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1.
Bruce Hapke 《Icarus》2008,195(2):918-926
It is well known that the bidirectional reflectance of a particulate medium such as a planetary regolith depends on the porosity, in contrast to predictions of models based on the equation of radiative transfer as usually formulated. It is shown that this failure to predict porosity dependence arises from an incorrect treatment of the light that passes between the particles. In this paper a more physically correct treatment that takes account of the necessity of preventing particles from interpenetrating is used together with the two-stream approximation to solve the radiative transfer equation and derive improved expressions for the bidirectional and directional-hemispherical reflectances. It is found that increasing the filling factor (decreasing the porosity) increases the reflectance of low and medium albedo powders, but decreases it for ones with very high albedos. The model agrees qualitatively with measured data. 相似文献
2.
The physics of scattering of electromagnetic waves by media in which the particles are in contact, such as planetary regoliths, has been thought to be relatively well understood when the particles are larger than the wavelength. However, this is not true when the particles are comparable with or smaller than the wavelength. We have measured the scattering parameters of planetary regolith analogs consisting of suites of well-sorted abrasives whose particles ranged from larger to smaller than the wavelength. We measured the variation of reflectance as the phase angle varied from 0.05° to 140°. The following parameters of the media were then deduced: the single scattering albedo, single scattering phase function, transport mean free path, and scattering, absorption, and extinction coefficients. A scattering model based on the equation of radiative transfer was empirically able to describe quantitatively the variation of intensity with angle for each sample. Thus, such models can be used to characterize scattering from regoliths even when the particles are smaller than the wavelength. The scattering parameters were remarkably insensitive to particle size. These results are contrary to theoretical predictions, but are consistent with earlier measurements of alumina abrasives that were restricted to small phase angles. They imply that a basic assumption made by virtually all regolith scattering models, that the regolith particles are the fundamental scattering units of the medium, is incorrect. Our understanding of scattering by regoliths appears to be incomplete, even when the particles are larger than the wavelength. 相似文献
3.
Jeffrey N. Cuzzi 《Icarus》1985,63(2):312-316
The optical thickness of the rings of Uranus has been thoroughly measured by many stellar occultations. However, we show that the optical thickness so obtained is larger by an extinction efficiency factor of 2 than the fractional area physically filled by particles which is commonly used to infer both particle reflectivity and particle size. By neglecting this factor, previous work has overestimated particle packing density and therefore underestimated individual particle reflectances and sizes (as well as overestimated collision frequencies). This has led to concern as to why the ring particles seemed unusually black and small. We present new estimates of particle reflectance which include both this effect and an improved radiative transfer treatment, and show that the ring particles, while still quite dark, are no longer mysteriously so. Particle sizes, while not strongly constrained, could easily lie in the macroscopic size range characteristic of other planetary rings. 相似文献
4.
In a recent paper Hapke et al. (Hapke, B., Shepard, M., Nelson, R., Smythe, W., Piatek, J. [2009]. Icarus 199, 210-218) performed bi-directional reflectance measurements on closely-packed particulate surfaces of micrometer-sized particles and compared these with both the Hapke IMSA photometric model, and a numerical radiative transfer algorithm, the MDYZ (Mishchenko, M., Dlugach, J., Yanovitskij, E., Zakharova, N. [1999a]. J. Quant. Spectrosc. Radiat. Trans. 63, 409-432). To account for the effects of close packing, Hapke et al. applied a diffraction truncation scheme to remove the diffraction spike and supplied the renormalized single scattering phase function to the IMSA. They found that the IMSA prediction is a better match with measurement than that of MDYZ. In this work we demonstrate that the diffraction truncation procedure outlined by Hapke et al. contains an error. By following Hapke et al.’s intended truncation scheme, we have found that the IMSA model is not sufficiently anisotropic to describe the reflectance pattern of measurements on surface reflectance of closely packed large spherical particles. 相似文献
5.
Over the last decade, considerable progress has been achieved in the theory of light scattering by morphologically complex
objects, which extends the potential of correct interpretation of photometric and polarimetric observations. This especially
concerns the backscattering domain, where the opposition effects in brightness and polarization are observed. Although the
equations of radiative transfer and weak localization (coherent backscattering) are rigorously valid only for sparse media,
the results of exact computer solutions of the Maxwell equations for a macroscopic volume filled with randomly positioned
particles show that their application area can be wider. In particular, the observations can be correctly interpreted if the
packing density of particles in the medium reaches 20–30%. The recently suggested approximate solution of the coherent backscattering
problem allowed interesting effects in the spectra of Saturn’s satellites to be explained. In the densely packed media, the
effects that are impossible in the sparse media and caused by the near-field contribution can be observed. To calculate the
characteristics of radiation reflected by such a medium, it is not sufficient to solve the radiative transfer and weak localization
equations, even if they are written in a form without the far-zone limitations. Nowadays, the influence of the interaction
of particles in the near field can be analyzed only for the restricted ensembles of particles. It shows that the substantial
increase of the packing density essentially changes the phase functions of intensity and polarization in the backscattering
domain. This allows the packing density of particles in the medium and their absorbing properties to be estimated from the
shape of the phase curves measured. However, the task of quantitative interpretation of the measurements of radiation reflected
by a densely packed medium, in terms of sizes of particles, their refractive index, and packing density, still remains unsolved. 相似文献
6.
