objects hidden by opaque scattering media

We report coherent imaging of objects behind opaque scattering media with only one piece of the power spectrum pattern. We solve the unique solution and improve algorithm speed for the inverse problem. Based on the proposed scattering-disturbance model, with only one piece of the Fourier transform power spectrum pattern under coherent illumination, we successfully reconstruct clear images of the objects fully hidden by an opaque diffuser. The experimental results demonstrate the feasibility of the reconstruction method and the scattering-disturbance model. Our method makes it possible to carry out snapshot coherent imaging of the objects obscured by scattering media, which extends the methodology of x-ray crystallography to visible-light scattering imaging for underwater and living biomedical imaging.

Bidirectional image transmission through physically thick scattering media using digital optical phase conjugation

We demonstrate the feasibility of bidirectional image transmission through a physically thick scattering medium within its memory effect range by digital optical phase conjugation. We show the bidirectional transmission is not simply the consequence of optical reciprocity. We observe that when the spatial light modulator (the device performing the digital optical phase conjugation) is relayed to the middle plane of the medium, the memory effect will be fully exploited and thus the transmitted images will have maximum field of view (FOV). Furthermore, we show that the FOV can be expanded n times by performing n times wavefront measurements.

Light scattering control in transmission and reflection with neural networks

Scattering often limits the controlled delivery of light in applications such as biomedical imaging, optogenetics, optical trapping, and fiber-optic communication or imaging. Such scattering can be controlled by appropriately shaping the light wavefront entering the material. Here, we develop a machine-learning approach for light control. Using pairs of binary intensity patterns and intensity measurements we train neural networks (NNs) to provide the wavefront corrections necessary to shape the beam after the scatterer. Additionally, we demonstrate that NNs can be used to find a functional relationship between transmitted and reflected speckle patterns. Establishing the validity of this relationship, we focus and scan in transmission through opaque media using reflected light. Our approach shows the versatility of NNs for light shaping, for efficiently and flexibly correcting for scattering, and in particular the feasibility of transmission control based on reflected light.

Reconstruction of structured laser beams through a multimode fiber based on digital optical phase conjugation

The digital optical phase conjugation (DOPC) technique is being actively developed for optical focusing and imaging through or inside complex media. Due to its time-reversal nature, DOPC has been exploited to regenerate different intensity targets. However, whether the targets with three-dimensional information through complex media could be recovered has not been experimentally demonstrated, to the best of our knowledge. Here, we present a method to regenerate structured laser beams based on DOPC. Although only the phase of the original scattered wave is time reversed, the reconstruction of a quasi-Bessel beam and vortex beams through a multimode fiber (MMF) is demonstrated. The regenerated quasi-Bessel beam shows the features of sub-diffraction focusing and a longer depth of field with respect to a Gaussian beam. Moreover, the reconstruction of vortex beams shows the fidelity of DOPC both in amplitude and phase, which is demonstrated for the first time, to the best of our knowledge. We also prove that the reconstruction results of DOPC through the MMF are indeed phase conjugate to the original targets. We expect that these results could be useful in super-resolution imaging and optical micromanipulation through complex media, and further pave the way for achieving three-dimensional imaging based on DOPC.

Non-invasive imaging through strongly scattering media based on speckle pattern estimation and deconvolution

Imaging through scattering media is still a formidable challenge with widespread applications ranging from biomedical imaging to remote sensing. Recent research progresses provide several feasible solutions, which are hampered by limited complexity of targets, invasiveness of data collection process and lack of robustness for reconstruction. In this paper, we show that the complex to-be-observed targets can be non-invasively reconstructed with fine details. Training targets, which can be directly reconstructed by speckle correlation and phase retrieval, are utilized as the input of the proposed speckle pattern estimation model, in which speckle modeling and constrained least square optimization are applied to estimate the distribution of the speckle pattern. Reconstructions for to-be-observed targets are realized by deconvoluting the estimated speckle pattern from the acquired integrated intensity matrices (IIMs). The qualities of reconstructed results are ensured by the stable statistical property and memory effect of laser speckle patterns. Experimental results show that the proposed method can reconstruct complex targets in high quality and the reconstruction performance is robust even much less data are acquired.

