We report the measurement of a large optical reflection matrix (RM) of a highly disordered medium. Incident optical fields onto a turbid sample are controlled by a spatial light modulator, and the corresponding fields reflected from the sample are measured using full-field Michelson interferometry. The number of modes in the measured RM is set to exceed the number of resolvable modes in the scattering media. We successfully study the subtle intrinsic correlations in the RM which agrees with the theoretical prediction by random-matrix theory when the effect of the limited numerical aperture on the eigenvalue distribution of the RM is taken into account. The possibility of the enhanced delivery of incident energy into scattering media is also examined from the eigenvalue distribution which promises efficient light therapeutic applications.
We demonstrate that polarization modulation of an illumination beam can effectively control the spatial profile of the light transmitted through turbid media. Since the transmitted electric fields are completely mingled in turbid media, polarization states of an illumination beam can be effectively used to control the propagation of light through turbid media. Numerical simulations were performed which agree with experimental results obtained using a commercial in-plane switching liquid-crystal display for modulating the input polarization states.
In this work we present a theoretical study on the propagation of light in heterogeneous systems with fluctuating optical properties. To understand the consequences of the fluctuations we perform numerical calculations with uniform and non uniforms systems using Monte Carlo simulations. We consider two distributions to represent a non-uniform medium: delta function and an exponential negative distributions.The results show that even with finite moments distributions, may require a large number of interactions for a convergence towards Gaussian statistics. This can be important when estimating …
In this Letter we present experimental results concerning the retrieval of images of absorbing objects immersed in turbid media via differential ghost imaging (DGI) in a backscattering configuration. The method has been applied, for the first time to our knowledge, to the imaging of small thin black objects located at different depths inside a turbid solution of polystyrene nanospheres and its performances assessed via comparison with standard imaging techniques. A simple theoretical model capable of describing the basic optics of DGI in turbid media is proposed.
We show that the Kubelka-Munk equations for the description of the intensity transfer of light in turbid media are equivalent to a one-dimensional diffusion equation, which is obtained by averaging the three-dimensional diffusion equation over the lateral directions. This enables us to identify uniquely the Kubelka-Munk parameters and derive expressions for diffuse reflection and transmission coefficients including the effect of internal reflections. Without internal reflections we recover the Kubelka-Munk formulas for these coefficients. We show that the Kubelka-Munk equations are the proper …
Focusing light through turbid media presents a highly fascinating challenge in modern biophotonics. The unique capability of optoacoustics for high resolution imaging of light absorption contrast in deep tissues can provide a natural and efficient feedback to control light delivery in scattering medium. While basic feasibility of using optoacoustic readings as a feedback mechanism for wavefront shaping has been recently reported, the suggested approaches may require long acquisition times making them challenging to be translated into realistic tissue environments. In an attempt to significantl…
We study the prospects of controlling transmission of broadband and bi-chromatic laser pulses through turbid samples. The ability to focus transmitted broadband light is limited via both the scattering properties of the medium, and the technical characteristics of the experimental set-up. There are two time scales, given by pulse stretching in the near- and far-field regions, which define the maximum bandwidth of a pulse amenable to focusing. In the geometric optics regime of wave propagation in the medium, a single set-up can be optimal for focusing light at frequencies w and nw simultaneousl…
Scattering has usually be considered as detrimental for optical focusing or imaging. Recently, more and more research has shown that strongly scattering materials can be utilized to focus coherent light by controlling or shaping the incident light. Here, purposeful focusing of second-harmonic waves, which are generated and scattered from nonlinear turbid media via feedback-based wavefront shaping is presented. This work shows a flexible manipulation of both disordered linear and nonlinear scattering signals, indicating more controllable degrees of freedom for the description of turbid media. T…
We discuss the far-field spatio-temporal cross-correlations of waves multiple-scattered in a turbid medium in which is embedded a hidden heterogeneous region (inclusion) characterized by a distinct scatterer dynamics (as compared to the rest of the medium). We show that the spatio-temporal correlation is affected by the inclusion which suggests a new method of imaging in turbid media. Our results allow qualitative interpretation in terms of diffraction theory: the cross-correlation of scattered waves behaves similarly to the intensity of a wave diffracted by an aperture.
