Scattering Transfer Function Research Articles

Clusters of Ultrasound Scattering Parameters for the Classification of Steatotic and Normal Livers

The study of ultrasound tissue interactions in fatty livers has a long history with strong clinical potential for assessing steatosis. Recently we proposed alternative measures of first- and second-order statistics of echoes from soft tissues, namely, the H-scan, which is based on a matched filter approach, to quantify scattering transfer functions and the Burr distribution to model speckle patterns. Taken together, these approaches produce a multiparameter set that is directly related to the fundamentals of ultrasound propagation in tissue. To apply this approach to the problem of assessing steatotic livers, these analyses were applied to in vivo rat livers (N=21) under normal feeding conditions or after receiving a methionine- and choline-deficient diet that produces steatosis within a few weeks. Ultrasound data were acquired at baseline and again at weeks 2 and 6 before applying the H-scan and Burr analyses. Furthermore, a classification technique known as the support vector machine was then used to find clusters of the five parameters that are characteristic of the different steatotic liver conditions as confirmed by histologic processing of excised liver tissue samples. With the in vivo multiparametric ultrasound measurement approach and determination of clusters, steatotic can be discriminated from normal livers with 100% accuracy in a rat animal model.

H-scan analysis of subtle changes in scattering

The H-scan analysis provides a matched filter approach to quantifying the scattering transfer function of tissue, at high resolution, in medical ultrasound. The approach yields quantitative estimates and high resolution images where color encodes the scattering information, and the results on normal and diseased tissues will be presented.

Scattering Signatures of Normal versus Abnormal Livers with Support Vector Machine Classification

Fifty years of research on the nature of backscatter from tissues has resulted in a number of promising diagnostic parameters. We recently introduced two analyses tied directly to the biophysics of ultrasound scattering: the H-scan, based on a matched filter approach to distinguishing scattering transfer functions, and the Burr distribution for quantification of speckle patterns. Together, these analyses can produce at least five parameters that are directly linked to the mathematics of ultrasound in tissue. These have been measured in vivo in 35 rat livers under normal conditions and after exposure to compounds that induce inflammation, fibrosis, and steatosis in varying combinations. A classification technique, the support vector machine, is employed to determine clusters of the five parameters that are signatures of the different liver conditions. With the multiparametric measurement approach and determination of clusters, the different types of liver pathology can be discriminated with 94.6% accuracy.

Fine-tuning the H-scan for discriminating changes in tissue scatterers

The H-scan approach (‘H’ denoting hue, or Hermite) is a recent matched filter methodology that aims to add information to the traditional ultrasound B-scan. The theory is based on the differences in the echoes produced by different classes of reflectors or scatterers. Matched filters can be created for different types of scatterers, whereby the maximum output indicates a match, and color schemes can be used to indicate the class of scatterer responsible for echoes, providing a visual interpretation of the results. However, within the theory of weak scattering from a variety of shapes, small changes in the size of the inhomogeneous objects will create shifts in the scattering transfer function. In this paper, we argue for a general power law transfer function as the canonical model for transfer functions from most normal soft vascularized tissues, at least over some bandpass spectrum illuminated by the incident pulse. In cases where scatterer size and distributions change, this produces a corresponding shift in center frequency, along with time and frequency domain characteristics of echoes, and these are captured by matched filters to distinguish and visualize in color the major characteristics of scattering types. With this general approach, the H-scan matched filters can be set to elicit more fine grain shifts in scattering types, commensurate with more subtle changes in tissue morphology. Compensation for frequency-dependent attenuation is helpful for avoiding beam softening effects with increasing depths. Examples from phantoms and normal and pathological tissues are provided to demonstrate that the H-scan analysis and displays are sensitive to scatterer size and morphology, and can be adapted to conventional imaging systems.

