Average Scattering Cross Section Research Articles

Monodisperse Versus Polydisperse Ultrasound Contrast Agents: Non-Linear Response, Sensitivity, and Deep Tissue Imaging Potential

It has been proposed that monodisperse microbubble ultrasound contrast agents further increase the signal-to-noise ratio of contrast-enhanced ultrasound imaging. Here, the sensitivity of a polydisperse pre-clinical agent was compared experimentally with that of its size- and acoustically sorted derivatives by using narrowband pressure- and frequency-dependent scattering and attenuation measurements. The sorted monodisperse agents had up to a two-orders-of-magnitude increase in sensitivity, that is, in the average scattering cross section per bubble. Moreover, we found, for the first time, that the highly non-linear response of acoustically sorted microbubbles can be exploited to confine scattering and attenuation to the focal region of ultrasound fields used in clinical imaging. This property is a result of minimal pre-focal scattering and attenuation and can be used to minimize shadowing effects in deep tissue imaging. Moreover, it potentially allows for more localized therapy using microbubbles through the spatial control of resonant microbubble oscillations.

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.

Three-dimensional graphic physically based simulator of rainbows together with the background scene.

This paper presents a single scattering 3D graphics simulator of rainbows that includes the thickness of the rain shaft and the background scenery. The simulator is devised so that we can find a good configuration of the sun, the viewers, and the volume of water drops in a complicated geometric setting. The background-scene geometry and light-reflecting properties are modelled using 3D graphics tools. The simulator allows both the light reflected from the background surface and the light scattered by water drops to contribute to the final image by taking the depth to the background surface into account. The simulator generates an image of the rainbow by using the radiative transfer equation (RTE). We use ray optics to compute the average scattering cross section and the average phase function of particles that are the main parameters of the RTE. Depending on the density distribution of the water drops, the rainbow is perceived to be translucent, and the background scene is visible through the rainbow. We simulate other effects of the variation of the water-dropdensity and the location of the viewer, e.g., the visibility of the secondary rainbow, the brightness of the sky around the rainbow, the close-up view of the rainbow, and the full-circle rainbow. We explain these effects partly by computing the luminance contrasts of the primary and secondary bows against their local backgrounds.

Effect of the age of the C60/N-methyl-2-pyrrolidone solution on the structure of clusters in the C60/N-methyl-2-pyrrolidone/water system according to the small-angle neutron scattering data

Fullerene clusters in the C60/N-methyl-2-pyrrolidone (NMP)/water system have been investigated by small-angle neutron scattering. It is shown that the scattering cross section corresponding to the size range 10–100 nm depends on the water content in the mixture. Addition of water to a C60/NMP solution in an amount exceeding 40% leads to a sharp increase in the average scattering cross section. This effect depends on the interval between the times of preparation of a C60/NMP solution and its dilution with water: the size of the clusters formed as a result of adding water increases with increasing the age of the initial solution. The reasons for this effect are discussed.

Scattering efficiency of aggregated clusters of spheres: dependence on configuration and composition

We study the orientation average scattering cross section of various isolated aggregates of identical spherical particles as functions of their size, optical properties, and spatial configurations. Two kinds of aggregates are studied: latex particles in water and rutile titanium dioxide pigments in a polymeric resin, with size parameters varying from 0.6 to 2.3. Calculations are performed by using a recursive centered T-matrix algorithm solution of the multiple scattering equation that we previously developed [J. Quant. Spectrosc. Radiat. Transfer 79-80, 533 (2003)]. We show that for a specific size of the constituent spheres, their respective couplings apparently vanish, regardless of the aggregate configuration, and that the scattering cross section of the entire cluster behaves as if its constituents were isolated. We found that the particular radius for which this phenomenon occurs is a function of the relative refractive index of the system. We also study the correlations between the strength of the coupling among the constituent spheres, and the pseudofractal dimension of the aggregate as it varies from 1 to 30.

Scattering efficiency of clusters composed by aggregated spheres

We present a detailed study of the variation of the average scattering cross section of various aggregates of titanium dioxide crystallites as a function of their sizes and shapes. To perform the analysis, we use a recursive T-matrix algorithm that we developed. We show how the aggregation phenomenon can tremendously decrease the local scattering properties of a white paint film and consequently affects its hiding power. We also compare the results with the equivalent spherical volume approximation which is used in particle size analysis using static or dynamic light-scattering methods. We show how the equivalent volume approximation used in those methods should be handled with care.