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
7.
Xinzhong Chen Edward A. Spiegel 《Monthly notices of the Royal Astronomical Society》2001,323(4):865-871
Viscous resistance to changes in the volume of a gas arises when different degrees of freedom have different relaxation times. Collisions tend to oppose the resulting departures from equilibrium and, in so doing, generate entropy. Even for a classical gas of hard spheres, when the mean free paths or mean flight times of constituent particles are long we find a non-vanishing bulk viscosity. Here we apply a method recently used to uncover this result for a classical rarefied gas to radiative transfer theory, and derive an expression for the radiative stress tensor for a grey medium with absorption and Thomson scattering. We determine the transport coefficients through the calculation of the comoving entropy generation. When scattering dominates absorption, the bulk viscosity may be much larger than either the shear viscosity or the thermal conductivity. 相似文献
8.
Predictions of two widely-used regolith reflectance models, a numerically exact computer code and an approximate analytic equation, based on the equation of radiative transfer were tested against the measured reflectance of a medium of close-packed spheres, whose properties supposedly can be well-characterized. Surprisingly, the approximate analytic model was a better match to the experimental data than the numerically exact computer solution. Other approximate regolith models were tested briefly with similar results. Discrepancies between the two models and between models and experiment can be explained if the phase functions and albedos of the spheres are not the same as when the particles are isolated. Differences include the absence of the Fraunhoffer diffraction peak, which is an intrinsic assumption of the approximate analytical model but not the exact numerical model, and increased scattering in the mid-range of phase angles, which the approximate analytic model fortuitously describes more accurately than the exact numerical model. These changes may be caused by the close proximity of surrounding particles. If they are taken into account, models based on the radiative transfer equation appear able to quantitatively predict the reflectances of regoliths and other particulate media. Interparticle perturbations are also predicted to cause a coherent backscatter opposition effect in the backward direction that was observed, but its angular width was found to be much larger than predicted by theories for sparsely-packed media. 相似文献
9.
Submicroscopic iron particles larger than about 50 nm, infused throughout mineral grains or glasses, are abundant in planetary materials altered by their environment such as shocked meteorites and lunar agglutinate glasses. Such particles darken their host material but do not redden their spectra but to date there has been no theoretical treatment of their optical effects. Using Mie theory, we modify the Hapke (2001) radiative transfer model of the effects of space weathering to include these effects. Comparison with laboratory measurements shows that the new treatment reproduces the relationship between submicroscopic iron size, abundance and reflectance. We apply this new model to near-IR spectra of Mercury recently obtained by the MESSENGER spacecraft and find that submicroscopic iron is much more abundant on Mercury than in lunar soils, with typical total submicroscopic iron abundances near 3.5 wt.% compared to about 0.5 wt.% for lunar soils We also find that the ratio of iron particles that darken but do not redden to the abundance of very small iron particles that impart the red slope to space weathered material is much larger than lunar (6 vs. 2). Both the total submicroscopic iron abundance and ratio of particle size fractions are consistent with the higher production of melt and vapor in micrometeorite impact on Mercury relative to the Moon (Cintala, 1992) that enables more accumulation of space weathering products before sequestration by regolith overturn. The radiative transfer model cannot directly constrain the abundance of opaque minerals on Mercury because of ambiguities between the darkening effects of opaques and submicroscopic iron particles larger than 50 nm, but assuming the opaques are the ultimate source of the submicroscopic iron, our results place a lower limit of 4-20 wt.% on opaque abundance on Mercury depending on the composition of the opaque phase and whether titanium metal also contributes to the space weathering effect. 相似文献
10.
11.
Björn J.R. DavidssonYuri V. Skorov 《Icarus》2002,156(1):223-248
A small but increasing volume of observations of cometary nuclei has accumulated during the past two decades. This development is accelerating with upcoming space missions such as Stardust, Contour, and Rosetta. In response to the growing need for a theoretical understanding of optical properties of cometary nuclei, we have calculated synthetic reflectance spectra in the wavelength region 0.2-2.0 μm, photometric colors in the Johnson-Kron-Cousins UBVRI system, and visual geometric albedos for a large number of porous ice-dust mixtures with differing composition, regolith grain sizes, and grain morphologies, such as core-mantle grains, dense clusters of such grains, and large irregular particles with internal scatterers. The calculations are based on Mie theory, the discrete dipole approximation, Hapke theory, and a numerical solution to the equation of radiative transfer in particulate media. In addition, wavelength-integrated directional-hemispherical albedos and flux attenuation profiles in the regolith as functions of depth have been calculated in order to improve the energy budget and treatment of energy boundary conditions in thermal models of cometary nuclei.Our results are compared with spectra and colors of observed cometary nuclei. Our main conclusions are that only regolith consisting of relatively large core-mantle grains, or clusters of smaller core-mantle grains, is capable of reproducing the red colors seen in comets; that ice-dust mixtures actually can be darker than ice-free regolith in certain circumstances; and that solar radiation sometimes penetrates to a depth that is comparable to the region in which diurnal temperature variations occur. 相似文献
12.
