Low-Frequency Scattering Research Articles

Stimulated Low-Frequency Scattering of Laser Radiation in an Aqueous Suspension of Viruses in the Frequency Range 1–60 GHz

Stimulated Low-Frequency Scattering of Laser Radiation in an Aqueous Suspension of Viruses in the Frequency Range 1–60 GHz

On a Novel Algorithmic Determination of Acoustic Low Frequency Coefficients for Arbitrary Impenetrable Scatterers

The calculation of low frequency expansions for acoustic wave scattering has been under thorough investigation for many decades due to their utility in technological applications. In the present work, we revisit the acoustic Low Frequency Scattering theory, and we provide the theoretical framework of a new algorithmic procedure for deriving the scattering coefficients of the total pressure field, produced by a plane wave excitation of an arbitrary, convex impenetrable scatterer. The proposed semi-analytical procedure reduces the demands for computation time and errors significantly since it includes mainly algebraic and linear integral operators. Based on the Atkinson–Wilcox theorem, any order low frequency scattering coefficient can be calculated, in finite steps, through algebraic operators at all steps, except for the last one, where a regular Fredholm integral equation with a continuous and separable integral kernel is needed to be solved. Explicit, ready to use formulae are provided for the first three low frequency scattering coefficients, demonstrating the applicability of the algorithm. The validation of the obtained formulae is demonstrated through recovering of the well-known analytical results for the case of a radially symmetric scatterer.

A Semi-Analytic, Numerically Efficient Model for Low-Frequency Sound Scattering by an Infinite Cylinder Located Near a Boundary

Scattering of sound by a target can be described as a wave radiated by virtual point sources inside the target. In the Rayleigh scattering regime, the strength of the virtual sources can be calculated analytically. When a target is located close to the ocean surface or another reflecting boundary, reflections of the incident and single-scattered waves from the boundary lead to multiple scattering from the target, with the target being insonified by nearby virtual sources. At low frequencies and for shallow targets, the distance from a virtual source to the target is not necessarily large compared to the acoustic wavelength or the target’s dimensions. Then, multiple orders of scattering make significant contributions and incident wave fields that cannot be approximated as a plane wave. This paper takes advantage of the virtual source concept and recently derived explicit analytic representations of 2D acoustic Green’s functions in unbounded fluids with inclusions of a circular cross-section, to develop a simple, intuitive, and numerically efficient model of multiple scattering. Scattering from soft, hard, and fluid targets is considered. The model is used to study the acoustic field in the vicinity of cylindrical targets near a pressure release surface or a hard bottom.

Low-Frequency Stimulated Scattering in an Aqueous Suspension of Dielectric Nanospheres

A low-frequency stimulated scattering (LFSS) signal caused by pulsations of nanospheres under an electromagnetic field is detected in an aqueous suspension of dielectric nanospheres of three diameters (∼74 nm, ∼292 nm, and ∼540 nm) at various particle concentrations. The frequency shifts of the scattering line, calculated based on the developed model, are in good agreement with the measurement results.

Stimulated Low-Frequency Scattering of Light in an Aqueous Suspension of the Tobacco Mosaic Virus

Stimulated low-frequency scattering of light by aqueous suspensions of the tobacco mosaic virus with the scattering frequency depending on the concentration of the virus is observed for the first time. For concentrations of ∼1 × 1012 and ∼2 × 1012 cm–3, the Stokes components of scattered light are shifted by ∼43.99 and ∼31.08 GHz, respectively. At the same time, the competing process of stimulated Brillouin scattering in these heterogeneous media is suppressed. The theory of stimulated emission resulting from normal-mode vibrations of solvent-molecule-loaded cylindrical nanoparticles driven by ponderomotive forces in the field of two copropagating pump electromagnetic waves is developed for the first time. The theoretically estimated frequency shift of the Stokes component is ∼50 GHz, which agrees with the experimental result. It remains unclear why a decrease in the thickness of the liquid layer with a simultaneous increase in concentration selectively favors a decrease in the frequency of coherent normal-mode vibrations of the virus participating in stimulated low-frequency scattering.

