Scattering Mean Free Path Research Articles

Reflection Measurement of the Scattering Mean Free Path at the Onset of Multiple Scattering.

Multiple scattering of waves presents challenges for imaging complex media but offers potential for their characterization. Its onset is actually governed by the scattering mean free path ℓ_{s} that provides crucial information on the medium microarchitecture. Here, we introduce a reflection matrix method designed to estimate this parameter from the time decay of the single scattering rate. Our method is first validated by an ultrasound experiment on a tissue-mimicking phantom before being applied invivo to a human liver. This Letter opens important perspectives for quantitative imaging of heterogeneous media with waves, whether it be for nondestructive testing, biomedical, or geophysical applications.

Harnessing forward multiple scattering for optical imaging deep inside an opaque medium

As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to in-depth optical microscopy, as it causes a drastic degradation of contrast, resolution and brightness of the resulting image beyond a few scattering mean free paths. However, the information about the inner reflectivity of the sample is not lost; only scrambled. To recover this information, a matrix approach of optical imaging can be fruitful. Here, we report on a de-scanned measurement of a high-dimension reflection matrix R via low coherence interferometry. Then, we show how a set of independent focusing laws can be extracted for each medium voxel through an iterative multi-scale analysis of wave distortions contained in R. It enables an optimal and local compensation of forward multiple scattering paths and provides a three-dimensional confocal image of the sample as the latter one had become digitally transparent. The proof-of-concept experiment is performed on a human opaque cornea and an extension of the penetration depth by a factor five is demonstrated compared to the state-of-the-art.

Bidirectional in-silico clearing approach for deep refractive-index tomography using a sparsely sampled transmission matrix.

Optical diffraction tomography (ODT) enables the label-free volumetric imaging of biological specimens by mapping their three-dimensional refractive index (RI) distribution. However, the depth of imaging achievable is restricted due to spatially inhomogeneous RI distributions that induce multiple scattering. In this study, we introduce a novel ODT technique named bidirectional in-silico clearing RI tomography. This method incorporates both forward and reversed in-silico clearing. For the reversed in-silico clearing, we have integrated an ODT reconstruction framework with a transmission matrix approach, which enables RI reconstruction and wave backpropagation from the illumination side without necessitating modifications to the conventional ODT setup. Furthermore, the framework employs a sparsely sampled transmission matrix, significantly reducing the requisite number of measurements and computational expenses. Employing this proposed technique, we successfully imaged a spheroid with a thickness of 263 µm, corresponding to 11.4 scattering mean free paths. This method was successfully applied to various biological specimens, including liver and colon spheroids, demonstrating consistent imaging performance across samples with varied morphologies.

Reciprocally tailored transparent artificial media for frequency and direction dependent light trapping

We propose a quasiperiodic leveled-wave structure whose reciprocal space is represented by spherical belt sections, designed to achieve scattering only for the defined wavelength and direction of incident light. At the same time light is scattered only towards directions of k-vectors for which the waves are trapped by total internal reflection in the structured slab. The trapped light is only weakly scattered and thus spends a long time inside the slab and is attenuated by weak absorption in the slab. The incident light of other direction and/or wavelength is transmitted through the slab almost undisturbed. We quantitatively estimated the scattering mean free paths for incident and trapped light from the first-order Born approximation and develop an analytical model which predicts the absorption for a given slab thickness, refractive index contrast and spherical belt parameters. Reducing the refractive index contrast and thickness of the belt, the selectivity can be increased and the absorption contrast for incident light of different wavelengths can reach 70%. We present numerical simulations with absorption contrast of 63% for refractive index contrast of 0.1, which is in good agreement with our analytical model.

