共查询到20条相似文献，搜索用时 31 毫秒
1.
K. Kawabata 《Astrophysics and Space Science》1980,69(1):189-216
We show that Hovenier's Exit Function equation describing reflection and transmission by a plane-parallel layer can be obtained from the Invariant Imbedding equations. As an immediate extension we obtain a similar equation for an Exit Function defined in terms of reflection and transmission functions for successive orders of scattering. These equations allow the reflection and transmission functions of a homogeneous atmosphere of arbitrary optical thickness to be obtained from angle integrations of only one function.A technique based on successive iterations is developed to solve Hovenier's equation. The numerical behavior of this equation is then investigated employing a few representative (i.e., isotropic, Rayleigh, and Henyey-Greenstein) phase functions with the following conclusions. (i) As long as the deviation from isotropy is small (cos 0.15), the Exit Function equation can be numerically solved with an efficiency comparable to that of the standard Doubling technique, which is one of the fastest algorithms available. (ii) The reflection function generated from the Exit Function is usually more accurate than the corresponding transmission function, particularly in the case of large optical thickness. (iii) As the degree of anisotropy increases, so does the difficulty in obtaining the numerical solution for the Exit Function. The solution of the equation depends sensitively on the treatment of the numerical singularities which arise from the integrands and also on the initial approximation employed for the iteration. An improved scheme is required for numerically obtaining the Exit Function in order for this method to yield accurate reflection and transmission functions for strongly anisotropic scattering. 相似文献
2.
A. G. Nikoghossian 《Astrophysics》2004,47(1):104-116
This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres. 相似文献
3.
A. G. Nikoghossian 《Astrophysics》2011,54(1):126-138
Group theory is used to describe a procedure for adding inhomogeneous absorbing and scattering atmospheres in a one-dimensional
approximation. The inhomogeneity originates in the variation of the scattering coefficient with depth. Group representations
are derived for the composition of media in three different cases: inhomogeneous atmospheres in which the scattering coefficient
varies continuously with depth, composite or multicomponent atmospheres, and the special case of homogeneous atmospheres.
We extend an earlier proposal to solve problems in radiative transfer theory by first finding global characteristics of a
medium (reflection and transmission coefficients) and then determining the internal radiation field for an entire family of
media without solving any new equations. Semi-infinite atmospheres are examined separately. For some special depth dependences
of the scattering coefficients it is possible to obtain simple analytic solutions expressed in terms of elementary functions.
An algorithm for numerical solution of radiative transfer problems in inhomogeneous atmospheres is described. 相似文献
4.
To improve the accuracy of calculations for the reflection and transmission functions, doubling techniques are in use. The central theme of this method is to derive the total reflection function when two portions of a medium are adjoined together. The synthesis is done by the use of star product techniques which require a knowledge of theS andT functions of both parts of the medium. Infinite series expansion is necessary to compute the total reflection. The method developed in this article splits the total reflected beam into two parts, one relating to that flux which suffers no scattering at all in the first portion of the medium and the second portion that undergoes at least one scattering in the first portion. The first part can be evaluated simply by knowing the reflection function of the second portion of the medium. The other part of the total reflection for variations of the thickness of the first portion of the medium is found to obey a simple Riccati type integro-differential equation with zero initial conditions. Knowledge of theT functions is not necessary and integration has to be performed over the interval corresponding to thickness of the first portion of the medium. Order-of-scattering analysis is also carried out. 相似文献
5.
Michael J. Price 《Icarus》1975,24(4):492-498
Quantitative predictions of the diffuse reflection and transmission properties of Saturn's rings, relevant to the September 1979 Pioneer 11 flyby, are presented. Predictions are based on an elementary anisotropic scattering model. Interparticle separations are considered to be sufficiently large that mutual shadowing is negligible. Likely ranges in both the single scattering albedo and perpendicular optical thickness of the ring are considered. Situations of pronounced back-scattering and of isotropic scattering are treated individually. Spacecraft measurement of the radiation suffering diffuse scattering by the ring can provide a useful test of the basic ring model. 相似文献
6.
In this paper we consider the time-dependent diffuse reflection and transmission problems for a homogeneous anisotropically-scattering atmosphere of finite optical depth and solve it by the principle of invariance. Also we consider the time-dependent diffuse reflection and transmission of parallel rays by a slab consisting of two anisotropic homogeneous layers, whose scattering and transmission properties are known. It is shown how to express the time-dependent reflected and transmitted intensities in terms of their components. In a manner similar to that given by Tsujita (1968), we assumed that the upward-directed intensities of radiation at the boundary of the two layers are expressed by the sum of products of some auxiliary functions depending on only one argument. Then, after some analytical manipulations, three groups of systems of simultaneous integral equations governing the auxiliary functions are obtained. 相似文献
7.
