Spherical Scatterers Research Articles

Spherical Harmonic-Based Anisotropic Point Scatterer Models for Radar Applications Using Inverse Optimization

High-performance computing-based electromagnetic (EM) emulators are used to simulate real-time complex EM wave interactions between multiple radar targets, transmitters, and receivers. The radar cross section (RCS) of the radar targets are required to be stored as a table; however, the needed storage size increases dramatically with the angle and frequency sampling density. In this article, we present an innovative approach of constructing a concise spherical harmonic-based anisotropic point scatterer model that the emulators can use as part of the computations. The point scatterer model is constructed directly from the precomputed RCS data. First, we use only the monostatic RCS data and compute the spherical harmonic-based monostatic point scatterer model by solving a linear least-squares problem which has a group sparsity constraint. Then, we further compute the spherical harmonic-based bistatic point scatterer model using the full bistatic RCS data. The problem is formulated as a bilinear least-squares problem. The problem is solved using the normalized iterative algorithm, which linearly solves two parameters in a back and forth manner. The results show that the point scatterer model can effectively represent the bistatic RCS data of a radar target.

Generalization and stabilization of exact scattering solutions for spherical symmetric scatterers

In a previous work the authors described a fast high-fidelity computer model for acoustic scattering from multi-layered elastic spheres. This work is now extended with a scaling strategy significantly mitigating the problem of overflow and thus expanding the useful frequency range of the model. Moreover, new boundary conditions and loads are implemented. Most important are the fluid–fluid and solid–solid couplings, which allow a completely general layering of the scattering object. Sound hard and sound soft boundary conditions are implemented for solids and fluids respectively. In addition to the existing acoustic excitation, mechanical excitation in the form of point-excitation and surface excitation are implemented. Attenuation in the form of hysteresis damping as well as viscous fluid layers are also included. Several numerical examples are included, with the purpose of validating the code against existing reference solutions. The examples include air bubbles, a coated steel shell and a point-exited steel shell.

Perceptual evaluation of approaches for binaural reproduction of non-spherical microphone array signals

Microphone arrays consisting of sensors mounted on the surface of a rigid, spherical scatterer are popular tools for the capture and binaural reproduction of spatial sound scenes. However, microphone arrays with a perfectly spherical body and uniformly distributed microphones are often impractical for the consumer sector, in which microphone arrays are generally mounted on mobile and wearable devices of arbitrary geometries. Therefore, the binaural reproduction of sound fields captured with arbitrarily shaped microphone arrays has become an important field of research. In this work, we present a comparison of methods for the binaural reproduction of sound fields captured with non-spherical microphone arrays. First, we evaluated equatorial microphone arrays (EMAs), where the microphones are distributed on an equatorial contour of a rigid, spherical 1. Second, we evaluated a microphone array with six microphones mounted on a pair of glasses. Using these two arrays, we conducted two listening experiments comparing four rendering methods based on acoustic scenes captured in different rooms2. The evaluation includes a microphone-based stereo approach (sAB stereo), a beamforming-based stereo approach (sXY stereo), beamforming-based binaural reproduction (BFBR), and BFBR with binaural signal matching (BSM). Additionally, the perceptual evaluation included binaural Ambisonics renderings, which were based on measurements with spherical microphone arrays. In the EMA experiment we included a fourth-order Ambisonics rendering, while in the glasses array experiment we included a second-order Ambisonics rendering. In both listening experiments in which participants compared all approaches with a dummy head recording we applied non-head-tracked binaural synthesis, with sound sources only in the horizontal plane. The perceived differences were rated separately for the attributes timbre and spaciousness. Results suggest that most approaches perform similarly to the Ambisonics rendering. Overall, BSM, and microphone-based stereo were rated the best for EMAs, and BFBR and microphone-based stereo for the glasses array.

Cautious note on using the discrete dipole approximation for inhomogeneous, spherical scatterers with high optical contrast

The discrete dipole approximation (DDA) is capable of treating scatterers with arbitrary shape and composition. However, large values of the refractive index require additional considerations. DDA calculations are performed for small spheres with a stronger absorbing inclusion and compared to T-matrix results. A natural phenomenon with strong optical contrasts is the melting of ice hydrometeors at microwave frequencies, and hence corresponding refractive indices are chosen. The obtained extinction and absorption efficiencies are found to depend mainly on the dipole size, whereas the phase function closely follows the T-matrix results by choosing a smaller stopping criterion and changing the polarizability formulation.

