Multiple-scattering Model Research Articles

Measurement of nuclear interaction cross sections towards neutron-skin thickness determination

The accuracy of reaction theories used to extract properties of exotic nuclei from scattering experiments is often unknown or not quantified, but of utmost importance when, e.g., constraining the equation of state of asymmetric nuclear matter from observables as the neutron-skin thickness. In order to test the Glauber multiple-scattering model, the total interaction cross section of ▪ on carbon targets was measured at initial beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The measurements were performed during the first experiment of the newly constructed R3B (Reaction with Relativistic Radioactive Beams) experiment after the start of FAIR Phase-0 at the GSI/FAIR facility with beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The combination of the large-acceptance dipole magnet GLAD and a newly designed and highly efficient Time-of-Flight detector enabled a precise transmission measurement with several target thicknesses for each initial beam energy with an experimental uncertainty of ±0.4%. A comparison with the Glauber model revealed a discrepancy of around 3.1% at higher beam energies, which will serve as a crucial baseline for the model-dependent uncertainty in future fragmentation experiments.

Monte Carlo simulations of charged particle transport in plasmas: A fast single-scattering model

When simulating a charged particle trajectory in plasmas with Monte Carlo methods, the traditional single-scattering model is accurate but computationally expensive. The traditional multiple-scattering model reduces the computation cost but assumes an exponential distribution of the scattering angle, which overestimates the cumulative scattering angle. In this paper, we develop a new Monte Carlo method for the charged particle transport simulations. The scattering angle is naturally sampled from a modified screened Rutherford scattering cross section, in which a greatly amplified minimum deflection angle is used. With this model, the simulations give the same scattering angle distribution with the single-scattering model but only take a comparable computation cost with the multiple-scattering model when the small scattering angle and Markovian approximations can be fulfilled. This model would be especially useful for the study of inertial-confinement-fusion, which is sensitive to the alpha-particle energy deposition.

Multiple-scattering model for the effective refractive index of dense suspensions offorward-scattering particles.

We present a multiple-scattering model for the effective refractive index of an arbitrarily dense suspension of forward-scattering particles. The model provides a very simple formula for the effective refractive index of such a suspension and reproduces with high accuracy available experimental results. Furthermore, the derivation we present herein is mathematically transparent and enables us to obtain information on the underlying physical processes rather than obscuring them. We also provide insight into the extent of the model's validity and a simple way to determine whether or not it will be valid for an arbitrary suspension. Due to its simplicity, analytical closedness, and wide range of applicability, we believe the model can be used as a diagnostic tool for complex materials of vastly different natures.

Multiple Scattering Model for Beam Synthesis With Reconfigurable Intelligent Surfaces

This article presents a method of synthetic beamforming for reconfigurable intelligent surfaces (RIS). The method uses a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> -matrix based multiple scattering model to compute the scattering from the RIS. We assume that the elements of the RIS are infinite circular cylinders. This allows us to make the model two-dimensional. Furthermore, we assume that the RIS elements satisfy the impedance boundary condition (IBC), the complex parameter of which adjusts the phase shift of the scattered field. We synthesize the beam both analytically and numerically. Both approaches rely on an approximation that assumes RIS elements that are small compared to the wavelength. We demonstrate the efficacy of the beam synthesis by applying it in a test case that features a linear array of RIS elements.

Impact of aerosols on the polarization patterns of full-sky background radiation.

Regarding aerosol particle-laded turbid atmospheres, full-sky background radiation polarization patterns can be adversely affected, an important factor limiting their effective near-ground observation and acquisition. We established a multiple-scattering polarization computational model and measurement system and conducted the following three tasks. (a) We thoroughly analyzed the impact of aerosol scattering characteristics on polarization distributions, calculating the degree of polarization (DOP) and angle of polarization (AOP) patterns for a more comprehensive set of atmospheric aerosol compositions and aerosol optical depth (AOD) values than calculated in previous studies. (b) We assessed the uniqueness of the DOP and AOP patterns as a function of AOD. (c) By employing a new polarized radiation acquisition system for measurements, we demonstrated that our computational models are more representative of the DOP and AOP patterns under actual atmospheric conditions. We found that under a clear sky without clouds, the impact of the AOD on the DOP was detectable. With increasing AOD, the DOP decreased, and the decreasing trend became increasingly obvious. When the AOD was above 0.3, the maximum DOP did not exceed 0.5. The AOP pattern did not change notably and remained stable, except for the contraction point at the sun position under an AOD of 2.

Three-dimensional bi-functional refractive index and fluorescence microscopy (BRIEF).

