Statistical properties of light reflected and transmitted by a thick horizontally inhomogeneous turbid layer.

The paper is devoted to the introduction of simple analytical relationships between statistical distributions of various radiative transfer characteristics for an inhomogeneous turbid layer with the extinction coefficient varying in the horizontal direction. Results are valid for an optically thick light-scattering layer having arbitrary local scattering laws and single-scattering albedos. It is shown that the statistical distribution of the optical thickness can be obtained directly from the measured statistical distribution of the reflectance or transmittance of a horizontally inhomogeneous light-scattering layer.

Reflection and polarization of light by semi-infinite turbid media: simple approximations.

The paper is devoted to the investigation of the accuracy of the Rozenberg approximation for the reflection function of a semi-infinite absorbing random media. We found that this approximation can be used at y<0.5, where y= square root (1-omega (0))/(3(1-g)) . Here omega(0) is the single scattering albedo and g is the asymmetry parameter. We also propose the modified approximation, which can be used at least up to y=1-2, depending on the observation geometry.

Multiple light scattering in laser particle sizing.

Multiple light scattering is an important issue in modern laser diffraction spectrometry. Most laser particle sizers do not account for multiple light scattering in a disperse medium under investigation. This causes an underestimation of the particle sizes in the case of high concentrations of scatterers. The retrieval accuracy is improved if the measured data are processed with multiple-scattering algorithms that treat multiple light scattering in a disperse medium. We evaluate the influence of multiple light scattering on light transmitted by scattering layers. The relationships among different theories to account for multiple light scattering in laser particle sizing are considered.

Angular spectrum of light transmitted through turbid media: theory and experiment.

Measurements of the angular spectrum of light transmitted through turbid slabs with monodispersions of polystyrene spheres have been performed. The results obtained are compared with theoretical calculations, based on the small-angle approximation of the radiative transfer theory. The experimental data and the theoretical results coincide with a high accuracy, which allows us to develop the laser diffraction spectroscopy of optically thick light-scattering layers.

Radiative transfer in chiral random media.

This paper is devoted to the investigation of polarization and radiative characteristics of coherent and diffused light beams in isotropic media with optically active particles. Simple solutions for the Stokes vectors of the direct and diffused beams are obtained in the framework of the vector radiative transfer theory. Results obtained can be used for the generalization of the circular dichroism and optical rotation dispersion spectroscopy for the case of disperse media.

Physically based parameterizations of the short-wave radiative characteristics of weakly absorbing optically thick media: application to liquid-water clouds.

We propose the physically based parameterization of the radiative characteristics of liquid-water clouds as functions of the wavelength, effective radius, and refractive index of particles, liquid-water path, ground albedo, and solar and observation angles. The formulas obtained are based on the approximate analytical solutions of the radiative transfer equation for optically thick, weakly absorbing layers and the geometrical optics approximation for local optical characteristics of cloud media. The accuracy of the approximate formulas was studied with an exact radiative transfer code. The relative error of the approximate formula for the reflection function at nadir observations was less then 15% for an optical thickness larger than 10 and a single-scattering albedo larger than 0.95.

Integral light-scattering and absorption characteristics of large, nonspherical particles.

We obtain and analyze simple analytical formulas for asymmetry parameters and absorption cross sections of large, nonspherical particles. The formulas are based on the asymptotic properties of these characteristics at strong and weak absorption of radiation inside particles. The absorption cross section depends on parameter phi, which determines the value of the light-absorption cross section for weakly absorbing particles. It is larger for nonspherical scatterers. The asymmetry parameter depends on two parameters. The first is the asymmetry parameter g(0) of a nonspherical, transparent particle with the same shape as an absorbing one. The second parameter, beta, determines the strength of the influence of light absorption on the value of the asymmetry parameter. Parameter beta is larger for nonspherical particles. One can find these three parameters (phi, g(0), and beta) using a ray-tracing code (RTC) for nonabsorbing and weakly absorbing particles. The RTC can then be used to check the accuracy of the equations at any absorption for hexagonal cylinders and spheroids. It is found that the error of computing the absorption cross section and 1 - g (g is the asymmetry parameter) is less than 20% at the refractive index of particles n = 1.333. Values for asymmetry parameters of large, nonabsorbing, spheroidal particles with different aspect ratios are tabulated for the first time to our knowledge. They do not depend on the size of particles and can serve as an independent check of the accuracy of T-matrix codes for large parameters.

Local optical parameters of spherical polydispersions: simple approximations.

New analytical solutions for the local optical characteristics (extinction and absorption coefficients, asymmetry parameters of phase functions) of spherical polydispersions composed of comparatively large particles are derived. The geometric optics (GO) approximation is used to solve the problem. For the accuracy of the GO approximation to be improved, the edge effects were taken into account. A comparison with the data obtained by the use of the Mie theory shows a satisfactory accuracy of our analytical formulas. The simple formulas for the cloud local optical characteristics are derived.

Analytical solution to the optical transfer function of a scattering medium with large particles.

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.