Simulation of Low-Frequency Scattering From Penetrable Objects in Layered Medium by Current and Charge Integral Equations

This paper presents a novel accurate and stable current and charge integral equation (CCIE) solver for the low-frequency scattering of penetrable objects in layered medium (LM). To the best of our knowledge, this is the first time to extend CCIE into LM simulations at low frequency. In order to integrate the matrix-friendly LM Green’s functions (LMGFs) into CCIE, we have rederived them to define new quasi-vector/scalar potentials, which are able to annihilate the frequency singularity in the original LMGFs. Moreover, an effective preconditioner is adopted to improve the conditioning of impedance matrices. In comparison with other perconditioners, this method performs much better. The excellent performance of this new CCIE solver is then demonstrated by numerical experiments.

Electrochemical behaviour in process of electrodeposition Ni–P alloy coating

An Ni–P alloy coating was obtained by electrodeposition on a 45 carbon steel substrate. The surface appearance of the coating was characterised by Hitachi S-4800 scanning electron microscope. The electrodeposition behaviour was investigated using electrochemical methods. The results showed that the Ni–P alloy coating was dense and smooth. The electrodeposition of the Ni–P alloy followed the mechanism of three-dimensional nucleation and subsequent grain growth. The main deposition process changed from heterogeneous nucleation/growth of Ni onto the 45 carbon steel substrate to heterogeneous nucleation/growth of Ni–P onto Ni film. There was low frequency scatter on electrochemical impedance spectroscopy plots, which can be attributed to the production of gas. With increasing negative bias voltage, the low frequency scatter became more obvious, and the charge transfer resistances Rct and Rp increased.

Single‐scan patient‐specific scatter correction in computed tomography using peripheral detection of scatter and compressed sensing scatter retrieval

X-ray scatter results in a significant degradation of image quality in computed tomography (CT), representing a major limitation in cone-beam CT (CBCT) and large field-of-view diagnostic scanners. In this work, a novel scatter estimation and correction technique is proposed that utilizes peripheral detection of scatter during the patient scan to simultaneously acquire image and patient-specific scatter information in a single scan, and in conjunction with a proposed compressed sensing scatter recovery technique to reconstruct and correct for the patient-specific scatter in the projection space. The method consists of the detection of patient scatter at the edges of the field of view (FOV) followed by measurement based compressed sensing recovery of the scatter through-out the projection space. In the prototype implementation, the kV x-ray source of the Varian TrueBeam OBI system was blocked at the edges of the projection FOV, and the image detector in the corresponding blocked region was used for scatter detection. The design enables image data acquisition of the projection data on the unblocked central region of and scatter data at the blocked boundary regions. For the initial scatter estimation on the central FOV, a prior consisting of a hybrid scatter model that combines the scatter interpolation method and scatter convolution model is estimated using the acquired scatter distribution on boundary region. With the hybrid scatter estimation model, compressed sensing optimization is performed to generate the scatter map by penalizing the L1 norm of the discrete cosine transform of scatter signal. The estimated scatter is subtracted from the projection data by soft-tuning, and the scatter-corrected CBCT volume is obtained by the conventional Feldkamp-Davis-Kress algorithm. Experimental studies using image quality and anthropomorphic phantoms on a Varian TrueBeam system were carried out to evaluate the performance of the proposed scheme. The scatter shading artifacts were markedly suppressed in the reconstructed images using the proposed method. On the Catphan©504 phantom, the proposed method reduced the error of CT number to 13 Hounsfield units, 10% of that without scatter correction, and increased the image contrast by a factor of 2 in high-contrast regions. On the anthropomorphic phantom, the spatial nonuniformity decreased from 10.8% to 6.8% after correction. A novel scatter correction method, enabling unobstructed acquisition of the high frequency image data and concurrent detection of the patient-specific low frequency scatter data at the edges of the FOV, is proposed and validated in this work. Relative to blocker based techniques, rather than obstructing the central portion of the FOV which degrades and limits the image reconstruction, compressed sensing is used to solve for the scatter from detection of scatter at the periphery of the FOV, enabling for the highest quality reconstruction in the central region and robust patient-specific scatter correction.