Amplifying nonresonant production of dark sector particles in scattering dominance regime

We investigate the enhancement of dark sector particle production within the scattering dominant regime. These particles typically exhibit a slight mixing with Standard Model particles through various portals, allowing for their generation through in-medium oscillation from Standard Model particle sources. Our analysis reveals that in the scattering dominance regime, with a significantly smaller scattering mean free path λsca compared to the absorption mean free path λabs, the nonresonant production of sterile states can experience an enhancement by a factor of λabs/λsca. This phenomenon is demonstrated within the context of kinetic mixing dark photon production at a reactor, precisely satisfying this condition. By incorporating this collisional enhancement, we find that the current sensitivity to the mixing parameter ε for dark photons in the TEXONO experiment can be significantly improved across a range spanning from tens of eV to MeV. This advancement establishes the most stringent laboratory constraint within this mass spectrum for the dark photon. Sterile neutrino production, however, does not exhibit such enhancement, either due to the failure to meet the scattering dominance criterion or the neutrino damping in resonant production. Published by the American Physical Society 2024

Velocities of transmission eigenchannels and diffusion

The diffusion model is used to calculate both the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered samples, such as a layer of paint or a tissue sample, the flux transmitted through the sample may be dramatically enhanced or suppressed relative to predictions of diffusion theory when the sample is excited by a waveform corresponding to a transmission eigenchannel. Even so, it is widely assumed that the velocity of waves is irretrievably randomized in scattering media. Here we demonstrate in microwave measurements and numerical simulations that the statistics of velocity of different transmission eigenchannels are distinct and remains so on all length scales and are identical on the incident and output surfaces. The interplay between eigenchannel velocities and transmission eigenvalues determines the energy density within the medium, the diffusion coefficient, and the dynamics of propagation. The diffusion coefficient and all scattering parameters, including the scattering mean free path, oscillate with the width of the sample as the number and shape of the propagating channels in the medium change.

Imaging objects hidden inside the strongly scattering media based on bidirectional ghost imaging.

We demonstrate a novel, to the best of our knowledge, method for imaging objects hidden inside the strongly scattering media based on bidirectional ghost imaging (GI). In this method, GI is performed separately on both sides of the object, resulting in two GI results. Through an autocorrelation operation to the two GI results, the convolution between the autocorrelation of the object and the point spread function (PSF) of the strongly scattering media can be recovered. Therefore, the object can be recovered by obtaining the PSF of the strongly scattering media through noninvasive measurement or numerical calculation. Simulation and experimental results show that bidirectional ghost imaging (BGI) can reconstruct high-quality images, particularly when the thickness of the strongly scattering media greatly exceeds the scattering mean free path.

Tracing multiple scattering trajectories for deep optical imaging in scattering media

Multiple light scattering hampers imaging objects in complex scattering media. Approaches used in real practices mainly aim to filter out multiple scattering obscuring the ballistic waves that travel straight through the scattering medium. Here, we propose a method that makes the deterministic use of multiple scattering for microscopic imaging of an object embedded deep within scattering media. The proposed method finds a stack of multiple complex phase plates that generate similar light trajectories as the original scattering medium. By implementing the inverse scattering using the identified phase plates, our method rectifies multiple scattering and amplifies ballistic waves by almost 600 times. This leads to a significant increase in imaging depth—more than three times the scattering mean free path—as well as the correction of image distortions. Our study marks an important milestone in solving the long-standing high-order inverse scattering problems.

Weak Localization of Light in a Magneto-Active Medium

The interference contribution to the optical conductance (total transmittance) of a sample of a disordered Faraday medium is calculated. The suppression of wave interference in a magnetic field is shown to be due to helicity-flip scattering events. The magnetic field does not destroy the interference of waves with a given helicity, but suppresses it if the helicity changes along different parts of the wave trajectory. This leads to a decrease in the interference contribution to the conductance with increasing the magnetic field. A similar phenomenon, negative magnetoresistance, is known as a consequence of weak localization of electrons in metals with impurities. It is found that, as the magnetic field increases, the change in the interference correction to the optical conductance tends to a certain limiting value, which depends on the ratio of the transport mean free path to the helicity-flip scattering mean free path. We also discuss the possibility of controlling the transition to the regime of strong “Anderson” localization in the quasi-one-dimensional case by means of the field.