Functional integral approach to the transfer function of a stochastic scattering channel

ABSTRACT We apply the formalism of functional integration to the calculation of the transfer function of a stochastic scattering channel formed by stationary, non-interacting point scatterers. The channel is described through a scattering amplitude density, defined over space, whose random component is characterized by a functional probability distribution. This random component induces in turn a probability distribution for the scattering transfer function, which we compute by means of functional integration in the case of Gaussian distributions. Some geometric configurations relevant to radar operation are worked out, as well as the statistical properties of the transfer function in the large-frequency limit. Extensions of the formulation in order to include scattering phase shifts, i.e. complex scattering amplitudes, and to consider non-Gaussian probability distributions are outlined.

Fading correlation modelling for troposcatter microwave propagation in array antenna detection applications

Microwave over-the-horizon (OTH) propagation through troposcatter is a valuable candidate for remote targets detection. Array antenna is promising to handle the contradiction between real-time wide spatial coverage requirement and high antenna gain to capture weak scattering signal. The detection tactics and performance of array receiving systems are significantly affected by the fading correlation between array antennas, but there is no analytical study which considers the fading correlation in troposcatter passive sensing environments for uncooperative targets. In this study, an analytical method based on a scattering transfer function is proposed to derive the channel fading correlation, and the result is a function of transmitter deviation and spatial, temporal, frequency, angular separations of receiving array antennas in uncooperative troposcatter circumstances. In addition, the OTH troposcatter array receiving signal model is derived by exploiting the fading correlation to form the covariance structure of the received array signal, adding up with the signal transmission loss. Existing experimental results validate the derived fading correlations, and the simulation results validate the OTH passive detection performance based on the provided signal model.

Multiple Bragg reflection by a thick mosaic crystal.

Symmetric Bragg-case reflections from a thick, ideally imperfect, crystal slab are studied mostly by analytical means. The scattering transfer function of a thin mosaic layer is derived and brought into a form that allows for analytical approximations or easy quadrature. The Darwin-Hamilton equations are generalized, lifting the restriction of wavevectors to a two-dimensional scattering plane. A multireflection expansion shows that wavevector diffusion can be studied independently of the real-space coordinate. Combining analytical arguments and Monte Carlo simulations, multiple Bragg reflections are found to result in a minor correction of the reflected intensity, a moderate broadening of the reflected azimuth angle distribution, a considerable modification of the polar angle distribution, and a noticeable shift and distortion of rocking curves.

垂直极化平行板有界波电磁脉冲模拟器辐射近场的快速估算方法

For fast estimating the time-domain near-fields of flat-plate bounded wave electromagnetic pulse(EMP) simulator with vertical polarization, scattering transfer function method is used in time-domain simulation of this kind of simulator. A Gaussian pulse, whose effective frequency domain is wider than that of a given pulse source, is found firstly. And the time-domain response of electric fields at some testing points in the simulator excited by the Gaussian pulse source can be got by finite-difference time-domain (FDTD) method. Then the transient response of electric field at each testing point as the simulator excited by the given pulse source can be computed by Fourier transform, system transfer function and inverse Fourier transform. The results are well consistent with those got by FDTD method as the simulator is excited by the given pulse source directly. The method in this paper is useful for fast estimating radiation near-fields of a fixed simulator with different exciting sources. It has the advantages of reducing FDTD simulation time, saving much computing time and CPU storage especially for medium or large simulators.

Combined lumped element network and transmission line synthesis for passive microwave structures

Abstract. Compact circuit models of electromagnetic structures are a valuable tool for embedding distributed circuits into complex circuits and systems. However, electromagnetic structures with large internal propagation delay are described by impedance functions with a large number of frequency poles in a given frequency interval and therefore yielding equivalent circuit models with a high number of lumped circuit elements. The number of circuit elements can be reduced considerably if in addition to capacitors, inductors, resistors and ideal transformers also delay lines are included. In this contribution a systematic procedure for the generation of combined lumped element/delay line equivalent circuit models on the basis of numerical data is described. The numerical data are obtained by numerical full-wave modeling of the electromagnetic structure. The simulation results are decomposed into two parts representing a lumped elements model and a delay line model. The extraction of the model parameters is performed by application of the system identification procedure to the scattering transfer function. Examples for the modeling of electromagnetic structures are presented.

Stimulated Brillouin scattering frequency-domain analysis in a single-mode optical fiber for distributed sensing.

