Showing papers on "Radiative transfer published in 1973"
Book•
01 Jan 1973
653 citations
TL;DR: The matrix operator approach contains the doubling method as a special case and numerous curves are given for both the reflected and transmitted radiance for Rayleigh scattering from a homogeneous layer.
Abstract: An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.
288 citations
TL;DR: In this article, an analysis of the heating of the deep chromosphere by a vertically descending beam of non-thermal electrons with power-law energy spectrum, in flares, is presented.
Abstract: Heating of the deep chromosphere by a vertically descending beam of non-thermal electrons with power-law energy spectrum, in flares, is analysed. In lower regions of the flare, radiative losses can balance the energy input and the flare structure is described in terms of instantaneous quasi-steady temperature/depth profiles. Motion of the optical flare material is at constant pressure and is constrained to be purely vertical by a vertical magnetic field. The ionisation of hydrogen is determined by the same non-LTE processes as in the quiet chromosphere. Temperature profiles are obtained for a wide range of electron beam intensities and spectral indices and are discussed in terms of optical flare observations. Due to the steepness of the electron spectra, typical densities in the optical flare vary only over a narrow range, despite the diversity of beam intensities, in agreement with observation. Above a certain region, the flare material cannot attain a radiatively steady state against the electron input but evaluation of the level at which this occurs leads to an estimate of the mass of material involved in the high temperature flare plasma in this model. Results, which are again insensitive to the electron beam parameters, are found to be in satisfactory agreement with observations of the mass of flare ejecta and of soft X-ray flare emission measures.
190 citations
TL;DR: In this paper, a detailed theoretical study of the radiative properties of water droplet and ice clouds at visible and infra-red wavelengths of 2·3, 3·5, 4·8 and 8·5 and 11 μm is presented.
Abstract: A detailed theoretical study of the radiative properties of water droplet and ice clouds at visible and infra-red wavelengths of 2·3, 3·5, 3·8 and 8·5 and 11 μm is presented. The radiative transfer computations have used a model atmosphere in which the microphysical properties of the clouds have been accurately incorporated. A range of physically realistic size distributions for the cloud particles have been used. The results have been presented in the form of tables of the emissivity, reflectivity and transmissivity, and their equivalent fluxes, at a particular wavelength, as a function of the optical thickness of the cloud layer. A simple scaling relationship enables these extensive tables to be used for any water content of the cloud layers. The results provide a detailed understanding of the radiative properties of terrestrial clouds at thermal infra-red window wavelengths.
The theoretical results are used to interpret infra-red observations of stratocumulus and cirrus clouds.
184 citations
TL;DR: The discrete-ordinate method for radiative transfer has been theoretically developed and numerically verified for use in solving the transfer of both solar and thermal infrared radiation through cloudy and hazy atmospheres.
Abstract: The discrete-ordinate method for radiative transfer introduced originally by Chandrasekhar has been theoretically developed and numerically verified for use in solving the transfer of both solar and thermal infrared radiation through cloudy and hazy atmospheres. This method differs from other radiative transfer approaches in the sense that the solution of the transfer equation can be explicitly derived by employing a finite set of discrete-streams representing the emergent angles in the integral term. Hence such a method is practical for deriving a simplified but reliable radiative transfer approximation for meteorological applications involving clouds and aerosols. Comprehensive comparisons with other rigorous means are carried out for the transmitted and reflected intensity and flux associated with isotropic, Rayleigh and anisotropic scattering. The comparisons reveal that close agreement of radiation computations can be achieved by using discrete-streams of 16. For flux calculations, it was fo...
159 citations
01 Jan 1973
TL;DR: In this article, the distribution of reduced radiation width, particularly for E1 and M1 radiation, in the less well-known “tail region” well below the peak of the E1 giant resonance was studied.
Abstract: The study of the energy dependence of multipole transition probabilities is a broad subject in which certain subfields have progressed much more rapidly than others. Thus for gamma rays ≲2 MeV, E1, M1, and E2 transition probabilities have been well studied (Per 66, SHR 66, SG 65), and at higher energies, ≳10 MeV, the absorption cross section and other properties of the E1 giant resonance are well known (Fir 70), but between these energies there are large gaps in our knowledge. In the present review we are concerned with the distribution of reduced radiation width, particularly for E1 and M1 radiation, in the less well-known “tail region” well below the peak of the E1 giant resonance. We will concentrate on elements with mass number A≳ 90, where a statistical description of radiative processes is appropriate, and on γ-ray energies above ~2 MeV.