Efficient framework of solving time-gated reflection matrix for imaging through turbid medium.

Imaging through turbid medium is a long pursuit in many research fields, such as biomedicine, astronomy and automatic vehicle, in which the reflection matrix-based method is a promising solution. However, the epi-detection geometry suffers from round-trip distortion and it is challenging to isolate the input and output aberrations in non-ideal cases due to system imperfections and measurement noises. Here, we present an efficient framework based on single scattering accumulation together with phase unwrapping that can accurately separate input and output aberrations from the noise-affected reflection matrix. We propose to only correct the output aberration while suppressing the input aberration by incoherent averaging. The proposed method is faster in convergence and more robust against noise, avoiding precise and tedious system adjustments. In both simulations and experiments, we demonstrate the diffraction-limited resolution capability under optical thickness beyond 10 scattering mean free paths, showing the potential of applications in neuroscience and dermatology.

Anisotropy effects on the quantum transport of atomic matter waves

We discuss effects of anisotropic scattering in transport properties of ultracold atoms in three-dimensional optical potentials. Within the realm of the first Born approximation, we calculate the self energy, the scattering mean free time, the scattering mean free path, and the anisotropy factor. The behavior of the diffusion constant as a function of the wavenumber is also examined in diffusive and weak localization regimes. We show that these quantities are affected by quantum corrections due to the interference caused by disorder. The dimensionless conductance is evaluated using the scaling theory of localization. Our results are compared with previous theoretical and the experimental results.

Investigating pulmonary edema in rat lungs using separation of multiple scattering and single scattering contribution

Lung ultrasound imaging is challenging due to multiple scattering (MS) from alveoli. Conventional B-mode does not provide lung microstructure images. However, MS signals can provide valuable information about structure and alveolar distribution and investigating conditions such as pulmonary edema. Lung edema results in fluid buildup in interstitial spaces and alveoli, affecting density of alveoli. Previously, we demonstrated that changes in the distribution of scatterers due to edema result in changes in the wave diffusion regime and the scattering mean free path was sensitive to lung injury due to induced edema in rodents. In the present study, we introduce a novel way of quantifying MS in lungs by isolating the single scattering (SS) and MS contributions and processing them separately. After inducing different severity of edema using ischemia reperfusion injury in 18 rats, full synthetic aperture transmit sequences were used to acquire backscattered signals. The SS/MS contributions were separated using singular value decomposition. The separated SS/MS intensities were calculated and a new parameter defined as the rate of decay in intensity with depth. To assess edema severity and method validation, ex vivo CT lung images were assigned scores compared with this novel biomarker (R = 0.47, p = 0.021). Lung wet/dry ratio was also compared (R = 0.52, p = 0.009).

Investigation of ultrasound propagation through dense glass bead packings immersed in water

Conventional ultrasound imaging generally relies on a single scattering assumption and a constant sound hypothesis. However, in dense granular sediments where the glass beads diameter is comparable to the wavelength (typically 500 μm), both hypothesizes are no longer valid, resulting in a loss of resolution and contrast, up to the situation where a target to image could totally vanish in the fog. To better characterize this strongly scattering medium, we have conducted several ultrasonic experiments in reflection and in transmission, either on the diffused wave or on the coherent one. Both the transport and scattering mean free paths are estimated in the imaging bandwidth (1–5 MHz), alongside with the phase velocity and extinction length of the coherent wave. These results are compared with an analytical model, i.e. Generalized Coherent Potential Approximation*, which considers a coated sphere buried in an effective medium. Finally, we show a dispersive beamformer which takes into account the measured phase and group velocity. This allows us to obtain a more resolved and contrasted image in such a scattering medium. * Jing X, Sheng P, Zhou M. Phys Rev Lett. 1991