Imaging of objects through a thin scattering layer using a spectrally and spatially separated reference

Incoherently illuminated or luminescent objects give rise to a low-contrast speckle-like pattern when observed through a thin diffusive medium, as such a medium effectively convolves their shape with a speckle-like point spread function (PSF). This point spread function can be extracted in the presence of a reference object of known shape. Here it is shown that reference objects that are both spatially and spectrally separated from the object of interest can be used to obtain an approximation of the point spread function. The crucial observation, corroborated by analytical calculations, is that the spectrally shifted point spread function is strongly correlated to a spatially scaled one. With the approximate point spread function thus obtained, the speckle-like pattern is deconvolved to produce a clear and sharp image of the object on a speckle-like background of low intensity.

Time-reversed magnetically controlled perturbation (TRMCP) optical focusing inside scattering media

Manipulating and focusing light deep inside biological tissue and tissue-like complex media has been desired for long yet considered challenging. One feasible strategy is through optical wavefront engineering, where the optical scattering-induced phase distortions are time reversed or pre-compensated so that photons travel along different optical paths interfere constructively at the targeted position within a scattering medium. To define the targeted position, an internal guidestar is needed to guide or provide a feedback for wavefront engineering. It could be injected or embedded probes such as fluorescence or nonlinear microspheres, ultrasonic modulation, as well as absorption perturbation. Here we propose to use a magnetically controlled optical absorbing microsphere as the internal guidestar. Using a digital optical phase conjugation system, we obtained sharp optical focusing within scattering media through time-reversing the scattered light perturbed by the magnetic microsphere. Since the object is magnetically controlled, dynamic optical focusing is allowed with a relatively large field-of-view by scanning the magnetic field externally. Moreover, the magnetic microsphere can be packaged with an organic membrane, using biological or chemical means to serve as a carrier. Therefore, the technique may find particular applications for enhanced targeted drug delivery, and imaging and photoablation of angiogenic vessels in tumours.

Wavefront Shaping and Its Application to Enhance Photoacoustic Imaging

Since its introduction to the field in mid-1990s, photoacoustic imaging has become a fast-developing biomedical imaging modality with many promising potentials. By converting absorbed diffused light energy into not-so-diffused ultrasonic waves, the reconstruction of the ultrasonic waves from the targeted area in photoacoustic imaging leads to a high-contrast sensing of optical absorption with ultrasonic resolution in deep tissue, overcoming the optical diffusion limit from the signal detection perspective. The generation of photoacoustic signals, however, is still throttled by the attenuation of photon flux due to the strong diffusion effect of light in tissue. Recently, optical wavefront shaping has demonstrated that multiply scattered light could be manipulated so as to refocus inside a complex medium, opening up new hope to tackle the fundamental limitation. In this paper, the principle and recent development of photoacoustic imaging and optical wavefront shaping are briefly introduced. Then we describe how photoacoustic signals can be used as a guide star for in-tissue optical focusing, and how such focusing can be exploited for further enhancing photoacoustic imaging in terms of sensitivity and penetration depth. Finally, the existing challenges and further directions towards in vivo applications are discussed.

High-speed single-shot optical focusing through dynamic scattering media with full-phase wavefront shaping

In biological applications, optical focusing is limited by the diffusion of light, which prevents focusing at depths greater than ∼1 mm in soft tissue. Wavefront shaping extends the depth by compensating for phase distortions induced by scattering and thus allows for focusing light through biological tissue beyond the optical diffusion limit by using constructive interference. However, due to physiological motion, light scattering in tissue is deterministic only within a brief speckle correlation time. In in vivo tissue, this speckle correlation time is on the order of milliseconds, and so the wavefront must be optimized within this brief period. The speed of digital wavefront shaping has typically been limited by the relatively long time required to measure and display the optimal phase pattern. This limitation stems from the low speeds of cameras, data transfer and processing, and spatial light modulators. While binary-phase modulation requiring only two images for the phase measurement has recently been reported, most techniques require at least three frames for the full-phase measurement. Here, we present a full-phase digital optical phase conjugation method based on off-axis holography for single-shot optical focusing through scattering media. By using off-axis holography in conjunction with graphics processing unit based processing, we take advantage of the single-shot full-phase measurement while using parallel computation to quickly reconstruct the phase map. With this system, we can focus light through scattering media with a system latency of approximately 9 ms, on the order of the in vivo speckle correlation time.

