Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements

The objective is to estimate the Rayleigh limit in bidirectional reflectance distribution function (BRDF) measurements caused by air in the laboratory, the wavelength, and the path length of light in the receiver field of view. Moreover, we intend to show the trend for the reduction of this limit by introducing a medium with small refractive index and by using a longer wavelength. Although the BRDF typically describes the angular distribution of scattered light from surfaces, the expression describing the equivalent BRDF caused by the optical scattering from gas molecules in the optical path is derived through the use of the Rayleigh scattering theory. The instrumentation is described, and the experimental results of the equivalent BRDF caused by gas scattering from molecules in clear air, nitrogen, and helium gases are reported. These results confirm the trends of the prediction.     

Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light

A Lambert surface would appear equally bright from all observation directions regardless of the illumination direction. However, the reflection from a randomly scattering object generally has directional variation, which can be described in terms of the bidirectional reflectance distribution function (BRDF). We measured the BRDF of a Spectralon white reflectance standard for incoherent illumination at 405 and 680?nm with unpolarized and plane-polarized light from different directions of incidence. Our measurements show deviations of the BRDF for the Spectralon white reflectance standard from that of a Lambertian reflector that depend both on the angle of incidence and the polarization states of the incident light and detected light. The non-Lambertian reflection characteristics were found to increase more toward the direction of specular reflection as the angle of incidence gets larger.     

Geometrical-optics approximation of forward scattering by gradient-index spheres

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.     

Modeling and simulating the bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks

A high-efficiency anisotropic model for bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks (SWCOS) was proposed. This model was set by combining a BRDF model for anisotropic rough sea surface whose slopes follow Gaussian distribution and the two-beam inference theory of a thin film. We have simulated the BRDFs of oil slicks by using the above model and the measured complex refractive index data of Romashkino crude oil. In addition, the relationships between the BRDF of oil slicks and the wind speed of sea surface, thickness of oil slick, complex refractive index of crude oil and the incident zenith angle were analyzed. Also, the differences between optical characteristics of clean water and of polluted water were discussed in the context of the optical contrast of SWCOS. With high simulation speed and reliable simulation precision, this model provides a theoretical basis for rapid detection of oil spill.     

亚微米级扁椭球颗粒群的散射特性

采用T矩阵方法计算亚微米级扁椭球随机取向分布颗粒群的散射特性,研究消光截面、散射截面、吸光截面、单散射反照率、非对称因子以及散射矩阵元素与颗粒的大小、折射率、长短轴比之间的关系。结果表明,随颗粒粒径增大,消光截面、散射截面、吸光截面、非对称因子都单调增加,散射相函数F11的角分布曲线特征可以区分颗粒的大小;颗粒越偏离球形,颗粒对入射光的衰减效率越低,后向散射光强越强,在轴比不大时,前向50°内的F22/F11值可以区分颗粒的形状;折射率变化主要是对后向散射光的分布产生影响,实部、虚部的变化可分别通过F34/F11的角分布曲线、F12/F11的第一个峰值来体现。     

Optical fiber design and the trapping of Cerenkov radiation

Cerenkov radiation is generated in optical fibers immersed in radiation fields and can interfere with signal transmission. We develop a theory for predicting the intensity of Cerenkov radiation generated within the core of a multimode optical fiber by using a ray optic approach and use it to make predictions of the intensity of radiation transmitted down the fiber in propagating modes. The intensity transmitted down the fiber is found to be dominated by bound rays with a contribution from tunneling rays. It is confirmed that for relativistic particles the intensity of the radiation that is transmitted along the fiber is a function of the angle between the particle beam and the fiber axis. The angle of peak intensity is found to be a function of the fiber refractive index difference as well as the core refractive index, with larger refractive index differences shifting the peak significantly toward lower angles. The angular range of the distribution is also significantly increased in both directions by increasing the fiber refractive index difference. The intensity of the radiation is found to be proportional to the cube of the fiber core radius in addition to its dependence on refractive index difference. As the particle energy is reduced into the nonrelativistic range the entire distribution is shifted toward lower angles. Recommendations on minimizing the quantity of Cerenkov light transmitted in the fiber optic system in a radiation field are given.     

Sensing polarization with variable coherence tomography

Variable coherence tomography (VCT) was recently developed by Baleine and Dogariu for the purpose of directly sensing the second-order statistical properties of a randomly scattering volume [J. Opt. Soc. Am. A21, 1917 (2004)]. In this paper we generalize the theory of VCT to include polarized inputs and anisotropic scatterers. In general the measurement of the scattered coherency matrix or Stokes vector is not adequate to describe the scattering, as these quantities depend on the coherence state of the incident beam. However, by controlling the polarized coherence properties of the source beam, VCT can be generalized to probe the polarimetric scattering properties of objects from a single-point Stokes vector or coherency matrix measurements. With polarized VCT, we are able to design a method that can measure analogous information to the polarimetric bidirectional reflection distribution function (BRDF), but do it from monostatic data. This capability would allow the BRDF to be measured remotely without having to adjust either the incident or observation angle with respect to the target.     

