Approximate solution for describing polarization characteristics of radiation in a Rayleigh scattering medium

An approximate analytical solution for the 4 × 4 Green’s matrix of the problem of polarized radiation transfer in a plane-parallel layer of an absorptive Rayleigh scattering medium is proposed. It permits one to perform fast estimates of angular distributions of the Stokes parameters that are created by an incident beam with an arbitrary polarization state at different levels in a layer when the layer thickness, absorption magnitude, and albedo of the underlying surface are varied. The developed solution is compared with data obtained by the numerical doubling method. The value of the scattering coefficient for a circularly polarized radiation is shown to be somewhat smaller than that for linearly polarized radiation.     

Application of the singularity-subtraction technique to isotropic scattering in a planar layer

A numerical procedure for solving a singular Fredholm integral equation, which describes radiative transfer in an absorbing and isotropically scattering layer exposed to collimated radiation, is studied. The integral equation is solved by subtracting out the singularity and then approximating the integral term by a Gaussian quadrature. Bidirectional and hemispherical properties are found from the source function. Any arbitrary directional distribution of incident radiation can be handled by superimposing the collimated radiation case. In particular, the case of isotropic incident radiation is presented. The method gives accurate results, even for the extreme conditions of large optical thickness and large angle of incidence.     

Light scattering in disperse layers with a high concentration of optically soft particles

A model describing the propagation of radiation in disperse close-packed layers of optically soft particles is proposed. The model is based on the radiative transfer equation used for describing a light field in the multiple scattering regime and on the interference approximation for describing collective scattering effects; it also takes into account the Fresnel reflection at the layer boundaries. To describe the single-scattering characteristics, the Mie formulas are used. The model allows one to consider scattering in layers of any optical thickness. Calculations of the angular structure of the radiation leaving the layer and estimates of the errors of the calculations were performed. The possibility of forming a maximum at small scattering angles in media with correlated particles is shown. The theoretical results are in good agreement with the available experimental data.     

Radiative transfer in a layer of magnetized plasma with random irregularities

The problem of radio wave reflection from an optically thick plane uniform layer of magnetized plasma is considered in the present work. The plasma electron density irregularities are described by a spatial spectrum of arbitrary form. The small-angle scattering approximation in invariant ray coordinates is proposed as a technique for the analytical investigation of the radiation transfer equation. The approximate solution describing the spatial and angular distribution of radiation reflected from a plasma layer is obtained. The solution obtained is investigated numerically for the case of ionospheric radio wave propagation. Two effects occur as a consequence of multiple scattering: a change in the reflected signal intensity and an anomalous refraction.     

Reconstruction of the characteristics of a light-scattering layer from its reflectance and transmittance: The neural network method

The problem of reconstructing the probability of photon survival, the optical layer thickness, and the parameter of asymmetry of the scattering indicatrix of an elementary volume from the dependence of the reflectance and the transmittance on the angle of incidence of radiation onto a layer of a medium with Fresnel reflection from the boundaries is considered. To solve this problem, a method based on the use of correlation neural networks is proposed. For training and control of the operation of neural networks, the reflectance and the transmittance of the layer calculated within the framework of the radiation transfer theory were used. For the simulation of the scattering characteristics of an elementary volume, the Mie theory was used. Estimates of errors in the reconstruction of the characteristics of the medium were performed.     

Applicability of approximate methods of calculation of the frequency-contrast characteristics of aerosol layers within the wavelength range of 0.4–14 μm

The spectral dependences of the optical characteristics governing radiation transfer in scattering media are analyzed within the wavelength range of 0.4–14 μm for three types of aerosols. The wavelength ranges where approximate methods of calculation of frequency-contrast characteristics are applicable are established; the corresponding limitting masses of aerosol particles in a layer per unit of surface area are determined for which approximate methods provide acceptable accuracy. B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 70 F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 419–425 May–June, 1998.     

半透明平板边界入射辐射热流密度的反问题

对一维半透明平板内辐射、导热及边界对流耦合换热过程进行了研究。提出了一种由一侧边界出射辐射强度反演另一侧边界入射辐射热流密度的方法。通过对各向异性散射、吸收系数、散射系数、边界外侧来流温度、对流换热系数、半透明平板的导热系数和平板厚度等参数对反演精度影响的分析表明,方法是可行的。     

Non-Fourier heat conduction with radiation in an absorbing, emitting, and isotropically scattering medium