Spectral analysis of scattering resonances with application on high-contrast nanospheres

In this paper, we provide further spectral analysis of the general asymptotic scattering resonances formula of small 3D dielectrics of arbitrary shape with high contrast, already derived in other works to a first-order approximation. To investigate the components of a full expansion of such resonances, a breakdown is presented for the case of high-contrast nanospheres, in terms of its radius h in the interval [0, 1]. We also derive, for radially symmetric fields, an exact resonance formula for a spherical scatterer in terms of its radius, not necessarily small, and dielectric susceptibility coefficient, not necessarily high. This formula is further developed and simplified in the case of high contrast nanospheres. Such formulas are useful in imaging applications to identify objects’ properties from frequency measurements. Another application is the study of negative refractive index materials, such as metamaterials, and the anomalous localized resonance phenomenon (ALR) that is associated with cloaking and superlensing.

Efficient electrical field Monte Carlo simulation of coherent backscattering

In this paper an efficient statistical solution approach for the quantitative description of the coherent backscattering (CBS) from turbid media based on an electrical field Monte Carlo method is presented. Spherical scatterers in a semi-infinite medium, which are illuminated with a defined polarization, are investigated. In particular, different variance reduction methods are reported, applied to the CBS and implemented. The obtained results are compared with a standard Monte Carlo method (SMCM). With the help of the presented methods, it is possible to efficiently obtain the spectrally resolved CBS on the basis of a single Monte Carlo simulation. A speed comparison of the SMCM with the Monte Carlo method, which includes the variance reduction methods, is made showing an acceleration of many orders of magnitude.

Analysis of Anapole States in Dielectric Spheres and Application to Near-Field Enhancement

Anapole states in isolated, homogeneous, and isotropic dielectric spheres are studied theoretically in accordance with Mie theory, numerically by full-wave electromagnetic simulations and by measurements at microwave and millimeter-wave frequency. Depending on the size and material properties of the dielectric spheres, the practical limitations of detection and possible applications of nonradiating anapole states are investigated. The electromagnetic signature, generated by anapole states of a spherical dielectric scatterer, in terms of finite extinction cross section, is verified by measurements, for both its electric and magnetic versions, in silicon and alumina spheres, respectively. In addition, the existence and the detection of higher order and hybrid anapole states are demonstrated. Finally, an approach to engineer electric field hotspots in a subwavelength-sized gap between two magnetic anapole coupled alumina ceramic spheres is demonstrated.

Calculating an Acoustic Trap for an Elastic Spherical Scatterer of Large Wave Size

Calculating an Acoustic Trap for an Elastic Spherical Scatterer of Large Wave Size

Asymmetric Bragg scattering of water-borne sound by identically oriented asymmetric inclusions

We report on the modeling, fabrication, and characterization of an innovative design for a heterogeneous material consisting of spherical scatterers with asymmetric material distribution embedded in a thin viscoelastic layer. The material properties of the scatterers are uniformly oriented with respect to the layer thickness. The inclusions consists of unequal parts iron (Fe) and polyetheylene glycol (PEG) with non-uniform distribution of Fe within each inclusion to leading to coupling between monopole and dipole scattering response from individual Fe-PEG scatterers in the long wavelength limit when embedded in a polydimethylsiloxane (PDMS) matrix. Experiments were conducted from 0.5–1.5 MHz in an ultrasonic tank on two different samples.

Invariance Principle for the Random Wind-Tree Process

Consider a point particle moving through a Poisson distributed array of cubes all oriented along the axes—the random wind-tree model introduced in Ehrenfest–Ehrenfest (1912) as reported by Ehrenfest, Ehrenfest (Begriffliche Grundlagen der statistischen Auffassung in der Mechanik Encykl. d. Math. Wissensch. IV 2 II, Heft 6, 90 S (1912) (Translated:) The conceptual foundations of the statistical approach in mechanics. Dover Books on Physics, 1912). We show that in the joint Boltzmann–Grad and diffusive limit this process satisfies an invariance principle. That is, the process converges in distribution to Brownian motion in a particular scaling limit. In a previous paper (2020) (Lutsko, Tóth in Commun. Math. Phys. 379:589–632, 2020) the authors used a novel coupling method to prove the same statement for the random Lorentz gas with spherical scatterers. In this paper we show that, despite the change in dynamics, a similar strategy with some modification can be used to prove the invariance principle for the random wind-tree model. The key differences from our previous work are that the individual path segments of the underlying Markov process are no longer fully independent and the geometry of recollisions is simpler.