153 citations
TL;DR: In this article, the question of quantum-electrodynamic radiative corrections to atomic transition frequencies was investigated, and it was shown that the Heisenberg equations of motion allow a novel and fruitful exploitation of the concept of radiation reaction.
Abstract: We investigate the question of quantum-electrodynamic radiative corrections to atomic transition frequencies. It is shown that the Heisenberg equations of motion allow a novel and fruitful exploitation of the concept of radiation reaction.
129 citations
TL;DR: In this article, a unique combination of properties in the host crystal BaY2F8 has made it possible to obtain laser emission from the Dy3+ ion at 3.022 μ.
Abstract: A unique combination of properties in the host crystal BaY2F8 has made it possible to obtain laser emission from the Dy3+ ion at 3.022 μ. The laser line lies close to the electronic transition from the lowest level of the 6H13/2 excited state at 3520 cm−1 to a ground manifold level at 216 cm−1, but the oscillation frequency is shifted by 5 cm−1 due to overlapping vibronic lines. The intensity of Dy3+ emission is enhanced by energy transfer from Er3+, Yb3+, Tm3+, and Ho3+. The restrictions imposed on the multiphonon decay rates for the operation of a Dy3+ laser at 3 μ are discussed. A comparison of radiative and nonradiative relaxation rates for rare‐earth ions in BaY2F8 indicates that an extension of laser emission to beyond 4 μ is unlikely.
126 citations
TL;DR: In this article, it was shown that the dimensionality of space-time serves as a cut-off for ultraviolet and infrared divergences, thus completely avoiding the introduction of a fictitious photon mass.
117 citations
TL;DR: In this article, a theoretical model describing radiative ignition of a solid fuel is constructed and numerically analyzed, including the effects of gas phase reaction and a finite value of the absorption coefficient of the solid (in-depth absorption of incident radiation).
Abstract: A theoretical model describing radiative ignition of a solid fuel is constructed and is numerically analyzed. The model includes the effects of gas phase reaction and a finite value of the absorption coefficient of the solid (in-depth absorption of incident radiation). It is found that the gas phase reaction must be included in the model in order to understand radiative ignition of a solid fuel and to find its ignition boundary. The in-depth absorption of the incident radiation by a solid fuel significantly affects the ignition delay time. The results indicate that there is a finite range of values for pyrolysis or gas phase reaction activation energy for which ignition will occur. This finding has a direct bearing on efforts to reduce material ignitability.
TL;DR: In this article, the authors considered the transfer of electronic energy between two molecules embedded in a host lattice and used a simple model for the electron phonon coupling and solved for the density matrix of the electronic system in the absence of radiative decay.
Abstract: In the present paper we consider the transfer of electronic excitation energy between two molecules embedded in a host lattice. We use a simple model for the electron phonon coupling and solve for the density matrix of the electronic system in the absence of radiative decay. We find, in the weak coupling limit, that the approach to equilibrium is in general complex but for large transfer rates becomes a simple exponential.
TL;DR: In this paper, the authors derived the escape factor for free-bound and bound-bound radiation in the case of Doppler and dispersion profiles, respectively, by solving the equation of radiative transfer with the assumption that the corresponding source functions are space-independent.
Abstract: Optical escape factors for bound-bound and free-bound radiation have been calculated by solving the equation of radiative transfer with the assumption that the corresponding source functions are space-independent. The general expression for bound-bound transitions yields for large optical depths—within a correction factor of order unity—Holstein's asymptotic expressions for the two limiting cases of a Doppler and a dispersion profile. Application to the more general case of a Voigt profile leads to an analytical formula which permits a rapid estimate of the escape factor for any optical depth. Numerical application to the resonance lines of neutral helium-which are broadened by Stark and Doppler effects—shows that under certain plasma conditions most of the higher members of the resonance series remain optically thin.—The general expression obtained for the escape factor of free-bound radiation has been applied to the resonance continuum of neutral helium. The numerical results show that the resonance continuum remains optically thin as long as the optical depth in the center of the He resonance line (λ = 584 A) remains smaller than 104 to 105. A similar result is obtained for atomic hydrogen.
TL;DR: The equations are sufficiently simple to be used for spectroscopic determination of the absorption and scattering coefficients and show very good agreement for all cases except for reflectance in the highly anisotropic case, where agreement is only fair.
