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1.
It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and micro-structures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from approximately 12 degrees on a 61m scale to approximately 7 degrees on a 216-272m scale. On the same scales, a value of the order of 2% has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness. 相似文献
2.
Photoclinometry is the most common method used to obtain high-resolution topographic maps of planetary terrain. We derive the likelihood function of photoclinometric surface slope from (1) the probability distribution of the measured photon count of natural sunlight through a Charge-Coupled Device (CCD) including uncertainty due to camera shot noise, camera read noise, small-scale albedo fluctuation and atmospheric haze, and (2) a photometric model relating photocount to surface orientation. We then use classical estimation theory to determine the theoretically exact biases and errors inherent in photoclinometric surface slope and show when they may be approximated by asymptotic expressions for sufficiently high sample size. We show how small-scale albedo variability often dominates biases and errors, which may become an order of magnitude larger than surface slopes when surface reflectance has a weak dependence on surface tilt. We provide bounds on the minimum possible error of any unbiased photoclinometric surface slope estimate, and compute the sample sizes necessary to constrain errors within desired design thresholds. 相似文献
3.
Robert L. Wildey 《Icarus》1975,25(4):613-626
The present investigation develops a new theory for the photoclinometric determination of topography when the photometric function of the planetary surface (or that which corresponds to the mean optical depth of emergent scattered solar radiation from an optically thick planetary atmosphere) is not restricted beyond the expectation that it is a function of phase angle, angle of incidence, and angle of emergence. Several versions of such an operational theory, which differ according to the auxiliary conditions employed to achieve mathematical determinacy, together with several approaches to the numerical analysis, have been evolved. The differences in the numerical methods arise from a variable trade-off between computing speed and stability and computer storage requirements. Although the computer encoding process is not yet fully operational, a first result has been worked out for an early frame in the Mariner 9 mission in which the dust-laden atmosphere appears to exhibit standing-wave patterns. Provided the assumption of homologous departures from plane-parallel atmospheric configuration is valid, the photoclinometric implication is that laminar flow lines in the optically viewable dust layer undergo a near-sinusoidal rise and fall of about 40 to 50m. Regardless of assumption, the resulting surface is a rigorous mean-emission surface. 相似文献
4.
A convenient photometric function for many particulate surfaces is the generalization of the Lommel-Seeliger law derived by Hapke (1963) and Irvine (1966). This generalization accounts for the effects of mutual shadowing among particles, but still assumes that multiple scattering within the surface layer can be neglected—an assumption which is evidently valid for dark surfaces. We describe a series of laboratory measurements which test the range of validity of this basic assumption, and the applicability of the Hapke-Irvine photometric function, for particulate surfaces whose normal reflectances ranges from 0.04 to 1.04. We find that multiple-scattering effects can be neglected, and that the Hapke-Irvine function can be used, for particulate surfaces whose normal reflectance is about 0.3, or less. The function is definitely inapplicable to surfaces whose normal reflectance exceeds 0.4. 相似文献
5.
A model for computing the brightness of a satellite in the shadow of a planet is described, which takes into account the Sun–planet–satellite–sensor geometry, the satellite bi-directional reflectance function, and the refraction of sunlight in the planetary atmosphere. Synthetic light curves for eclipse ingress or egress of the five large satellites of Uranus are generated. The model luminosities can be fitted to photometric observations in order to calculate a precise distance between the centers of the satellite and the planet. Alternately, when the satellite ephemeris is accurately known the atmospheric state of the planet can be studied. 相似文献
6.