Efficient computation of arbitrary beam scattering on a sphere: Comments and rebuttal, with a review on the angular spectrum decomposition

The present paper may be viewed as built from comments concerning a recently published paper in Journal of Quantitative Spectroscopy and Radiative Transfer, and actually constitutes as well a rebuttal of some of the claims it contains. The issue considered concerns the computation of scattering properties of the interaction between an arbitrary electromagnetic shaped beam and a homogeneous sphere. Our discussion of the issue may be easily extended as well to more general cases, beyond the simplest case of a homogeneous spherical scatterer, up to the case of arbitrary shaped particles in the framework of T-matrix formulation. Finally, we take the opportunity of the present paper to review the use of the angular spectrum decomposition in light scattering.

Spherical harmonic decomposition of a sound field based on observations along the equator of a rigid spherical scatterer.

We present a method for computing a spherical harmonic representation of a sound field based on observations of the sound pressure along the equator of a rigid spherical scatterer. Our proposed solution assumes that the captured sound field is height invariant so that it can be represented by a two-dimensional (2D) plane wave decomposition (PWD). The 2D PWD is embedded in a three-dimensional representation of the sound field, which allows for perfectly undoing the effect of the spherical scattering object. If the assumption of height invariance is fulfilled, then the proposed solution is at least as accurate as a conventional spherical microphone array of the same spherical harmonic order, which requires a multiple of the number of sensors. Our targeted application is binaural rendering of the captured sound field. We demonstrate by analyzing the binaural output signals that violations of the assumptions that the solution is based on-particularly height invariance and consequently also horizontal propagation-lead to errors of moderate magnitude.

Spectral expansions of open and dispersive optical systems: Gaussian regularization and convergence

Resonant states (RS), also known as quasi-normal modes, arise in spectral expansions of linear response functions of open systems. Manipulation of these spatially ‘divergent’ oscillating functions requires a departure from the usual definitions of inner product, normalization and orthogonality typical in the studies of closed systems. A multipolar Gaussian regularization method for RS inner products is introduced in the context of light scattering and shown to provide analytical results for the crucial RS inner product integrals in the problematic region exterior to the scattering system. We detail the applicability of this method to arbitrary scattering geometries while providing semi-analytic benchmark results for spherical scatterers. This formulation is then used to highlight the lack of ‘convergence’ in directly truncated RS spectral expansions and the necessity of adding non-resonant contributions to the RS spectral expansions. Solutions to these difficulties are illustrated in the case of dispersive media spheres, but these methods should prove generalizable to arbitrary RS spectral expansions.

Measuring Droplets Expelled During Endoscopy to Investigate COVID-19 Transmission Risk

Measuring Droplets Expelled During Endoscopy to Investigate COVID-19 Transmission Risk

An analytic BRDF for materials with spherical Lambertian scatterers

AbstractWe present a new analytic BRDF for porous materials comprised of spherical Lambertian scatterers. The BRDF has a single parameter: the albedo of the Lambertian particles. The resulting appearance exhibits strong back scattering and saturation effects that height‐field‐based models such as Oren‐Nayar cannot reproduce.

Switching the angular direction of radiation by the handedness of a circular dipole in the vicinity of a subwavelength Mie scatterer

We study the radiation of a circular dipole nearby a subwavelength spherical particle. The circular dipole spins in a plane containing a great circle of the spherical particle (meridional plane). We derive general conditions for which radiation vanishes in any direction lying in the meridional plane, yielding directional radiation whose angular orientation can be changed by switching the handedness of the circular dipole. The radiative response (far field) of this dipole-scatterer system can be synthesized as arising from an effective electric dipole in the meridional plane and an effective magnetic dipole perpendicular to the meridional plane; both dipoles are located at the center of the sphere. We consider a nonabsorbing sphere and explore the radiative characteristics (radiation pattern, directivity, radiated power, and spin angular momentum) in which radiation is nullified along two particular axes lying in the meridional plane; particular geometrical configurations and dielectromagnetic properties of the dipole-scatterer system are given. The directional radiation and spin angular momentum patterns can be rotated $\ensuremath{\pi}\phantom{\rule{0.16em}{0ex}}\mathrm{rad}$ around the axis joining the dipole position and the center of the spherical scatterer by changing the handedness of the circular dipole, excepting for the cases of null radiation in the forward and backward directions. Our work might have implications for transferring quantum spin states to electromagnetic modes, controlling of radiation by emitters, routing of light in networks, manipulating of light propagation with metasurfaces, and sensing and locating molecules.

