Single-scattering Approximation Research Articles

Application of Slip Interface Conditions in the Elastic Parabolic Equation

The parabolic equation method is the most effective approach for solving wave propagation problems in environments with strong vertical variations and gradual horizontal variations. This approach efficiently provides accurate solutions for problems involving sloping fluid-fluid interfaces, sloping solid-solid interfaces, and sloping solid boundaries. There remains a need for improvement for the case of sloping fluid-solid interfaces. The most promising approach to date is the combination of a single-scattering approximation and the treatment of part of the fluid layer as a solid layer with low shear speed. This is a singular perturbation, which results in rapid oscillations near the interface between the low-speed layer and the true solid layer. It is demonstrated here that the rapid oscillations may be eliminated by using slip conditions at the interface between the low-speed layer and the true solid layer. Stability problems were encountered when attempting to directly implement the slip conditions, but this problem was resolved by using an equivalent condition involving the normal derivative of the tangential displacement. This progress does not fully resolve the case of the sloping fluid-solid interface. There remains a need to find a vertical interface condition that is compatible with the slip conditions and that provides accurate results for problems involving sloping fluid-solid interfaces.

Laser light propagation in a turbid medium: solution including multiple scattering effects

We have shown that solutions to the radiative transfer equation for a homogeneous slab yield a zenith radiance reflectance that for collimated beam incidence in the nadir direction can be expressed in terms of the lidar ratio, defined as the extinction coefficient divided by the 180^circ backscattering coefficient. The recently developed QlblC method, which allows one to quantify layer-by-layer contributions to radiances emerging from a slab illuminated with a collimated beam of radiation, was used to show explicitly that in the single-scattering approximation the attenuated backscatter coefficient estimated by the new QlblC method gives the same result as the lidar equation. Originally developed for the continuous wave (CW) lidar problem, we have extended the new QlblC method to apply to the pulsed lidar problem. A specific example is provided to illustrate the challenge encountered for ocean property retrievals from space observations due to the fact that a very significant fraction of the signal is due to aerosol scattering/absorption; typically only about 10% (or less) comes from the ocean.Graphical abstract

A note on Marchenko-linearised full waveform inversion for imaging

SUMMARY Full waveform inversion and least-squares reverse time migration are the leading technologies for imaging with seismic waves. Both of them usually rely (in one way or another) on a single-scattering approximation, i.e. the Born approximation, to compute gradients and obtain an updated model. This approximation linearises the relation between modelled data and model by ignoring multiple scattering. We propose to use the Marchenko integral, an equation originating from inverse scattering theory, to obtain an alternative linear equation. Using the Marchenko method we can retrieve Green’s functions, including all orders of scattering, for virtual sources anywhere within the volume of interest – without prior knowledge of the high-wavelength model variations that induce scattering. Plugging these estimated Green’s functions into the Lippmann–Schwinger integral delivers a Marchenko-linearised relation between the full waveform data and the model. We present this new linearisation strategy and illustrate its advantages and disadvantages by comparing numerical results for different inversion kernels. Our new linearisation is exact, i.e. it does not exclude any orders of scattering, however, it relies on the quality of the Marchenko-derived Green’s functions. These Marchenko-based Green’s functions require an estimate of the first arrivals of the Green’s functions – commonly obtained by modelling in a background medium. Although these first arrival estimates strongly bias our results for inaccurate background models, we find the Marchenko-linearisation to deliver overall slightly better inverted models than the single-scattering approximation.

On the colour of noctilucent clouds

Abstract. The high-latitude phenomenon of noctilucent clouds (NLCs) is characterised by a silvery-blue or pale blue colour. In this study, we employ the radiative transfer model SCIATRAN to simulate spectra of solar radiation scattered by NLCs for a ground-based observer and assuming spherical NLC particles. To determine the resulting colours of NLCs in an objective way, the CIE (International Commission on Illumination) colour-matching functions and chromaticity values are used. Different processes and parameters potentially affecting the colour of NLCs are investigated, i.e. the size of the NLC particles, the abundance of middle atmospheric O3 and the importance of multiply scattered solar radiation. We affirm previous research indicating that solar radiation absorption in the O3 Chappuis bands can have a significant effect on the colour of the NLCs. A new result of this study is that for sufficiently large NLC optical depths and for specific viewing geometries, O3 plays only a minor role for the blueish colour of NLCs. The simulations also show that the size of the NLC particles affects the colour of the clouds. Cloud particles of unrealistically large sizes can lead to a reddish colour. Furthermore, the simulations show that the contribution of multiple scattering to the total scattering is only of minor importance, providing additional justification for the earlier studies on this topic, which were all based on the single-scattering approximation.