偏振状态下球形粒子的散射相位函数研究

本文根据散射相位函数的定义,得到了偏振状态下单个粒子散射相位函数的表达式,并且通过研究发现以下规律:1)粒子半径越小,极值差随散射角越趋向于对称分布;2)散射角在0～0.025π以及O.997π～π之间,散射相位函数随极化角基本不变;3)散射角在O.025π～0.997π之间,散射相位函数随极化角变化明显.同时比较了偏振状态下多粒子和单粒子散射相位函数随散射角和极化角的分布.最后从大气中光传输理论出发,建立了非偏振状态与偏振状态下散射相位函数的关系,为大气散射回波功率测量以及近似散射相位函数的研究提供参考.     

Physically based reflectance model utilizing polarization measurement

A surface bidirectional reflectance distribution function (BRDF) depends on both the optical properties of the material and the microstructure of the surface and appears as combination of these factors. We propose a method for modeling the BRDF based on a separate optical-property (refractive-index) estimation by polarization measurement. Because the BRDF and the refractive index for precisely the same place can be determined, errors cased by individual difference or spatial dependence can be eliminated. Our BRDF model treats the surface as an aggregation of microfacets, and the diffractive effect is negligible because of randomness. An example model of a painted aluminum plate is presented.     

Comparison of near-forward light scattering on oceanic turbulence and particles

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1 degrees . The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1 degrees . In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.     

Scattering by random particles on optical surfaces

An analytical technique has been developed for calculating the angle-resolved light scattering by contaminant particles on smooth opaque surfaces. The analytical method was tested by a comparison of measured and calculated bidirectional reflectance distribution function (BRDF) values for contaminated surfaces. BRDF values were calculated from particle sizes, shapes, and areal densities obtained from scanning electron microscope images of the contaminated surfaces by a Princeton gamma-tech image analyzer. Measured and calculated BRDF values agreed to within the uncertainty associated with the particle characterization process for most scattering angles.     

Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section

An alternative to using the traditional scattering angle theta to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(theta/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of theta. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter rho = 2kR/m - 1/, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when p < 1 and follows simple patterns for p > 1, which evolve predictably as a function of p. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.     

Simultaneous retrieval of aerosol refractive index and particle size distribution from ground-based measurements of direct and scattered solar radiation

Ground-based sunphotometer observation of direct and scattered solar radiation is a traditional tool for providing data on aerosol optical properties. Spectral transmission and solar aureole measurements provide an optical source of aerosol information, which can be inverted for retrieval of microphysical properties (particle size distribution and refractive index). However, to infer these aerosol properties from ground-based remote-sensing measurements, special numerical inversion methods should be developed and applied. We propose two improvements to the existing inversion techniques employed to derive aerosol microphysical properties from combined atmospheric transmission and solar aureole measurements. First, the aerosol refractive index is directly included in the inversion procedure and is retrieved simultaneously with the particle size spectra. Second, we allow for real or effective instrumental pointing errors by including a correction factor for scattering angle errors as a retrieved inversion parameter. The inversion technique is validated by numerical simulations and applied to field data. It is shown that ground-based sunphotometer measurements enable one to derive the real part of the aerosol refractive index with an absolute error of 0.03-0.05 and to distinguish roughly between weakly and strongly absorbing aerosols. The aureole angular observation scheme can be refined with an absolute accuracy of 0.15-0.19 deg. Offset corrections to the scattering angle error are generally found to be small and consistently of the order of -0.17. This error magnitude is deduced to be due primarily to nonlinear field-of-view averaging effects rather than to instrumental errors.     

Optical method for measuring optical rotation angle and refractive index of chiral solution

Based on the phenomena of Brewster's angle and the principles of common-path heterodyne interferometry, we present an optical method for measuring the optical rotation angle and the refractive index of a chiral solution simultaneously in one optical configuration. A heterodyne light beam and a circularly polarized heterodyne light beam are separately guided to project onto the interface of a semicircle glass and a chiral solution. One of the beams is transmitted through the solution, and the other is reflected near Brewster's angle at the interface. Then the two beams pass through polarization components respectively for interference. The phase differences of the two interference signals used to determine the rotation angle and the refractive index become very high with the proper azimuth angles of some polarization components, hence achieving an accurate rotational angle and a refractive index. The feasibility of the measuring method was demonstrated by our experimental results. This method should bear the merits of high accuracy, short sample medium length, and simpler operational endeavor.     

Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices

The finite-difference time-domain (FDTD) technique is examined for its suitability for studying light scattering by highly refractive dielectric particles. It is found that, for particles with large complex refractive indices, the FDTD solution of light scattering is sensitive to the numerical treatments associated with the particle boundaries. Herein, appropriate treatments of the particle boundaries and related electric fields in the frequency domain are introduced and examined to improve the accuracy of the FDTD solutions. As a result, it is shown that, for a large complex refractive index of 7.1499 + 2.914i for particles with size parameters smaller than 6, the errors in extinction and absorption efficiencies from the FDTD method are generally less than ~4%. The errors in the scattering phase function are less than ~5%. We conclude that the present FDTD scheme with appropriate boundary treatments can provide a reliable solution for light scattering by nonspherical particles with large complex refractive indices.     

