Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements (original) (raw)
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An identification procedure is developed for obtaining spectral radiative properties of highly scattering dispersed materials such as porous ceramics. Traditional techniques based on measurements of the directional-hemispherical reflectance and transmittance are of limited use because of difficulties in fabricating sufficiently thin and mechanically stable samples to obtain reliable values of directional-hemispherical transmittance. However, one can use the directional-hemispherical reflectance measurements for optically thick samples to obtain the transport scattering albedo. A one-dimensional analytical solution employs the modified two-flux approximation for the identification of transport scattering albedo. An additional transmittance measurement is required to identify the transport extinction coefficient. Bi-normal narrow cone transmittance is measured for this purpose. Because the one-dimensional analytical solution is not applicable to model the bi-normal narrow cone transmi...
Generalized method for evaluating scattering parameters used in radiative transfer models
Journal of The Optical Society of America A-optics Image Science and Vision, 1997
The effective scattering and absorption coefficients used to describe the optical properties of particulate materials in radiative transfer models are determined by the average path-length parameter of the diffuse radiation, as well as by the fraction of energy that each particle scatters into the forward and backward hemispheres relative to the direction of the impinging radiation. Until now, there were no well-established methods to calculate these parameters. We have devised an approach for evaluating average path-length parameters and forward-scattering ratios for both forward and backward diffuse radiation intensities. Single-scattering processes are described by Lorenz-Mie theory, and multiple-scattering effects have been taken into account by a generalization of Hartel theory. As a consequence of the formalism, the Kubelka-Munk scattering and absorption coefficients are explicitly related to average path-length parameters and forward-scattering ratios. These parameters display an optical depth dependence, characterized by values smoothly increasing or decreasing from the perpendicularly illuminated interface and saturation values at large optical depths.
Computational Thermal Sciences, 2012
An identification procedure is developed for obtaining spectral radiative properties of highly scattering dispersed materials such as porous ceramics. Traditional techniques based on measurements of the directional-hemispherical reflectance and transmittance are of limited use because of difficulties in fabricating sufficiently thin and mechanically stable samples to obtain reliable values of directional-hemispherical transmittance. However, one can use the directionalhemispherical reflectance measurements for optically thick samples to obtain the transport scattering albedo. A onedimensional analytical solution employs the modified two-flux approximation for the identification of transport scattering albedo. An additional transmittance measurement is required to identify the transport extinction coefficient. Binormal narrow cone transmittance is measured for this purpose. Because the one-dimensional analytical solution is not applicable to model the binormal narrow cone transmittance, the Monte Carlo ray-tracing technique is used to identify the transport extinction coefficient. The identification procedure is applied to obtain near-infrared radiative properties of porous ceria ceramics used in solar thermochemical reactors. The identified transport scattering coefficient is shown to be in good agreement with theoretical estimates based on the Mie theory for polydisperse pores and grains. This verifies the applicability of a model based on independent scattering and Mie theory for theoretical predictions of radiative properties of two types of ceria ceramics with porosity of 0.08 and 0.72, and for extrapolating the properties of both ceramics in a limited near-infrared range to the range of significant absorption.
Teplofizika Vysokikh Temperatur
A two-step approximate analytical solution for the normal emittance of a plane layer of an absorbing, scattering and refracting medium is derived analytically. The analysis is based on the transport approximation and the two-step solution method for radiative transfer. The high accuracy of the approximate solution, examined by comparing its results to those obtained independently by the discrete ordinates and Monte Carlo methods, makes it suitable for application in combined experimental-analytical studies to identify selected spectral radiative properties of dispersed media in the range of semi-transparency.
2008
We derive an analytical approximation in the framework of the radiative transfer theory for use in the analysis of diffuse reflectance measurements. This model uses two parameters to describe a material, the transport free path length, l, and the similarity parameter, s. Using a simple algebraic expression, s and l can be applied for the determination of the absorption coefficient K abs , which can be easily compared to absorption coefficients measured using transmission spectroscopy. l and K abs can be seen as equivalent to the S and K parameters, respectively, in the Kubelka-Munk formulation. The advantage of our approximation is a clear basis in the complete radiative transfer theory. We demonstrate the application of our model to a range of different paper types and to fabrics treated with known levels of a dye.