Modal formulation and paraxial approximation for acoustic wave propagation in waveguides with surface perturbations.

We propose a modal approach developed in the framework of the paraxial approximation to investigate the effects of deterministic surface perturbations in a planar waveguide. In the first part, the sensitivity of the modal amplitudes is theoretically formulated for a three-dimensional perturbation at the air-water interface. When applied to a broadband ultrasonic signal in a laboratory tank experiment, this approach results in travel-time and amplitude fluctuations that are successfully compared to experimental data recorded between two vertical source-receiver arrays that span the ultrasonic waveguide. The nonlinear shape of the modal amplitude fluctuations is of particular interest and is due to the three-dimensional nature of the surface perturbation. In the second part, a time-harmonic inversion method is built in the paraxial single-scattering approximation to image the dynamic surface perturbation from the modal transmission matrix between two source-receiver arrays. Again, the inversion results for capillary-gravity surface perturbations are successfully compared to similar inversions performed from experimental data processed with a complete set of eigenbeams extracted between the two arrays.

Empirical model of multiple-scattering effect on single-wavelength lidar data of aerosols and clouds

Abstract. We performed extensive Monte Carlo (MC) simulations of single-wavelength lidar signals from a plane-parallel homogeneous layer of atmospheric particles and developed an empirical model to account for the multiple scattering in the lidar signals. The simulations have taken into consideration four types of lidar configurations (the ground based, the airborne, the CALIOP, and the ATLID) and four types of particles (coarse aerosol, water cloud, jet-stream cirrus, and cirrus). Most of the simulations were performed with a spatial resolution 20 m and particle extinction coefficients εp between 0.06 and 1.0 km−1. The resolution was 5 m for high values of εp (up to 10.0 km−1). The majority of simulations for ground-based and airborne lidars were performed at two values of the receiver field of view (RFOV): 0.25 and 1.0 mrad. The effect of the width of the RFOV was studied for values up to 50 mrad. The proposed empirical model is a function that has only three free parameters and approximates the multiple-scattering relative contribution to lidar signals. It is demonstrated that the empirical model has very good quality of MC data fitting for all considered cases. Special attention was given to the usual operational conditions, i.e. low distances to a layer of partices, small optical depths, and quite narrow receiver fields of view. It is demonstrated that multiple-scattering effects cannot be neglected when the distance to a layer of particles is about 8 km or higher, and the full RFOV is 1.0 mrad. As for the full RFOV of 0.25 mrad, the single-scattering approximation is acceptable; i.e. the multiple-scattering contribution to the lidar signal is lower than 5 % for aerosols (εp≲1.0 km−1), water clouds (εp≲0.5 km−1), and cirrus clouds (εp≤0.1 km−1). When the distance to a layer of particles is 1 km, the single-scattering approximation is acceptable for aerosols and water clouds (εp≲1.0 km−1, both RFOV = 0.25 and RFOV = 1 mrad). As for cirrus clouds, the effect of multiple scattering cannot be neglected even at such low distances when εp≳0.5 km−1.

Multi-Parameter True-Amplitude Generalized Radon Transform Inversion for Acoustic Transversely Isotropic Media With a Vertical Symmetry Axis

In anisotropic media, the compressional wave scattering phenomena is governed by several parameters and can be simulated using a good kinematic approximation. How to retrieve anisotropic properties from recorded seismic data free of shear waves for exploration geophysics is interesting and challenging. We present an approach to infer the material properties in acoustic transversely isotropic (TI) media with a vertical axis of symmetry (VTI) described by a combination of the normal-moveout velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v_{n}$ </tex-math></inline-formula> and anisotropic parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> . The method we consider is based on the true-amplitude generalized Radon transform (GRT) inversion strategy. Because the scattering integral is at the kernel of the inversion engine, we start our investigation from a fourth-order pseudo-acoustic VTI equation instead of the conventionally coupled system of second-order wave equations. With the single-scattering approximation and high-frequency asymptotic analysis, the integral representation of P-wave scattered wavefield is incorporated into a weighted GRT operator that contains VTI scattering patterns of each parameter perturbation, which leads the way in constructing an acoustic VTI amplitude-preserving GRT pseudo-inverse operator. We describe an appropriate survey design by shooting a fan of rays from the target area toward the acquisition system, which is necessary when calculating the pseudo-inverse operator. Numerical test results from 2-D synthetic data verify the effectiveness of our method.

