Homodyne and heterodyne imaging through a scattering medium

We introduce a novel two-dimensional (2D) homodyne and heterodyne technique for imaging objects through or embedded in a scattering medium. Our imaging approach is based on heterodyning of light with different Doppler broadenings that is scattered from objects of two different textures or from an opaque object and a textured scattering medium. We report on the initial demonstration of pulling signals out of noise for an object hidden behind a scattering medium. Enhancements of signal-to-noise ratio of the order of 50 have been achieved by use of a 2D holographic phase-sensitive detector. We also discuss the experimental feasibility of this approach for objects embedded in a scattering medium.     

Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.     

Nonlinear scatterers in nonlinear media: Born approximation and local perturbation method

Wave scattering by inhomogeneous nonlinear particles placed in a nonlinear host medium is studied. In the case of weak scattering the scattering indicatrix is calculated in the first Born approximation. Scattering from small nonlinear particles loaded in a medium with saturation of permittivity is studied by the local perturbation method. A small perturbation method is developed for nonlinear equations of rather general type with a random, intensity-dependent, scattering potential.     

Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics

We study light scattering by Gaussian-random-sphere particles that are large compared to the wavelength of the incident light using ray optics that, in addition to Fresnellian reflection and refraction, accounts for diffuse scattering. We consider two types of diffusely scattering media. One type of media constitutes a uniform medium inside the particle, i.e. a diffuse internal medium. The second type of media constitutes a layer on the surface of the particle that is thin compared to the particle dimensions and acts as a diffuse external medium mimicking the particle surface roughness. We illustrate the effects of the diffuse media on the scattering characteristics for both cases and show that incorporating diffuse scatterers allows us to explain the scattering matrices measured experimentally for Saharan sand particles large compared to the wavelength.     

Effective response and scattering cross section of spherical inclusions in a medium

The Maxwell-Garnett theory for a right-handed homogeneous system is extended in order to investigate the effective response of a medium consisting of low density distributed 3-dimensional inclusions. The polarisability factor is modified to account for inclusions with binary layered volumes and it is shown that such a configuration can yield doubly negative effective permittivity and permeability. Terms representing second-order scattering interactions between binary inclusions in the medium are derived and are used to reformulate conventional effective medium theory. In the appropriate limit, the one-body theory of Maxwell-Garnett is recovered. The scattering cross section of the spherical inclusions is determined and comparison is made to homogeneous dielectric scatterers in the Rayleigh limit. It is found that the scattering resonances can be manipulated using the inclusion parameters. Furthermore, the effect that two-interacting spherical inclusions in a medium have on the scattering cross section is investigated via higher order dipole moments while the issue of reducing the scattering cross section to zero is also examined.     

Nonlinear scatterers in nonlinear media: Born approximation and local perturbation method

Abstract

Wave scattering by inhomogeneous nonlinear particles placed in a nonlinear host medium is studied. In the case of weak scattering the scattering indicatrix is calculated in the first Born approximation. Scattering from small nonlinear particles loaded in a medium with saturation of permittivity is studied by the local perturbation method. A small perturbation method is developed for nonlinear equations of rather general type with a random, intensity-dependent, scattering potential.     

散射介质中层间杂质检测效率的影响因素及分析

散射介质中层间杂质检测是一个非常重要的研究课题.改进现有的Monte Carlo方法,模拟大量光子在散射介质中的传输,得到入射光强、杂质埋藏深度、介质折射率、介质散射系数和各向异性因子对光学透反射成像法检测层间杂质效率的影响规律.结果表明,入射光强、杂质埋藏深度和介质折射率对透反射成像检测结果均有影响,且影响规律相似.增加入射光强、减小杂质埋藏深度或减小介质折射率均可提高反射光成像的检测效率;增大入射光强、减小介质折射率、减小介质散射系数或增大各向异性因子均可提高透射光成像的检测效率.这些规律对散射介质中层间杂质检测具有一定指导意义.     

