The scattering matrix of transparent particles of random shape in the geometrical optics approximation

A numerical model that allows one to calculate elements of the scattering matrix for transparent particles of random shape in the geometrical optics approximation is presented. It is shown that a deviation from sphericity, which, in particular, is modeled by a reduction of the number of triangular facets approximating a sphere, essentially affects the magnitude, position, and width of peaks of the photometric and polarimetric indicatrices. Thus, when 1500 facets were used for the approximation, the amplitude of the polarimetric peak associated with the first rainbow, which is located close to the scattering angle 160°, decreases by a factor of two. Calculations showed that, in the region of backscattering, for particles of an arbitrary shape, the linear polarization ?F ₁₂/F ₁₁ has no negative branch, which is well observed for spherical particles. In going from spherical to nonspherical particles, the backscattering peak also disappears. The indicatrices for particles of irregular shape that were calculated for small distances from the center of a particle noticeably differ from the indicatrices at infinity. Thus, when simulating multiple scattering in dense powderlike media, the use of particle scattering indicatrices that were calculated for infinite distances is incorrect even in the geometrical optics approximation.     

Metallic foams: Radiative properties/comparison between different models

The aim of this study is to determine the radiative properties, which are the extinction coefficient, the scattering albedo and the scattering phase function, of highly porous open-cell aluminium foam, using more-or-less simple predictive models, and to compare all these models. The radiative properties are predicted using geometric optics laws to model the interaction of radiation with the particles forming the foam. Moreover, the particles forming the foam are large compared with the considered wavelength and are supposed to be sufficiently distant from each other to scatter radiation independently. Thus, the radiative characteristics of the foam can be determined by adding the contributions of each particle. A particular attention is paid on microstructure analysis and modelling. We considered different kinds of cell shapes and struts cross-section, using microscopic and tomographic analysis. Furthermore, a new phase function modelling is presented. Finally, we compare the results of each method with the radiative properties obtained from experimental measurements of directional and hemispherical transmittances and hemispherical reflectance.     

Numerical simulation of multiple light scattering in layers consisting of opaque particles with a dull surface (geometrical optics approximation)

A numerical model is presented which allows one, in the geometrical optics approximation, to calculate scattering contributions of specified multiplicity in layers comprised of opaque particles with dull surfaces. For definiteness, the particles are assumed to be spherical with the Lambertian law of light scattering by the particle surface. The greatest scattering multiplicity is restricted, in this model, only by computer capacity. In this paper, the scattering multiplicities up to the sixth order inclusively are studied. Layers of moderate optical thickness, as well as the case of a semi-infinite medium with different particle packing densities, are analyzed for different geometries of illumination and observation. It is shown that for conservative scattering by the particle surface, the contribution of higher-order scattering decreases with increasing order number, which is related to the shadow-hiding effect. The scattering indicatrices of higher orders approach the isotropic case. The even and odd scattering orders show a systematic difference between themselves.     

Polarimetric weak-localization effect in scattering of natural light in the region of small phase angles

Results of laboratory measurements and interpretations of the polarimetric effect of weak localization (negative polarization) appearing under scattering of natural light by a dark ultradisperse surface (soot with albedo of 2.5%) are presented. The measurements were carried out in red light in a range of phase angles of 0.2°–4.2°. It was revealed that the soot, despite the low albedo, shows the polarimetric weak-localization effect inherent in bright surfaces such as the surface formed by smoked MgO. The results of measurements are interpreted using numerical simulation of multiple light scattering in a medium consisting of particles whose characteristics are close to those observed for soot. As the result of simulation, it was found that the scattering with the multiplicity exceeding two can give rise to a negative polarization branch, which becomes narrower with increasing scattering order. For the case of soot, four orders of scattering is sufficient to describe the observed polarimetric effect of weak localization with a necessary accuracy.     

