A note on the scattering geometry from infinite cylinders
Light scattering geometry from infinite cylinder shown consistent with Rayleigh-Gans formalism
Craven, P. D.↗
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Results for “scattering geometry”
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The effects of scattering geometry on the spectrophotometric properties of powdered material
The characteristics of reflectance spectra are being used as a basis in investigations to infer the composition of planetary surfaces. However, the reflectance spectra of powdered materials depend not only on the composition of these materials, but also on other variables. A description is presented of the results of an exploratory series of measurements designed to investigate the importance of scattering geometry as a variable in determining the shapes of spectral reflectance curves, taking into account half a dozen materials of planetary interest. It is noted that the considered results are consistent with those reported by Adams and Felice (1967), especially the results on the variation with phase angle of the Red/Blue color ratio for various silicate materials. The measurements demonstrate in detail that scattering geometry does affect the shapes of spectral reflectance curve. In some cases this effect is quite significant.
Gradie, J.↗
Effective path length corrections in beam-beam scattering experiments
The effect of the change of scattering geometry with scattering angle in beam-beam experiments is investigated. Atomic (molecular) target distributions associated with static gas, orifice, tube, capillary array (with and without further collimation), and jet sources have been considered in model calculations for a number of commonly used electron scattering geometries. The relationship between scattering intensity, cross section, and the geometrical integral called 'effective path length' is derived. Volume correction factors (the reciprocal of effective path length) have been calculated for sample cases to illustrate the effect of various beam and scattering geometry characteristics. The validity of the model calculation has been experimentally verified. Most of the commonly used scattering geometries require significant correction of the scattering intensity distributions, but with proper planning scattering geometries can be designed such that the intensity and the cross section angular distribution are identical within 1%.
Brinkmann, R. T.↗
The SAGEX review on scattering amplitudes Chapter 7: Positive geometry of scattering amplitudes
Abstract Scattering amplitudes are both a wonderful playground to discover novel ideas in quantum field theory and simultaneously of immense phenomenological importance to make precision predictions for e.g. particle collider observables and more recently also for gravitational wave signals. In this review chapter, we give an overview of some of the exciting recent progress on reformulating QFT in terms of mathematical, geometric quantities, such as polytopes, associahedra, Grassmanians, and the amplituhedron. In this novel approach, standard notions of locality and unitarity are derived concepts rather than fundamental ingredients in the construction which might give us a handle on a number of open questions in QFT that have evaded an answer for decades. We first give a basic summary of positive geometry before discussing the associahedron—one of the simplest physically relevant geometric examples—and its relation to tree-level scattering amplitudes in bi-adjoint ϕ 3 theory. Our second example is the amplituhedron construction for scattering amplitudes in planar maximally supersymmetric Yang–Mills theory.
Physics↗
Geometries and focal properties of two electron-lens systems useful in low-energy electron or ion scattering
Geometries and focal properties are given for two types of electron-lens system commonly needed in electron scattering. One is an electron gun that focuses electrons from a thermionic emitter onto a fixed point (target) over a wide range of final energies. The other is an electron analyzer system that focuses scattered electrons of variable energy onto a fixed position (e.g., the entrance plane of an analyzer) at fixed energy with a zero final beam angle. Analyzer-system focusing properties are given for superelastically, elastically, and inelastically scattered electrons. Computer calculations incorporating recent accurate tube-lens focal properties are used to compute lens voltages, locations and diameters of all pupils and windows, filling factors, and asymptotic rays throughout each lens system. Focus voltages as a function of electron energy and energy change are given, and limits of operation of each system discussed. Both lens systems have been in routine use for several years, and good agreement has been consistently found between calculated and operating lens voltages.