Low-Frequency Scattering by a Semi-Infinite Lattice of Cylinders

Acoustic wave scattering by a semi-innite lattice of sound-soft cylinders is considered in the long-wave limit. The problem is rst reduced an innite linear system of algebraic equations, and this in turn is solved via the discrete Wiener{Hopf technique. A complete description of the far eld is given, rst for the case where there is no propagation through the lattice, and then for the situation in which Bloch waves are excited. Finally, we apply the principle of conservation of energy, which leads to useful identities that serve as a check on the validity of our results.

Two-Term Ritz–Galerkin Solution for the Low Frequency Scattering by a Rectangular Trough in a Soft Ground Plane

An analytic form is derived for the diffracted field that originates when a transverse-magnetic plane-wave excites a rectangular trough cut in a ground plane. The low-frequency analysis is valid for trough apertures that are less than half a free-space wavelength in width. Trough depth is arbitrary. The quasi-static nature of the long wave problem is exploited by approximating the aperture field as a complex superposition of decoupled symmetric and antisymmetric solutions to Laplace's equation in the vicinity of the aperture, subject to Dirichlet boundary conditions. Geometrical contributions to the final algebraic expressions for the two aperture coefficients arise from two sources: A rapidly convergent series governs the aperture interaction with the trough modes and the effect of the half-space is embodied in a small number of terms of low powers in kappaalpha and factors of In kappaalpha.

Variational Low Frequency Scattering by a Rectangular Trough in a Hard Ground Plane

A set of analytical expressions are presented for the diffraction from a rectangular trough when excited by a transverse-electric polarized plane-wave. The final explicit forms are appropriate for applications requiring efficient computation, making minimal use of special functions and requiring no matrix inversions. The solution is arrived at via a quasi-static variational technique wherein the aperture field is represented by a linear combination of three simple functions suggested by the solution to Laplace's equation in the channel geometry. Comparison with an independent moment method indicates that the variational solution to the dynamic problem is highly accurate for troughs of general depth. The upper limit on the frequency corresponds to a total aperture width of one-half of a free-space wavelength.

Low Frequency Scattering by Circular Dielectric Cylinder: New Polarizability Tensor

SUMMARY This paper considers the low-frequency scattering by a circular dielectric cylinder and modifies the exact polarizability tensor to extend the valid region of the known low-frequency solution. When compared to the traditional formulation, the proposed solution is shown to be valid for cylinders with a higher dielectric constant and larger radius.

A Generalized Overrelaxation Method for Solving Singular Volume Integral Equations in Low-Frequency Scattering Problems

A Generalized Overrelaxation Method for Solving Singular Volume Integral Equations in Low-Frequency Scattering Problems

Component-Based Normalization for Panel Detector PET Scanners

We present a component-based normalization method for a PET scanner with a rotating array of panel detectors. The normalization procedure is designed to robustly normalize sinograms acquired with different levels of scattered radiation and at different count rates, flattening the response and removing artifactual detector-block patterns, which if uncorrected could cause ring artifacts in images and intensity variations along the scanner axis. Coincidence events are binned during acquisition into a 3-D sinogram S(r,/spl phi/,z,seg) where r is radius, /spl phi/ is angle, z is the axial position, and seg is the segment. In its simple form, the normalization N, defined by the equation S(normalized)=N*S(unnormalized), is assumed to take the angle-independent form N=1/(g(r,seg)*f(r,z,seg)*c(z,seg)), where the f term contains only low radial frequencies. The g and f terms are derived from a scan of a scatter-free uniform source. The c term, derived from a scan of a cylindrical phantom that scatters radiation and fills the axial field of view, removes high-frequency axial features in the sinogram but does not correct for the low-frequency scatter features which are handled by the reconstruction software. As the count rate changes, one finds that sinograms normalized by this simple procedure are afflicted by a high-frequency axial pattern due to a count rate dependent sensitivity change at the edges of blocks. This artifact is addressed by a multiplicative correction of the form /spl gamma/=/spl gamma/(S,z), where S is the singles counting rate and /spl gamma/ is a periodical function with the periodicity of the array of detector blocks.