High-speed single-shot optical focusing through dynamic scattering media with full-phase wavefront shaping

In biological applications, optical focusing is limited by the diffusion of light, which prevents focusing at depths greater than ∼1 mm in soft tissue. Wavefront shaping extends the depth by compensating for phase distortions induced by scattering and thus allows for focusing light through biological tissue beyond the optical diffusion limit by using constructive interference. However, due to physiological motion, light scattering in tissue is deterministic only within a brief speckle correlation time. In in vivo tissue, this speckle correlation time is on the order of milliseconds, and so the wavefront must be optimized within this brief period. The speed of digital wavefront shaping has typically been limited by the relatively long time required to measure and display the optimal phase pattern. This limitation stems from the low speeds of cameras, data transfer and processing, and spatial light modulators. While binary-phase modulation requiring only two images for the phase measurement has recently been reported, most techniques require at least three frames for the full-phase measurement. Here, we present a full-phase digital optical phase conjugation method based on off-axis holography for single-shot optical focusing through scattering media. By using off-axis holography in conjunction with graphics processing unit based processing, we take advantage of the single-shot full-phase measurement while using parallel computation to quickly reconstruct the phase map. With this system, we can focus light through scattering media with a system latency of approximately 9 ms, on the order of the in vivo speckle correlation time.

Focusing light through scattering media by polarization modulation based generalized digital optical phase conjugation

Optical scattering prevents light from being focused through thick biological tissue at depths greater than ∼1 mm. To break this optical diffusion limit, digital optical phase conjugation (DOPC) based wavefront shaping techniques are being actively developed. Previous DOPC systems employed spatial light modulators that modulated either the phase or the amplitude of the conjugate light field. Here, we achieve optical focusing through scattering media by using polarization modulation based generalized DOPC. First, we describe an algorithm to extract the polarization map from the measured scattered field. Then, we validate the algorithm through numerical simulations and find that the focusing contrast achieved by polarization modulation is similar to that achieved by phase modulation. Finally, we build a system using an inexpensive twisted nematic liquid crystal based spatial light modulator (SLM) and experimentally demonstrate light focusing through 3-mm thick chicken breast tissue. Since the polarization modulation based SLMs are widely used in displays and are having more and more pixel counts with the prevalence of 4 K displays, these SLMs are inexpensive and valuable devices for wavefront shaping.

Focusing light through scattering media by transmission matrix inversion

Focusing light through scattering media has broad applications in optical imaging, manipulation and therapy. The contrast of the focus can be quantified by peak-to-background intensity ratio (PBR). Here, we theoretically and numerically show that by using a transmission matrix inversion method to achieve focusing, within a limited field of view and under a low noise condition in transmission matrix measurements, the PBR of the focus can be higher than that achieved by conventional methods such as optical phase conjugation or feedback-based wavefront shaping. Experimentally, using a phase-modulation spatial light modulator, we increase the PBR by 66% over that achieved by conventional methods based on phase conjugation. In addition, we demonstrate that, within a limited field of view and under a low noise condition in transmission matrix measurements, our matrix inversion method enables light focusing to multiple foci with greater fidelity than those of conventional methods.