Electromagnetic wave scattering from real-life rough-surface profiles and profiles based on an averaged spectrum

We investigate random rough-surface scattering with surface profiles of three different kinds. For each surface profile we calculate the scattering cross section exactly, and the average scattering cross section is taken over realizations. In the first method, we use a limited number of real-life measured profiles of natural surfaces. In the second method, the average surface spectrum of the measured profiles of the first method is found. With the use of the averaged spectrum, many profiles are generated, the scattering cross sections of which are calculated. In the third method, the averaged rough-surface power spectral density found in the second method is fitted with a spectrum (e.g., power law). From the filted spectrum, many profiles are generated, and the average scattering cross section is calculated. We find that the back-scattering levels of Method 3 and Method 1 can have differences (e.g., 6 dB). Method 2 generally gives reasonable results within 1.1 dB of Method 1. Examples are taken from soil, snow, and rock surfaces. © 1996 John Wiley & Sons, Inc.

Small angle neutron scattering by melted superconducting vortex lines

The small angle scattering by the melted vortex lines in superconductors is discussed. The average scattering cross section in the refraction range of scattering is calculated. It is shown that this cross section consists of two contributions. One is due to the refraction and another is due to the Fraunhofer diffraction. It is pointed out that there is a range of the transfer momentum where the Fraunhofer diffraction predominates over the refraction.

Electromagnetic resonant scattering by multiple objects

Electromagnetic scattering by multiple objects in the resonance region is investigated numerically with particular emphasis on direct application to object characterization. The influence of coupling between objects on scattering properties is demonstrated. The average scattering cross section is suggested as a tool to extract useful information about an unknown object adjacent to other known objects from total scattering data measured from multiple scatterers.

Light scattering by perfectly conducting statistically irregular particles

By means of a perturbation method the average scattering cross section of an ensemble of randomly oriented irregular particles is calculated; the material of the particles is perfectly conducting, and their deviation from the spherical shape is assumed to be small. The novel idea consists in pursuing a statistical approach: instead of an ensemble, a single particle with statistical surface irregularities is considered; this approach resembles some well-known methods for treating scattering from rough planar surfaces, e.g., the Rayleigh–Rice method. It turns out that the surface autocorrelation function and the sizeparameter uniquely determine the average scattering behavior of the particles. The scattering cross sections result as expansions in generalized spherical functions, which are of importance in the theory of radiative transfer of polarized light. Limiting cases of long and short wavelengths are discussed and are shown to agree with results found in the literature.

The effect of slight surface roughness on the scattering properties of convex particles

The average scattering cross section for reflection of electromagnetic waves by an ensemble of randomly oriented convex particles is calculated. The particles are assumed to be large compared to the incident wavelength and to have a slightly rough surface such that the deviations from a smooth surface are smaller than wavelength. A perturbation expansion resulting from the Rayleigh–Rice approach leads to incoherent and coherent corrections to the zero-order specularly reflected light. The quantity that in this limit completely determines the scattering behavior of the particles is the two-point correlation function ρ(r) of the roughness structure. The main effect of roughness is a diminution of the reflected intensity for a wide range of the scattering angle θ and a shifting of the maximum of the polarization curve to larger θ. It turns out that measurements of the backscattered intensity in some wavelength limits provide information on the correlation function ρ(r). For conducting material, knowledge of the cross-polarized backscatter intensity over a wide frequency range even enables one, at least in principle, to calculate the complete shape of the correlation function.

Rough surface scattering using specular point theory

The expression for the average scattering cross section for a random surface is derived using the stationary phase approximation for the scattered field due to specular points on a finitely conducting rough surface. A previous error in the literature is corrected by showing that the proper result is proportional to the average value of the product of the number of specular points per unit area and the principal radii of curvature at the specular point, rather than the product of the average value of the number of specular points and the average value of the radii of curvature. When the correct expression for the average value of the product is inserted in the expression for the scattering cross section, the result is in total agreement with the answers obtained when the averaging and stationary phase processes are interchanged. This analysis explicitly accounts for shadowing.

Density and temperature effects on electron mobility in gaseous, critical, and liquid ethane