Abstract: Equations are derived to determine the diffuse reflectance and transmittance of inhomogeneous materials. The equations are valid for collimated incident radiation for any angle of incidence. The effects of boundary reflectance and anisotropic scattering are included. The equations are derived from the equation of radiative transport, using the Schuster-Schwartzchild approximation. They are sufficiently simple to be used for spectroscopic determination of the absorption and scattering coefficients. Numerical comparison with more exact solutions of the equation of radiative transfer show very good agreement for all cases except for reflectance in the highly anisotropic case, where agreement is only fair.
01 Jan 1973
TL;DR: In this paper, the authors describe the flow, heat-transfer, and chemical-reaction processes occurring within a gaseous-fired furnace, using a four-flux model of radiative heat transfer.
Abstract: Calculations are described of the flow, heat-transfer, and chemical-reaction processes occurring within a gaseous-fired furnace. A particular feature of the computations is the incorporation of a four-flux model of radiative heat transfer. The calculation procedure is a two-dimensional one, in which the main hydrodynamic variables are the vorticity and stream function. The turbulent transport properties are obtained from a two-equation turbulence model, in which turbulence energy and energy-dissipation rate are the dependent variables. Mass-transfer and chemical reactions are calculated from a model which assumes a single-step chemical reaction, and physical control: the effects of these processes thus embodied in a single differential equation for the mixture fraction. Heat transfer is determined by solution of differential equations for the specific enthalpy, and for the sums of the radiative fluxes for each of the coordinate directions. Calculations are performed for the conditions of the “M1 Trials” carried out on the furnaceof the International Flame Foundation, IJmuiden. Encouraging agreement is obtained between the predicted and measured distributions of temperature and radiant heat transfer along the furnace walls. However, the agreement within the flow is unsatisfactory, due, it is believed, to neglect in the computations of the effects of the “unmixedness” phenomenon.
TL;DR: The infrared spectral reflectance of a semi-infinite medium composed of irregular particles of different materials is calculated in terms of the sizes, shapes, and complex refractive indices of the particles.
Abstract: The infrared spectral reflectance of a semi-infinite medium composed of irregular particles of different materials is calculated in terms of the sizes, shapes, and complex refractive indices of the particles. For particles larger than the wavelength, the scattering and absorption are computed mainly by geometrical optics but with important wave-optical corrections for the additional absorption caused by edges and asperities, which are represented by dipoles distributed over the surface of the particle. For particles smaller than the wavelength, a Lorentz-Lorenz model is used to derive the average complex index of the medium, the particles being treated as ellipsoids with a wide range of shapes. The average scattering of an individual ellipsoidal particle is then found from the relative refractive index of the particle with respect to the Lorentz-Lorenz medium. For both large and small particles the single-particle scattering is represented by six discrete beams. Calculation of the reflectance is then facilitated by a radiative transfer method that also involves six beams. For particles of intermediate size a suitable formula bridging the results for large and small particles is found to be satisfactory.
01 Jan 1973
TL;DR: In this article, a radiative transfer model was used to correct Apollo photographic imagery for degradation arising from atmospheric scattering using aircraft scanner data, and an extrapolation was then made to spacecraft altitudes.
Abstract: Description of a radiative transfer model which has been used to correct Apollo photographic imagery for degradation arising from atmospheric scattering. The model was tested using aircraft scanner data, and an extrapolation was then made to spacecraft altitudes. Using standard meteorological data for the region of interest, it is possible to determine transmittance, path radiance, and total radiance from calculations made with the multiple scattering atmospheric model. Simple algorithms are presented which allow potential users of spacecraft sensor data to correct imagery for the deleterious effects due to the scattering of radiation under clear or hazy atmospheric conditions.
Journal Article•
TL;DR: In this paper, a new numerical method for solving the general equation of radiative transfer is presented, which replaces the integral term over angle in the transfer equation by a quadrature sum, and an estimate of the error involved is obtained and this error can then be used to evaluate a corection to the radiation field originally determined.
Abstract: A new numerical method is presented for solving the general equation of radiative transfer. The approximation, which replaces the integral term over angle in the transfer equation by a quadrature sum, is studied; an estimate of the error involved is obtained and this error, which may be thought of as a further source or sink of photons (depending upon the sign), can then be used to evaluate a corection to the radiation field originally determined. This process may then be continued as a perturbation series. The method is found to give a final solution, when starting from the Eddington approximation, at least as accurate as that obtained using variable Eddington factors. Furthermore, the technique involves very little extra computing over that required using the Eddington approximation, and may be trivially generalized to any radiative transfer problem. It can also be used in conjunction with any of the existing methods for solving the equation of transfer. Examples are given in the context of spectral line formation in slab geometry.