Fluorescence microscopy is a powerful tool for imaging biological samples with molecular specificity. In contrast, phase microscopy provides label-free measurement of the sample's refractive index (RI), which is an intrinsic optical property that quantitatively relates to cell morphology, mass, and stiffness. Conventional imaging techniques measure either the labeled fluorescence (functional) information or the label-free RI (structural) information, though it may be valuable to have both. For example, biological tissues have heterogeneous RI distributions, causing sample-induced scattering that degrades the fluorescence image quality. When both fluorescence and 3D RI are measured, one can use the RI information to digitally correct multiple-scattering effects in the fluorescence image. Here, we develop a new computational multi-modal imaging method based on epi-mode microscopy that reconstructs both 3D fluorescence and 3D RI from a single dataset. We acquire dozens of fluorescence images, each 'illuminated' by a single fluorophore, then solve an inverse problem with a multiple-scattering forward model. We experimentally demonstrate our method for epi-mode 3D RI imaging and digital correction of multiple-scattering effects in fluorescence images.

Computationally Efficient Millimeter-Wave Scattering Models: A Multiple-Scattering Model

Backscattering by objects is a relevant phenomenon in millimeter-wave (mm-wave) propagation. Accordingly, computationally efficient models characterizing this process are now available in the literature. However, these models are restricted to single-surface contributions. In this article, we propose a multiple-scattering model for calculating backscattered fields due to consecutive interactions with several smooth electrically-large rectangular surfaces. The model is fundamentally based on the cascading of single-scattering events. In addition, the model is later extended to capture single-scattering blockage between backscattering events. The model is implemented using a Fresnel-integral-based method and validated by means of electromagnetic (EM) simulations and measurements. Furthermore, insight on the effects of the model parameters—number of surfaces, frequency, surface size, surface height-to-width ratio, surface displacement, and antenna-to-surface and surface-to-surface distances—is provided. Due to its computational efficiency, the proposed model can be suitable for system- and link-level simulations of wireless systems, particularly when Monte Carlo simulations are applied.

High-fidelity intensity diffraction tomography with a non-paraxial multiple-scattering model.

We propose a novel intensity diffraction tomography (IDT) reconstruction algorithm based on the split-step non-paraxial (SSNP) model for recovering the 3D refractive index (RI) distribution of multiple-scattering biological samples. High-quality IDT reconstruction requires high-angle illumination to encode both low- and high- spatial frequency information of the 3D biological sample. We show that our SSNP model can more accurately compute multiple scattering from high-angle illumination compared to paraxial approximation-based multiple-scattering models. We apply this SSNP model to both sequential and multiplexed IDT techniques. We develop a unified reconstruction algorithm for both IDT modalities that is highly computationally efficient and is implemented by a modular automatic differentiation framework. We demonstrate the capability of our reconstruction algorithm on both weakly scattering buccal epithelial cells and strongly scattering live C. elegans worms and live C. elegans embryos.

Broadband Negative Reflection of Underwater Acoustic Waves from a Simple Metagrating: Modeling and Experiment

Metagratings are periodic arrays of subwavelength scatterers, or atoms, engineered to refract or reflect waves toward anomalous directions with unit efficiency. Here, we design and build a metagrating to control the reflection direction of waterborne ultrasound waves impinging on a rigid or free surface. The grating and its atoms are designed to cancel the specular reflection and to redirect acoustic power toward a negative-reflection direction, through the first-negative-order Floquet mode. Despite a simple design, based on C-shaped brass particles acting as Helmholtz resonators, the grating is efficient ($&gt;90\mathrm{%}$) over a relatively broad range of frequencies (74--103 kHz) for a broad range of incidence angles (${14}^{\ensuremath{\circ}}$--${54}^{\ensuremath{\circ}}$). This good performance is obtained by tuning the distance between the atoms and the reflective surface. A multiple-scattering analytical model is presented to explain the phenomenon and a finite-element model is developed to further investigate the performance of the proposed design. Predictions from the model are confirmed experimentally in a water tank. The simplicity, reconfigurability, and scalability of the design, as well as its high efficiency, broadband behavior, and robustness to the incidence angle are all features that make the grating potentially useful for various applications in underwater acoustics, such as telemetry, communication, or noise mitigation.