The effect of deformation of absorbing scatterers on Mie-type signatures in infrared microspectroscopy

Mie-type scattering features such as ripples (i.e., sharp shape-resonance peaks) and wiggles (i.e., broad oscillations), are frequently-observed scattering phenomena in infrared microspectroscopy of cells and tissues. They appear in general when the wavelength of electromagnetic radiation is of the same order as the size of the scatterer. By use of approximations to the Mie solutions for spheres, iterative algorithms have been developed to retrieve pure absorbance spectra. However, the question remains to what extent the Mie solutions, and approximations thereof, describe the extinction efficiency in practical situations where the shapes of scatterers deviate considerably from spheres. The aim of the current study is to investigate how deviations from a spherical scatterer can change the extinction properties of the scatterer in the context of chaos in wave systems. For this purpose, we investigate a chaotic scatterer and compare it with an elliptically shaped scatterer, which exhibits only regular scattering. We find that chaotic scattering has an accelerating effect on the disappearance of Mie ripples. We further show that the presence of absorption and the high numerical aperture of infrared microscopes does not explain the absence of ripples in most measurements of biological samples.

Merging Mie solutions and the radiative transport equation to measure optical properties of scattering particles in optical phantoms.

We present a new method to calculate the complex refractive index of spherical scatterers in a novel optical phantom developed by using homemade monodisperse silica nanospheres embedded into a polyester resin matrix and an ethanol-water mixture for applications in diffuse imaging. The spherical geometry of these nanoparticles makes them suitable for direct comparison between the values of the absorption and reduced scattering coefficients (μa and μs', respectively) obtained by the diffusion approximation solution to the transport equation from scattering measurements and those obtained by the Mie solution to Maxwell's equations. The values of the optical properties can be obtained by measuring, using an ultrafast detector, the time-resolved intensity distribution profiles of diffuse light transmitted through a thick slab of the silica nanosphere phantom, and by fitting them to the time-dependent diffusion approximation solution to the transport equation. These values can also be obtained by Mie solutions for spherical particles when their physical properties and size are known. By using scanning electron microscopy, we measured the size of these nanospheres, and the numerical results of μa and μs' can then be inferred by calculating the absorption and scattering efficiencies. Then we propose a numerical interval for the imaginary part of the complex refractive index of SiO2 nanospheres, ns, which is estimated by fixing the fitted values of μa and μs', using the known value of the real part of ns, and finding the corresponding value of Im(ns) that matches the optical parameters obtained by both methods finding values close to those reported for silica glass. This opens the possibility of producing optical phantoms with scattering and absorption properties that can be predicted and designed from precise knowledge of the physical characteristics of their constituents from a microscopic point of view.

New views of tissue scattering

What causes scattering of ultrasound from normal soft tissues such as the liver, thyroid, and prostate? Commonly, the answer is formulated around the properties of spherical scatterers, related to cellular shapes and sizes. However an alternative view is that the closely packed cells forming the tissue parenchyma create the reference media, and the long cylindrical-shaped fluid vessels serve as the scattering sites. Under a weak scattering or Born approximation for the extracellular fluid in the vessels, and assuming an isotropic distribution of cylindrical channels across a wide range of diameters, consistent with a fractal branching pattern, some theoretical predictions can be made. Our model predicts that backscatter increases as a power law of frequency, where the power law is determined by the fractal dimension. These results are consistent with the pioneering measurements of Campbell and Waag. Furthermore, the normalized histogram of echo amplitudes is found to be related to the classical Burr distribution, with the key power law parameter directly related to the fractal dimension, expected in the range of 2 to 3 for normal vasculature. Thus, the first and second order statistics of backscatter from soft vascularized tissues appear to be determined by fractal branching cylindrical vessels.

Быстрый метод анализа возмущения электромагнитного поля малыми сферическими рассеивателями

Быстрый метод анализа возмущения электромагнитного поля малыми сферическими рассеивателями