Modelling shock-like injections of solar energetic particles with 3D test particle simulations

Context. Solar energetic particle (SEP) acceleration and injection into interplanetary space during gradual SEP events is thought to take place at coronal mass ejection (CME)-driven shocks. Various features of measured intensity profiles at 1 au have been attributed to properties of the radial, longitudinal, and latitudinal SEP injections at the shock. Focussed transport models are typically used to model acceleration at a CME-shock and subsequent propagation. Test particle simulations are an alternative approach but so far they have been carried out only with instantaneous injection near the Sun. Aims. We develop the first temporally extended shock-like injection for our 3D test particle code and investigate how the spatial features of injection at a shock affect SEP intensity and anisotropy profiles for observers at 0.3 and 1.0 au. Methods. We conducted simulations of a monoenergetic population of 5 MeV protons considering three different radial injection functions and two longitudinal and latitudinal injection functions. We considered a range of scattering conditions with scattering mean free path values ranging from λ = 0.1 − 1.0 au, and determined intensity and anisotropy profiles at six observers at different longitudinal locations. Results. We find that the radial, longitudinal, and latitudinal injection functions play a relatively minor role in shaping the SEP intensity profiles. The dependence of intensity profiles on the value of the scattering mean free path is also weak, unlike what is found from 1D focussed transport models. Spatial factors, such as the times of observer-shock connection and disconnection as well as the time of shock passage have a much stronger influence on SEP intensities and anisotropies. Persistent anisotropies, until shock passage, are seen in our simulations. Comparing instantaneous and shock-like injections, we find that the link between the duration of injection and the duration of the SEP event is very weak, unlike what is commonly assumed.

Impact of corotation on gradual solar energetic particle event intensity profiles

Context. The corotation of particle-filled magnetic flux tubes is generally thought to have a minor influence on the time-intensity profiles of gradual solar energetic particle (SEP) events. For this reason, many SEP models solve the focussed transport equation within the corotating frame, thus neglecting corotation effects. Aims. We use simulations to study the effects of corotation on gradual SEP intensity profiles at a range of observer longitudinal positions relative to the solar source. We study how corotation affects the duration and decay time constant of SEP events as well as the variation in the peak intensity with the observer’s position. Methods. We used a 3D full-orbit test particle code with time-extended SEP injection via a shock-like source. In contrast to the case of focussed transport models, the test particle approach enables us to easily switch corotation on and off. While shock acceleration and downstream features are not modelled directly, our methodology allows us to study how corotation and the time-varying observer-shock magnetic connection influence the intensity profiles detected at several observers. Results. We find that corotation has a strong effect on the SEP intensity profiles for a monoenergetic population of 5 MeV protons, having a dominant influence during the decay phase. Simulations that include corotation display dramatically shortened durations for western events, compared to ones where it is not included. When corotation effects are taken into account, for both eastern and western events, the decay time constant is reduced and its dependence on the value of the scattering mean free path becomes negligible. Corotation reduces the SEP peak intensity for western events and enhances it for eastern ones, thus making the east-west asymmetry in peak intensity stronger, compared to the non-corotation case. Modelling SEP intensity profiles without carefully accounting for the effects of corotation leads to artificially extended decay phases during western events, leading to profiles with a similar shape regardless of the observer’s longitudinal position.

In-depth polarisation resolved SHG microscopy in biological tissues using iterative wavefront optimisation.