Imaging with optical resolution through highly scattering media is a long sought-after goal with important applications in deep tissue imaging. Although being the focus of numerous works, this goal was considered impractical until recently. Adaptive-optics techniques which are effective in correcting weak wavefront aberrations, were deemed inadequate for turbid samples, where complex speckle patterns arise and light is scattered to a large number of modes that greatly exceeds the number of degrees of control. This conception changed after the demonstration of focusing coherent light through tu…
Brillouin microscopy has recently emerged as powerful technique to characterize the mechanical properties of biological tissue, cell and biomaterials. However, the potential of Brillouin microscopy is currently limited to transparent samples, because Brillouin spectrometers do not have sufficient spectral extinction to reject the predominant non-Brillouin scattered light of turbid media. To overcome this issue, we developed a spectrometer composed of a two VIPA stages and a multi-pass Fabry-Perot interferometer. The Fabry-Perot etalon acts as an ultra-narrow band-pass filter for Brillouin ligh…
We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.
Dynamics light scattering (DLS) is a widely used techniques to characterize dynamics in soft phases. Evanescent Wave DLS refers to the case of total internal reflection DLS that probes near interface dynamics. We here investigate the use of EWDLS for turbid sample. Using combination of ray-tracing simulation and experiments, we show that a significant fraction of the detected photons are scattered once and has phase shifts distinct from the multiple scattering fraction. It follows that the measured correlation can be separated into two contributions: a single scattering one arising from the ev…
In Polarization Discrimination Imaging, the amplitude of a sinusoid from a rotating analyzer, representing residual polarized light and carrying information on the object, is detected with the help of a lock-in amplifier. When turbidity increases beyond a level, the lock-in amplifier fails to detect the weak sinusoidal component in the transmitted light. In this work we have employed the principle of Stochastic Resonance and used a 3-level quantizer to detect the amplitude of the sinusoids, which was not detectable with a lock-in amplifier. In using the three level quantizer we have employed t…
Optical coherence tomography (OCT) is a powerful biomedical imaging technology that relies on the coherent detection of backscattered light to image tissue morphology in vivo. As a consequence, OCT is susceptible to coherent noise (speckle noise), which imposes significant limitations on its diagnostic capabilities. Here we show a method based purely on light manipulation that is able to entirely remove the speckle noise originating from turbid samples without any compromise in resolution. We refer to this method as Speckle-Free OCT (SFOCT). Using SFOCT, we succeeded in revealing small structu…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings, and good agreement is found. The role of step correlations is discussed, and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous syst…
Diffraction-limited imaging through complex scattering media is a long sought after goal with important applications in biomedical research. In recent years, high resolution wavefront-shaping has emerged as a powerful approach to generate a sharp focus through highly scattering, visually opaque samples. However, it requires a localized feedback signal from the target point of interest, which necessitates an invasive procedure in all-optical techniques. Here, we show that by exploiting optical nonlinearities, a diffraction-limited focus can be formed inside or through a complex sample, even whe…
We provide a new analytic expression and an innovative experimental method to isolate the effect of multiple scattering (MS) in Brillouin investigation of highly turbid media. On the one hand, an analytic model is given to describe the spectrum in case of ill-defined exchanged wave-vector. On the other hand, a new experimental method, named Polarization Gated Brillouin Spectroscopy (PG-BS), is proposed for selecting the MS contribution through light polarization. Both experimental and analytic methods are tested against a benchmark material, milk, demonstrating their capability to extract reli…
Gwangju Institute of Science and Technology（光州科学技术院）；Korea University（高丽大学）
The input numerical aperture (NA) of multimode fiber (MMF) can be effectively increased by placing turbid media at the input end of the MMF. This provides the potential for high-resolution imaging through the MMF. While the input NA is increased, the number of propagation modes in the MMF and hence the output NA remains the same. This makes the image reconstruction process underdetermined and may limit the quality of the image reconstruction. In this paper, we aim to improve the signal to noise ratio (SNR) of the image reconstruction in imaging through MMF. We notice that turbid media placed i…
Duke University（杜克大学）；Tsinghua University（清华大学）；Lund University（隆德大学）；Tsinghua Shenzhen International Graduate School（清华大学深圳国际研究生院）
Noninvasive optical imaging through dynamic scattering media has numerous important biomedical applications but still remains a challenging task. While standard diffuse imaging methods measure optical absorption or fluorescent emission, it is also well-established that the temporal correlation of scattered coherent light diffuses through tissue much like optical intensity. Few works to date, however, have aimed to experimentally measure and process such temporal correlation data to demonstrate deep-tissue video reconstruction of decorrelation dynamics. In this work, we utilize a single-photon …
