Polarization-based range-gated imaging in birefringent medium:Effect of size parameter

We have investigated the effect of size parameter of the scatterer on the image quality obtained with polarization-based range-gated imaging in birefringent turbid medium. Both linearly and circularly polarized light were utilized for imaging.The simulated results indicate that the improvement of visibility is more pronounced using circularly polarized light for the birefringent medium composed of smaller-sized scatterers at lower values of optical thickness and the birefringent medium comprising larger-sized scatterers. In contrast, linearly polarized light provides better image quality for the birefringent medium composed of smaller-sized scatterers at larger values of optical thickness. The evolution of the polarization characteristics of backscattered light and target light under the conditions mentioned above was measured to account for these numerical results.     

Coherent opposition effects for semi-infinite discrete random medium in the double-scattering approximation

The rigorous equations of the theory of multiple scattering of light by a layer of disordered medium have been used in the double-scattering approximation for semi-infinite medium to determine the influence of the particle properties on the coherent opposition effects. The effects were found to be strongly dependent on the concentration of scatterers in the medium. The polarization opposition effect is more sensitive to the properties of the scatterers than the photometric opposition effect. The interference of waves could result in the negative polarization at the backscattering direction as well as in the positive polarization.     

含金属散射体的中红外无序介质的光子定域化理论研究

基于Mie散射理论发现,各种金属在中红外区的各个频率点上的散射行为均极为相近,是一种在中红外区反照率高但散射效率较低的散射体.在浓度为10%时,介质的定域化参量最小只能达到6.6,并且与体系的常用基质材料无关.数值研究揭示了这种金属散射体系统与低吸收、高折射率散射体系统间的内在联系 关键词： 光子定域化 无序介质 中红外 Mie散射 金属     

Generalized Foldy-Lax formulation

We present a method for numerical wave propagation in a heterogeneous medium. The medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers. By extending the classic Foldy-Lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension. In the method that we set forth multiple scattering among the point scatterers and the extended target is fully taken into account via a boundary integral formulation coupled with the Foldy-Lax formulation. This formulation forms the basis for our numerical procedure.     

Localization of a small change in a multiple scattering environment without modeling of the actual medium

A method to actively localize a small perturbation in a multiple scattering medium using a collection of remote acoustic sensors is presented. The approach requires only minimal modeling and no knowledge of the scatterer distribution and properties of the scattering medium and the perturbation. The medium is ensonified before and after a perturbation is introduced. The coherent difference between the measured signals then reveals all field components that have interacted with the perturbation. A simple single scatter filter (that ignores the presence of the medium scatterers) is matched to the earliest change of the coherent difference to localize the perturbation. Using a multi-source/receiver laboratory setup in air, the technique has been successfully tested with experimental data at frequencies varying from 30 to 60 kHz (wavelength ranging from 0.5 to 1 cm) for cm-scale scatterers in a scattering medium with a size two to five times bigger than its transport mean free path.     

Effect of pulse entrapping on diffuse reflection from a resonant random medium: exact solution to the scalar albedo problem

A recently derived radiative transfer equation with three Lorentzian delay kernels is applied to an albedo problem of the scalar wave field produced by the diffuse reflection of a quasi-monochromatic pulse from a semi-infinite random medium consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar H-function H(μλ), extended analytically into the complex single-scattering albedo λ plane. The resulting analytic solution for the time evolution of a diffusely reflected short pulse is used to study on the whole time axis the effect of the redistribution of the energy of the propagated pulse from the front to the rear of the pulse in cases where the pulse may for most of the propagation time through the medium be 'entrapped' inside resonant scatterers. By considering the power flux through unit area of the boundary of the medium and unit solid angle, it is shown that the relative shift of an 'energy centroid' ('centre of mass') of the pulse diffusely reflected from the resonant random medium (compared with the pulse energy centriod in the non-resonant case) is equal to the parameter describing the energy accumulation inside the scatterers. This result may be used for experimental study of resonant random media with the aid of a short-pulse technique.     

Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers

The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and Berry's [Proc. Phys. Soc. London 91, 678-688 (1967)], the latter being limited to fluid host media, and it is the three-dimensional counterpart of that derived by Conoir and Norris [Wave Motion 47, 183-197 (2010)] for cylindrical scatterers in an elastic host medium.     

Green's function estimation in speckle using the decomposition of the time reversal operator: application to aberration correction in medical imaging

The FDORT method (French acronym for decomposition of the time reversal operator using focused beams) is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their Green's function. It is particularly useful when focusing in a heterogeneous medium. This paper generalizes the theory of the FDORT method to random media (speckle), and shows that it is possible to extract Green's functions from the speckle signal using this method. Therefore it is possible to achieve a good focusing even if no point scatterers are present. Moreover, a link is made between FDORT and the Van Cittert-Zernike theorem. It is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well-known focusing criterion. The concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of FDORT in speckle. Applications to aberration correction are presented. The reduction of the variance of the Green's function estimate is discussed. Finally, it is shown that the method works well in the presence of strong interfering scatterers.     