This article numerically analyses the combined conductive and radiative heat transfer in an absorbing, emitting, and isotropically scattering medium. The non-Fourier heat conduction equation, which includes the time lag between heat flux and the temperature gradient, is used to model the conductive heat transfer in the medium. It predicts that a temperature disturbance will propagate as a wave at finite speed. The radiative heat transfer is solved using the P₃ approximation method. In addition, the MacCormack's explicit predictor-corrector scheme is used to solve the non-Fourier problem. The effects of radiation including single scattering albedo, conduction-to-radiation parameter, and optical thickness of the medium on the transient and steady state temperature distributions are investigated in detail. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature. The thermal wave nature in the combined non-Fourier heat conduction with radiation is more obvious for large values of conduction-to-radiation parameter, small values of optical thickness and higher scattering medium. The results from non-Fourier-effect equation are also compared to those obtained from the Fourier equation. Non-Fourier effect becomes insignificant as either time increases or the effect of radiation increases.     

Scattering and active acoustic control from a submerged piezoelectric-coupled orthotropic hollow cylinder

A general exact analysis for three-dimensional scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent, which is composed of a cylindrically orthotropic axially polarized piezoelectric inner layer perfectly bonded to an orthotropic outer layer, is presented. An approximate laminate model in the context of the so-called state space formulation along with the classical T-matrix solution technique involving a system global transfer matrix is employed to solve for the unknown modal scattering and transmission coefficients. Numerical example is given for an air-filled and water-submerged two-layered elasto-piezoelectric hybrid (steel/PZT4) hollow cylinder insonified by an obliquely incident unit-amplitude plane sound wave. Following the acoustic resonance scattering theory (RST), the total form function amplitude together with the associated global scattering, the far-field inherent background, and the resonance scattering coefficients of the nth normal mode are computed as a function of dimensionless frequency for selected angles of incidence, piezoelectric layer thickness parameters, and electrical boundary conditions (i.e., open/closed circuit or active). Also, the electrical voltage coefficients required for partial or complete cancellation of the reflected sound field are calculated. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

Radiative Transfer in a Layer of Oriented Spheroidal Particles with Oblique Incidence of Light

The results of numerical modeling of diffuse reflection and transmission by layers of oriented spheroidal particles (whose rotation axes are normal to the layer surface) with oblique incidence of a parallel beam of radiation on the layer are presented. To describe the properties of particles in the elementary act of scattering, the Rayleigh-Gans approximation is used. To describe the propagation of radiation in the layer, the radiative transfer equation in which the characteristics of the medium depend on the direction of radiation propagation is used. The influence of Fresnel reflection at the layer boundaries and the influence of the substrate are taken into account. Calculations of the luminance factors at the layer boundaries over a wide range of characteristics of the medium and layer thicknesses have been made.     

Polarization imaging of multiply-scattered radiation based on integral-vector Monte Carlo method

A new integral-vector Monte Carlo method (IVMCM) is developed to analyze the transfer of polarized radiation in 3D multiple scattering particle-laden media. The method is based on a “successive order of scattering series” expression of the integral formulation of the vector radiative transfer equation (VRTE) for application of efficient statistical tools to improve convergence of Monte Carlo calculations of integrals. After validation against reference results in plane-parallel layer backscattering configurations, the model is applied to a cubic container filled with uniformly distributed monodispersed particles and irradiated by a monochromatic narrow collimated beam. 2D lateral images of effective Mueller matrix elements are calculated in the case of spherical and fractal aggregate particles. Detailed analysis of multiple scattering regimes, which are very similar for unpolarized radiation transfer, allows identifying the sensitivity of polarization imaging to size and morphology.     

混浊大气介质调制传递函数的一般特征

基于混浊介质的调制传递函数(MTF)和在各向同性漫射光源照射下平行平面混浊介质出射光强度分布之间的等效原理,利用辐射传输算法DISORT数值计算了几种典型的均匀大气混浊介质的MTF,获得了整个空间频域内MTF的一般特征.结果显示,大气介质的MTF不但依赖于介质的光学厚度(散射和吸收),也依赖于介质的散射相函数.给出了大...     

Determination of optical characteristics of biological tissues by temporal distribution of an ultrashort laser pulse passed through homogeneous scattering layer

The determination of optical characteristics of biological tissues by the temporal distribution of an ultrashort laser pulse passed through a homogeneous scattering layer is considered. Four nonstationary models used to describe passing of laser pulses through a highly scattering medium are compared for the first time. The domains of applicability for the diffusion models are determined. It has been shown that the determination of optical characteristics of highly scattering media by experimental temporal distributions leads to different numerical values depending on the used model. Nevertheless, any of these models can be used because the performed study does not permit one to give preference to any of them. However, in determining optical characteristics of the scattering samples, it is necessary to specify the used model, as well as the conditions under which the initial experimental data (in particular, the thickness of the layer of a studied sample) are obtained.     