Theory of Low-Frequency Scattering of Light by Superionic Glasses with Nanosize Structure

In the Raman spectra of glasses of (AgI)x(Ag2O · nB2O3)1 – x type, along with so-called “boson” peak (at frequencies of about 10 cm–1), a wide central component is pronounced even at room temperature. The component is similar to that in the spectra of crystalline superionic α-AgI. The emergence of such a central component in the spectra for glasses containing AgI indicates that size effects, which are associated with the glass structure, can significantly modify the relaxation modes associated with ionic conduction. For the first time, low-frequency spectra of superionic glasses are theoretically analyzed taking into account that, in nanocrystalline AgI, the mobile ion concentration is increased. A theoretical treatment of experimental spectra can provide information on important physicochemical characteristics of such glasses.

Low Frequency Scattering

This book for the first time unifies the theories of acoustic, electromagnetic, and elastic waves and discusses the many physical and geometric aspects of their interactions with obstacles. It offers a complete introduction to scattering theory, and goes on to discuss low frequency scattering in particular. A significant number of results are previously unpublished, and the book fills many gaps in the existing literature. Included is an extended bibliography covering the whole existing literature on low frequency scattering, making this an invaluable reference for researchers.

Relationship Between High-Frequency Diffraction and Low-Frequency Scattering From a Sharp Wedge

ABSTRACT This article describes a new relationship between the two-dimensional high-frequency and low-frequency waves scattered by an obstacle with a sharp wedge. It is shown that these two extremal waves have a unique correspondence in the underlying description of electromagnetic fields. The low-frequency field, which is given as a quasi-static field, is represented in terms of a function of complex variable z = x + iy. The high-frequency field can also be represented in terms of this complex function. The time-harmonic electromagnetic scattered or diffracted fields varying with exp(jωt) are thus bicomplex, which contains two imaginary units i and j. Basic concepts for this bicomplex calculations were discussed in the early paper. To illustrate the new solution in comparison with the exact one, the result is extended here to a half-plane diffraction known as a canonical problem. The same idea is tested to obtain a uniform solution that has no geometric-optical singularity in the far zone.

An Analytic Solution for Low-Frequency Scattering by Two Soft Spheres

A plane wave is scattered by two small spheres of not necessarily equal radii. Low-frequency theory reduces this scattering problem to a sequence of potential problems which can be solved iteratively. It is shown that there exists exactly one bispherical coordinate system that fits the given geometry. Then R-separation is utilized to solve analytically the potential problems governing the leading two low-frequency approximations. It is shown that the Rayleigh approximation is azimuthal independent, while the first-order approximation involves the azimuthal angle explicitly. The leading two nonvanishing approximations of the normalized scattering amplitude as well as the scattering cross-section are also provided. The Rayleigh approximations for the amplitude and for the cross-section involve only a monopole term, while their next order approximations are expressed in terms of a monopole as well as a dipole term. The dipole term disappears whenever the two spheres become equal, and this observation provide...

The low frequency scatter of SH waves by a rough interface in an elastic plate

The study of the reflection and transmission of low frequency SH waves incident upon a rough interface in an elastic plate is undertaken by employing a theory of acoustic wave scattering from rough surfaces originally due to Biot and subsequently generalised to the case of elastic media. In this theory the interface is replaced by a distribution of voids/asperities whose individual size is small compared to the excitation wavelength. We plot the absolute values of the reflection and transmission coefficients versus frequency when a single symmetric SH plate mode is used as the input excitation. The different types of inclusions are used to simulate the rough surface are the hollow, fluid filled and aluminum spheres. Lastly, the loss of energy due to scattering is also estimated for the different inclusion distributions considered.

Oscillations in cell morphology and redox state

Fluctuations in the intensity of light scattered and absorbed by cells in suspension have been analysed by smoothing, periodogram and power spectrum methods to reveal oscillations attributed to changes in cell morphology and the redox state of NADH and FAD (periods 10 s to 30 min). The rhythms are themselves periodically modulated in amplitude at a similar frequency and exhibit burst characteristics. The low frequency scatter dynamics are provisionally attributed to oscillations in gross morphology and the high frequency variation to changes at the cell surface. Agents, such as insulin and transferrin, affect the dynamics. The scatter results suggest that rhythmic changes in cell morphology associated with locomotion are largely inherent in the cell and not due to periodic attachment and detachment from a surface.