Scattering prevents light from being focused in turbid media. The effect of scattering can be negated through wavefront shaping techniques when a localized form of feedback is available. Even in the absence of such a localized reporter, wavefront shaping can blindly form a single diffraction-limited focus when the feedback response is nonlinear. We developed and experimentally validated a model that accurately describes the statistics of this blind focusing process. We show that maximizing the nonlinear feedback signal does not always result in the formation of a focus. Using our model, we can…
Purpose: Visualization and monitoring of capillary loops in dermis and mucosa are interesting for various clinical applications, including rheumatology, early cancer, and shock detection. However, the limitations of existing imaging technologies are not well understood. Therefore, this study aimed to elucidate peculiarities of the subsurface defect visualization in realistic skin imaging geometries. Methods: We used a perturbation approach for the light propagation in turbid tissues with mismatched boundaries. Defects were considered as negative light sources immersed in homogeneous media, whi…
We propose a new method to image fluorescent objects through turbid media base on Airy beam scanning. This is achieved by using the non-diffractive nature of Airy beams, namely their ability to maintain their shape while penetrating through a highly scattering medium. We show, that our technique can image fluorescent objects immersed in turbid media with higher resolution and signal to noise than confocal imaging. As proof-of-principle, we demonstrate imaging of 1$μ$m sized fluorescent beads through a dense suspension of yeast cells with an attenuation coefficient of 51cm$^{-1}$ at a depth of …
In turbid media, scattering of light scrambles information of the incident beam and represents an obstacle to optical imaging. Noninvasive imaging through opaque layers is challenging for dynamic and wide-field objects due to unreliable image reconstruction processes. We here propose a new perspective to solve these problems: rather than using the full point-spread-function (PSF), the wave distortions in scattering layers can be characterized with only the phase of the optical-transfer-function (OTF, the Fourier transform of PSF), with which diffraction-limit images can be analytically solved.…
One challenge that has long held the attention of scientists is that of clearly seeing objects hidden by turbid media, as smoke, fog or biological tissue, which has major implications in fields such as remote sensing or early diagnosis of diseases. Here, we combine structured incoherent illumination and bucket detection for imaging an object completely embedded in a turbid medium. A sequence of low-intensity microstructured light patterns is launched onto the object, whose image is accurately reconstructed through the light fluctuations measured by a single-pixel detector. Our technique is non…
We introduce a simple but practical method to measure the optical transmission matrix (TM) of complex media. The optical TM of a complex medium is obtained by modulating the wavefront of a beam impinging on the complex medium and imaging the transmitted full-field speckle intensity patterns. Using the retrieved TM, we demonstrate the generation and linear combination of multiple foci on demand through the complex medium. This method will be used as a versatile tool for coherence control of waves through turbid media.
From multi-photon imaging penetrating millimeters deep through scattering biological tissue, to super-resolution imaging conquering the diffraction limit, optical imaging techniques have greatly advanced in recent years. Notwithstanding, a key unmet challenge in all these imaging techniques is to perform rapid wide-field imaging through a turbid medium. Strategies such as active wave-front correction and multi-photon excitation, both used for deep tissue imaging; or wide-field total-internal-refection illumination, used for super-resolution imaging; can generate arbitrary excitation patterns o…
The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated. Here we demonstrate experimentally that the reflected and transmitted speckle patterns are correlated, even for opaque media with thickness much larger than the transport mean f…
Non-invasive and single-shot holographic imaging through complex media is technically challenging due to random light scattering which significantly scrambles optical information. Recently, several methods have been presented to address this issue. However, they require complicated measurements of optical transmission matrices, or existing techniques do only retrieve intensity information. Here we propose and experimentally demonstrate a holographic approach for single-shot imaging through a scattering layer based on digital in-line holography in combination with the autocorrelation of the spe…
Graded index media whose electric susceptibility satisfies the spatial Kramers-Kronig relations are known to be one-way reflectionless to electromagnetic radiation, for all angles of incidence. We demonstrate how a family of these media, in addition to being reflectionless, also have negligible transmission. To this end, we discuss how the transmission coefficient for the propagation of waves through a medium whose permittivity is built from poles in the complex position plane, with residues that sum to infinity, can be controlled by tuning the positions and residues of the poles. In particula…