Polarised nonlinear microscopy has been extensively developed to study molecular organisation in biological tissues, quantifying the response of nonlinear signals to a varying incident linear polarisation. Polarisation Second harmonic Generation (PSHG) in particular is a powerful tool to decipher sub-microscopic modifications of fibrillar collagen organisation in type I and III collagen-rich tissues. The quality of SHG imaging is however limited to about one scattering mean free path in depth (typically 100 micrometres in biological tissues), due to the loss of focus quality, induced by wavefront aberrations and scattering at even larger depths. In this work, we study how optical depth penetration in biological tissues affects the quality of polarisation control, a crucial parameter for quantitative assessment of PSHG measurements. We apply wavefront shaping to correct for SHG signal quality in two regimes, adaptive optics for smooth aberration modes corrections at shallow depth, and wavefront shaping of higher spatial frequencies for optical focus correction at larger depths. Using nonlinear SHG active nanocrystals as guide stars, we quantify the capabilities of such optimisation methods to recover a high-quality linear polarisation and investigate how this approach can be applied to in-depth PSHG imaging in tissues, namely tendon and mouse cranial bone.

Semi-analytical prediction of phonon mean free path utilizing stochastic behavior at nanostructure interfaces

A semi-analytical method is developed to predict the phonon-boundary scattering mean free path (MFP) in nanostructured materials. Based on the segmentation of phonon displacements for each phonon collision event, the proposed solution enables us to evaluate the MFP with the geometrical and phonon-boundary scattering information of nanostructures. The validity of the method is confirmed by comparing its results with the MFP in polycrystalline nanostructures calculated using phonon transport simulations, which shows that it effectively predicts the MFP. Therefore, the proposed method can be used to efficiently determine the phonon MFP in nanostructures with sufficient accuracy.

Analytical models for phonon mean free path in polycrystalline nanostructures based on mean square displacement

In this study, a numerical simulation method and analytical models for predicting the boundary scattering mean free path (MFP) of phonons in polycrystalline nanostructures are developed. The grain morphologies are assumed to be approximately equiaxed, i.e., forbidding needle-like or pancake-like morphologies. Adapting a technique from rarefied gas dynamics, the method evaluates the MFP from the mean square displacements of phonons that experience random motion and interface collisions in nanostructures. We confirm that the MFP in simple cubic polycrystalline nanostructures obtained by the simulations agrees with that reported in a previous study; this result supports the validity of the method. Two analytical models for high and low interfacial transmission probabilities at the crystal interfaces are also derived by considering the mean square displacements. We find that the grain-boundary intercept length distribution of polycrystalline structures is an essential parameter for determining this boundary scattering MFP. These analytical models reproduce the MFPs in simple cubic and Voronoi diagram polycrystalline nanostructures calculated by the numerical simulations. This result indicates that the boundary scattering MFP of phonons in polycrystalline nanostructures can be obtained once the intercept length distribution is evaluated, without any additional numerical simulations.

Stellar Energetic Particle Transport in the Turbulent and CME-disrupted Stellar Wind of AU Microscopii

Energetic particles emitted by active stars are likely to propagate in astrospheric magnetized plasma and disrupted by the prior passage of energetic coronal mass ejections (CMEs). We carried out test-particle simulations of ∼GeV protons produced at a variety of distances from the M1Ve star AU Microscopii by coronal flares or traveling shocks. Particles are propagated within a large-scale quiescent three-dimensional magnetic field and stellar wind reconstructed from measured magnetograms, and within the same stellar environment following the passage of a 1036 erg kinetic energy CME. In both cases, magnetic fluctuations with an isotropic power spectrum are overlayed onto the large-scale stellar magnetic field and particle propagation out to the two innnermost confirmed planets is examined. In the quiescent case, the magnetic field concentrates the particles into two regions near the ecliptic plane. After the passage of the CME, the closed field lines remain inflated and the reshuffled magnetic field remains highly compressed, shrinking the scattering mean free path of the particles. In the direction of propagation of the CME lobes the subsequent energetic particle (EP) flux is suppressed. Even for a CME front propagating out of the ecliptic plane, the EP flux along the planetary orbits highly fluctuates and peaks at ∼2–3 orders of magnitude higher than the average solar value at Earth, both in the quiescent and the post-CME cases.

Determination of scattering mean free path in magnetic nanoparticle suspensions

Determination of scattering mean free path in magnetic nanoparticle suspensions