A Novel Fast Multiple-Scattering Approximate Model for Oceanographic Lidar

An effective lidar simulator is vital for its system design and processing algorithms. However, laser transmission is a complex process due to the effects of sea surface and various interactions in seawater such as absorption, scattering, and so on. It is sophisticated and difficult for multiple scattering to accurately simulate. In this study, a multiple-scattering lidar model based on multiple-forward-scattering-single-backscattering approximation for oceanic lidar was proposed. Compared with previous analytic models, this model can work without assuming a homogeneous water and fixed scattering phase function. Besides, it takes consideration of lidar system and environmental parameters including receiver field of view, different scattering phase functions, particulate sizes, stratified water, and rough sea surface. One should note that because the scattering phase function is difficult to determine accurately, the simulation accuracy may be reduced in a complex oceanic environment. The Cox–Munk model used in our method simulates capillarity waves but ignores gravity waves, and the pulse stretching is not included. The wide-angle scattering occurs in the dense subsurface phytoplankton, which sometimes makes it hard to use this model. In this study, we firstly derived this method based on an analytical solution by convolving Gaussians of the forward-scattering contribution of layer dr and the energy density at R in the small-angle-scattering approximation. Then, the effects of multiple scattering and water optical properties were analyzed using the model. Meanwhile, the validation with Monte Carlo model was implemented. Their coefficient of determination is beyond 0.9, the RMSE is within 0.02, the MAD is within 0.02, and the MAPD is within 8%, which indicates that our model is efficient for oceanographic lidar simulation. Finally, we studied the effects of FOV, SPF, rough sea surface, stratified water, and particle size. These results can provide reference for the design of the oceanic lidar system and contribute to the processing of lidar echo signals.

Unsupervised single-image dehazing using the multiple-scattering model

An unsupervised single-image dehazing method using a multiple scattering model is proposed. The method uses an undegraded atmospheric multiple scattering model and unsupervised learning to implement dehazing on single real-world image. The atmospheric multiple scattering model can avoid the influence of multiple scattering on the image and the unsupervised neural network can avoid the intensive operation on the data set. In this method, three unsupervised learning branches and a blur kernel estimation module estimate the scene radiation layer, transmission layer, atmospheric light layer, and blur kernel layer, respectively. In addition, the unsupervised loss function is constructed by prior knowledge to constrain the unsupervised branches. Finally, the output of the three unsupervised branches and the blur kernel estimation module synthesizes the haze image in a self-supervised way. A large number of experiments show that the proposed method has good performance in image dehazing compared with the six most advanced dehazing methods.

FMCW Laser Fuze Multiple Scattering Model and Accurate Fixed-Distance Algorithm in a Smoke Environment.

In a smoke environment, suspended particles can scatter and absorb laser photons, making target echo signals extremely weak and difficult to extract and identify, which causes obvious difficulty in fixed-distance of laser fuze. In this paper, the multiple scattering model of frequency-modulated-continuous-wave (FMCW) laser fuze in a smoke environment was established. This model simulates multi-path propagation and multiple scattering of photons. At the same time, we use the correntropy spectral density (CSD) algorithm for accurate fixed-distance of FMCW laser fuze. The absolute error of distance does not exceed 0.15 m in smoke interference environment.

Multi-layer Born multiple-scattering model for 3D phase microscopy

We propose an accurate and computationally efficient 3D scattering model, multi-layer Born (MLB), and use it to recover the 3D refractive index (RI) of thick biological samples. For inverse problems recovering the complex field of thick samples, weak scattering models (e.g., first Born) may fail or underestimate the RI, especially with a large index contrast. Multi-slice (MS) beam propagation methods model multiple scattering to provide more realistic reconstructions; however, MS does not properly account for highly oblique scattering, nor does it model backward scattering. Our proposed MLB model uses a first Born model at each of many slices, accurately capturing the oblique scattering effects and estimating the backward scattering process. When used in conjunction with an inverse solver, the model provides more accurate RI reconstructions for high-resolution phase tomography. Importantly, MLB retains a reasonable computation time that is critical for practical implementation with iterative inverse algorithms.

Image Conditions for Elliptical-Coordinate Separation-of-Variables Acoustic Multiple Scattering Models with Perfectly Reflecting Flat Boundaries: Application to in Situ Tunable Noise Barriers