散射相函数对一维介质内辐射传递的影响规律

采用有限体积法研究了一维线性各向异性散射介质内散射相函数对辐射传递的影响规律.经与理论解、辐射元法、蒙特卡洛法计算结果比较表明,有限体积法的计算结果更可靠,且不同散射相函数的辐射换热系统中,其无因次热流之比与光学厚度之间存在某种单调变化的函数关系,利用该函数关系可以检验模型的准确度.     

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping(i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.     

A parametric study of radiative transfer with anisotropic scattering in a one-dimensional system

Radiative heat transfer in an absorbing, emitting, anistropically-scattering, one-dimensional medium is analyzed. Unlike many of the existing works, the present analysis does not require a known temperature distribution within the medium. Assuming a model of linear anistropic scattering, the transfer equation and the energy equation are solved simultaneously by utilizing a recently developed successive approximation technique. Closed-form approximate solutions and accurate higher-order results are both presented. Calculations show that the relative importance of the anistropic scattering effect generally decreases with decreasing wall emissivity and decreasing optical thickness. For radiative equilibrium without internal heat generation, it is demonstrated that the anistropic-scattering heat-transfer results can be approximated quite adequately by the isotropic-scattering result with the introduction of the concept of an effective optical thickness. For media with internal heat generation, an interesting effect of the scattering albedo is observed. It is established that, in the limit of a large scattering albedo, the temperature of the medium approaches a constant value that is independent of anistropic-scattering effects and wall emissivity. The exact limiting expressions for the temperature and apparent emissivity of an isothermal slab are found.     

Speckle diagnostics of multiple scattering media with the use of frequency-modulated laser radiation

A method for probing randomly inhomogeneous multiple scattering media with the use of frequency-modulated laser radiation is considered. The method is based on analysis of the dependence of the blinking index of time-averaged speckles formed upon scattering of the probing radiation in a medium on the frequency modulation depth of the probing radiation. In the case of a binary frequency modulation, the blinking index of the detected speckle-modulated radiation is determined by the cosine Fourier transform of the probability density of the optical path-length difference of partial components of the scattered field in the probed medium. The values of the probability density of the optical path-length difference reconstructed with the use of the proposed method from the measured blinking index of speckles for model scattering media (fluoroplastic layer and layer of TiO₂ particles on a glass substrate) are in a good agreement with the results of statistical simulation of the probing radiation transfer in multiple scattering media.     

Explaining the polarization signal from rain dichroic effects

Radiative transfer simulations for a dichroic medium consisting of horizontally oriented spheroid raindrops in a cloud have been performed to better understand the polarization properties of the radiation field in such kind of media. A successive order of scattering methodology is employed to obtain exact and approximate equations of the rain medium in order to evaluate the contribution of the different scattering orders to the polarization signal for a 1D geometry approximation at all cloud levels. Then a Monte Carlo technique is used to evaluate the impact of 3D effects in the polarization of the downwelling/upwelling radiation field at the bottom/top of the dichroic layer. An accurate analysis of the impact of the emission term onto the total polarization signal is carried out. The 3D effects seem to be more relevant in polarization signatures when the emission/absorption processes dominate.     

热防护层覆盖弹体目标雷达散射截面的修正的等效电流近似法和图形计算电磁学法分析

将修正的等效电流近似法与图形计算电磁学法相结合引入到热防护层覆盖弹体目标的电磁散射问题的研究中.应用修正的等效电流近似法对介质和有耗表面进行散射计算,结合图形计算电磁学法,借助于计算机显示技术,将三维目标图形在计算机屏幕上投影,由图形加速卡完成遮挡和消隐工作,利用图形计算电磁学的积分公式,把三维空间的计算转化为二维空间的计算,大大降低了计算时间和复杂度.计算结果表明:当入射波频率较低时,热防护层的厚度不会影响弹体雷达截面值的大小,当频率升高,随着热防护层厚度的增加,弹体雷达截面值不断减小,说明热防护涂层为有耗介质,介电常数的虚部越大其消耗能量的能力越强,弹体雷达截面变化越明显;当热防护层中存在孔隙,热防护层厚度一定,孔隙率越大,雷达截面值越大,孔隙率为零时,雷达截面值最小.当孔隙率相同,热防护层越薄,其雷达截面值越大;当弹体在高空中出现脱粘现象,对弹体的雷达截面值影响不大.