The effective medium for a cylinder with cylindrical inclusions.

In this paper, the scattering from a fluid-filled (infinite length) cylinder is considered. This cylinder, C, has a different interior sound speed and density than the surrounding water. Within the cylinder's interior, there are a number of smaller cylinders, inclusions, with yet other sound speeds and densities. The mean coherent field scattered from C is computed using Monte Carlo simulations with respect to the random realizations of the inclusion positions and compared to the results computed using an effective sound speed for C. An original formula for the effective sound speed is derived by equating the reflection coefficient for C (without inclusions) to the expected coherent scattered field from C with inclusions, assuming a single-scattering approximation. A single realization of inclusions is also considered with the backscattered spectra averaged azimuthally over the angle of the source/receiver pair. This result is then compared to the coherent fields predicted by the effective medium theory. This is performed for both spectra and the computed time series.

Investigation of the single scattering approximation through direct electromagnetic scattering simulation

In this work, we investigate quantitatively the applicability conditions of single scattering approximation (SSA) through direct simulation of electromagnetic scattering by small volume elements filled with randomly distributed spherical particles. The influences of size parameter x, volume fraction fv, complex refractive index m and number N of particles on the nondimensional extinction cross section ηext and absorption cross section ηabs of particle groups are discussed. For non-absorbing particles with small size parameters (x = 0.1 and 0.2 in this study), due to the small phase shift across particles, the particle refractive index has almost no influence on the criteria for SSA. However, when the particle size increases or particle absorption is enhanced, the criteria for SSA will be closely related to the particle complex refractive index. Moreover, when the particle size is small, due to the weak multiple scattering between particles, the criteria for SSA can be regarded as the criteria for independent scattering approximation (ISA). But as the particles increase to relatively large sizes (x = 4.0 in this study), because of the enhancement of multiple scattering, the criteria for SSA and ISA should be treated differently. The widely used criteria obtained for bispheres may not be applicable to particle groups composed of lots of particles, and the optical thickness of dispersed media is not suitable for evaluating the applicability conditions of SSA. For particle groups composed of different particle numbers, due to the differences in dependent scattering and multiple scattering, the criteria for SSA are obviously different and the particle volume fraction should be small enough to make the SSA sufficiently accurate.

Temperature-dependent particle stability behavior and its effect on radiative transfer in water/SiO2 nanofluids

Radiative transfer is one of the methods of energy transport that includes in a wide range of applications and we feel it in our daily lives. Thermal radiation transfer plays an effective role in the utilization of renewable energy. The radiative and optical properties, as well as the nature of the radiative scattering, are the basic principles of the thermal radiation transfer. The unique properties of nanofluids offer the unmatched potential for use in energy utilization, the working temperature has a dominant effect on the stability and radiative properties of such type of suspensions. In this research, the radiative transfer (optical properties, the independent and dependent scattering, and radiative properties) in water/SiO2 nanofluids are investigated; taking into consideration the effect of working temperature on the stability of the particles. The effect of the temperature on the stability ratio and particle agglomeration is determined by estimating the radius of gyration of particle agglomerates using the scaling law based on the stability (DLVO) method. The single-scattering approximation (SSA) is used to calculate the radiative properties in the case of independent scattering, while the quasi-crystalline approximation (QCA) is used for this purpose in the case of dependent scattering. The results show that the temperature has a significant effect on the stability of particles and radiative transfer in nanofluids. It was observed by comparing the results from the two approximation methods in the Rayleigh regime. Particle size affects the physical and scattering cross-sectional areas which give a general understanding of the scattering mechanism from small to large particles.

Radiative analysis of luminescence in photoreactive systems: Application to photosensitizers for solar fuel production.