I. A. Dulova S. I. Skuratovsky N. V. Bondarenko Yu. V. Kornienko 《Solar System Research》2008,42(6):522-535
The possibility of reconstructing the surface topography from single images with the photometric method in the linear approximation is analyzed. The photometric method or surface topography Reconstruction employs a statistical approach to the problem formulation and is the most mathematically correct. This method allows determination of the most probable surface topography given specific observational data. When only one image is available, the photometric method is superior in comparison with the currently available photoclinometry. The processing of test surface topography with the photometric method shows that, under typical conditions, the error of surface relief reconstruction is of higher than 40% in terms of the standard deviation of the surface height. The surface relief of some Martian areas are reconstructed from HRSC images obtained by the Mars Express spacecraft. It is shown that the image-reconstructed surface topography is in good agreement with the topographic information for the same Martian areas obtained by the MOLA altimeter. 相似文献
7.
In many cases, the derivation of high-resolution digital terrain models (DTMs) from planetary surfaces using conventional digital image matching is a problem. The matching methods need at least one stereo pair of images with sufficient texture. However, many space missions provide only a few stereo images and planetary surfaces often possess insufficient texture.This paper describes a method for the generation of high-resolution DTMs from planetary surfaces, which has the potential to overcome the described problem. The suggested method, developed by our group, is based on shape-from-shading using an arbitrary number of digital optical images, and is termed “multi-image shape-from-shading” (MI-SFS). The paper contains an explanation of the theory of MI-SFS, followed by a presentation of current results, which were obtained using images from NASA's lunar mission Clementine, and constitute the first practical application with our method using extraterrestrial imagery. The lunar surface is reconstructed under the assumption of different kinds of reflectance models (e.g. Lommel-Seeliger and Lambert). The represented results show that the derivation of a high-resolution DTM of real digital planetary images by means of MI-SFS is feasible. 相似文献
8.
John K. Hillier 《Icarus》1997,130(2):328-335
It has been proposed that composite particles containing internal scatterers may provide the explanation for the fact that most photometric studies of planetary surfaces based on Hapke's model of bidirectional reflectance have found the planetary particles to exhibit moderately backscattering phase functions. However, an implicit assumption made in this explanation is that the scattering by composite particles containing multiple internal inclusions in a planetary surface can still be adequately computed using standard radiative transfer theory assuming the composite particles to be the fundamental individual scatterers even though such particles are necessarily in close proximity to each other. In this paper, this assumption is explored by examining the effects of close packing on the light scattering by spherical particles containing isotropic internal scatterers using a Monte Carlo routine. As expected, classical radiative transfer (assuming a random distribution of scattering particles) coupled with the assumption that the composite particle is the fundamental scatterer provides a good approximation in the high porosity limit. However, even for porosities as high as 90% the effects of close packing are clearly seen with the radiative transfer calculation underestimating the scattering by ∼10% at high incidence, emission, and phase angles. As the porosity is lowered further, the discrepancy becomes more severe and can reach 50% or more. In contrast, assuming the individual scatterer properties in the radiative transfer calculation leads to a substantial overestimate of the scattering even for porosities as low as 27.5%. This suggests that parameters derived using the classical radiative transfer theory will yield results intermediate between those of the composite as a whole and those of the internal scatterers. Thus, one should exercise caution in interpreting the results of models based on classical radiative transfer theory in terms of the physical properties of the surface particles and, where possible, the bidirectional reflectance of densely packed composite particles should be computed using more accurate methods such as the stochastic radiative transfer theory. 相似文献
9.
The results of investigations of the surface relief of Mercury with a classical photometric method are reported. A subject of the photometric method is the intensity of light reflected by the surface of the planet. The main data for the photometric study are the high-resolution images of Mercury received from the MESSENGER space station during its first flyby over Mercury. The images of the surface of Mercury were downloaded from the NASA web-site (http://messenger.jhuapl.edu) and converted to a digital form for photometric measurements. The reflectance characteristics of the surface were calculated according to the model of a three-dimensional scattering phase function (Shevchenko, 1979; 2004a; 2006). From the photometric processing of the space-borne images, the reflectance of four morphologic types of the surface structure of Mercury was determined. With the Hapke model of the bidirectional reflectance (Hapke, 2001), the structural inhomogeneity of the regions of the morphologic forms with centimeter-sized rough-ness was estimated. 相似文献
10.