Ultrasound speckle analysis based on the K distribution

The departure of speckle magnitude from Rayleigh statistics was applied to examine insonated phantoms with both low and high concentrations of scatterers. A mathematical model, the K distribution of Jakeman, was used to characterize non-Rayleigh statistics. This model contains a parameter, alpha, which characterizes the clustering of the scattering sites in a medium. It is shown from phantom experiments that alpha is linearly proportional to the log-scaled scatterer concentration in a range from about 1 to 30 scatterers per sample volume.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

Localization of radiation in two-dimensional random media of finite extent

The localization of electromagnetic waves in a two-dimensional random medium composed of strong scatterers is studied theoretically. It is shown that an allowance for the spatial radiation intensity distribution inside the medium, along with an analysis of the distance dependence of the transmission coefficient, is needed to reveal the localization states in media of finite extent.     

随机非球形粒子全极化散射的时间相关Mueller矩阵解

从与时间相关的矢量辐射传输方程推导一阶Mueller矩阵解,用来模拟Gauss型平面脉冲波入射下,一层随机、非均匀取向非球形粒子的全极化双站散射.数值计算了同极化和去极化脉冲响应,与入射脉冲进行了比较,说明了随机介质的物理参数,如粒子的取向和占空比、入射角、极化以及层厚等对脉冲响应的影响 关键词： 平面脉冲波 非球形粒子 Mueller矩阵     

On optical properties of nonspherical inhomogeneous particles

To solve the problem of light scattering by multilayer scatterers of an arbitrary axisymmetric shape, a separation of variables method that involves special scalar potentials and their expansions in spherical functions is developed. The approach is shown to yield highly exact results even for particles that have 100 layers or more. A graphic library that illustrates the optical properties of layered and homogeneous (with an effective refractive index) spheroids, spheres, and Chebyshev particles of various shapes and sizes (about 650 figures) is created and is put on the Internet. It is noted that the linear polarization of radiation transmitted forward through a polydisperse medium containing partially oriented nonspherical porous particles strongly depends on the structure of scatterers. It is shown that the difference between the degrees of polarization of layered and corresponding homogeneous scatterers can exceed 200–300%.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Theory of transfer with delay for trapping of nonstationary acoustic radiation in a resonant randomly inhomogeneous medium

The propagation of a quasimonochromatic wave packet of acoustic radiation in a discrete randomly-inhomogeneous medium under the condition that the carrier frequency of the packet is close to the resonance frequency of Mie scattering by an isolated scatterer is studied. The two-frequency Bethe-Salpeter equation in the form of an exact kinetic equation that takes account of the accumulation of the acoustic energy of the radiation inside the scatterers is taken as the initial equation. This kinetic equation is simplified by using the model of resonant point scatterers, the approximation of low scatterer density, and the Fraunhofer approximation in the theory of multiple scattering of waves. This leads to a new transport equation for nonstationary radiation with three Lorentzian delay kernels. In contrast to the well-known Sobolev radiative transfer equation with one Lorentzian delay kernel, the new transfer equation takes account of the accumulation of radiation energy inside the scatterers and is consistent with the Poynting theorem for nonstationary acoustic radiation. The transfer equation obtained with three Lorentzian delay kernels is used to study the Compton-Milne effect—trapping of a pulse of acoustic radiation diffusely reflected from a semi-infinite resonant randomly-inhomogeneous medium, when the pulse can spend most of its propagation time in the medium being “trapped” inside the scatterers. This specific albedo problem for the transfer equation obtained is solved by applying a generalized nonstationary invariance principle. As a result, the function describing the scattering of a diffusely reflected pulse can be expressed in terms of a generalized nonstationary Chandrasekhar H-function, satisfying a nonlinear integral equation. Simple analytical asymptotic expressions are found for the scattering function for the leading and trailing edges of a diffusely reflected δ-pulse as functions of time, the reflection angle, the mean scattering time of the radiation, the elementary delay time, and the parameter describing the accumulation of radiation energy inside the scatterers. These asymptotic expressions demonstrate quantitatively the retardation of the growth of the leading edge and the retardation of the decay of the trailing edge of a diffusely reflected δ-pulse when the conventional radiative transfer regime goes over to a regime of radiation trapping in a resonant randomly-inhomogeneous medium. Zh. éksp. Teor. Fiz. 113, 432–444 (February 1998)     

Spatio-temporal invariants of the time reversal operator

The decomposition of the time reversal operator, known by the French acronym DORT, is a technique to extract point scatterers' monochromatic Green's functions from a medium. It is used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. A limitation of the method arises from its single-frequency nature, when the signals used in acoustics are often broadband. Reconstruction of the broadband Green's functions from the single-frequency Green's functions can be very difficult when numerous scatterers are present in the medium. Moreover, the method does not take advantage of the axial resolution associated with broadband signals. Time domain methods are investigated here as an answer to these problems. It is shown that the time reversal operator in the time domain takes the form of a tensor. The properties of the invariants are discussed. It is shown they do not have all the expected properties. Another method is proposed that requires a priori information on the medium.     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.