TL;DR: In this paper, the positions, intensities, half widths and ground state energies of approximately 1700 of the strongest spectral limes in the ν2 band of ammonia and its first overtone are presented.
Abstract: Data are presented on the positions, intensities, half widths and ground state energies of approximately 1700 of the strongest spectral limes in the ν2 band of ammonia and its first overtone. The values are used to compute the transmission function for dilute mixtures of ammonia in hydrogen, approximating the Jovian environment, and these are compored to laboratory measured transmissions for the same conditions. The application of the data to theoretical studies of radiative transfer in the atmosphere of Jupiter and the interpretation of observations in the 8–20 μ range is discussed.
TL;DR: Arguments are presented to show that in clearest ocean water the upwelling field above the surface can provide information only about the upper 25 m of the medium.
Abstract: The radiative transfer equation has been solved by a Monte Carlo technique for a flat homogeneous ocean with two different incident radiance distributions. The irradiance reflectivity R for photons that penetrate the ocean is presented as a function of the single scattering albedo ω0, and the scattering phase function P(θ) of the medium. The P(θ)’s used are based on experimental observations. The results clearly show that R depends strongly on both ω0 and P(θ) but apparently not on the form of the incident radiance distribution. Arguments are presented to show that in clearest ocean water the upwelling field above the surface can provide information only about the upper 25 m of the medium.
TL;DR: In this paper, the equivalence of the two formulations is shown and some new results obtained from the reformulation are presented, and the relation between the quenching constant and the cross-section is discussed.
Abstract: the excited donor and the ground state acceptor on the rate of energy transfer. In this paper, the equivalence of the two formulations is shown and some new results obtained from the reformulation are presented. The inelastic collision cross-sections for singlet-singlet, triplet-singlet, and triplet-triplet transfers have been obtained by using the first Born approximation. The relation between the quenching constant and the quenching cross-section is discussed. It is shown that for singlet-singlet and triplet-singlet transfers in the gas phase, both Coulomb and exchange interactions are important. The energy transfer probability in the solid phase and the quenching constants in the collisional energy transfer are compared. Some experimental results of the energy transfer measurements in the gas phase are discussed. In a previous paper Lin (97i a) reformulated in a preliminary way the DexterF'rster theory (Forster I948; Dexter I953) so that it can be used to discuss explicitly effects of temperature, isotope substitution and the energy gap between the excited donor and the ground state acceptor on the rate of energy transfer. Both formulations use the golden rule expression for the energy transfer probability; while Dexter and Forster normalize the wavefunctions on an energy scale as for a, continuum system, Lin regards the Born-Oppenheimer levels as a dense quasicontinuum of vibronic levels and proceed to the derivation of the expression for the energy transfer probability by using the same theoretical technique as that dLeveloped for the treatment of radiationless transitions (Lin 1966; Lin & Bersohn 1968; Freed & Jortner 1970). The purpose of this paper is twofold; first, to show that our formulation can be reduced to that of Forster and Dexter's and also to present some new results of the energy transfer in the solid phase obtained from our formulation; and second, we shall extend the Dexter-Forster theory to the energy transfer in the gas phase and compare the energy transfer in the solid and gas phases. In the gas phase, the energy transfer is collisional. For inelastic collisions which we are concerned with, the exact analytical expression of collisional cross-sections is not available except for the simplest systems. For the purpose of comparison, the analytical expression
TL;DR: In this article, it was shown that the radiation-reaction concept, which explains classical radiative effects, cannot be used exclusively to explain atomic radiative effect, and must be supplemented by consideration of the vacuum field.
Abstract: It is shown that the radiation-reaction concept, which explains classical radiative effects, cannot be used exclusively to explain atomic radiative effects, and must be supplemented by consideration of the vacuum field.
TL;DR: In this paper, the authors compared the performance of radiative and Auger processes and showed that the recombination coefficients for both processes take the form of Cr(α 0a0)3/t0, CAuga0 6/t 0, where the dimensionless numbers Cr, CAug lie between 1 and 1010, α 01/137, a 0 is the Bohr radius and t 0 is an atomic unit of time.