Adaptive optics can focus light through opaque media by compensating the random phase delay acquired while crossing a scattering curtain. The technique is commonly exploited in many fields, including astrophysics, microscopy, biomedicine and biology. A turbid lens has the capability of producing foci with a resolution higher than conventional optics, however it has a fundamental limit: to obtain a sharp focus one has to introduce a strongly scattering medium in the optical path. Indeed a tight focusing needs strong scattering and, as a consequence, high resolution focusing is obtained only for…
Optical diffraction tomography (ODT) has emerged as a powerful label-free three-dimensional (3D) bioimaging techniques for observing living cells and thin tissue layers. We report a new reflection-mode ODT (rODT) method for imaging thick biological specimens with 500 nm lateral resolution and 1 μm axial resolution. In rODT, multiple scattering background is rejected through spatio-temporal gating provided by dynamic speckle-field interferometry, while depth-resolved refractive index maps are reconstructed by developing a comprehensive inverse scattering model that also considers specimen-induc…
We present a numerical study on the minimum reflection channel in a disordered waveguide and its modification by coherent amplification of light. The minimum reflection channel is formed by destructive interference of quasi-normal modes at the front surface of the random medium. While the lowest reflection eigenvalue increases with gain in most random realizations, the minimum reflection channel can adjust its modal composition to enhance the destructive interference and slow down the growth of reflectance with gain. Some of the random realizations display a further reduction of the minimum re…
Focusing light through dynamically varying heterogeneous media is a sought-after goal with important applications ranging from free-space communication to nano-surgery. The underlying challenge is to control the optical wavefront with a large number of degrees-of-freedom (DOF) at timescales shorter than the medium dynamics. Recently, many advancements have been reported following the demonstration of focusing through turbid samples by wavefront-shaping, using spatial light modulators (SLMs) having >1000 DOF. Unfortunately, SLM-based wavefront-shaping requires feedback from a detector/camera an…
Reflection statistics have not been well studied for optical random media whose mean refractive indices do not match with the refractive indices of their surrounding media. Here, we theoretically study how this refractive index mismatch between a one dimensional (1D) optical sample and its surrounding medium affects the reflection statistics in the weak disorder limit, when the fluctuation part of the refractive index (dn) is much smaller than the mismatch as well as the mean refractive index of the sample (dn << <n>). In the theoretical derivation, we perform a detailed calculation that resul…
We demonstrate bending of light on the same side of the normal in a free standing corrugated metal film under bi-directional illumination. Coherent perfect absorption (CPA) is exploited to suppress the specular zeroth order leading to effective back-bending of light into the `-1' order, while the `+1' order is resonant with the surface mode. The effect is shown to be phase sensitive yielding CPA and superscattering in the same geometry.
We report a method to design at will the spatial profile of transmitted coherent light after propagation through a scattering sample. We compute an operator based on the experimentally measured transmission matrix, obtained by numerically adding an arbitrary mask in the Fourier domain prior to focusing. We demonstrate the strength of the technique through several examples: propagating Bessel beams, thus generating foci smaller than the diffraction limited speckle grain, donut beams, and helical beams. We characterize the 3D profile of the achieved foci and analyze the fundamental limitations o…
Sensing and manipulating targets hidden under scattering media are universal problems that take place in applications ranging from deep-tissue optical imaging to laser surgery. A major issue in these applications is the shallow light penetration caused by multiple scattering that reflects most of incident light. Although advances have been made to eliminate image distortion by a scattering medium, dealing with the light reflection has remained unchallenged. Here we present a method to minimize reflected intensity by finding and coupling light into the anti-reflection modes of a scattering medi…
Optical logic gates are fundamental blocks of optical computing to accelerate information processing. While significant progress has been achieved in recent years, existing implementations typically rely on dedicated structures that are predesigned to modulate the phases and intensities of optical beams accurately for specific logic functions. Thus, these optical gates usually lack reconfigurability and are incapable within or through dynamic complex media/environment, such as fog and turbid water. In this work, as a conceptual demonstration, we propose reconfigurable optical logic operations …
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane electromagnetic waves in ordinary dielectrics, the kinematical and dynamical aspects of these phenomena are studied, such as the intensity of the various wave components and the change in the polarization of the wave as it crosses the boundary. As a prerequisite of this, we show that the plane wave solution must be written as a suitable superposition of the cir…