Ray model of light scattering by flake pigments or rough surfaces with smooth transparent coatings

We derive expressions for the intensity and polarization of light singly scattered by flake pigments or a rough surface beneath a smooth transparent coating using the ray or facet model. The distribution of local surface normals is used to calculate the bidirectional reflectance distribution function (BRDF). We discuss the different distribution functions that can be used to characterize the distribution of local surface normals. The light-scattering model is validated by measurements of the BRDF and polarization by a metallic flake pigmented coating. The results enable the extraction of a slope distribution function from the data, which is shown to be consistent over a variety of scattering geometries. These models are appropriate to estimate or predict the appearance of flake pigment automotive paints.     

Application of dynamic light scattering to the study of small marine particles

Small particles ranging from approximately 0.1 μm to several micrometers in size, which include detrital material, bacteria, and other planktonic microorganisms, make a significant contribution to light scattering in the upper ocean. The scattering properties of these particles are strongly dependent on their size, which is difficult to measure in the submicrometer range with commonly used electronic resistive counters and microscopic techniques. We examined the size of small marine particles by application of the dynamic light scattering (DLS) method. In this method the time-dependent autocorrelation function of scattered intensity by particles undergoing Brownian motion provides information about the size of particles. The samples were collected in clear oceanic waters off the coast of Southern California. The mean hydrodynamic diameter of particles, determined from the DLS measurements at a scattering angle of 45°, was 0.54μ m. This indicates that the major contribution to scattering at this angle comes rom submicrometer particles. We also described an inverse method for estimating the general slope of the size distribution of small marine particles from the mean hydrodynamic diameter. This method is based on calculations of the size distribution weighted by distribution from Mie theory and assumes that a power-law approximation represents the actual particle scattered intensity. These calculations suggested that particulate assemblage in our seawater samples was best characterized by a differential size distribution with a slope of -4.35. This estimation was supported by independent measurements of particle size distribution and the spectral beam attenuation coefficient taken from the same samples as those used for the DLS measurements. We also demonstrated that multiangle DLS measurements may be used to determine the representative value of the refractive index of particles.     

Optical properties (bidirectional reflectance distribution function) of shot fabric

To study the optical properties of materials, one needs a complete set of the angular distribution functions of surface scattering from the materials. Here we present a convenient method for collecting a large set of bidirectional reflectance distribution function (BRDF) samples in the hemispherical scattering space. Material samples are wrapped around a right-circular cylinder and irradiated by a parallel light source, and the scattered radiance is collected by a digital camera. We tilted the cylinder around its center to collect the BRDF samples outside the plane of incidence. This method can be used with materials that have isotropic and anisotropic scattering properties. We demonstrate this method in a detailed investigation of shot fabrics. The warps and the fillings of shot fabrics are dyed different colors so that the fabric appears to change color at different viewing angles. These color-changing characteristics are found to be related to the physical and geometrical structure of shot fabric. Our study reveals that the color-changing property of shot fabrics is due mainly to an occlusion effect.     

Light scattering and absorption caused by bacterial activity in water

There is a growing class of elementary particle detectors, large-water ?erenkov detectors, that have a body of water (thousands of tons) as a sensitive medium. Particles are detected when they interact with the water and produce ?erenkov light, so detection efficiency relies on the transparency of the water. These detectors are active typically for many years, so biological activity (primarily bacterial growth) is one of the means by which the transparency of the water may be reduced. We present the results of a measurement of light scattering and absorption from a population of Escherichia coli in water, which is used as a model for bacteria in general. One can separate the scattering and absorption by varying the refractive index of the medium by using a solute of high molecular weight. We show that the results can be understood simply in terms of light scattering from small spheres (radius ≈ wavelength) with an effective refractive index, n(b), plus a small amount of absorption in the ultraviolet. We compare his scattering with Rayleigh scattering in pure water.     

Numerical evaluation of droplet sizing based on the ratio of fluorescent and scattered light intensities (LIF/Mie technique)

The dependence of fluorescent and scattered light intensities from spherical droplets on droplet diameter was evaluated using Mie theory. The emphasis is on the evaluation of droplet sizing, based on the ratio of laser-induced fluorescence and scattered light intensities (LIF/Mie technique). A parametric study is presented, which includes the effects of scattering angle, the real part of the refractive index and the dye concentration in the liquid (determining the imaginary part of the refractive index). The assumption that the fluorescent and scattered light intensities are proportional to the volume and surface area of the droplets for accurate sizing measurements is not generally valid. More accurate sizing measurements can be performed with minimal dye concentration in the liquid and by collecting light at a scattering angle of 60° rather than the commonly used angle of 90°. Unfavorable to the sizing accuracy are oscillations of the scattered light intensity with droplet diameter that are profound at the sidescatter direction (90°) and for droplets with refractive indices around 1.4.