Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

Abstract

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.     

Gaussian beam scattering from arbitrarily shaped objects with rough surfaces

Abstract

The scattered field of Gaussian beam scattering from arbitrarily shaped dielectric objects with rough surfaces is investigated for optical and infrared frequencies by using the plane wave spectrum method and the Kirchhoff approximation, and the formulae for the coherent and incoherent scattering cross sections are obtained theoretically based on geometrical optics and tangent plane approximations. The infrared laser scattering cross sections of a rough sphere are calculated at 1.06 μm, and the influence of the beam size is analysed numerically. It is shown that when the beam size is much larger than the size of the object, the results in this paper will be close to those of an incident plane wave.     

On the incoherent scattering of an acoustic or electromagnetic wave

A random configuration of objects in space, or a stochastically rough boundary, is considered to scatter an incident acoustic or electromagnetic wave having harmonic time dependencee ^iwt . In the case of a stochastic surface, Beckmann has compared the Kirchhoff solution with his approach, which employs random walk. The latter approach is used to demonstrate the Rayleigh-distributed amplitude of a field scattered by a very rough surface. This demonstration requires the conjecture that large standard deviations in the random phases of the scattered elementary waves result in an incoherent scattered field. Beckmann's conjecture has not been rigorously proven. However, in this paper, incoherence of the scattered field and broad distributions, over many cycles, in the phases of the elementary waves are both shown to be implied by a third condition, which is defined. Furthermore, the random phase of an incoherent field is shown to be statistically independent of its amplitude and uniformly distributed on a 2-rad interval.     

Enhanced wavefront reconstruction by random phase modulation with a phase diffuser

A phase retrieval technique for enhanced wavefront reconstruction using random phase modulation and a phase diffuser is proposed. The speckle field generated is sampled at multiple axially displaced planes and the speckle patterns are used in an iterative algorithm based on the optical wave propagation in free space. The presentation of this technique is carried out using two setups. In the first setup, a diffuser plate is placed at the image plane of a metallic test object. The benefit of randomizing the phase of the object wave is the enhanced intensity recording due to high dynamic range of the diffusely scattered beam. The use of demagnification optics will also allow the investigations of relatively large objects. In the second setup, a transparent object is illuminated using a wavefront with random phase and constant amplitude by positioning the phase diffuser close to the object. The benefit of phase-only modulation is the increased resolution of the phase structures of the transparent test objects.     

Non-Gaussian statistical models for scattering calculations

Abstract

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Scattering contrast of X-ray radiation

It is experimentally established that, in the majority of cases, the X-ray radiation scattered on different constituent parts of a weakly absorbing object provides sufficient information on inner structure, different types of structural inhomogeneities, and morphological characteristics, such as shapes, sizes, and location of invisible defects of the object. In this study, a new method for investigation of the inner structure of noncrystalline materials is developed. The method is based on recording of the scattered X-ray radiation. It is demonstrated that the image contrast, formed by the X-ray radiation scattered on weakly absorbing objects, can be considerably higher than the absorption contrast.     

Multiple scattering effects on the radar cross section (RCS) of objects in a random medium including backscattering enhancement and shower curtain effects

Abstract

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second–order moments by using the circular complex Gaussian assumption. The stochastic Green's functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.     

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

Abstract

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.     

Scattering and diffraction of a plane wave by a randomly rough half-plane*

Abstract

The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the D^a-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral along the steepest descent path and a branch-cut integral, which are evaluated numerically. Then, intensities of the coherently scattered wave and incoherent wave are calculated in the region near the edge and illustrated in figures.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

Abstract

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Method of phase-dispersion introscopy

A method is described for studying the internal structure of noncrystalline objects which are weak x-ray absorbers. The method uses the conventional arrangement of plane-wave topography. The object to be investigated is immersed in a monochromatic pseudoplane wave formed by a highly asymmetric reflection off a perfect crystal or several crystals and introduces phase disruptions at the wave front. A perfect single crystal mounted behind the object in a Laue arrangement reveals these disturbances, forming a contrast image of the boundaries of the structural components of the object. The possibilities of the method are illustrated by photographs of objects of various natures. The features of the image contrasts are discussed and confirmed by experiments on test objects. Zh. Tekh. Fiz. 67, 68–77 (January 1997)     