TL;DR: In this article, a modified diffusion approximation of the Fokker-Planck equation was proposed to study the impact-radiation recombination in a low-temperature plasma, taking into account the real energy structure of the atom, the influence of the radiative transitions, and the relationship between the non-equilibrium distributions of the atoms over the levels and of the electrons over the energies.
Abstract: The theory of impact-radiation recombination (ionization) in a low-temperature plasma is based on the representation of this process as a random walk of a recombining (released) electron in the discrete space of the atom's energy levels. Different methods of studying recombination (ionization) are considered. The described modified diffusion approximation, combining the possibilities of the previously developed approaches, takes into account the real energy structure of the atom, the influence of the radiative transitions, and the relationship between the non-equilibrium distributions of the atoms over the levels and of the electrons over the energies. A solution is presented for the Fokker-Planck equation expressed in finite-difference form, and analytic expressions are obtained for the ionization and recombination coefficients. The results are compared with the published experimental data.
TL;DR: In this article, a one-dimensional model of the Martian planetary boundary layer over sloping terrain is analyzed under a variety of conditions and the results for the steady and diurnal components of the temperature and wind fields are found when a Boussinesq model with a Newtonian cooling law is considered.
Abstract: A one-dimensional model of the Martian planetary boundary layer over sloping terrain is analyzed under a variety of conditions. Analytical results for the steady and diurnal components of the temperature and wind fields are found when a Boussinesq model with a Newtonian cooling law is considered. These results form a basis for understanding the numerical results which include more realistic representations for the heating and parametrizations for the eddy transfer of momentum and heat. The diurnal boundary layer thickness is determined primarily by radiative processes, and the amplitudes of the wind and temperature oscillations are found to depend in an important way on the latitude and slope magnitude. Typically, oscillations in the temperature of plus or minus 15 K and in the upslope wind of plus or minus 25 m/sec are found 1 km above a Martian slope of 0.005.
TL;DR: Matrix operator theory is used to calculate the reflected and transmitted radiance of photons that have interacted with plane-parallel maritime haze layers and the results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick.
Abstract: Matrix operator theory is used to calculate the reflected and transmitted radiance of photons that have interacted with plane-parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo are tabulated. The forward peak and other features in the single scattered phase function cause the radiance in many cases to be very different from that for Rayleigh scattering. In particular the variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked and the relative limb darkening under very thick layers is greater for haze M than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = 0 is always greater and the cloud albedo is always less for haze M than for Rayleigh layers.
TL;DR: In order to investigate experimentally the applicability of a previously developed two-flux radiative transfer model that takes into account surface reflections and collimated incidence, pulverized and sintered scattering standards prepared from a glass of known absorption coefficient variation are measured.
Abstract: Separation of the scattering contribution from the total optical attenuation is necessary to determine the absorption portion of nonhomogeneous media such as naturally occurring minerals. In order to investigate experimentally the applicability of a previously developed two-flux radiative transfer model that takes into account surface reflections and collimated incidence, we have measured pulverized and sintered scattering standards prepared from a glass of known absorption coefficient variation. The new model produces an accuracy improvement up to a factor of 2.5 over the Kubelka-Munk theory. Off-axis scattering measurements were made with improved instrumentation between 0.33 microm and 2.7 microm. The model was then applied to the mineral rhodochrosite in this range to obtain accurate values of scattering and absorption.
TL;DR: In this article, a perturbation solution for a vibronic model for the relaxed excited state of the $F$ center, in the limiting case of weak electron-phonon coupling, was given.
Abstract: A perturbation solution is given for a vibronic model for the relaxed excited state of the $F$ center, in the limiting case of weak electron-phonon coupling. The resulting predictions of the model are compared with available data on radiative lifetimes, Stark effects, magnetic circular polarization, and stress-induced polarization of $F$-band luminescence in alkali halides. It is shown that a consistent quantitative interpretation of most of these data is possible on this basis if the $2s$ electronic state lies below the $2p$ state in the relaxed cubic configuration by an energy difference which is \ensuremath{\sim} 0.09 eV for KCl and \ensuremath{\sim} 0.15 eV for KF. The long radiative lifetime should then be attributed predominantly to the $2s$ state being only weakly coupled to the $2p$ state by the phonons, rather than to spatial diffuseness of the $2p$ state. The model also accounts for the observed ratio of the electric-field-induced change in the radiative lifetime to the field-induced polarization of the luminescence, for the temperature dependence of the radiative lifetime and field-induced polarization, and for the absence of any such temperature dependence in the stress-induced polarization.