The problem of remote sensing of the surface through a planetary atmosphere is considered. An efficient approach to the atmospheric correction of satellite information is developed. A model for the atmospheric transfer properties is represented as a linear functional—the superposition integral underlying the classical linear-system approach. The optical transfer operator is constructed mathematically rigorously and physically correctly by the method of influence functions and spatial-frequency characteristics. The influence functions and spatial-frequency characteristics of an atmosphere–planetary surface system are the kernels of the functionals and objective characteristics, which are invariant to specific structures of the objects being sensed and to illumination and observing conditions. The spatial-frequency characteristics are introduced as Fourier transforms of the influence function in horizontal coordinates. The foundations of the spatial-filtering theory are outlined for the problem of remote sensing, which have a wide range of applications. The main problems of the theory and mathematical modeling of three-dimensional radiative transfer are pointed out. 相似文献
13.
We present a numerical model that allows us to calculate the contribution of a specified scattering order in the geometric optics approximation for media composed of large particles with an arbitrary phase function. It has been demonstrated that the correlated propagation of the incident and emergent rays, which is disregarded in the classical radiative-transfer theory, markedly affects the contributions of different orders of scattering, especially the first-order scattering. If the theory describing the photometric properties of regolith-like media ignores the shadowing effect, the errors of its application may reach several tens of percent even for bright surfaces. The packing density of a medium essentially influences the phase dependence of the first-order scattering, although its effect on the value and the phase curve of the higher scattering orders is relatively weak. The backscattering peaks calculated on the basis of the Hapke theory are narrower than those obtained from the numerical simulations, because the Hapke theory is an approximate approach. 相似文献
14.
Stephen J. Keihm 《Icarus》1982,52(3):570-584
The effects of volume scattering on the lunar microwave brightness temperature spectrum are evaluated for a broad range of plausible scattering fragment populations. Mie-scattering phase functions and the radiative transfer method are utilized. Results indicate that emission darkening of ～1–7°K is to be expected over the wavelength range 3–30 cm, dependent on the total volume fraction of centimeter-sized and larger fragments. Spectral variations can occur if the size distribution of scatterers is nonuniform in a power law sense. For mare regions representative of the Surveyor III, V, and VI sites, an increase in brightness temperature with wavelength is predicted which is smaller than the predicted spectral variation due to planetary heat flow. The amplitude of lunation variation in brightness temperature is particularly sensitive to the fraction of fragments in the upper 10-cm diurnal layer. Deductions of electrical loss based on purely absorptive models can overestimate loss tangent values by a factor of 1.5 or more if scattering effects are not accounted for. The absence of anomalies exceeding ～2°K in lunar night-time γ3.55-cm brightness temperature maps requires a remarkable uniformity of the surface layer (upper 10 cm) scattering properties on a 250-km scale. 相似文献
15.
Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles. 相似文献
16.
A classical problem in the theory of radiative transfer is considered: calculating the radiation field within a plane scattering
atmosphere. The recently proposed albedo-shifting method is used to calculate the source function both in a semi-infinite
atmosphere and in an atmophere of finite optical depth, illuminated by parallel rays. The method enables one to “suppress”
scattering and obtain iterative solutions of the integral equation for the source function in only a few direct lambda iterations,
even when the average number of photon scatterings in the atmosphere is very large.
Translated from Astrofizika, Vol. 42, No. 4, pp. 485–500, October–December, 1999. 相似文献
17.
The infinite medium Green’s function is used to solve the half-space albedo, slab albedo and Milne problems for the unpolarized Rayleigh scattering case; these problems are the most classical problems of radiative transfer theory. The numerical results are obtained and are compared with previous ones. 相似文献
18.
We present measurements of ratios of elements of the scattering matrix of martian analogue palagonite particles for scattering angles ranging from 3° to 174° and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0° to 180°. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty martian atmosphere. 相似文献
19.
It is shown that a lower limit exists on the microwave brightness of the rings of Saturn, if they are assumed to be composed of Mie scatterers of geological composition. The lower limit (about 15°K) is due to scattering of planetary microwave emission. Significant variation of brightness with azimuth along the rings is expected if the particles are typically of 2–3cm radius. Implications for the multiple-scattering hypothesis of the radar cross section of the rings are noted. 相似文献
20.
Viik Tõnu 《Earth, Moon, and Planets》1989,46(3):261-284
The vector equation of radiative transfer is solved both for conservative and non-conservative planetary atmospheres using the method of discrete ordinates. The atmosphere, bounded by a Lambert bottom, is considered plane-parallel and homogeneous. The scattering in the atmosphere obeys the Rayleigh or Rayleigh-Cabannes law. The compiled package of FORTRAN codes allows us to find the Stokes parameters for such an atmosphere at arbitrary optical depth. 相似文献