Interleaved segment correction achieves higher improvement factors in using genetic algorithm to optimize light focusing through scattering media

Focusing and imaging through scattering media has been proved possible with high resolution wavefront shaping. A completely scrambled scattering field can be corrected by applying a correction phase mask on a phase only spatial light modulator (SLM) and thereby the focusing quality can be improved. The correction phase is often found by global searching algorithms, among which Genetic Algorithm (GA) stands out for its parallel optimization process and high performance in noisy environment. However, the convergence of GA slows down gradually with the progression of optimization, causing the improvement factor of optimization to reach a plateau eventually. In this report, we propose an interleaved segment correction (ISC) method that can significantly boost the improvement factor with the same number of iterations comparing with the conventional all segment correction (ASC) method. In the ISC method, all the phase segments are divided into a number of interleaved groups; GA optimization procedures are performed individually and sequentially among each group of segments. The final correction phase mask is formed by applying correction phases of all interleaved groups together on the SLM. The ISC method has been proved significantly useful in practice because of its ability to achieve better improvement factors when noise is present in the system. We have also demonstrated that the imaging quality is improved as better correction phases are found and applied on the SLM. Additionally, the ISC method lowers the demand of dynamic ranges of detection devices. The proposed method holds potential in applications, such as high-resolution imaging in deep tissue.

Scatter-plate microscope for lensless microscopy with diffraction limited resolution

Scattering media have always been looked upon as an obstacle in imaging. Various methods, ranging from holography to phase compensation as well as to correlation techniques, have been proposed to cope with this obstacle. We, on the other hand, have a different understanding about the role of the diffusing media. In this paper we propose and demonstrate a ‘scatter-plate microscope’ that utilizes the diffusing property of the random medium for imaging micro structures with diffraction-limited resolution. The ubiquitous property of the speckle patterns permits to exploit the scattering medium as an ultra-thin lensless microscope objective with a variable focal length and a large working distance. The method provides a light, flexible and cost effective imaging device as an alternative to conventional microscope objectives. In principle, the technique is also applicable to lensless imaging in UV and X-ray microscopy. Experiments were performed with visible light to demonstrate the microscopic imaging of USAF resolution test target and a biological sample with varying numerical aperture (NA) and magnifications.

Polarization recovery through scattering media

The control and use of light polarization in optical sciences and engineering are widespread. Despite remarkable developments in polarization-resolved imaging for life sciences, their transposition to strongly scattering media is currently not possible, because of the inherent depolarization effects arising from multiple scattering. We show an unprecedented phenomenon that opens new possibilities for polarization-resolved microscopy in strongly scattering media: polarization recovery via broadband wavefront shaping. We demonstrate focusing and recovery of the original injected polarization state without using any polarizing optics at the detection. To enable molecular-level structural imaging, an arbitrary rotation of the input polarization does not degrade the quality of the focus. We further exploit the robustness of polarization recovery for structural imaging of biological tissues through scattering media. We retrieve molecular-level organization information of collagen fibers by polarization-resolved second harmonic generation, a topic of wide interest for diagnosis in biomedical optics. Ultimately, the observation of this new phenomenon paves the way for extending current polarization-based methods to strongly scattering environments.

Non-invasive three-dimension control of light between turbid layers using a surface quasi-point light source for precorrection

Manipulating light non-invasively through inhomogeneous media is an attractive goal in many disciplines. Wavefront shaping and optical phase conjugation can focus light to a point. Transmission matrix method can control light on multiple output modes simultaneously. Here we report a non-invasive approach which enables three-dimension (3D) light control between two turbid layers. A digital optical phase conjugation mirror measured and conjugated the diffused wavefront, which originated from a quasi-point source on the front turbid layer and passed through the back turbid layer. And then, because of memory effect, the phase-conjugated wavefront could be used as a carrier wave to transport a pre-calculated wavefront through the back turbid layer. The pre-calculated wavefront could project a desired 3D light field inside the sample, which, in our experiments, consisted of two 220-grid ground glass plates spaced by a 20 mm distance. The controllable range of light, according to the memory effect, was calculated to be 80 mrad in solid angle and 16 mm on z-axis. Due to the 3D light control ability, our approach may find applications in photodynamic therapy and optogenetics. Besides, our approach can also be combined with ghost imaging or compressed sensing to achieve 3D imaging between turbid layers.