Since one does not know the photometric functions of various parts of Io, one cannot convert the observed geometric albedo of the satellite to a parameter more directly measurable in the laboratory. One must therefore convert laboratory reflectances to geometric albedos before quantitative comparisons between Io's surface and a laboratory sample are made. This procedure involves determining the wavelength dependence of the sample's photometric function. For substances such as sulfur, whose reflectance varies strongly with wavelength, it is incorrect to assume that the photometric function, and hence the ratio (laboratory reflectance/geometric albedo) is independent of wavelength. To illustrate this point, measurements of the color dependence of this ratio for sulfur are presented for the specific case in which the measured laboratory reflectance is the sample's normal reflectance. In general, unless the laboratory reflectance is precisely the geometric albedo, a wavelength-dependent correction factor must be determined before the laboratory sample can be compared quantitatively with Io's surface. 相似文献
11.
The effects of various types of topography on the shadow-hiding effect and multiple scattering in particulate surfaces are studied. Two bounding cases were examined: (1) the characteristic scale of the topography is much larger than the surface particle size, and (2) the characteristic scale of the topography is comparable to the surface particle size. A Monte Carlo ray-tracing method (i.e., geometric optics approximation) was used to simulate light scattering. The computer modeling shows that rocky topographies generated by randomly distributed stones over a flat surface reveal much steeper phase curves than surface with random topography generated from Gaussian statistics of heights and slopes. This is because rocks may have surface slopes greater than 90°. Consideration of rocky topography is important for interpreting rover observations. We show the roughness parameter in the Hapke model to be slightly underestimated for bright planetary surfaces, as the model neglects multiple scattering on large-scale topographies. The multiple scattering effect also explains the weak spectral dependences of the roughness parameter in Hapke's model found by some authors. Multiple scattering between different parts of a rough surface suppresses the effect of shadowing, thus the effects produced by increases in albedo on the photometric behavior of a surface can be compensated for with the proper decreases in surface roughness. This defines an effective (photometric) roughness for a surface. The interchangeability of albedo and roughness is shown to be possible with fairly high accuracy for large-scale random topography. For planetary surfaces that have a hierarchically arranged large-scale random topography, predictions made with the Hapke model can significantly differ from real values of roughness. Particulate media with surface borders complicated by Gaussian or clumpy random topographies with characteristic scale comparable to the particle size reveal different photometric behaviors in comparison with particulate surfaces that are flat or the scale of their topographies is much larger than the particle size. 相似文献
12.
R.M. Nelson R.H. Brown B.W. Hapke W.D. Smythe L. Kamp M.D. Boryta F. Leader K.H. Baines G. Bellucci J.-P. Bibring B.J. Buratti F. Capaccioni P. Cerroni R.N. Clark M. Combes A. Coradini D.P. Cruikshank P. Drossart V. Formisano R. Jaumann Y. Langevin D.L. Matson T.B. McCord V. Mennella P.D. Nicholson B. Sicardy C. Sotin 《Planetary and Space Science》2006,54(15):1540-1551
The Visual and Infrared Mapping Spectrometer (VIMS) instrument on the Cassini Saturn Orbiter returned spectral imaging data as the spacecraft undertook six close encounters with Titan beginning 7 July, 2004. Three of these flybys each produced overlapping coverage of two distinct regions of Titan's surface. Twenty-four points were selected on approximately opposite hemispheres to serve as photometric controls. Six points were selected in each of four reflectance classes. On one hemisphere each control point was observed at three distinct phase angles. From the derived phase coefficients, preliminary normal reflectances were derived for each reflectance class. The normal reflectance of Titan's surface units at 2.0178 μm ranged from 0.079 to 0.185 for the most absorbing to the most reflective units assuming no contribution from absorbing haze. When a modest haze contribution of τ=0.1 is considered these numbers increase to 0.089–0.215. We find that the lowest three reflectance classes have comparable normal reflectance on either hemisphere. However, for the highest brightness class the normal reflectance is higher on the hemisphere encompassing longitude 14–65° compared to the same high brightness class for the hemisphere encompassing 122–156° longitude. We conclude that an albedo dichotomy observed in continental sized units on Titan is due not only to one unit having more areal coverage of reflective material than the other but the material on the brighter unit is intrinsically more reflective than the most reflective material on the other unit. This suggests that surface renewal processes are more widespread on Titan's more reflective units than on its less reflective units.