At applied electric-field strengths below a threshold value ${(\frac{E}{n})}_{\mathrm{thr}}$ the mobility of electrons is independent of field strength. At strengths just above the threshold the sign of the mobility-field coefficient $\frac{d\ensuremath{\mu}}{\mathrm{dE}}$ is positive in the low-density gas, negative in the high-density gas and low-density liquid [$1.0<(\frac{n}{{10}^{21}})<8$], and positive in the normal liquid. The temperature coefficient of mobility $\frac{d\ensuremath{\mu}}{\mathrm{dT}}$ is positive at all densities. The change of sign of $\frac{d\ensuremath{\mu}}{\mathrm{dE}}$ going from $n=0.9 \mathrm{to} 1.0$ (${10}^{21}$ molecule/${\mathrm{cm}}^{3}$) is attributed to destructive interference of long-range attractive interactions, which tends to reduce the effective scattering cross sections at the lower velocities. The sign of $\frac{d\ensuremath{\mu}}{\mathrm{dT}}$ remains positive because quasilocalization of electrons occurs at density fluctuations of suitable magnitude in this region of $n$. Quasilocalization is characterized by large negative values of $\ensuremath{\Delta}{H}^{\ensuremath{'}}$ and $\ensuremath{\Delta}{S}^{\ensuremath{'}}$, with $\ensuremath{\Delta}{G}^{\ensuremath{'}}\ensuremath{\simeq}0$. The density-normalized mobility $\ensuremath{\mu}n$ changes by less than a factor of 2 while increasing $n$ from the low-density gas to the liquid at $n=7\ifmmode\times\else\texttimes\fi{}{10}^{21}$ molecule/${\mathrm{cm}}^{3}$. At $n>8\ifmmode\times\else\texttimes\fi{}{10}^{21}$ the value of $\ensuremath{\mu}n$ plunges, due to the formation of more stable localized states; field-assisted delocalization of the electrons causes $\frac{d\ensuremath{\mu}}{\mathrm{dE}}$ to become positive again. Electron behavior in fluid ethane is quite different from that in fluid methane. The differences are attributed to the difference in molecular shape; methane is much more spherelike than ethane. The less spherelike molecule has a lower average scattering cross section for electrons at 300 K in the low-density gas, a Ramsauer-Townsend minimum in ${\ensuremath{\sigma}}_{\ensuremath{\nu}}$ lying at a lower energy, a larger ratio of threshold drift velocity to the speed of sound $\frac{{v}_{d}^{\mathrm{thr}}}{{c}_{o}}$, and more stable localized states of electrons in the liquid.

Storage density limitation of a volume-type hologram memory: theory

The maximum storage density of a volume-type hologram memory obtainable with a prescribed signal-to-noise ratio is discussed. In the theoretical analysis, a microscopic particle model of a phase hologram is considered; the refractive index variation is assumed to be caused by the density variation of bleached silver particles distributed spatially at random. The signal and noise intensities are derived from the analysis based upon this model. The theoretical limit of the storage density and the optimum hologram thickness are then derived in terms of the signal-to-noise ratio. The maximum storage density is finally given as a function of the average scattering cross section of the particles, the light wavelength, and the prescribed signal-to-noise ratio. Some practical cases are also discussed on the basis of measured material parameters.

Scattering of electromagnetic waves from a layer with rough front and plane back (small perturbation method by Rice)

Rice's small perturbation method is extended to obtain first- and second-order terms of the field scattered from a rough layer. The first-order terms are utilized to obtain average scattering cross sections. Lossy and lossless layers are considered for horizontal and vertical polarizations.

Rough Surface Scattering Based on the Specular Point Theory

The average number of specular points per unit area for a two-dimensionally rough surface is derived in terms of the surface statistics. Expressions for the average of the product of the principal radii of curvature of the specular point are also obtained. These quantities are then substituted into the average scattering cross section per unit area derived from the stationary-phase approach, and two probability models are considered. The results are general and apply to bistatic as well as backscatter, and are valid for finitely as well as perfectly conducting surface materials.

Thermal Conductivity of Potassium Chloride Crystals Containing Calcium

The details of the phonon scattering produced by point imperfections in insulating crystals has been determined from measurements of the thermal conductivity of six single crystals of KCl from 3\ifmmode^\circ\else\textdegree\fi{}K to 30\ifmmode^\circ\else\textdegree\fi{}K as a function of the concentration of point imperfections. These imperfections were produced by the addition of Ca${\mathrm{Cl}}_{2}$, which was incorporated into the KCl crystals as a substitutional impurity during growth from the melt. At temperatures above 15\ifmmode^\circ\else\textdegree\fi{}K the mean free path of the phonons decreases inversely with increasing calcium concentration. The average scattering cross section of a calcium ion---potassium ion vacancy complex increases as the fourth power of the temperature for low temperatures, and becomes equal to the geometrical cross section of the vacancy at a temperature of about $\frac{{\ensuremath{\theta}}_{D}}{6}$. Below 15\ifmmode^\circ\else\textdegree\fi{}K the phonon scattering by colloids of precipitated calcium chloride produces a large thermal resistivity in the impure crystals. The thermal conductivity of "pure" KCl at low temperatures is limited mainly by isotope and boundary scattering. The theoretical expressions as given by Klemens for combining thermal resistivities which possess different temperature dependences have been calculated, and have been applied to the present results. The agreement between Klemens' theory and the present experiment as to both the magnitude and the temperature dependence of the thermal resistivity is considered to be satisfactory.