Chutjian, A.↗
On positive geometry and scattering forms for matter particles
We initiate the study of positive geometry and scattering forms for tree-level amplitudes with matter particles in the (anti-)fundamental representation of the color/flavor group. As a toy example, we study the bi-color scalar theory, which supplements the bi-adjoint theory with scalars in the (anti-)fundamental representations of both groups. Using a recursive construction we obtain a class of unbounded polytopes called open associahedra (or associahedra with certain facets at infinity) whose canonical form computes amplitudes in bi-color theory, for arbitrary number of legs and flavor assignments. In addition, we discuss the duality between color factors and wedge products, or "color is kinematics", for amplitudes with matter particles as well.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Coupling of fully symmetric As phonon to magnetism in Ba(Fe 1-x Au x ) 2 As 2
In this work, we study the coupling of the fully symmetric vibration mode of arsenic atoms to magnetism in a Ba ( Fe 1 - x Au x ) 2 As 2 system by polarization-resolved Raman spectroscopy and neutron diffraction. In this system, there are two phase transitions: a tetragonal-to-orthorhombic structural phase transition at temperature T S and a magnetic phase transition into collinear spin-density wave (SDW) state at temperature T N ( ≤ T S ). T S and T N almost coincide in the pristine compound, whereas they differ by as much as 8 K for compounds with dilute gold substitution for iron. Raman coupling to the A g (As) phonon is forbidden for the X Y scattering geometry in the tetragonal phase above T S , whereas it becomes allowed in the orthorhombic phase below T S : The emerging mode's intensity indicates the lattice orthorhombicity. Furthermore, we find that upon cooling below T S , first, weak A g (As) phonon mode intensity appears in the X Y scattering geometry spectra; however, the mode's intensity is significantly enhanced in the magnetic phase below T N . The A g (As) phonon also shows an asymmetric line shape below T N and an anomalous linewidth broadening upon Au doping. We describe the anomalous behavior of the A g (As) mode in the X Y scattering geometry using a Fano model involving the A g (As) phonon interacting with the B 2 g ( D 4 h )-symmetry-like electron-hole continuum. We conclude that the temperature dependence of light coupling amplitude to the A g (As) phonon follows the evolution of the magnetic order parameter M ( T ) . We propose that the intensity enhancement of the A g (As) phonon in the X Y scattering geometry below T N is due to electronic anisotropy induced by the collinear SDW order parameter.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Multiple scattering calculations - Geometry for spherical atmospheres
Geometric relationships involved in multiple scattering calculations for spherical planets
Shipley, E. N.↗
GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning
This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. Further, an extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.
42 ENGINEERING↗
Photometric properties of powdered sulfur
Particle size, temperature, thermal history, and scattering geometry are shown by the present laboratory investigation of the spectrophotometric properties of three particle-size fractions of sulfur to influence the spectral reflectance of both normal and quenched molten samples of sulfur. A scattering law that consists of a linear combination of lunar-like and Lambertian terms adequately describes the data for all particle sizes. Near opposition, sulfur particles closely follow a Minnaert limb darkening law except where the reflectance is low, as in the strong UV absorption band of the larger particle size fractions. The present data indicate that quantitative comparisons between disk-integrated observations of Io and laboratory measurements of flat sulfur samples are inadequate unless temperature effects and scattering geometry changes are included.
Gradie, J.↗
Interference by rain scatter
The data from Japan and the U.S. (the Virginia Precipitation Scatter Experiment) show excellent agreement between the two-component rain scatter model predictions and bistatic scatter measurements. In employing the model, all the scattering geometries should be classified as backscattering as defined by Crane (1974). The forward scatter model should only be used for great circle paths with both antennas pointed at the horizon and at each other in a typical troposcatter communication system geometry. The forward scatter model can also be used for main-lobe, side-lobe coupling when one antenna is pointed toward the other along the great circle path. The forward scatter observations made over the Prospect Hill - Mt Tug path show that the two-component model is incomplete. Much stronger signals were observed at Ku-band than expected based on simultaneous C-band measurements. The discrepancies may be due to: (1) scattering by ice/snow at height (posssible in April) at the 1 km height of the scattering volume), (2) the coherent effects of turbulent fluctuations in the hydrometeor number densities and (3) errors in the modeling of the statistical relationship between attenuation along the path and scattering in the common volume.