Most chemical reactions promoted by light and using a photosensitizer (a dye) are subject to the phenomenon of luminescence. Redistribution of light in all directions (isotropic luminescence emission) and in a new spectral range (luminescence emission spectrum) makes experimental and theoretical studies much more complex compared to a situation with a purely absorbing reaction volume. This has a significant impact on the engineering of photoreactors for industrial applications. Future developments associated with photoreactive system optimization are therefore extremely challenging, and require an in-depth description and quantitative analysis of luminescence. In this study, a radiative model describing the effect of luminescence radiation on the calculation of absorptance is presented and analyzed with the multiple inelastic-scattering approach, using Monte Carlo simulations. The formalism of successive orders of scattering expansion is used as a sophisticated analysis tool which provides, when combined with relevant physical approximations, convenient analytical approximate solutions. Its application to four photosensitizers that are representative of renewable hydrogen production via artificial photosynthesis indicates that luminescence has a significant impact on absorptance and on overall quantum yield estimation, with the contribution of multiple scattering and important spectral effects due to inelastic scattering. We show that luminescence cannot be totally neglected in that case, since photon absorption lies at the root of the chemical reaction. We propose two coupled simple and appropriate analytical approximations enabling the estimation of absorptance with a relative error below 6% in every tested situation: the zero-order scattering approximation and the gray single-scattering approximation. Finally, this theoretical approach is used to determine and discuss the overall quantum yield of a bio-inspired photoreactive system with Eosin Y as a photosensitizer, implemented in an experimental setup comprising a photoreactor dedicated to hydrogen production.

Effective elastic properties of porous rocks with fluid-filled vugs

The problem of determination of the effective elastic properties, particularly, the velocity and attenuation of the compressional wave propagating in porous rocks containing fluid-filled vugs is considered. Usually the correct interpretation of double- or triple-porosity formations using sonic logs is a complex problem, even nowadays with the use of the most advanced inversion algorithms and the contribution of other petrophysical tools. In this work, the proposed model considers spherical inclusions filled with viscous or ideal fluids aimed to represent geological vugs. This approach also considers the cases of “open” and “closed” interfaces at the boundary between the porous rock and the vug. To describe the propagation of elastic waves in porous rocks, the well-known Biot's theory is implemented. The calculations were fulfilled for the incidence of plane compressional harmonic waves. As the first step of performed calculations the so-called one-particle problem is solved. Then, the first order (single-scattering) approximation is applied to calculate the effective wave number of elastic waves propagating in a poroelastic rock containing sets of randomly distributed vugs. The results reported here show that the hydrodynamic effects associated with the fluid filtration at the boundaries between the vugs and the porous rock at the scale of the incident compressional wave, lead to significant frequency dispersion of the effective elastic wave velocity and its correspondent Q-factor. These hydrodynamic effects on the elastic properties are clearly appreciated at the sonic log frequency range. From the findings of this paper, it can be sustained that the elastic response of the fluid viscosity in the vugs is not so significant. This implies that it is possible to use the simple model of an ideal fluid in the vugs.

Linearized scattering problem in acoustic transversely isotropic media with a vertical symmetry axis

The ray-based generalized Radon transform (GRT) inversion/migration strategy is studied in this paper for acoustic transversely isotropic media with a vertical symmetry axis (VTI media) represented by the P-wave normal moveout velocity, Thomsen parameter δ, anelliptic parameter η, and density. The multi-parameter GRT inversion solutions for multi-shot/multi-offset acquisition geometries are derived from the single-scattering approximation of the wavefields and an elliptically anisotropic background. Results from classical two-dimensional numerical tests show the true amplitude properties of the GRT backprojection operators.

WawHelioGlow: A Model of the Heliospheric Backscatter Glow. I. Model Definition

Abstract The helioglow is the fluorescence of interstellar atoms inside the heliosphere, where they are excited by the solar EUV emission. So far, the helioglow of interstellar H and He has been detected. The helioglow features a characteristic distribution in the sky, which can be used to derive the properties of both interstellar neutral (ISN) gas and the solar wind. This requires a simulation model capable of catching with sufficient realism the essential coupling relations between the solar and interstellar factors. The solar factors include the solar wind flux and its variation with time and heliolatitude, as well as the heliolatitude and time variation of the solar EUV output. The ISN gas inside the heliosphere features a complex distribution function, which varies with time and location. The paper presents the first version of a WawHelioGlow simulation model for the helioglow flux using an optically thin, single-scattering approximation. The helioglow computations are based on a sophisticated kinetic treatment of the distribution functions of interstellar H and He provided by the (n)WTPM model. The model takes into account the heliolatitudinal and spectral variations of the solar EUV output from observations. We present a formulation of the model and the treatment of the solar spectral flux. The accompanying Paper II illustrates details of the line-of-sight evolution of the elements of the model and a brief comparison of results of the WawHelioGlow code with selected sky maps of the hydrogen helioglow, obtained by the SWAN instrument on board the Solar and Heliospheric Observatory mission.

