Spherical Scatterers Research Articles

Anechoic lesion detection in a strongly scattering medium: Application to pulmonary nodules

We present an imaging methodology to detect the presence of an anechoic lesion in a highly scattering medium consisting of spherical air scatterers. Classical imaging methods have failed to image such media. In the method presented here, the incoherent backscattered intensity is extracted and the linear growth of the diffusive halo is tracked. Sudden changes in this growth indicates the presence of a target. This algorithm combined with the algorithm of Winslow et al. on contour detection enables us to predict the presence and the location of such a lesion. This method has been developed to detect the presence of pulmonary nodules and ground glass opacities in the lung parenchyma. Using a 128-element linear array transducer operating at 5 MHz, experimental results were obtained from a sponge phantom with an air volume fraction of 50%, in which gelatin nodules of diameter 5 mm and 8 mm were implanted at depths of 15 mm and 20 mm, respectively. The diameter of the nodules could be predicted within an error margin of ±25%. FDTD simulations were also carried out with nodule sizes of 6mm and 11 mm, in media with 20% and 50% air volume fractions. The coordinates of the center of the lesion could be predicted within a tolerance of ±7%.

Longitudinal Optical Fields in Light Scattering from Dielectric Spheres and Anderson Localization of Light

Recent research has shown that coupling between point scatterers in a disordered medium by longitudinal electromagnetic fields is harmful for Anderson localization of light. However, it has been unclear if this feature is generic or specific for point scatterers. The present work demonstrates that the intensity of longitudinal field outside a spherical dielectric scatterer illuminated by monochromatic light exhibits a complicated, nonmonotonous dependence on the scatterer size. Moreover, the intensity is reduced for a hollow sphere, whereas one can adjust the parameters of a coated sphere to obtain a relatively low longitudinal field together with a strong resonant scattering efficiency. Therefore, random arrangements of structured (hollow or coated) spheres may be promising three‐dimensional disordered materials for reaching Anderson localization of light.

Plane-wave decomposition and ambisonics output from spherical and nonspherical microphone arrays

Any acoustic sensor embedded in a baffle disturbs the spatial acoustic field to a certain extent, and the recorded field is different from a field that would have existed if the baffle were absent. Recovery of the original (incident) field is a fundamental task in spatial audio. For some sensor baffle geometries, such as the sphere, the disturbance of the field by the sensor can be characterized analytically and its influence can be undone to recover the incident field. However, for arbitrary shaped baffles, numerical methods have to be employed. In the current work, the baffle influence on the field is characterized using boundary element methods, and a framework to recover the incident field from measurements from sensors embedded on the baffle in the plane-wave function basis is developed. Field recovery also allows generation of high-order ambisonics representations of the spatial audio scene. Experimental results using both complex and spherical scatterers will be presented.

Experimental implementation of a synthesized two-dimensional phased array for transcranial imaging with aberration correction

Ultrasound (US) imaging of brain structures is a challenging, but highly promising diagnostic technology in medical ultrasound. Recent advances in transcranial US therapy suggest the potential to implement diagnostic US at higher frequencies, ideally for full brain imaging. In this work. we present experimental results of ultrasound imaging of spherical and tubular scatterers placed behind a skull phantom. The phantom was produced from a casting compound with acoustic properties matching those of skull. Phantom shape was defined from CT data of a human skull and 3D printing of a mold. A two-dimensional ultrasound array was simulated by mechanical translation of the focal spot of a broadband single-element 2 MHz transducer over the phantom surface. This synthesized array mimicked a 2D flexible phased array placed on the top of the patient's head. A pulse-echo technique was used for reconstructing the thickness of the skull phantom and detecting backscattered signals from the test objects. Transcranial image reconstruction was performed using a delay-and-sum technique that accounts for refraction and absorption inside the phantom. It was demonstrated that aberration correction using either straight rays or more accurate refracted raytracing yields significant improvement of image quality. [Work supported by RSF-14-15-00665.]

Effect of scattering on coherent anti-Stokes Raman scattering (CARS) signals.

We develop a computational framework to examine the factors responsible for scattering-induced distortions of coherent anti-Stokes Raman scattering (CARS) signals in turbid samples. We apply the Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method combined with the radiating dipole approximation to compute the effects of scattering-induced distortions of focal excitation fields on the far-field CARS signal. We analyze the effect of spherical scatterers, placed in the vicinity of the focal volume, on the CARS signal emitted by different objects (2μm diameter solid sphere, 2μm diameter myelin cylinder and 2μm diameter myelin tube). We find that distortions in the CARS signals arise not only from attenuation of the focal field but also from scattering-induced changes in the spatial phase that modifies the angular distribution of the CARS emission. Our simulations further show that CARS signal attenuation can be minimized by using a high numerical aperture condenser. Moreover, unlike the CARS intensity image, CARS images formed by taking the ratio of CARS signals obtained using x- and y-polarized input fields is relatively insensitive to the effects of spherical scatterers. Our computational framework provide a mechanistic approach to characterizing scattering-induced distortions in coherent imaging of turbid media and may inspire bottom-up approaches for adaptive optical methods for image correction.