椭球模型下通过雾场的多重光散射谱

由于雾滴的非球形、多重散射特性以及几何光学效应,光通过实际雾场的散射问题成为一个研究难点. 建立了近于实际的椭球雾滴模型,考虑光的衍射、透射及反射特性后,利用辐射传播方程得到了在不同的雾滴大小分布 及不同的雾滴形状分布下通过雾场的多重散射光强公式.在两种特例下与已有的结果较为相符,说明了方法的可靠性. 计算表明:与随机取向的非球形颗粒场的散射谱呈圆形特征不同,通过椭球形雾滴场的散射谱呈椭圆特征, 不同方位角的散射光强角分布有所差异,雾滴的形状因子越接近于1,差异越小;与单散射不同, 散射谱中的条纹随光学厚度增大逐步消失;对于不同大小分布及不同形状分布的雾滴场, 在不同方位角及不同观察角的散射光强随光学厚度τ的增加总是先增大再减小,光强的极大值位置在τ = 1.0---3.0 范围内.计算同时还表明,由于多数情况下实际雾场的雾滴大小偏差较大, 因而通过雾场的散射谱将呈现以中央亮斑为中心向四周弥散的图样.     

Analysis of eccentric photorefraction by Fourier optics

Eccentric photorefraction usually is used as early eyesight diagnostic test of infants and small children. Unlike currently approved geometrical optical model of eccentric photorefractometer, the crescent formation and the light-intensity distribution in the pupil image of a myopic eye are analyzed by Fourier optics with the assumption of an isotropic scattering retina. In the case of little circular light source and rectangular slit, the simulation results of different myopic diopters are obtained by geometrical optical theory and Fourier optics respectively. It is found that the simulation results by Fourier optics are similar as those obtained by geometrical optics, and all simulations are almost corresponding to the experimental result.The result demonstrates that the new method presented here is feasible.     

Computer simulations for multiple scattering of light rays in systems of opaque particles

A new computer model for multiple light scattering in arbitrary systems of opaque diffusely scattering particles is considered. For ray tracing and scattering in such systems, the geometric optics approximation is used. Semi-infinite media and clusters with spherical and irregular shaped particles are investigated. The irregular particles are approximated with a discrete set of small triangular facets attached to each other. The particle surface is supposed to scatter by the Lambertian indicatrix. Scattering of the first six orders is considered, but the model can be effectively used for calculations of higher orders too. Phase-angle curves of scattering for media and clusters with different packing density are calculated. It is shown that the contributions of scattering orders rapidly diminish as the order grows even for non-absorbing particulate surfaces. Only the first scattering order shows the opposition effect and is rather sensitive to packing density. Higher orders do not show any features near zero phase angle. The contributions of high orders increase slightly, when the packing density increases. The form of particles is important mostly for the second scattering order. For clusters of particles both packing density and number of particles are important for phase function behavior. Clusters consisting of 100 particles show weak phase-angle dependences of high orders of scattering. These dependences become more prominent with increase of number of particles. Phase curves for spherical and cubic clusters are compared. It turns out that the influence of cluster shape is only a minor factor.     

Direct simulation Monte Carlo ray tracing model of light scattering by a class of real particles and comparison with PROGRA experimental results

The Direct Simulation Monte Carlo (DSMC) model is presented for three-dimensional single scattering of natural light by suspended, randomly oriented, optically homogeneous and isotropic, rounded and stochastically rough cubic particles. The modelled particles have large size parameter that allows geometric optics approximation to be used. The proposed computational model is simple and flexible. It is tested by comparison with known geometric optics solution for a perfect cube and Lorenz–Mie solution for a sphere, as extreme cases of the class of rounded cubes. Scattering and polarization properties of particles with various geometrical and optical characteristics are examined. The experimental study of real NaCl crystals with new Progra² instrument in microgravity conditions is conducted. The experimental and computed polarization and brightness phase curves are compared.     

