Distribution Of Scattered Intensity Research Articles

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.

Intensity distribution and impact of scatter for dual-source CT

Apart from forward scatter, which is given for all CT scanners, dual-source CT (DSCT) is also affected by cross-scatter photons from the second tube–detector system arranged at 90°. We investigated the magnitude and distribution of scatter for DSCT and its impact on image quality. Simulations and measurements of homogeneous and anthropomorphic phantoms were conducted for a DSCT scanner (SOMATOM Definition, Siemens Medical Solutions, Forchheim, Germany) at tube voltages of 80 and 120 kV. The simulations of forward scatter were carried out using combined analytical and Monte Carlo simulation methods for a collimation of 19.2 mm for both tube–detector systems. Measurements of cross scatter were performed by switching one tube off, still reading out the corresponding detector. The relative scatter fractions and the distribution of cross scatter were registered for various imaging conditions. Additionally, a detailed noise analysis with respect to the correction of cross-scatter artifacts is provided to evaluate the performance of correction algorithms. The forward-scatter fraction increased with increasing phantom diameter from 0.02 up to 0.11 for PMMA phantoms of 80 to 400 mm diameter. For cross scatter, the mean intensity was equivalent to forward scatter for small phantoms but was larger for increased phantom size and resulted in severe artifacts in the reconstructed images. The outer dimensions and shape of the object are decisive for the cross-scatter intensity distribution whereas the influence of the degree of inhomogeneity of the respective phantom appears to be negligible. Scatter correction suppressed cross-scatter artifacts but increased noise as a function of the cross-scatter fraction. The magnitude of scatter is not negligible for DSCT systems and dedicated corrections are necessary for the assurance of unimpaired image quality.

Fluctuation correlation spectroscopy and photon histogram analysis of light scattered bygold nanospheres

Fluorescence correlation spectroscopy (FCS) is a valuable tool in biological research. In recentyears there has been growing interest in using light scattered from metallic colloids in placeof organic fluorophores. Metallic colloids display optical cross sections for scattering thatare orders of magnitude brighter than fluorophores. We used the FCS method to study thescattering properties of varying sizes of gold colloids 38–100 nm in diameter. The opticalcross sections of the gold colloids increase rapidly with size, as can be seen by both theG(0) value of the autocorrelation function and the scattering intensity distributions. In mixturesof different size gold colloids the autocorrelation function is dominated by thelarger (brighter) colloids, even when present at a small fractional population.We show that it is possible to detect one 100 nm gold colloid in the presence of103–104 smaller 39 nm diameter colloids. Because the scattering cross sections of colloids willincrease with aggregation, we believe that FCS can be used to detect a small number ofassociated bio-labeled colloids in the presence of a much larger population ofnon-associated colloids.

Geometrical-optics approximation of forward scattering by gradient-index spheres

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

Coherence effects in the scattering from domain structures

Scattering techniques with x-rays or neutrons are most effective for studyingdomain and domain wall structures on a mesoscopic scale. For small domain sizesand small strains between adjacent domains, coherence effects can give rise tosignificant modifications of the scattering intensity distribution which cannot generallybe neglected. Additional or missing peaks, peak shifts and peak narrowing canlead to false conclusions concerning assignments to multiple phases, lower orhigher symmetries, wrong lattice constants and domain sizes, respectively. This isdemonstrated by examples calculated with a simple scattering theory outlined.

Characterization of chemically etched indium phosphide surfaces with light scattering

Scattering of light from chemically etched InP surfaces is studied in the present paper. A model is developed to describe the randomly rough surfaces produced by chemical etching and this model is used in a numerical simulation using the Kirchhoff approximation to calculate the scattered intensity distribution from the surfaces. Comparisons between the numerical results and experimental measurements for an incident wavelength of 633 nm show good agreement. Numerical simulation results are presented to show the variation of the scattered intensity distribution for surfaces with different times of chemical etching. These results are useful for characterization or control of this type of surface.

Diffuse x-ray scattering from a crystal modulated by surface acoustic wave

The process of diffuse x-ray scattering from a crystal modulated by surface acousdtic wave is considered. It is shown that the angular distribution of the diffuse scattering intensity depends on variation of the gradient of the ultrasonic wave amplitude in depth of the crystal. This distribution is formed both in the vicinity of the main diffraction peak and around its satellites. Theoretical reciprocal space maps of the diffuse scattering intensity distribution are obtained and compared to the experimental data.

Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators

We report transmission spectra and mode-field distributions of a waveguide-coupled spiral-shaped microdisk resonator on a silicon nitride-on-silica substrate. Our measured and simulated transmission spectra reveal reciprocal transmissions between clockwise and counterclockwise travelingwaves of such microcavity that lacks mirror symmetry. Our measured out-of-plane scattering intensity distributions and simulated steady-state mode-field patterns, however, indicate asymmetric modal distributions that depend on the sense of lightwave circulations and the input-coupling mechanisms. We discuss implications of the observed reciprocal transmissions with asymmetric modal distributions to unidirectional lasing from spiral-shaped microcavities reported in the literature.

Rigorous analysis of spheres in Gauss-Laguerre beams

In this paper we develop a rigorous formulation of Gauss- Laguerre beams in terms of Mie scattering coefficients which permits us to quasi-analytically treat the interaction of a spherical particle located in the focal region of a possibly high numerical aperture lens illuminated by a Gauss-Laguerre beam. This formalism is used to study the scattered field as a function of the radius of a spherical scatterer, as well as the translation of a spherical scatterer through the Gauss-Laguerre illumination in the focal plane. Knowledge of the Mie coefficients provides a deeper insight to understanding the scattering process and explaining the oscillatory behaviour of the scattered intensity distribution.

A Faster Approximation of Forward Scattering by Gradient-index Particles

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 - {60 - ) for gradient-index particles illuminated by acollimated ted incident beam. The incident angle of the re∞ected light is derived from the scattering angle to improve the approximation precision. This method proves efiective for transparent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. With the given index model, the geometrical optics approximation is efiective only for forward small angles, typically less than 10 - or so when the refractive index difierence of a particle is greater than a certain value. DOI: 10.2529/PIERS061023013549

Protein Interactions Studied by SAXS: Effect of Ionic Strength and Protein Concentration for BSA in Aqueous Solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, SSC(q), or an attractive square-well structure factor, SSW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I < 0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >or= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.

Kinetics of Different Processes in Human Insulin Amyloid Formation

Human insulin has long been known to form amyloid fibrils under given conditions. The molecular basis of insulin aggregation is relevant for modeling the amyloidogenesis process, which is involved in many pathologies, as well as for improving delivery systems, used for diabetes treatments. Insulin aggregation displays a wide variety of morphologies, from small oligomeric filaments to huge floccules, and therefore different specific processes are likely to be intertwined in the overall aggregation. In the present work, we studied the aggregation kinetics of human insulin at low pH and different temperatures and concentrations. The structure and the morphogenesis of aggregates on a wide range of length scales (from monomeric proteins to elongated fibrils and larger aggregates networks) have been monitored by using different experimental techniques: time-lapse atomic force microscopy (AFM), quasi-elastic light-scattering (QLS), small and large angle static light-scattering, thioflavin T fluorescence, and optical microscopy. Our experiments, along with the analysis of scattered intensity distribution, show that fibrillar aggregates grow following a thermally activated heterogeneous coagulation mechanism, which includes both tip-to-tip elongation and lateral thickening. Also, the association of fibrils into bundles and larger clusters (up to tens of microns) occurs simultaneously and is responsible for an effective lag-time.

Computation for angular distribution of scattered light on a coated bubble in water

The bubbles in sea water are mostly coated with a layer of oil, of which the effect on scattered light has usually been ignored in previous studies. This paper aims to propose an equation of scattering intensity by coated bubbles in water, based on geometrical optics theories. During the research, a PC was used to generate a two-dimensional curve that models the angular distribution of scattered intensity, namely the volume scattering function (VSF), by a coated bubble with a diameter larger than 200 μm. The curve reveals the far-field characteristics of light scattered by the coated bubble, as well as the refractive rays that have the main influence on the scattering intensity. It is seen from the simulation results that the scattering intensity distribution of an uncoated bubble and a coated bubble are very similar. But the oil layer weakens the forward scattering effect of the coated bubble while it strengthens the backward scattering effect.

X-ray diffuse scattering from stacking faults in thick 3C-SiC single crystals

Stacking faults in thick (001)- and (111)-oriented 3C-SiC single crystals are studied by high resolution x-ray diffraction. The authors demonstrate that the analysis of the diffuse scattering intensity distribution can be used as a nondestructive means to accurately determine the densities of Shockley-type stacking faults. The diffuse scattering intensity is simulated with a scattering model based on a difference-equation description of faulting in fcc materials. It is shown that the (001) SiC crystals exhibit an anisotropic fault distribution, whereas the (111) SiC crystals exhibit an isotropic fault distribution, in excellent quantitative agreement with transmission electron microscopy observations.