Coherent wave propagation in viscoelastic media with mode conversions and pair-correlated scatterers

The influence of correlation between scatterers on coherent waves propagation is studied in the case of a viscoelastic medium hosting a random configuration of either spherical or cylindrical scatterers. A distinction is made between the hole correction and the additional disturbances to the pair correlation function beyond the excluded volume via a radial and concentration dependent Ursell function. The effect of the Ursell function on the effective wavenumber is shown to be of order 3 in concentration and order 2 in scattering, and the corresponding formulas generalize those of Caleap et al. (2012) for an ideal fluid host medium. The whole order 3 in concentration is calculated; its other part is of order 3 in scattering. Both parts of the order 3 in concentration are the sum of two terms, one related to mode conversions, the other not. The numerical study is performed mostly for aluminum spheres in epoxy, which is a rather illustrative situation of the different phenomena that participate to the coherent propagation. The Ursell function effect is enhanced at low frequency, while counteracted partly at higher frequency, by the other term of order 3 in concentration. The most visible effects of both terms are on the attenuation. The Ursell term related to mode conversions is larger than the one with no mode conversions included in the low frequency regime.

Far-field coherent backscatter enhancement from random aggregations of scatterers and comparisons to backscattering from single isolated spheres.

Coherent backscatter enhancement (CBE), a multiple scattering phenomenon, may cause an enhancement of up to a factor of two in the average intensity backscattered from a random aggregation of scatterers. In the ocean, CBE may occur when a fish school or a bubble cloud is remotely illuminated. The research reported here explored the possibility that CBE might be used to remotely discriminate between an aggregation of many scatterers and a single isolated scattering object. For this investigation, the far-field harmonic acoustic pressure backscattered from aggregations of randomly placed omnidirectional point scatterers was determined from numerical solution of the equations from Foldy [(1945) Phys. Rev. 67(3,4), 107-119], and compared to equivalent results from single spherical scatterers having hard surfaces, pressure-release surfaces, or aggregation-matched effective-medium properties. Interestingly, CBE causes a spherical aggregation to backscatter as much or more sound than a single perfectly reflecting sphere of the same size when (ka)1/2(ks)-4/5(kσs1/2)3/4 ≥ 2.3, where k is the acoustic wave number, a is the aggregation radius, s is the average spacing between scatterers, and σs is a scatterer's cross section. And, backscattered intensity samples (in dB) from all simulated aggregations followed an extreme value distribution, a finding that supports the conventional use of backscatter statistics for remote aggregation-versus-single-object discrimination.

Water Interaction in Faujasite Probed by in Situ X-ray Powder Diffraction

Using in situ X-ray diffraction and the Rietveld method combined with the maximum entropy method, we investigated the interaction of water with sodium faujasite and determined the sodium and water sorption sites as a function of water content. From the information contained in the lowest diffraction-angle peaks, we found that water also interacts with faujasite, forming a shell-like layer inside the supercages located at a mean distance of 2.8 A from the pore-wall oxygens. For water-saturated faujasite, this shell has a surface density comparable to liquid water. The ion-exchange sites and ordered water found inside the supercage are embedded in this layer. We included the water shell contribution in Rietveld refinements by modeling it as a hollow sphere scatterer inside the faujasite supercages, and the refined water and cation quantities have agreed with nominal values.

Effects of Composition and Melting Time on the Phase Separation of Poly(3-hydroxybutyrate)/Poly(propylene carbonate) Blend Thin Films.

In this study, the effect of composition and melting time on the phase separation of poly(3-hydroxybutyrate)/poly(propylene carbonate) (PHB/PPC) blend thin films was investigated. Optical microscopy under phase contrast confirms the occurrence of phase separation of PHB/PPC blends at 190 °C. Polarized optical and scanning electron microscopies (POM and SEM) demonstrate that phase separation takes place along both horizontal and vertical film planes, which should be attributed to the two different interfaces and immiscible blends. A low PPC content (e.g. 30 wt %) results in the formation of compact PHB spherulites filling the whole space, whereas the noncrystallizable PPC spherical microdomains scatter in the PHB region, and their size shows a remarkable melting-time dependence. With the increasing PPC component and melting time, it is observed from POM that the separated PHB domains scattered in the continuous PPC phase, like the island structure. However, it can be revealed by SEM micrographs that the PHB thick domains are actually connected by its thin layer under the PPC layer. The real situation is, therefore, a large amount of PPC aggregates to the surface to form a network uplayer, whereas the PHB thick domains connected by its thin layer form a continuous PHB region, leading to a superimposed bilayer structure. There is also a small amount of PHB small domains scattered in the PHB phase. The PHB thick domains crystallize cooperatively with the PHB- or PHB-rich sublayer in a way just like the growth of pure PHB spherulites. This superimposed bilayer by interplay between phase separation and crystallization may provide availability to tailor the final structure and properties of crystalline/amorphous polymer blends.