High spectral resolution atmospheric radiative transfer: Application of the equivalence theorem
Journal of Geophysical Research, 2000
This paper introduces several new variations of the equivalence theorem of Irvi,.e [1964] which lnay increase the speed and accuracy of spectral radiative tra, nsfer models tha, tca. lcula. te spectral radiance or flux. Using this theory, spectral gaseous, cloud, and surface a. bsorptions a. re accommodated by integrating or summing over photon path length and scattering probability density functions (pdfs) after the completion of the multiple-scattering calculation. This procedure can be performed for absorption coefficients a,t any spectral resolution within a wavelength interva,1 in which scattering properties of the atmosphere can be considered consta. nt. This technique eliminates the need to run the multiple-scat•ering portion of a, model more than once for each interval in lieu of integration a. nd/or summation. If this procedure can be perforlned efficiently, dramatic increases in model speed ma,y be realized. Also, because absorption coefficient spectral resolution can be extremely fine, the need for approximations or parameterizations is eliminated, increasing model accuracy. Unlike the origina.1 derivation, the new version of the gaseous absorption equa,tion allows the use of colnplex model scattering atmospheres. An approximation is introduced which allows the use of gas profiles which wry in the vertical. Because employment of the complete theory requires a relatively large amount of computer melnory, a, pdf a. pproximation is introduced to ma, ke it tractable. Va. lida,tion of ea, ch relation is presented using a, Monte C, arlo model simulating shortwave flux. An example of shortwave flux transmitted through a. three-dimensional model a.tmosphere obtained from the Monte Carlo/equivalence theorem (MC/ET) model is shown along with all a. nalysis of the effect of constant scattering property wavelength interval size on the resulting broadband flux,
Journal of the Optical Society of America A, 2002
Recently it has been shown that the perturbation technique, based on joint use of both the direct and the adjoint solutions of the radiative transfer equation, is a powerful tool to solve and analyze various timeindependent one-dimensional problems of atmospheric physics such as the calculation of weighting functions, prediction of radiative effects, and development of retrieval algorithms. Our primary goal is to obtain a general formulation of the perturbation technique for the most general case of the radiative transfer problem: time-dependent problems, with regard to polarization, and any possible external sources of radiation such as laser beams and solar illumination. Possible areas of application of the perturbation technique are discussed, and several examples to illustrate them are provided. The accuracy of this technique is discussed by considering the particular examples.
Journal of Geophysical Research, 1997
A fast and numerically accurate model for monochromatic transfer in scattering atmospheres has been developed to extend the capabilities of the existing LBLRTM line-by-line model to the treatment of clouds and aerosols. The algorithm is based on the adding-doubling method and is specifically designed to perform radiance calculations in both the thermal and the solar regimes using any specified number of computational streams. The efficient implementation of the adding-doubling scheme makes it possible to use the multiple-scattering algorithm in retrieval applications, an essential requirement for the intended use of the algorithm in atmospheric validation studies. The algorithm is applied to observations of water clouds from the ground-based high spectral resolution atmospheric emitted radiance interferometer (AERI) made during the daytime. Retrieval of cloud mode radius, cloud liquid water, and effective cloud fraction is required to model the AERI radiance measurements in the 520-1500 cm-• band and in the 1800-3020 cm-• band which contains significant scattered solar energy. An initial assessment is made of the spectral information content of the AERI measurements for water cloud properties and of the quality of the spectral fits obtainable with those three parameters in the two spectral bands. reproduce in the laboratory, and the direct comparison of model calculations with high spectral resolution atmospheric radiance measurements is an important strategy to validate and improve the physics of relevant radiative mechanisms. Unlike the laboratory environment, the atmospheric environment cannot be controlled. Several complications arise in this type of atmospheric validation due to the large number of optically active molecular species with overlapping radiance contributions, the vertical inhomogeneities in pressure and temperature, and the presence of solid matter in suspension. An essential attribute of the line-by-line approach, often not fully appreciated, is that there is no other known method that ensures sufficient numerical accuracy at any spectral resolution in vertically inhomogeneous media and that rigorously treats the contribution of overlapping optically active species. Because it is important that numerical errors do not interfere with Copyright 1997 by the American Geophysical Union. Paper number 97JD01551. 