In the present paper, with the aid of invariance principles in connection with the scattering matrix, we get the exact solution of diffuse reflection and transmission problems by finite inhomogeneous, anisotropically scattering atmospheres bounded by reflecting sufaces. On making use of the reflection and transmission integral operators, we show how to obtain the non-linear integro-differential equations for these operators, which do not depend on the initial condition. Then, we have a system of the required integro-differential equations for the scattering and transmission functions. The obtained result is new, so far as we know. Finally, using the scattering matrix, we reduce the diffuse reflection and transmission problems for planetary atmospheres with reflecting surfaces to the standard diffuse reflection and transmission problems.Supported by the National Science Foundation under Grant No. GP29049 and the Atomic Energy Comminission, Division of Research under Contract No. AT(40-3)-133, Project 19. 相似文献
8.
Multiple-scattering computations are carried out to explain the variation of the observed brightness of the A and B rings of Saturn with declination of the Earth and Sun. These computations are performed by a doubling scheme for a homogeneous plane-parallel scattering medium. We test a range of choices for the phase function, albedo for single scattering, and optical depth of both the rings. Isotropic scattering and several other simple phase functions are ruled out, and we find that the phase function must be moderately peaked in both the forward and backward directions. The tilt effect can be explained by multiple scattering in a homogeneous layer, but, for ring B, this requires a single-scattering albedo in excess of 0.8. The brightest part of ring B must have an optical depth greater than 0.9. We find that the tilt effect for ring A can be reproduced by particles having the same properties as those in ring B with the optical depth for the A ring in the range 0.4 to 0.6. 相似文献
9.
H. Domke 《Astronomische Nachrichten》1978,299(2):87-93
Linear FREDHOLM integral equations are derived for the STOKES vector of the radiation emerging from a scattering plane parallel medium of finite optical thickness. The integral equations are obtained by means of imbedding the slab in an infinite medium. They are formulated in terms of GREEN 's function matrices and renormalized for the asymptotic eigenmode. Explicitly, linear integral equations are given for the reflection and transmission matrices. The reciprocity principle is employed to obtain integral equations also for the mean intensity of the inner radiation field in the case of the slab albedo problem. 相似文献
10.
K. L. Coulson 《Planetary and Space Science》1959,1(4):277-284
The solution of the equation of radiative transfer in a medium exhibiting Rayleigh scattering, as developed by S. Chandrasekhar, has been used for an extensive series of computations(3) of the characteristics of the scattered and diffusely reflected radiation emerging from the top of an atmospheric model which corresponds in many respects to the sunlit portion of the earth's atmosphere. The first part of this two-part discussion dealt with the intensity, degree of polarization, plane of polarization and the neutral points of the emergent light as functions of sun elevation, direction in the downward hemisphere, optical thickness of the model atmosphere and reflectivity of the underlying surface. This second part is concerned with the upward flux obtained by an integration of the intensity over the entire hemisphere, for the incident radiation (a) being independent of wavelength or (b) having the spectral distribution of the extra-terrestrial solar radiation. Integration with respect to wavelength in the latter case, together with an approximation for the sphericity of the atmosphere, yields a value of 7.6 per cent for the earth's planetary albedo due to scattering by the clear atmosphere. An approximation for ozone absorption decreases the computed albedo to 6.9 per cent. 相似文献
11.
The coupling of magnetoacoustic waves at a plane interface that separates two semiinfinite collisionless fluids is studied. The fluids are characterized by different temperatures along and transverse to the ambient magnetic field. Continuum equations obtained by Chewet. al. (1956) are used and expressions for the reflection and transmission coefficients are derived. Extensive numerical computations are done to study the variation of the reflection coefficient, with the angle of incidence, for various temperature anisotropies of the media. Relevance of these investigations to the magnetosphere-solar wind boundary is discussed. 相似文献
12.
Equations connecting the transmission and reflection functions of a finite medium to the reflection function of a semi-infinite one are used to get the albedos in the slowing-down region. The transport equation is solved by the modified Eddington method using Fermi's backward-forward scattering model, modulated to allow for different orders of backward-forward and isotropic scattering. Numerical results for the energy albedos are obtained and compared.On leave of absence from Atomic Energy Center, Inchass, Egypt. 相似文献
13.