Crane, Robert K.↗
Electron scattering by highly polar molecules. III - CsCl
Utilizing a crossed electron-beam-molecular-beam scattering geometry, relative values of differential electron scattering cross sections for cesium chloride at 5 and 20 eV electron impact energies and at scattering angles between 10 and 120 deg have been measured. These relative cross sections have been normalized to the cross section at 15 deg scattering angle calculated by the hybrid S-matrix technique. In the angular range between 0 and 10 deg and between 120 and 180 deg extrapolations have been made to obtain integral and momentum transfer cross sections. An energy-loss spectrum is also presented which gives various spectral features lying between the 4 and 10 eV regions in CsCl.
Vuskovic, L.↗
Multislice forward modeling of coherent surface scattering imaging on surface and interfacial structures
To study nanostructures on substrates, surface-sensitive reflection-geometry scattering techniques such as grazing incident small angle X-ray scattering are commonly used to yield an averaged statistical structural information of the surface sample. Grazing incidence geometry can probe the absolute three-dimensional structural morphology of the sample if a highly coherent beam is used. Coherent surface scattering imaging (CSSI) is a powerful yet non-invasive technique similar to coherent X-ray diffractive imaging (CDI) but performed at small angles and grazing-incidence reflection geometry. A challenge with CSSI is that conventional CDI reconstruction techniques cannot be directly applied to CSSI because the Fourier-transform-based forward models cannot reproduce the dynamical scattering phenomenon near the critical angle of total external reflection of the substrate-supported samples. To overcome this challenge, we have developed a multislice forward model which can successfully simulate the dynamical or multi-beam scattering generated from surface structures and the underlying substrate. The forward model is also demonstrated to be able to reconstruct an elongated 3D pattern from a single shot scattering image in the CSSI geometry through fast-performing CUDA-assisted PyTorch optimization with automatic differentiation.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
A Fast Evaluation of PDA Experimental Parameters Using Mie Scattering to Enhance the Measurement Accuracy of Droplet Size Distributions
The Phase Doppler technique (PDA) and its implementation generally relies on a geometric optics formulation for light scattering to estimate drop sizes from the measured phase differences between Doppler signals from two or more detectors. Although this limits experimental PDA scattering geometries to those where only one component of the geometric scatter is dominant, the calculations are relatively simple. This TM describes a fast method to evaluate PDA experimental parameters analytically using Mie scattering that provides a performance estimate of all possible configurations. The best configurations are fully tested using a Monte Carlo simulation to obtain a more accurate capability estimate for each one.
PDA↗
General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I
This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.
36 MATERIALS SCIENCE↗
A model for microwave intensity propagation in an inhomogeneous medium
A combined analytic and phenomenological approach, utilizing Maxwell's equations in the Born approximation with radiative transfer theory, is used to describe the propagation of microwave intensity in a scattering medium characterized by three-dimensional random fluctuations in refractive index, as well as nonrandom variations in permittivity, temperature, and loss. This approach yields microwave intensities as a function of polarization, direction, and position. Numerical techniques are presented to solve the transport equations, which include cases of spatially varying coefficients, and highly peaked phase functions. Some computed results illustrating the behavior of microwave intensity in various media are presented. Included are the angular and frequency spectra of thermal emission from semi-infinite media, and the diffuse transmission and reflection response of a scattering layer. The effects of scatterer geometry and scale sizes; correlation function; and gradients in temperature, loss, and scattering parameters are also demonstrated. This model should be particularly useful in interpreting active and passive remote sensing data.
Fisher, A. D.↗
Influence of a finite scattering volume on the determination of electron-impact coherence parameters
Superelastic electron scattering from laser-excited Ba-138 ...6s6p (1)P is investigated both theoretically and experimentally. The theoretical framework is developed and incorporated into a model of a realistic scattering geometry of finite spatial extent. Model calculations predict that the dependence of the superelastic scattering intensity on the linear polarization direction of the laser beam can be severely distorted due to the existence of a finite scattering volume. Measurements obtained confirm the presence of this distortion and are well described by the model calculations. Conclusions are drawn concerning the influence of this effect on the extraction of electron-impact coherence parameters.
Zetner, P. W.↗