We note that one of our photometric control points has increased in reflectance by 12% relative to the surrounding terrain from July of 2004 to April and May of 2005. Possible causes of this effect include atmospheric processes such as ground fog or orographic clouds; the suggestion of active volcanism cannot be ruled out.
Several interesting circular features which resembled impact craters were identified on Titan's surface at the time of the initial Titan flyby in July of 2004. We traced photometric profiles through two of these candidate craters and attempted to fit these profiles to the photometric properties expected from model depressions. We find that the best-fit attempt to model these features as craters requires that they be unrealistically deep, approximately 70 km deep. We conclude that despite their appearance, these circular features are not craters, however, the possibility that they are palimpsests cannot be ruled out.
We used two methods to test for the presence of vast expanses of liquids on Titan's surface that had been suggested to resemble oceans. Specular reflection of sunlight would be indicative of widespread liquids on the surface; we found no evidence of this. A large liquid body should also show uniformity in photometric profile; we found the profiles to be highly variable. The lack of specular reflection and the high photometric variability in the profiles across candidate oceans is inconsistent with the presence of vast expanses of flat-lying liquids on Titan's surface. While liquid accumulation may be present as small, sub-pixel-sized bodies, or in areas of the surface which still remain to be observed by VIMS, the presence of large ocean-sized accumulations of liquids can be ruled out.
The Cassini orbital tour offers the opportunity for VIMS to image the same parts of Titan's surface repeatedly at many different illumination and observation geometries. This creates the possibility of understanding the properties of Titan's atmosphere and haze by iteratively adapting models to create a best fit to the surface reflectance properties. 相似文献
13.
Knut Stamnes 《Planetary and Space Science》1982,30(7):727-732
By appealing to the reciprocity principle simple expressions are derived for the plane albedo and the transmissivity of a vertically inhomogeneous, plane parallel atmosphere. The plane albedo is shown to equal the angular distribution of the reflected intensity for isotropie Illumination of unit intensity incident at the top of the atmosphere, while the transmissivity equals the angular distribution of the transmitted intensity for isotropie illumination of unit Intensity incident at the bottom of the atmosphere. Chandrasekhar's solution of the planetary problem (including a Lambert reflecting lower boundary) in terms of the solution to the standard problem (no reflecting ground) is extended to apply to an inhomogeneous atmosphere resting on a surface that reflects radiation anisotropically but with no dependence on the direction of incidence (anisotropic Lambert reflector). The computational aspects are discussed and a procedure for computing the planetary albedo and transmissivity Is outlined for a vertically inhomogeneous, anisotropically scattering atmosphere overlying a partially reflecting surface. Numerical verification and illustration are also provided and it is shown that the assumed vertical variation of the single scattering albedo strongly affects the plane albedo but only weakly the transmissivity. 相似文献
14.
Sub-pixel slope variations can have significant effects on the intensity of light scattered from a planetary surface. As a result, determination of the surface slope from the apparent brightness of a given pixel can be confounded by uncertainly in such variations. Under a wide range of conditions, the average slope across the pixel may be different from what is inferred by photoclinometry. Because topography is derived from photoclinometry by integrating the slope across an image composed of many pixels, topographic elevation could in principle be distorted considerably by this effect. As actually applied, photoclinometry generally includes strategies designed to mitigate these effects substantially. Nevertheless, the potential always exists for unknown variations in the character of sub-pixel topography (among other uncertainties such as albedo variations) to introduce errors. The results shown here show the importance of the mitigating strategies and of considering the magnitude of uncertainties in determination of topography. 相似文献
15.