Anomalous diffraction of light with geometrical path statistics of rays and a Gaussian ray approximation

The anomalous-diffraction theory (ADT) of extinction of light by soft particles is shown to be determined by a statistical distribution of the geometrical paths of individual rays inside the particles. Light extinction depends on the mean and the mean-squared geometrical paths of the rays. Analytical formulas for optical efficiencies from a Gaussian distribution of the geometrical paths of rays are derived. This Gaussian ray approximation reduces to the exact ADT in the intermediate case of light scattering for an arbitrary soft particle and describes well the extinction of light from a system of randomly oriented and (or) polydisperse particles. The implications for probing of the sizes and shapes of particles by light extinction are discussed.     

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.     

Light scattering by particulate media of irregularly shaped particles: laboratory measurements and numerical simulations

We present a light-scattering simulation based on geometrical optics to study the bidirectional reflectance of particulate media observed from laboratory measurements. The simulation model is built so that the arrangement of composing particles of the media and characteristics of the particles (i.e. size, irregularity of shape and refractive index) can be given as parameters. From the results of simulations and comparison with laboratory measurements, we have found the following: (1) The media of irregular-shaped particles show flatness in the angular change of the reflectance compared with those of more rounded particles. (2) The media of smaller particles with diameters of show brighter reflectance than those of , similarly as observed in laboratory measurements. (3) The reflectance in small (<30) and large (>120) phase angles increases with increasing surface porosity (i.e. enhancements of backscattering and forward scattering). The former can be ascribed to the first order of scattering in contrast with the latter to the first plus the second order of scattering, where the first order of scattering is the total sum of the scattered rays from the first particle hit by the incident ray, and the second means that from the second particle hit by the sub-rays from the first particle.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Modeling the nadiral low-frequency pulse return of one-dimensionally rough surfaces

Measurements of radar pulse return waveforms are known to provide information on properties of the observed surface, and are commonly used in oceanographic altimetry. In such applications, the convolution model (also called the “Brown model”) is widely applied for waveform analysis. This model describes pulse return waveforms as a multiple convolution of the “flat surface impulse response”, the surface's height probability density function, and the radar's point target response. The flat surface impulse response is typically determined by an integration of scattering contributions from incremental surface elements weighted by a geometrical optics (GO) prediction of the normalized radar cross-section of the elemental surfaces.

Recent interest in the analysis of pulse return waveforms at VHF and lower frequencies for ice sheet sensing applications motivate reconsideration of the convolution model. While the ultimate goal of this effort is the development of a model to be utilized for interpreting VHF radar measurements over ice sheets, it is important first to establish the validity of the convolution model for these applications. Such an investigation, which involves the comparison of convolution model predictions with those of a method that does not require a separation of surface length-scales into “elemental” and large-scale regions, is most easily performed for one-dimensional surfaces.

This paper describes a derivation of the convolution model for one-dimensionally rough surfaces that is applicable at low frequencies, primarily through the replacement of GO surface scattering coefficients with those of a physical optics theory. The method is validated by comparing its predictions with a Monte Carlo physical optics approach. Results show the convolution model to provide reasonable estimates of the pulse return waveform, so that a similar method can be utilized to develop a convolution model for two-dimensional surface pulse return waveforms in ice-sheet sensing applications. The results also suggest the possibility of retrieving surface profile statistical information from waveform measurements.     

The physical optics integral on the scatterer's unlit surface

The scattering integrals of the modified theory of physical optics are redefined according to the illuminated and unlit surfaces of the scattering object. With this aim the canonical problem of wedge diffraction is taken into account. It is shown that the new scattering integral contain two geometrical optics and diffracted fields. One of the geometrical optics waves is the reflected field component that propagates in the real space. The other one transmits to an imaginary space through the scattering surface and does not have any influence in the real space. The diffracted waves exist in the real space and satisfy the related boundary condition on the scattering surfaces. The resultant field expressions are compared with the exact series solution of the problem numerically.     