基于赝热光照明的单发光学散斑成像

散射介质对光的散射是当前限制光学成像深度或距离的一个严重的问题.本文首先数值模拟比较了光透过随机散射介质成像研究中常用的基于光学记忆效应(memory effect, ME)和自相关(autocorrelation, AC)方法的HIOER算法和乒乓(Ping-Pang, PP)算法的优缺点.通过对HIOER算法和PP算法的恢复效果和迭代次数进行比较,发现PP算法在保持较高恢复效果的前提下拥有更快的运行速度.实验中,利用连续HeNe激光器和旋转毛玻璃产生赝热光源,通过物镜对随机散射介质后数毫米距离内的不同形状物体进行了单帧成像,并采用PP算法成功地恢复出微米量级物体的实际图像.这一研究结果将进一步促进ME和AC方法在深层生物组织医学成像研究上的应用.最后,实验研究了不同的物镜和散射介质的间距对成像恢复的放大率、分辨率和图像强度的影响特性,并进行了详细研究.     

Propagation of acoustic waves scattered in a lossy three-dimensional channel

Abstract

In previous papers we discussed the scattering of acoustic waves by random sound-speed fluctuations in lossless two- and three-dimensional channels. Here we include the effect of bottom loss in a three-dimensional channel. The bottom loss is included by replacing the rigid bottom condition by one allowing for loss. We find an asymptotic solution for the angular distribution of the scattered acoustic energy and the characteristic propagation distance at which the asymptotic solution is valid. Beyond this characteristic distance the angular distribution saturates and is no longer dependent on the propagation distance. Before the mathematical development is given a simple physical argument is presented which shows why a saturation region is expected.     

Singularities in forward scattering through random media

Abstract

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ ^z , and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q _c , the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

Spectral Changes of Light Produced by Multiple Scattering from Space-Time Fluctuating Random Media under the Born Approximation

Changes in the spectrum of light scattered by space-time fluctuating random media are investigated theoretically within the accuracy of the second-order Born approximation, as a continuation of the previous paper [Opt. Commun. 123 (1996) 234]. Effects of multiple scattering on the resultant field are manifested by a number of illustrative examples. It is shown, in particular, that the spectrum of the scattered light to be observed under practical circumstances is distorted by the process of multiple scattering. Comparison between spectra of both single and multiple scattering lights is also presented in the framework of the dynamic scattering.     

Quantitative method for determining the angles of deflection of light rays reconstructed from the hologram of a phase object

A quantitative method is proposed to study the reconstructed wave front from a single hologram of a phase object. The method is designed to study coarse inhomogeneities in phase objects. Results of an experimental test of this method, confirming its efficiency, are presented. Zh. Tekh. Fiz. 67, 39–42 (March 1997)     

A novel method for non-destructive Compton scatter imaging based on the genetic algorithm

Compton scattering tomography is widely used in numerous applications such as biomedical imaging, nondestructive industrial testing and environmental survey, etc. This paper proposes the use of the genetic algorithm (GA), which utilizes bio-inspired mathematical models, to construct an image of the insides of a test object via the scattered photons, from a voxel within the object. A NaI(Tl) scintillation detector and a 185 MBq ¹³⁷Cs gamma ray source were used in the experimental measurements. The obtained results show that the proposed GA based method performs well in constructing images of objects.     

Subsurface detection of a buried object using angular correlation function measurement

Abstract

A new technique is proposed for subsurface detection of buried objects using the angular correlation function (ACF) measurement of scattered waves. Compared with the traditional detection technique which relies on radar cross section (intensity) measurement, this new ACF-based technique results in better signal-to-clutter ratio and thus higher target visibility. Laboratory experiments were conducted at millimetre-wave (80–105 GHz) and X-band (7–13 GHz) frequencies to illustrate the potential effectiveness of this new correlation approach over the traditional cross section approach.