SummaryTwo-dimensional time-harmonic multiple scattering problems are addressed for a finite number of elliptical objects placed in wedge-shaped acoustic domains including half-plane and right-angled corners. The method of separation of variables in conjunction with the addition theorems is employed in the elliptical coordinates. The wavefunctions are represented in terms of radial and angular Mathieu functions. The method of images is applied to consider the effect of the infinitely long flat boundaries which are perfectly reflecting: either rigid or pressure release. The wedge angle is $\pi/n$ rad with integer $n$; image ellipses must be appropriately rotated to realise the mirror reflection. Then, the ‘image conditions’ are developed to reduce the number of unknowns by expressing the unknown expansion coefficients of image scattered fields in terms of real counterparts. Use of image conditions, therefore, leads to the $4n^2$-fold reduction in the size of a matrix for direct solvers and $2n$-times faster computation in building the system of linear equations than the approach without using them. Multiple scattering models using image conditions are formulated for rigid, pressure release and fluid ellipses under either plane- or cylindrical-wave incidence, and are numerically validated by the boundary element method. Furthermore, potential applications are presented: arrays of elliptically shaped scatterers make in situ tunable noise barriers by rotating scatterers. Finally, polar-coordinate image conditions (for circular objects) are also discussed when coordinates local to circles are also rotated. In Appendix, analytic formulae are provided, which permits the elliptical-coordinate addition theorems used in this article to be calculated by summation instead of numerical integration.

Multiple scattering model considering the vibration effect

The independent atomic (IAM) and the multiple scattering (MS) models are recently adopted to extract the molecular geometrical structures from the electron diffraction images, especially, in the laser-induced electron diffraction. In this study, firstly, we clarify the working range of the MS and the IAM models by comparing its diffraction images at various collision energies. We claim that the MS model is effective at low energy of incident electron while both MS and IAM models give similar results at high collision energy. Secondly, we successfully develop the MS model by numerically including the molecular vibration. By comparing with the diffraction patterns calculated within the IAM model at considerably high collision energy, we verify the accuracy of the developed MS model. We show that the diffraction curves simulated by the MS and IAM methods considering the vibration effect are consistent with each other. Moreover, the extracted interatomic distance from diffraction images well agrees with the initial input. This evidence proves that the MS model with the vibration effect is reliable.

三维云层遥感辐射传输中的水平方向邻域多次散射近似模型

三维云层遥感辐射传输中的水平方向邻域多次散射近似模型

Three-dimensional kernel-based coda attenuation imaging of caldera structures controlling the 1982-84 Campi Flegrei unrest

Coda-wave attenuation imaging has risen as a state-of-the-art technique to depict volcanic structures using their dispersion effects. The 1982–84 seismic and deformation unrest at Campi Flegrei caldera (Italy) is a unique example of non-eruptive volcanic activity in a structured caldera. Here, we propose the first application of 3D coda-attenuation kernels to image caldera structures at multiple frequencies during unrest. Using sensitivity kernels is necessary to assess the effective resolution of coda imaging in highly heterogeneous volcanoes. The technique relies on the solution of Paasschens' equations in the framework of radiative transfer theory. The results map coda attenuation in the 3D space without need of pre-existent velocity models. The resolution and stability of the inversion solutions were examined by changing the damping parameters and outputting the corresponding images, inverting for different node spacings and performing checkerboard tests. These tests show that the resolution of the multiple-scattering model is much lower than that provided by a standard isotropic-scattering and/or single scattering technique. The best resolution in our model is obtained between depths of 1 km and 3 km in the centre of the model, between Pozzuoli town and Solfatara crater. The results are discussed at a frequency of 3 Hz, due to both longer coda durations and broader kernel illumination: in this frequency range, coda-based 3D imaging had so far failed to provide stable results. The interpretation is performed based on the extensive geological and geophysical knowledge of the caldera. High-attenuation anomalies below Solfatara and Monte Nuovo mark areas either saturated with water or enriched in molten rocks, feeding the respective fumarole fields. The flattening and horizontal elongation of these anomalies below 2 km depth is a manifestation of the blocking and spreading around of the rising hot magmatic fluids below a previously-inferred high-velocity, low-attenuation and highly-deforming caprock. This caprock is not uniform, likely due to the remnants of erupted structure. A SW-to-NE-trending low-attenuation and high-velocity anomaly deeps down to 3 km under Pozzuoli. We infer that the high seismicity in the region is a consequence of the stress sustained by the caprock from a 4-km-deep deformation source in 1983–84. On top of this source, high coda attenuation corresponds to high Vp/Vs ratios and high direct-wave attenuation. The region's characteristics are likely due to the accumulation of magmatic fluids above a magmatic sill.