Spectral power determinations of compressibility and density variations in model media and calf liver using ultrasound

A model of scattering is used to relate average differential scattering cross section and power spectra of scattering medium variations. The model expresses the average differential scattering cross section as a sum of the power spectrum of medium compressibility variations, the power spectrum of density variations weighted by the square of the cosine of the scattering angle, and the cross-power spectrum of compressibility and density variations weighted by twice the cosine of the scattering angle. Known values of the average differential scattering cross section at a minimum of three different scattering angles and temporal frequencies corresponding to the same spatial frequency are used to calculate each of the three power spectra. Since noise and statistical fluctuations are present in actual measurements of average differential scattering cross section, the calculations of power spectra are obtained from an overdetermined set of equations to which a solution is found by using a singular value decomposition. Data derived from a model for scattering from a cloud of correlated particles are employed to show the influence of additive noise. Calculations are also made from measurements of scattering from three suspensions of particles that have a different average radius in each suspension but are similarly modeled by scattering from a cloud. Additionally, the calculations are applied to measurements of average differential scattering cross section of calf liver. The results show that determination of the power spectra of scattering medium variations can be made under practical conditions, and also imply that density variations contribute significantly to scattering by calf liver.     

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.     

Determination of g and mu using multiply scattered light in turbid media

We propose an inversion scheme to reconstruct the scattering coefficient mu and the anisotropy factor g that characterize the optical properties of a turbid medium. It is based on a theory for the scattering of light inside the medium from an angularly collimated light source. We demonstrate the feasibility of this method using light scattering data obtained from a Monte Carlo simulation.     

Radiative properties of scattering and absorbing dense media: theory and experimental study

We investigate the validity of the radiative transfer equation to model transmission of light through an absorbing and scattering medium. Assuming that radiative transfer equation is valid, the inverse scattering problem for non-polarized radiative transfer in one-dimensional absorbing and scattering media is solved using a parameter identification method. We discuss how to identify the albedo, phase function and extinction coefficient of the medium. We present experimental data that confirm that this approach is robust and can be used to make reliable predictions of the behavior of scattering absorbing systems.     

Radiative heat transfer in a planar medium with anisotropic scattering and directional boundaries

Radiation heat transfer in an absorbing, emitting and scattering medium has been the subject of many previous investigations. Most solutions are numerically complex and the existing analytical solutions are restricted in application by the simplifying assumptions involved. A plane-parallel medium is considered which scatters anisotropically. The boundaries are considered to be specular reflectors, as predicted by Fresnel's relations, while the diffusely incident radiation is refracted according to Snell's law. The emission is restricted to a medium with a uniform temperature distribution. Approximate closed-form solutions for the radiative heat flux and incident intensity are presented for dielectric layers and linear anisotropic scattering. Numerical results are also presented and show that the effects of directional boundaries, anisotropic scattering, scattering albedo and optical depth are accurately predicted by the approximate solution.     

Adding and invariant imbedding equations in matrix notation for all the scattering functions

Previous work by the author introduced a radiative formulation, containing a delta interior illumination, that allowed scattering solutions driven by internal sources to be handled in complete analogy to those for the standard problem (external delta illumination scattering through a medium). This analogy was made explicit by defining the three levels of scattering functions, S_s-level, $\text{S}$_s- and S_F-level, and $\text{S}$_F-level, that characterize scattering through, into and out of, and within a finite medium, respectively. For an inhomogeneous medium the invariant imbedding method was employed to solve for these functions. This paper continues the work by showing that: (1) Adding equations can be derived for all the scattering functions using one superposition formula. (2) Adding and invariant imbedding computational methods are closely related and should be used in combination for efficient calculations. (3) A new set of functions can be defined that represent scattering out of a medium driven by thermal sources. (4) All scattering functions can be converted to represent a planetary problem by one adding step. References are given for numerical results using this formulation.     

Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium

We propose an analytical model of the spatio-temporal structure of a short laser pulse transmitted through a layer of an optically inhomogeneous medium with high anisotropy of scattering. The light-field brightness in the medium is represented as a finite series in terms of multiplicities of the small-angle scattering, while the contribution from the higher-order scattering is allowed for as a quasi-diffuse component. The scattered-pulse structure is calculated on the basis of solving the radiative-transfer equation in the small-angle approximation with allowance for the effect of multipath light propagation. Compared with the first approximation of the multiple-scattering theory (attenuated nonscattered light plus the diffuse component), this approach makes it possible to describe more correctly the transformation of the spatio-angular distribution of light in the medium when passing from the single-scattering to multiple-scattering regime, as well as specify the temporal profile of the scattered pulse. The temporal profile of the femtosecond pulse transmitted through a layer of model scattering medium with various concentrations of scatterers is studied experimentally. The blurred-pulse structure is studied with the help of nonlinear optical gating in the case of noncollinear generation of the second harmonic. Good agreement between the theoretical and experimental time profiles of the scattered pulse is shown for the optical-thickness intervals corresponding to both the predominantly low multiplicity scattering and multiple small-angle scattering, which allows us to use the proposed analytical model for solving the inverse problem of the pulse sounding of a homogeneous turbid medium. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 333–348, April 2008.     

光的散射定律及其证明

本文从完全新的角度出发,建立起散射介质的整体散射模型,从而发现了普遍适用的光的散射定律,并且开拓了测量介质散射率的新的研究领域。     

A multi-dimensional differential approximation for absorbing/emitting and anisotropically scattering media with collimated irradiation

By considering the intensity within a medium to consist of a collimated and a fairly diffuse part, the overall problem of radiative transfer is reduced to two simpler ones: first the collimated intensity is obtained (equivalent in complexity to a nonscattering medium); for the evaluation of the diffuse part of the radiation (due to emission and scattering), a new differential approximation has been developed. To demonstrate the accuracy and simplicity of the present method, two sample cases are presented for which some exact solutions can be found in the literature: results are presented (i) for cosine-varying irradiation incident upon a two-dimensional, isotropically scattering slab and (ii) for irradiation with a Gaussian intensity distribution of a two-dimensional, anisotropically scattering semi-infinite cylindrical medium.     

一维带限Weierstrass分形分层地面与矩形截面导体柱复合电磁散射FDTD研究

运用时域有限差分方法研究一维带限分形分层粗糙地面与矩形截面导体柱的复合电磁散射,计算复合电磁散射的双站散射系数,得到复合散射系数随散射角的变化,讨论粗糙面高度起伏均方根、分维、中间层介质、下层介质及矩形截面导体柱的参数等对复合散射系数的影响.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning-Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Refocusing and locating effect of fluorescence scattering field

Optical imaging deep inside scattering medium has always been one of the challenges in the field of bioimaging, which significantly drawbacks the employment of con-focal microscopy system. Although a variety of feedback techniques, such as acoustic or nonlinear fluorescence-based schemes have realized the refocusing of the coherent light, the problems of non-invasively refocusing and locating of linearly-excited fluorescent beads inside the scattering medium have not been thoroughly explored. In this paper, we linearly excited the fluorescent beads inside a scattering medium by using our homemade optical con-focal system, collected the fluorescence scattering light as the optimized target, and established a theoretical model of target contrast enhancement, which is consistent with the experimental data. By improving both the cost function and variation rate within the genetic algorithm, we could refocus the fluorescence scattering field while improving the contrast enhancement factor to 12.8 dB. Then, the positions of the fluorescent beads are reconstructed by sub-pixel accuracy centroid localization algorithm, and the corresponding error is no more than 4.2 μ with several fluorescent beads within the field of view. Finally, the main factors such as the number of fluorescent beads, the thickness of the scattering medium, the modulating parameter, the experimental noise and the system long-term stability are analyzed and discussed in detail. This study proves the feasibility of reconstructing fluorescent labeled cells inside biological tissues, which provides certain reference value for deep imaging of biological tissues.     

偏振相移与相位共轭结合的散射光聚焦技术研究

散射介质对光的随机散射作用是制约其光学聚焦和成像的重要因素，光学相位共轭技术能够通过对散射光场共轭还原实现透过散射介质的光学聚焦和成像，其中散射光场相位的获取是共轭还原的核心。阐述了偏振相移的基本原理，将偏振相移与相位共轭技术相结合，设计了新的基于偏振相移的数字光学相位共轭系统。采用633 nm的HeNe激光器作为系统光源，毛玻璃作为散射介质开展散射光聚焦实验研究。实验结果表明:该装置能够成功实现透过散射介质的光学聚焦，其中聚焦点与背景光强的比值可达约400倍。