A numerical and experimental analysis of the stimulated Brillouin scattering in a single-mode optical fiber for distributed sensing applications is carried out in the frequency domain. The theoretical model describing the Brillouin interaction is solved by taking into account the temporal dynamics of the acoustic wave that is involved. The simulations and the experimental results reveal the role played by the ac component of the acoustic wave, which is responsible for significant changes of the small-signal stimulated Brillouin scattering transfer function that occur when the modulation frequency rises above the natural Brillouin gain spectrum linewidth. One should take these effects into account to perform accurate signal processing of frequency-domain signals in high-resolution distributed sensing applications.

Hybrid STF-FDTD approach for EM scattering analysis with an extremely slow-decaying pulse incidence

In this paper, we present a hybrid scattering transfer function (STF) and finite-difference time-domain (FDTD) approach for the calculation of electromagnetic transient responses with the incidence of an extremely slow-decaying pulse, e.g., a double-exponential pulse. We first introduce a scattering transfer function (STF) into the scattering system based on the principle of the linear system theory by using a fast-decaying pulse as the incident wave with the bandwidth of interest. Next, we derive the scattering response for an extremely slow-decaying pulse incidence with the help of the Fourier and inverse Fourier transforms. We have demonstrated the feasibility and superiority of the presented approach by analyzing some practical transient scattering cases. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 247–251, 2001.

Phase characteristics of scattering transfer functions of a sphere

Phase characteristics of scattering transfer functions of a sphere

Phase characteristics of scattering transfer functions of a sphere

Phase characteristics of scattering transfer functions of a sphere

Generalized Darlington synthesis

The existence of a has been the topic of vigorous debate since the time of Darlington's original attempts at synthesizing a lossy input impedance through a lossless cascade of sections terminated in a unit resistor. This paper gives a survey of present insights in that existential question. In the first part it considers the multiport, time invariant case, and it gives the necessary and sufficient conditions for the existence of the Darlington embedding, namely that the matrix transfer scattering function considered must satisfy a special property of analyticity known as pseudomeromorphic continuability (of course aside from the contractivity condition which ensures lossiness). As a result, it is reasonably easy to construct passive impedances or scattering functions which do not possess a Darlington embedding, but they will not be rational, i.e. they will have infinite dimensional state spaces. The situation changes dramatically when time-varying systems are concerned. In this case also Darlington synthesis is possible and attractive, but the anomalous case where no synthesis is possible already occurs for systems with finite dimensional state spaces. We give precise conditions for the existence of the Darlington synthesis for the time-varying case as well. It turns out that the main workhorse in modern Darlington theory is the geometry of the so called Hankel map of the scattering transfer function to be embedded. This fact makes Darlington theory of considerably larger importance for the understanding of systems and their properties than the original synthesis question would seem to infer. Although the paper is entirely devoted to the theoretical question of existence of the Darlington embedding and its system theoretic implications, it does introduce the main algorithm used for practical Darlington synthesis, namely the 'square root algorithm' for external or inner-outer factorization, and discusses some of its implications in the final section.

Radiative transfer in vegetation canopies with anisotropic scattering

The governing equation and various leaf models for photon transport in vegetation canopies that scatter anisotropically are presented. For idealized leaf-angle distributions and for simple canopy scattering models, the general transport equation and its azimuthal average are shown to reduce to standard forms encountered in radiative transfer and particle transport problems. In general, however, standard transport descriptions are not directly applicable to canopy problems. A realistic anisotropic and non-rotationally invariant scattering transfer function is examined and exact scattering models are derived. A variant of the discrete- ordinates method is then proposed for solving the canopy transport equation numerically. Finally, numerical results for a variety of agricultural canopies are compared with various theoretical and measured results.

Transfer functions interpolating an ideal amplitude with arbitrary phase and delay

AbstractA method is presented to generate polynomials with phase values and delay (first derivative) specified at given frequencies. Then a closed form solution is described for the scattering transfer function S12(p) of a resistively terminated lossless reciprocal two‐port network with ideal amplitude and arbitrary phase and delay.