Fast Hyper-Spectral Radiative Transfer Model Based on the Double Cluster Low-Streams Regression Method

Fast radiative transfer models (RTMs) are required to process a great amount of satellite-based atmospheric composition data. Specifically designed acceleration techniques can be incorporated in RTMs to simulate the reflected radiances with a fine spectral resolution, avoiding time-consuming computations on a fine resolution grid. In particular, in the cluster low-streams regression (CLSR) method, the computations on a fine resolution grid are performed by using the fast two-stream RTM, and then the spectra are corrected by using regression models between the two-stream and multi-stream RTMs. The performance enhancement due to such a scheme can be of about two orders of magnitude. In this paper, we consider a modification of the CLSR method (which is referred to as the double CLSR method), in which the single-scattering approximation is used for the computations on a fine resolution grid, while the two-stream spectra are computed by using the regression model between the two-stream RTM and the single-scattering approximation. Once the two-stream spectra are known, the CLSR method is applied the second time to restore the multi-stream spectra. Through a numerical analysis, it is shown that the double CLSR method yields an acceleration factor of about three orders of magnitude as compared to the reference multi-stream fine-resolution computations. The error of such an approach is below 0.05%. In addition, it is analysed how the CLSR method can be adopted for efficient computations for atmospheric scenarios containing aerosols. In particular, it is discussed how the precomputed data for clear sky conditions can be reused for computing the aerosol spectra in the framework of the CLSR method. The simulations are performed for the Hartley–Huggins, O2 A-, water vapour and CO2 weak absorption bands and five aerosol models from the optical properties of aerosols and clouds (OPAC) database.

Applicability of the single-scattering approximation for the ocean acoustic sounding

A mathematical model in the work that describes the process of pulsed high-frequency acoustic sounding in a fluctuating ocean is considered. The inverse problem for the non-stationary equation of acoustic radiative transfer is investigated. It consists in finding the coefficient of volume scattering from the angular distribution of the radiation flux density at a given point in space. In the single scattering approximation, a formula is obtained to find the scattering coefficient. A series of computational experiments was carried out to substantiate its use in acoustic sensing of a fluctuating water medium. A numerical analysis has shown that the application of the single scattering approximation is justified at least at a sensing range of the order of 100 meters. Moreover, double and triple scattered fields have the main effect on the error.

Simulation of High-Altitude Nuclear Electromagnetic Pulse Using a Modified Model of Scattered Gamma

High-altitude electromagnetic pulse (HEMP) generated by the photons from nuclear explosions is a threat to electronic and power systems. During the generation of HEMP, besides the gamma rays released directly by the nuclear devices, the scattered gamma rays can also produce recoil electrons that contribute to the Compton current and further conduction current. Therefore, the gamma-ray model containing both direct and scattered gamma is more accurate to be used in the simulation of HEMP environments. In this article, the modified gamma-ray model based on single-scattering approximation which considers the effects of scattered gamma is presented and the results of the modified model and the traditional prompt-gamma-only model are compared. It is concluded that the scattered gamma rays have little effect on the peak value and rising edge of HEMP. However, the scattered gamma rays influence the electric field at the end of early-time HEMP greatly. This method is also an approach to the scattered gamma component of intermediate-time HEMP.

Elsepa—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules (New Version Announcement)