Tõnu Viik 《Astrophysics and Space Science》1995,232(1):49-64
The determination of the average path-length of photons emerging from a finite planeparallel atmosphere with molecular scattering is discussed. We examine the effects of polarisation on the average path-length of the emergent radiation by comparing the results with those obtained for the atmosphere where the scattering obeys the scalar Rayleigh function. Only the axial radiation field is considered for both cases.To solve this problem we have used the integro-differential equations of Chandrasekhar for the diffuse scattering and transmission functions (or matrices). By differentiation of these equations with respect to the albedo of single scattering we obtain new equations the solution of which gives us the derivatives of the intensities of the emergent radiation at the boundaries.As in the case of scalar transfer the principles of invariance by Chandrasekhar may be used to find an adding scheme to obtain both the scattering and transmission matrices and their derivatives with respect to the albedo of single scattering. These derivatives are crucial in determining the average path length.The numerical experiments have shown that the impact of the polarisation on the average pathlength of the emergent radiation is the largest in the atmospheres with optical thickness less than, or equal to, three, reaching 6.9% in the reflected radiation. 相似文献
14.
15.
The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan’s atmosphere between 2.0 and 2.8 μm and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab. This potentially reduces the need for a full three-dimensional Monte Carlo code for calculating transmission spectra of atmospheres that contain forward-scattering particles. 相似文献
16.
Marek Gierli&#;ski Chris Done Kim Page 《Monthly notices of the Royal Astronomical Society》2009,392(3):1106-1114
We build a simple model of the optical/ultraviolet (UV) emission from irradiation of the outer disc by the inner disc and coronal emission in black hole binaries. We apply this to the broad-band Swift data from the outburst of the black hole binary XTE J1817−330 to confirm previous results that the optical/UV emission in the soft state is consistent with a reprocessing a constant fraction of the bolometric X-ray luminosity. However, this is very surprising as the disc temperature drops by more than a factor of 3 in the soft state, which should produce a marked change in the reprocessing efficiency. The easiest way to match the observed constant reprocessed fraction is for the disc skin to be highly ionized (as suggested 30 yr ago by van Paradijs), so that the bulk of the disc flux is reflected and only the hardest X-rays heat the disc. The constant reprocessed fraction also favours direct illumination of the disc over a scattering origin as the optical depth/solid angle of any scattering material (wind/corona) over the disc should decrease as the source luminosity declines. By contrast, the reprocessed fraction increases very significantly (by a factor of ∼6) as the source enters the hard state. This dramatic change is not evident from X-ray/UV flux correlations as it is masked by bandpass effects. However, it does not necessarily signal a change in emission, for example, the emergence of the jet dominating the optical/UV flux as the reflection albedo must change with the dramatic change in spectral shape. 相似文献
17.
H. V. Pikichian 《Astrophysics》2010,53(2):251-267
The major results for the linear problem of diffuse reflection and transmission of radiation by a layer of finite thickness
are carried over to the nonlinear case by successive application of Ambartsumyan’s approach for a one dimensional anisotropic
medium. Formulas are given for nonlinear addition of layers which can be used to construct recurrence calculation procedures
for uniform, periodic, and arbitrary stratified media. A complete set of differential equations for invariant imbedding is
derived with the aid of these formulas. These equations are used to obtain a system of total invariance equations, which,
in turn, offer the possibility of reducing the nonlinear problem of diffuse reflection and transmission during irradiation
of a layer from both sides to the simpler problem of illuminating this medium from only one side, with the thickness of the
layer remaining only as a fixed parameter. Finally, it is shown that the results obtained for the single frequency case (two-level
atom) remain valid in the polychromatic case (multilevel atom), which is important for interpreting astrophysical data. 相似文献
18.
The problem of the passage of a plane electromagnetic wave through an arbitrary, inhomogeneous dielectric layer bounded on two sides by two different homogeneous, semi-infinite media is considered. Algebraic relations are obtained between the amplitudes of transmission and reflection (the scattering amplitudes) for the problem under consideration and the wave scattering amplitudes when the layer is bounded on both sides by a vacuum. It is shown that for s and p polarized fields the scattering problem (a boundary-value problem) can be formulated as a Cauchy problem directly for the s and p wave equations. It is also shown that the problem of finding the field inside the layer also reduces to a Cauchy problem in the general case. 相似文献
19.
It is supposed that solar rays are incident uniformly on the top of a plane-parallel, anisotropically scattering, and homogeneous atmosphere, whose bottom is bounded by a specular reflector. An initial-value solution for the scattering and transmission functions is obtained, starting with an auxiliary equation. Some results of numerical experiments for given optical parameters are presented in Figures. 相似文献
20.
Ultraviolet complex refractive index of Martian dust: Laboratory measurements of terrestrial analogs
The optical complex index of refraction of four candidate Martian surface materials has been determined between 0.185 and 0.4 μm using a modified Kubelka-Munk scattering theory. The candidate materials were limonite, andesite, montmorillonite, and basalt. The effect of scattering has been removed from the results. Also presented are diffuse reflection and transmission data on these samples. 相似文献