0148-0227/97/97JD-01551509.00 the more fundamental errors of physical origin, the line-by-line approach constitutes the method of choice for this type of application. Computational efficiency is a critical requirement for lineby-line models. To properly validate radiative transfer calculations with spectral measurements, the validations should be performed over extended spectral regimes to ensure that the relevant temperatures, pressures, applicable surface properties, trace gas concentrations, and most importantly, the scattering constituents are properly specified. The spectral resolution at which these calculations must be made is that appropriate to the gaseous absorption at the lowest pressure involved. These requirements impose a significant computational burden to correctly interpret the measurements over broad spectral intervals. The LBLRTM model [Clough and Iacono, 1995; Clough et al., 1992] is an example of a line-by-line code that has been specifically designed to satisfy the above requirements in nonscattering atmospheres. It is the objective of this development to extend this capability to the treatment of multiple scattering in the same rigorous and efficient manner as the clear-sky calculations. Existing multiple-scattering radiative transfer algorithms of general applicability do not adequately address the computational requirements for monochromatic radiance and flux calculations at a single level over an extended spectral range. For instance, DISORT [Stamnes et al., 1988], a radiative transfer algorithm based on the discrete ordinate method, has the capability to provide fluxes at all levels, facilitating cooling rate calculations, and to provide radiances at several arbitrarily specified angles in a single run. However, no computational gain can be achieved with DISORT by restricting the problem to the calculation of radiance. In addition, DISORT is not optimized for performing calculations over a large number of 21,853
Applied Optics, 2009
We present computationally efficient and accurate semiempirical models of light transfer suitable for real-time diffuse reflectance spectroscopy. The models predict the diffuse reflectance of both (i) semiinfinite homogeneous and (ii) two-layer media exposed to normal and collimated light. The two-layer medium consisted of a plane-parallel slab of finite thickness over a semi-infinite layer with identical index of refraction but different absorption and scattering properties. The model accounted for absorption and anisotropic scattering, as well as for internal reflection at the medium/air interface. All media were assumed to be nonemitting, strongly forward scattering, with indices of refraction between 1.00 and 1.44 and transport single-scattering albedos between 0.50 and 0.99. First, simple analytical expressions for the diffuse reflectance of the semi-infinite and two-layer media considered were derived using the twoflux approximation. Then, parameters appearing in the analytical expression previously derived were instead fitted to match results from more accurate Monte Carlo simulations. A single semiempirical parameter was sufficient to relate the diffuse reflectance to the radiative properties and thickness of the semiinfinite and two-layer media. The present model can be used for a wide range of applications including noninvasive diagnosis of biological tissue. pend on the concentrations of oxyhemoglobin and deoxyhemoglobin . Light transfer through turbid media, such as biological tissues, is governed by the radiative transfer equation (RTE). The latter expresses an energy balance in a unit solid angle dΩ, about the directionŝ at locationr. The steady state RTE in a homogeneous, absorbing, scattering, but nonemitting, medium is expressed as
Journal of the Optical Society of America A, 2004
The auxiliary function method consists of taking full advantage of the expansion of the phase function on spherical harmonics in order to deduce an integral equation from the radiative transfer equation. In contrast to the discrete-ordinate method, it is free of the channel concept, the unknowns being a function only of the optical depth. After presenting the method, we show that it is very accurate and particularly well fitted when the scattering medium is continuously inhomogeneous in albedo and phase function and also for sublayers with different refractive index.