A new version of the Fortran program elsepa, which calculates differential and integrated cross sections for elastic scattering of electrons and positrons, is presented. Details of the program and its applications are given in the original paper [Comput. Phys. Commun.165 (2005) 157–190]. Dirac phase shifts are now calculated by using the recently published subroutine package radial (Salvat and Fernández-Varea, 2019), which solves the radial wave equation for real or complex central potentials by means of a robust and accurate power-series method. In addition, elastic collisions with atoms in elemental solids are described by using the muffin-tin optical model potential proposed by Bote et al., (2009), which is somewhat more elaborate and flexible than that in the original elsepa code and allows adjusting the absorption potential to give inelastic cross sections in close agreement with empirical data. With the use of the radial subroutines, the work of elsepa is reduced to (1) the definition of the interaction potential and (2) the summation of the partial-wave series of the scattering amplitudes. The structure of the new code has been simplified and stricter criteria for the convergence of the partial-wave series have been adopted. The distribution package includes gnuplot scripts for easy visualization of the calculation results. Program summaryProgram Title:elsepaCPC Library link to program files:https://doi.org/10.17632/w4hm5vymym.1Licensing provisions: CC BY NC 3.0Programming language: Fortran 90Journal reference of previous version: Comput. Phys. Commun. 165 (2005) 157–190Does the new version supersede the previous version?: YesReasons for the new version: This new version offers increased accuracy, and a more flexible modeling of elastic collisions of electrons and positrons with atoms in elemental solids.Summary of revisions: The calculation of phase shifts is now performed by the generic subroutines of the radial package [1]. A more flexible optical-model potential for scattering in solids is included [2]. Stricter criteria for convergence of the partial-wave series are applied. The distribution package has been reorganized, with the numerical database files now placed in a separate directory; scripts for direct visualization of the calculation results with the plotting program gnuplot (http://www.gnuplot.info) are also included.Nature of problem: The code calculates differential cross sections, total cross sections and transport cross sections for single elastic scattering of electrons and positrons by neutral atoms, positive ions and randomly oriented molecules. When the energy of the projectile is less than about 5 MeV, the programs also compute scattering amplitudes and spin polarization functions.Solution method: The effective interaction between the projectile and the target atom is represented by a local central potential that can optionally include an imaginary (absorptive) part to account approximately for the coupling with inelastic channels. For projectiles with kinetic energy less that about 5 MeV, the code performs a conventional relativistic Dirac partial-wave analysis. For higher kinetic energies, where the convergence of the partial-wave series is too slow, approximate factorization methods are used. The programs only admit kinetic energies higher than 5 eV, a practical lower limit that may be changed by editing the source files.Additional comments including restrictions and unusual features: The calculations are based on the static-field approximation. The optional correlation-polarization and inelastic absorption corrections are obtained from approximate, semi-empirical models. elsepa allows considering an absorption potential only for projectiles with energies less than about 1 MeV; for higher energies, the absorption potential is set to zero to prevent the occurrence of numerical instabilities. Calculations for molecules are based on a single-scattering independent-atom approximation. To ensure accuracy of the results for scattering by ions, the electron density of the ion must be supplied by the user; it can be generated, e.g., by running the program dhfs of the radial package [1].AcknowledgmentsWe are indebted to Dr John Villarrubia for pointing out various cases of incomplete convergence of the original code. Financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades / Agencia Estatal de Investigación, Spain / European Regional Development Fund , European Union, (project no. RTI2018-098117-B-C22) is gratefully aknowledged.

Comprehensive measurements of cross sections and spin observables of the three-body break-up channel in deuteron-deuteron scattering at 65\xa0MeV/nucleon

Detailed measurements of five-fold differential cross sections and a rich set of vector and tensor analyzing powers of the ^{2}mathrm{H}({varvec{d}},dp){n} break-up process using polarized deuteron-beam energy of 65 MeV/nucleon with a liquid-deuterium target are presented. The experiment was conducted at the AGOR facility at KVI using the BINA 4pi -detection system. We discuss the analysis procedure including a thorough study of the systematic uncertainties. The results can be used to examine upcoming state-of-the-art calculations in the four-nucleon scattering domain, and will, thereby, provide further insights into the dynamics of three- and four-nucleon forces in few-nucleon systems. The results of coplanar configurations are compared with the results of recent theoretical calculations based on the Single-Scattering Approximation (SSA). Through these comparisons, the validity of SSA approximation is investigated in the Quasi-Free (QF) region.

Iterative Algorithms for Joint Scatter and Attenuation Estimation From Broken Ray Transform Data

The single-scatter approximation is fundamental in many tomographic imaging problems including x-ray scatter imaging and optical scatter imaging for certain media. In all cases, noisy measurements are affected by both local scatter events and nonlocal attenuation. Prior works focus on reconstructing one of two images: scatter density or total attenuation. However, both images are media specific and useful for object identification. Nonlocal effects of the attenuation image on the data are summarized by the broken ray transform (BRT). While analytic inversion formulas exist, poor conditioning of the inverse problem is only exacerbated by noisy measurements and sampling errors. This has motivated interest in the related star transforms incorporating BRT measurements from multiple source-detector pairs. However, all analytic methods operate on the log of the data. For media comprising regions with no scatter a new approach is required. We are the first to present a joint estimation algorithm based on Poisson data models for a single-scatter measurement geometry. Monotonic reduction of the log-likelihood function is guaranteed for our iterative algorithm while alternating image updates. We also present a fast algorithm for computing the discrete BRT forward operator. Our generalized approach can incorporate both transmission and scatter measurements from multiple source-detector pairs. Transmission measurements resolve low-frequency ambiguity in the joint image estimation problem, while multiple scatter measurements resolve the attenuation image. The benefits of joint estimation, over single-image estimation, vary with problem scaling. Our results quantify these benefits and should inform design of future acquisition systems.