Acoustic radiation force of a quasi-Gaussian beam imparted to a solid spherical scatterer in a fluid

The radiation force generated upon the scattering of a quasi-Gaussian acoustic beam on a homo-geneous elastic sphere in a fluid is investigated. It is shown that the force depends nonmonotonically on the ratio between the sphere’s diameter and the beam’s waist. For a given beam power, the radiation force has its maximum value when the diameters are roughly egual to each other. This is due to the resonant excitation of shear waves on the sphere’s surface under the impact of acoustic wave in the surrounding fluid.

Multiple scattering in random dispersions of spherical scatterers: Effects of shear-acoustic interactions.

The propagation of acoustic waves through a suspension of spherical particles in a viscous liquid is investigated, through application of a multiple scattering model. The model is based on the multiple scattering formulation of Luppé, Conoir, and Norris [J. Acoust. Soc. Am. 131, 1113-1120 (2012)] which incorporated the effects of thermal and shear wave modes on propagation of the acoustic wave mode. Here, the model is simplified for the case of solid particles in a liquid, in which shear waves make a significant contribution to the effective properties. The relevant scattering coefficients and effective wavenumber are derived in analytical form. The results of calculations are presented for a system of silica particles in water, illustrating the dependence of the scattering coefficients, effective wavenumber, speed, attenuation on particle size and frequency. The results demonstrate what has already been shown experimentally; that the shear-mediated processes have a very significant effect on the effective attenuation of acoustic waves, especially as the concentration of particles increases.

A method for estimating the 3-D structure function from 2-D histology sections

Understanding the fundamental scattering mechanism(s) in tissues is critical to the success of Quantitative Ultrasound (QUS) imaging. From a discrete scatterer point of view, the ultrasound scattered power depends not only on the properties of the individual scatterers (modeled by the form factor) but also on the spatial correlation among the scatterers (modeled by the structure function). Previously, the structure function was obtained from the ultrasound backscatter data for dense cell pellet biophantoms. This study introduces a method for obtaining the 3-D structure function from the digitized hematoxylin & eosin (H&E) stained histology images. The method starts with calculating the 2-D pair correlation function using the scatterer positions determined from a histology image. Assuming isotropic media with spherical scatterers, the 3-D pair correlation function is then estimated by numerically solving a stereological function that relates the 3-D pair correlation function with the 2-D pair correlation f...

Transverse spin and transverse momentum in scattering of plane waves.

We study the near field to the far field evolution of spin angular momentum (SAM) density and the Poynting vector of the scattered waves from spherical scatterers. The results show that at the near field, the SAM density and the Poynting vector are dominated by their transverse components. While the former (transverse SAM) is independent of the helicity of the incident circular polarization state, the latter (transverse Poynting vector) depends upon the polarization state. It is further demonstrated that the interference of the transverse electric and transverse magnetic scattering modes enhances both the magnitudes and the spatial extent of the transverse SAM and the transverse momentum components.

A numerical study of super-resolution through fast 3D wideband algorithm for scattering in highly-heterogeneous media

We present a wideband fast algorithm capable of accurately computing the full numerical solution of the problem of acoustic scattering of waves by multiple finite-sized bodies such as spherical scatterers in three dimensions. By full solution, we mean that no assumption (e.g. Rayleigh scattering, geometrical optics, weak scattering, Born single scattering, etc.) is necessary regarding the properties of the scatterers, their distribution or the background medium. The algorithm is also fast in the sense that it scales linearly with the number of unknowns. We use this algorithm to study the phenomenon of super-resolution in time-reversal refocusing in highly-scattering media recently observed experimentally (Lemoult et al., 2011), and provide numerical arguments towards the fact that such a phenomenon can be explained through a homogenization theory.

Effects of a near-field rigid sphere scatterer on the performance of linear microphone array beamformers.