Considering the complex reflection amplitude R=|R|exp(iθ) of a light wave, real delay time τ_r (i.e., sojourn or Wigner delay time), which is the energy derivative of the real phase (τ_r =dθ/cdk), and complex delay time τ_i , which is the energy derivative of the reflection coefficient (τ_i=dθ_i/cdk, |R|=r^1/2=exp(-θ_i)), have the same statistical form and a mirror image with a shift in time in weak disorder and short length regime. Real delay time statistics obtained from the reflection coefficient can be attributed to the strong correlation between the reflection coefficient and its phase in…
Light wave reflection from optical disordered media is always associate with its phase, and the phase statistics influence the reflection statistics. We report a detailed numerical study of the statistics of the reflection coefficient RR* and its associated phase(theta) for plane electromagnetic waves reflected from one dimensional (1D) Gaussian white-noise optical disordered media, ranging from weak to strong disordered regimes. We solve numerically the full Fokker-Planck (FP) equation for the joint probability distribution in the RR* - phase(theta) space for different lengths of the sample w…
Previously we considered the effect of experimental parameters on optimized transmission through opaque media using spatial light modulator (SLM)-based wavefront shaping. In this study we consider the opposite geometry, in which we optimize reflection from an opaque surface such that the backscattered light is focused onto a spot on an imaging detector. By systematically varying different experimental parameters (genetic algorithm iterations, bin size, SLM active area, target area, spot size, and sample angle with respect to the optical axis) and optimizing the reflected light we determine how…
Angle-resolved reflection and emission spectra of metal gratings consisting of sub-wavelength grooves and immersed into rhodamine B and rhodamine 19 solutions are presented. The measured reflection and emission dispersion diagrams reveal the surface plasmon polaritons positions and strong plasmon mediated emission enhancement, respectively. The same grating could be easily re-used for the characterization of different dye-molecules.
Optical imaging through complex scattering media is one of the major technical challenges with important applications in many research fields, ranging from biomedical imaging, astronomical telescopy, and spatially multiplex optical communications. Although various approaches for imaging though turbid layer have been recently proposed, they had been limited to two-dimensional imaging. Here we propose and experimentally demonstrate an approach for three-dimensional single-shot imaging of objects hidden behind an opaque scattering layer. We demonstrate that under suitable conditions, it is possib…
A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and reflection are obtained even in cases where classical effective medium theory breaks down. Magnetoelectric coupling accounts for symmetry breaking in reflection and transmission when a non-symmetric structure is illuminated from two opposite sides.
A Physics-Guided Neural Framework for Rheology Measurement from Dynamical Laser Speckles
Technical University of Munich（慕尼黑工业大学）；University of Oxford（牛津大学）；TUM University Hospital, Technical University of Munich（慕尼黑工业大学附属塔姆大学医院）；Peking University Third Hospital（北京大学第三医院）；China Jiliang University（中国计量大学）
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part of free space is distorted in some desired manner. The coordinate transformation is then applied to the permittivity and permeability tensors to yield the specification for a complex medium with desired functionality. The transformation optical structures proposed to date, such as electromagnetic "invisibility" cloaks and concentrators, are inherently reflect…
We present a theoretical study of frequency correlations of light backscattered from a random scattering medium. This statistical quantity provides insight into the dynamics of multiple scattering processes accessible both, in theoretical and experimental investigations. For frequency correlations between field amplitudes, we derive a simple expression in terms of the path length distribution of the underlying backscattering processes. In a second step, we apply this relation to describe frequency correlations between intensities in the regime of weak disorder. Since, with increasing disorder …
Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and numerically, that in quasi one-dimensional ($1$D) diffusive samples, their behavior is governed mostly by the asymmetry in the reflections of the sample edges rather than by the absolute values of the reflection coefficients themselves. We show that there exists a threshold value of the asymmetry parameter, below which high transmission eigenchannels exist, giving…
The scattering of light observed through the turbid underwater channel is often regarded as the leading challenge when designing underwater electro-optical imaging systems. There have been many approaches to address the effects of scattering such as using pulsed laser sources to reject scattered light temporally, or using intensity modulated waveforms and matched filters to remove the scattered light spectrally. In this paper, a new method is proposed which primarily uses the backscattering asymmetry property for object detection and geometric profiling. In our approach, two parallel and ident…
Specular reflection is known to play an important role in many fields of scattering applications, e.g., in remote sensing, computer graphics, optimization of visual appearance of industrial products. Usually it can be assumed that the object has a solid surface and that the properties of the surface will dictate the behavior of the specular component. In this study I will show that media consisting of wavelength-sized particles can also have a quasi-specular reflection in cases where there is ordered structure in the media. I will also show that the quasi-specular reflection in particulate med…