Analytical simulator of proton radiography and tomography for different detector configurations

PurposeAn analytical simulator of ion Radiography (iRad) and Computed Tomography (iCT) for protons is proposed to serve as imaging benchmark for different detector configurations. MethodsThe analytical simulator is applied to an anthropomorphic phantom and provides iRad and iCT benchmarks. Proton trajectories are traced relying on the Most Likely Path (MLP) algorithm. To simulate the proton trajectories the Multiple Coulomb Scattering (MCS) model embedded in the MLP algorithm is extended to non-uniform water equivalent materials according to variable substitution in the well-known statistical description in uniform water. The proton trajectories are instead estimated relying on the typical assumption of uniform water, thus causing intrinsic inaccuracies of the MLP algorithm. In this work the analytical simulator is used to explore and firstly compare the imaging performances of list-mode and integration-mode detector configurations with proton pencil beam scanning. ResultsThe intrinsic inaccuracies of the MLP algorithm affect the imaging performances of list-mode detector configuration, which nevertheless remains superior to integration-mode detector configuration for iCTs. For relatively higher proton statistics, comparable or better imaging performances are offered by integration-mode detector configuration for iRads (upto 29.2% of WET difference). Uncertainties of proton trajectories due to beam spot size are shown to compromise the imaging performances of integration-mode detector configuration, but also to affect the accuracy of the MLP algorithm for list-mode detector configuration. ConclusionsBased on MCS model in non-uniform water equivalent materials, the proposed simulation environment can serve for development and testing of dedicated imaging methodologies prior to and in combination with realistic Monte Carlo simulations.

Image conditions and addition theorems for prolate and oblate spheroidal-coordinate separation-of-variables acoustic multiple scattering models with perfectly-reflecting flat surfaces

Abstract Three-dimensional time-harmonic acoustic multiple scattering problems are considered for a finite number of prolate and oblate spheroidal objects adjacent to flat surfaces. Wave propagation by spheroids is modelled by the method of separation of variables equipped with the addition theorems in the spheroidal coordinates. The effect of flat surfaces is accounted for by using the method of images; hence, the flat surfaces are of (semi-)infinite extent and perfectly reflecting: either rigid or pressure release. Wedge-shaped acoustic domains are constructed including half-space and right-angled corners with the wedge angle of $\pi /n$ rad with positive integer $n$. First, Euler angles are implemented to rotate image spheroids to realize the mirror reflection. Then, the ‘image conditions’ are developed to reduce the number of unknowns by expressing the unknown expansion coefficients of image-scattered fields in terms of real counterparts. Use of image conditions to 2D wedges, therefore, leads to the $4n^2$-fold reduction in the size of a matrix for direct solvers and $2n$-times faster computation than the approach without using them; for 3D wedges, the savings are $16n^2$-fold and $4n$-times, respectively. Multiple scattering models (MSMs) are also formulated for fluid, rigid and pressure-release spheroids under either plane- or spherical-wave incidence; novel addition theorems are also derived for spheroidal wavefunctions by using two rotations of spherical wavefunctions and a $z$-axis translation in-between, which is shown numerically more efficient than other addition theorems based on an arbitrary-direction translation and a single rotation. Finally, MSMs using image conditions are numerically validated by the boundary element method for a configuration populated with both prolate and oblate spheroids.

On the accuracy and efficiency of condensed history transport in magnetic fields in GEANT4

The purpose of this work was to investigate the accuracy and efficiency of electron transport in GEANT4 with and without a magnetic field present. Fano cavity simulations were performed in GEANT4 version 10.02 and 10.04.p01 using two multiple scattering (MSC) algorithms for two slab and one pseudo-ion chamber geometries. An iterative approach was used to optimize the transport parameters to obtain agreement with theory. Similar to previous works, the step lengths had to be severely restricted to obtain agreement with theory when using the Urban MSC model in GEANT4 v10.02. Using the Goudsmit–Saunderson MSC model with the UseSafetyPlus MSC step limitation in GEANT4 v10.04.p01 limited the maximum discrepancy from theory to 0.5%. Minor adjustments to the transport parameters were needed to obtain agreement within 0.16% of theory for all simulation configurations without a magnetic field present. The maximum deviation from theory was within 2% for all simulation configurations in the presence of a magnetic field except for two setups that exhibited discrepancies of up to 10.8%. This anomalous behavior was mitigated by forcing single scattering within the detector gas volume. Further adjustments to the transport parameters resulted in agreement with theory at the 0.21% level. Agreement with theory in the absence of a magnetic field can be obtained without significantly restricting the step size if the Goudsmit–Saunderson MSC model is used with the UseSafetyPlus MSC step limitation in GEANT4 v10.04.p01. The large discrepancies from theory observed for two simulation setups with a magnetic field present were attributed to an issue with energy loss sampling over a step when strict magnetic field transport parameters are used. This problem can be corrected by forcing single scattering within the detector gas volume; however, more work is needed to identify the cause of this anomalous behavior. This work has shown that GEANT4 can perform accurate electron transport with and without a magnetic field present without applying significant step-size reductions.