Beamformers enable a microphone array to capture acoustic signals from a sound source with high signal to noise ratio in a noisy environment, and the linear microphone array is of particular importance, in practice, due to its simplicity and easy implementation. A linear microphone array sometimes is used near some scattering objects, which affect its beamforming performance. This paper develops a numerical model with a linear microphone array near a rigid sphere for both far-field plane wave and near-field sources. The effects of the scatterer on two typical beamformers, i.e., the delay-and-sum beamformer and the superdirective beamformer, are investigated by both simulations and experiments. It is found that the directivity factor of both beamformers improves due to the increased equivalent array aperture when the size of the array is no larger than that of the scatter. With the increase of the array size, the directivity factor tends to deteriorate at high frequencies because of the rising side-lobes. When the array size is significantly larger than that of the scatterer, the scattering has hardly any influence on the beamforming performance.

An accelerated derivation of the acoustic low‐frequency expansion: the penetrable sphere

The well‐known low‐frequency expansion of the total acoustic field in the exterior of a penetrable spherical scatterer is revisited in view of the Atkinson Wilcox theorem. The corresponding low‐frequency approximations of any order are calculated following a purely algebraic algorithmic procedure, based on the spectral decomposition of the problem's far field pattern. As an indication of its accuracy and effectiveness, the proposed algebraic procedure is shown to recover already known low‐frequency coefficients and also to deduce higher order of approximations. The proposed track of calculations leads to a closed‐form expression of any such coefficient and has been recently applied on impenetrable spherical scatterers as well, offering equally accurate results. The effectiveness of the proposed procedure indicates an underlying general efficient method applicable to a wider class of starshaped scatterers. Copyright © 2016 John Wiley & Sons, Ltd.

A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers

By means of the expansion of the nondiffracting beams on plane waves with help of the Whittaker integral, an exact analytical expression of the far-field form function of the scattering of the acoustic and optical nondiffracting Lommel beams propagating in a medium containing spherical particles, considered as rigid and single spheres, is investigated in this work. The form function of the scattering of the high order Bessel beam by a rigid and isolated sphere is deduced, from our finding, as a special case. The effects of the wave number-sphere radius product (ka), the polar angle (φ), the propagation half-cone angle (β) and the scattering angle (θ) on the far-field form function of the scattered wave have been analyzed and discussed numerically. The numerical results show that the illumination of a rigid sphere by Lommel beams produces asymmetrical scattering.

Plasmon-driven large Hall photon currents in light scattering by a core–shell magnetoplasmonic nanosphere

The conditions for the occurrence of strong magnetotransverse anisotropy in light scattering by a single gyrotropic sphere are investigated by means of rigorous full electrodynamic multipole calculations. It is shown that composite magnetoplasmonic spherical scatterers with a core–shell morphology can induce large and tunable plasmon-driven Hall photon currents, which appear even in the case of subwavelength particles. Explicit results for silver-coated bismuth-substituted yttrium iron garnet nanospheres are presented and analyzed.

Symmetry relations in the generalized Lorenz–Mie theory for lossless negative refractive index media

In this paper we present a theoretical analysis of the generalized Lorenz–Mie theory for negative refractive index (NRI) media and spherical scatterers, extending the well-known concepts and definitions found in the literature involving dielectric or positive refractive index (PRI) particles. The consequences of a negative phase velocity and an anti-parallelism of the wave vector with respect to the Poynting vector are investigated and interpreted in this framework and, together with the symmetries found for the beam-shape coefficients when compared to the conventional PRI case, it is shown that the description of plane waves, Gaussian beams and, more generally, on-axis azimuthally symmetric waves along a NRI medium, their fields and all physical properties can be conveniently correlated with that of dielectric media once the electromagnetic response functions are replaced by their corresponding dielectric counterparts.

Constructing ultrasonic images of soft spherical scatterers

The paper considers specific features of ultrasonic visualization of gas bubbles in a liquid or a medium of like soft biological tissue type under conditions when the size of scatterers is comparable to the acoustic wavelength. It was proposed to use styrofoam specimens as the experimental model of stationary gas bubbles. Patterns of ultrasound scattering by a styrofoam sphere in water were obtained experimentally. It was shown that the measurement results agree well with the prediction of the classical theoretical model of scattering of a plane wave by a perfectly soft sphere. Several experiments were performed illustrating the specific features of visualizing millimeter-sized bubbles. A Terason commercial ultrasonic scanner was used; gelatin specimens with embedded styrofoam spheres served as the objects of study. The simulation and experimental results showed that when bubbles with diameters of <1 mm are visualized, it is impossible to measure the diameter of scatterers because bubbles of different diameters are imaged as bright spots of identical diameter, which is equal to the scanner resolution. To eliminate this difficulty, it is recommended to use the results of theoretical simulation performed in this study, which revealed a monotonic increase in the backscattered signal intensity with an increase in bubble radius. An ultrasonic visualization mode is proposed in which the brightness of scattered signals is used to differentiate between bubbles of different size.