Viscoelastic effects on early stage of spinodal decomposition in dynamically asymmetric polymer blends

Spinodal decomposition induced by a rapid pressure change was investigated for a dynamically asymmetric polymer blend [deuterated polybutadiene (DPB)/polyisoprene (PI)] with a composition of 50/50 wt/wt by using time-resolved small angle neutron scattering. The time change in the scattered intensity distribution with wave number (q) during the spinodal decomposition was found to be approximated by the Doi-Onuki theory [M. Doi and A. Onuki, J. Phys. II 2, 1631 (1992)]. The theoretical analysis yielded the q dependence of the Onsager kinetic coefficient which is characterized by the q(-2) dependence at qxive > 1 with the characteristic length xive being much larger than the radius of gyration of DPB or PI. The estimated xive agrees well with that obtained previously in the relaxation processes induced by pressure change within the one phase region for the same blend.

Computation of the scattering intensity distribution for natural light scattered by an air bubble in water

This paper aims to propose an equation for calculating the distribution of light scattered when a collimated beam is incident upon a spherical air bubble in water. As it neglects the attenuation factor G, the formula is much simpler than that of the Davis model. One application of the formula is providing a model using which one can computer generate the angular distribution of radiation scattered by air bubbles. During the research, a curve that models the angular distribution of the radiation scattered by a bubble is generated by use of a PC. The typical computations are for a bubble radius of R = 200??m andthe relative refractivity of water at 15??C of n = 1.33. It is found that the forward scattering effect is far greater than the backward scattering one. The conclusion is that as long as the bubble radius is much larger than the wavelength of light, the angular distribution of the scattered light is not influenced by the change of bubble radius. However, increase of the relative refractive index in the transmitting media weakens the forward scattering while it strengthens the backward scattering on the bubble surface.

Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section

An alternative to using the traditional scattering angle theta to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(theta/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of theta. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter rho = 2kR/m - 1/, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when p < 1 and follows simple patterns for p > 1, which evolve predictably as a function of p. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.

Unified Interpretation of the Short- and Long-Range Ordered States in Cu–Pt Alloys

This paper describes a unified interpretation of unusual short-range order diffuse scattering intensity distribution, the appearance of intensity maxima simultaneously at the special points L and X of the reciprocal space, and of the formation of a variety of long-range ordered structures, including less common structures, in the face-centered cubic Cu–Pt alloys. Reassessment is first made of the ordered structures on the Pt-rich composition side and then it is shown that all the structures in the alloys are systematically described adopting the static concentration wave model, originally developed by Khachaturyan, with the two kinds of waves, L1 1 wave and L1 2 wave, and their combination. These waves are assumed to be still alive at temperatures above the order–disorder transition point with appreciably decreased amplitude and coherency length and lead to the appearance of the two types of diffuse intensity maxima. Comparison is made with the ordering behaviors in the well-known Cu–Au alloys, in which o...

Effective Long-Range Attraction between Protein Molecules in Solutions Studied by Small Angle Neutron Scattering

Small angle neutron scattering intensity distributions taken from cytochrome C and lysozyme protein solutions show a rising intensity at a very small wave vector Q, which can be interpreted in terms of the presence of a weak long-range attraction between protein molecules. This interaction has a range several times that of the diameter of the protein molecule, much greater than the range of the screened electrostatic repulsion. We show evidence that this long-range attraction is closely related to the type of anion present and ion concentration in the solution.

Asphaltenic aggregates are polydisperse oblate cylinders

Small-angle neutron scattering (SANS) has proven to be very useful for deducing the sizes and morphologies of asphaltenic aggregates in solution. A wide variety of intra-particle structure factors have previously been applied to SANS scattering spectra, but the studies often provided limited information concerning the quality of the fits and the Q range over which the models were applied. Selection of an appropriate form factor that closely approximates the structure of asphaltenic aggregates is important for determining the properties of asphaltenic aggregates, such as the radius of gyration ( R G ), molar mass, and apparent fractal dimension. This study evaluates various mono- and polydisperse intra-particle structure factor models as applied to four asphaltene scattering spectra. Agreement of the model fit parameters ( I 0 and R G ) with those obtained from Guinier analyses suggests that such a form factor model is physically reasonable. Reduced χ 2 values for each non-linear least squares fit indicates how well a given model fits to the entire Q range studied for the scattering intensity distribution. In the polydispersity analyses, an analytical function is introduced to model the scattering behavior of oblate cylinders with a Schultz distribution of radii. Results indicate that the polydisperse radius oblate cylinder model best approximates the shape of asphaltenic aggregates.