Holographic imaging through a scattering layer using speckle interferometry

Optical imaging through complex scattering media is one of the major technical challenges with important applications in many research fields, ranging from biomedical imaging to astronomical telescopy to spatially multiplexed optical communications. Various approaches for imaging through a turbid layer have been recently proposed that exploit the advantage of object information encoded in correlations of the random optical fields. Here we propose and experimentally demonstrate an alternative approach for single-shot imaging of objects hidden behind an opaque scattering layer. The proposed technique relies on retrieving the interference fringes projected behind the scattering medium, which leads to complex field reconstruction, from far-field laser speckle interferometry with two-point intensity correlation measurement. We demonstrate that under suitable conditions, it is possible to perform imaging to reconstruct the complex amplitude of objects situated at different depths.

Image restoration in fiber-coupled imagers using space-variant impulse response characterization

Fiber-coupled image sensors have attracted interest in recent years for high-resolution conformal image transfer, including mapping of the spherical image surface of a monocentric wide-angle lens to one or more flat focal plane sensors. However, image resolution is lost due to fiber bundle defects, moiré from lateral fiber-sensor misalignment, and blur due to the nonzero gap between fiber bundle and the image sensor. Here we investigate whether subpixel impulse response characterization of the strongly shift-variant impulse response can be used with existing image-processing techniques to recover the resolution otherwise lost in image transfer. We show that the submicrometer impulse response is experimentally repeatable, and can be used to recover image data and reveal fine features of the input surface structure of a 2.5 μm pitch fiber bundle.

Three-dimensional focusing through scattering media using conjugate adaptive optics with remote focusing (CAORF)

The small correction volume for conventional wavefront shaping methods limits their application in biological imaging through scattering media. We demonstrate large volume wavefront shaping through a scattering layer with a single correction by conjugate adaptive optics and remote focusing (CAORF). The remote focusing module can maintain the conjugation between the adaptive optical (AO) element and the scattering layer during three-dimensional scanning. This new configuration provides a wider correction volume by better utilization of the memory effect in a fast three-dimensional laser scanning microscope. Our results show that the proposed system can provide 10 times wider axial field of view compared with a conventional conjugate AO system when 16,384 segments are used on a spatial light modulator. We also demonstrate three-dimensional fluorescence imaging, multi-spot patterning through a scattering layer and two-photon imaging through mouse skull tissue.

Lensless wide-field single-shot imaging through turbid media based on object-modulated speckles

The need to image objects through light-scattering materials is common in a range of applications. Different methods have been investigated to acquire the image of the object when diffusers are presented. In this paper, we demonstrate the object reconstruction with single-shot imaging based on the correlography principle and phase retrieval algorithm with coherent illumination. We prove the possibility of reconstructing positive and negative objects in both transmission and reflection modes with collimated and scattered light. Formulas for calculating the size of the object from the reconstructed image are presented. We also prove that the object can be retrieved from a small section of the raw speckle image. These interesting features will have broad potential applications in many areas (such as biomedicine, security and sensing).

Optical Phase Conjugation with Less Than a Photon per Degree of Freedom

We demonstrate experimentally that optical phase conjugation can be used to focus light through strongly scattering media even when far less than a photon per optical degree of freedom is detected. We found that the best achievable intensity contrast is equal to the total number of detected photons, as long as the resolution of the system is high enough. Our results demonstrate that phase conjugation can be used even when the photon budget is extremely low, such as in high-speed focusing through dynamic media or imaging deep inside tissue.

Exploiting scattering media for exploring 3D objects

Scattering media, such as diffused glass and biological tissue, are usually treated as obstacles in imaging. To cope with the random phase introduced by a turbid medium, most existing imaging techniques recourse to either phase compensation by optical means or phase recovery using iterative algorithms, and their applications are often limited to two-dimensional imaging. In contrast, we utilize the scattering medium as an unconventional imaging lens and exploit its lens-like properties for lensless three-dimensional (3D) imaging with diffraction-limited resolution. Our spatially incoherent lensless imaging technique is simple and capable of variable focusing with adjustable depths of focus that enables depth sensing of 3D objects that are concealed by the diffusing medium. Wide-field imaging with diffraction-limited resolution is verified experimentally by a single-shot recording of the 1951 USAF resolution test chart, and 3D imaging and depth sensing are demonstrated by shifting focus over axially separated objects.