Brightness distribution in a model atmosphere with continuous and broken cloud

This paper describes a method and apparatus for the simulation of various experimental situations which are often required for the solution of problems of optics and spectroscopy of light-scattering media. The depth distribution of brightness within light-scattering materials, their albedo, indicatrix, etc., can be investigated. The investigations can be made at any optical depths and with different underlying surfaces. It is also possible to simulate horizontally in-homogeneous and vertically stratified media, which it has not been possible to simulate before. The brightness indicatrices obtained on a model of the earth's atmosphere with broken cloud of different density, stratification, extent of cloud cover, and above different underlying surfaces are illustrated.Translated from Izvestiya VUZ. Fizika, No. 1, pp. 34–42, January, 1972.     

取向比对椭球气溶胶粒子散射特性的影响

利用T矩阵和离散坐标法研究了取向比对椭球粒子散射特性的影响, 计算了小尺度范围内椭球粒子的散射特征参量, 包括消光效率因子、不对称因子、单次散射反照率、散射相矩阵及双向反射函数(BRDF). 结果表明, 椭球粒子的散射特性与取向比密切相关, 粒子取向比会影响散射参量的振荡频率和振幅, 与球形粒子散射参量的相对差异也呈周期振荡趋势. 研究还发现, 某些特殊粒子尺寸的散射参量与粒子取向比基本无关. 在多次散射条件下, 分析不同取向比粒子群的BRDF随反射角和光学厚度的变化特性. 结果显示: 不同取向比粒子群的BRDF随反射角的变化趋势基本一致, 球形粒子群比非球形粒子群的BRDF曲线波动振幅更大; 球形-非球形粒子的BRDF相对差异随光学厚度和取向比的增大而减小, 随入射角的增大而增大.     

高功率激光传输过程中散射点对光束质量的影响

为了研究高功率激光传输过程中不透明颗粒引起的光束调制,通过分析这些不透明颗粒的形状和分布特点,建立了位置呈随机分布的高斯状散射点模型,从光束的衍射理论和干涉叠加理论出发,得到该模型下散射点对传输光束质量影响的解析式。数值分析了高斯状散射点的大小、密度、散射面积比及其传输距离对输出光束的近场分布、位相分布和光束透过率的影响,结果显示亚毫米量级散射点的衍射效应引起最大调制可达1．4,光学元件散射面积比小于0．003时才能满足元件透过率大于99．5％的需求。该结果可用于评价高功率激光装置光学元件的加工状况,并对光学元件加工要求和激光装置的洁净度要求有指导意义。     

Statistical approach to light scattering by convex ice crystals

Within the geometric optics approximation, the phase functions of randomly oriented ice crystals are calculated as a series relative to multiplicity of internal collisions of light inside the particles. In the case of convex crystals, it is shown that the coefficients of the series provide the most information about the crystal shapes, while the angular functions of this series are weakly dependent on the shapes. The prevailing role of the term corresponding to one internal collision is emphasized. Three numbers describing a distribution of the single-collision scattered light among the aureole and halos of 22 degrees and 46 degrees prove to be the basic parameters by which to characterize scattering by hexagonal ice crystals.     

Temperature response in participating media with anisotropic scattering caused by pulsed lasers

It is not by isotropic scattering but by anisotropic scattering that radiant energy is redistributed in some materials containing real particles, fibers, or impurities. In some instances, great difference can be caused in transient thermal behavior between isotropic scattering and anisotropic scattering media. Ray tracing method combined with Hottel's zonal method is introduced to deduce thermal radiative source term for various optical boundary conditions induced by collimated incidence passing through translucent boundary. Temperature response caused by laser pulse at non-incident side of participating and anisotropic scattering media is examined. We investigate effects of scattering albedo, scattering phase function, initial temperature of media and thickness of media on temperature response. Results obtained for anisotropic scattering media are compared with those for isotropic scattering one and show that anisotropic scattering must be considered in the simulating measurement of thermophysical properties by the laser flash method for some materials with big scattering albedo which behave anisotropically, or big error will be introduced; forward scattering can increase excess temperature and backward scattering can decrease it at non-incident side of the considered sample irradiated by laser pulse.