A detailed study to evaluate ground-based photographs of Mercury has been carried out. Models of the surface scattering properties have been assumed and smeared with a Gaussian function for direct comparison with center-to-limb scans along Mercury's intensity equator. Data from a range of phase angles from 31° to 92° have been compared with smeared models assuming a Lambert surface, a surface which obeys the Lommel-Seeliger law and one which is Minnaertian, having a variable coefficient. Within the limits of the observations a lunar Minnaert surface yields the most consistent interpretation. An objective evaluation of the resolution of the photographs is obtained in terms of Gaussian half-widths. 相似文献
16.
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
17.
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
18.
Photometric correction is a necessary step in planetary image pre-processing since the images of planetary surfaces are acquired by orbiting spacecraft at various observational geometries. In this study, visible (748 nm) and near-infrared (948 nm) bands of Hyper Spectral Imager (HySI) onboard Chandrayaan-1 have been used to derive a preliminary photometric correction for lunar data. The purpose of the proposed photometric correction for HySI is to convert observations taken at solar incidence (i), sensor emission (e), and the solar phase angles (α) to a fixed geometry by applying i?=?α?=?30° and e?=?0° to each image. The Lommel–Seeliger function was used to model the lunar limb darkening effect, while topography data from the merged Digital Elevation Model of Lunar Reconnaissance Orbiter—Lunar Orbiter Laser Altimeter (LRO-LOLA) and SELENE Terrain Camera (TC) was used to correct local topographic effects. Data from Moon Mineralogy Mapper (M3), SELENE Multiband Imager (MI) and Clementine Ultraviolet and Visible Camera (UV/VIS) were also used to compare radiance, reflectance and phase functions derived from HySI. Our analysis reveals that HySI is darker than M3 primarily due to low surface radiance conditions observed by HySI. The derived phase functions for the two HySI bands indicate a good correlation between the derived reflectance and phase angle as well as with the phase functions derived for the empirically corrected M3 data. This approach led to the derivation of a photometric correction for maria regions. Finally, it is expected that the proposed correction would be applicable to all HySI images covering the lunar mare region.
相似文献19.
Bjarne S. Haugstad 《Icarus》1978,35(3):410-421
Turbulence in planetary atmospheres leads to both fluctuating and systematic errors in atmospheric profiles derived from Doppler measurements during radio occultation. If the upper atmospheres of Venus and Jupiter are about as turbulent as the earth's troposphere, we deduce rms fractional errors in temperature and pressure of less than ～ 10?2 for the Mariner 10 and Pioneer 10/11 occultation experiments. Fractional systematic errors are typically of the order of 10?6. These estimates depende rather weakly on quantities characterizing the atmosphere and the occultation, and it is conjectured that turbulence-induced errors in atmospheric profiles derived from Doppler measurements are always very small in the weak scattering limit 相似文献
20.
V. V. Shevchenko 《Solar System Research》2004,38(6):441-448
The integral photometric properties of Mercury and the Moon were studied, and the similarities in the reflectance characteristics of small surface areas determined by centimeter-sized irregularities were found. The relations obtained were used to pattern the surface of the Hermean soil on a specified scale. In a first approximation, the resulting image shows the character of the photometric relief of Mercury and the fine-grained structure of the surface in a range of phase angles, where the shadow function of centimeter-sized irregularities most affects the brightness of the mantle material. Probable variations of the photometric-relief types were revealed in processing the images selected from a series obtained from the Mariner 10 flyby. According to the data analysis, three main types of photometric relief were distinguished, which correspond to different morphological types of the Hermean surface formations. The relationship between the morphological types and the properties of the surface structure of the Hermean mantle material was revealed via morphological studies.Translated from Astronomicheskii Vestnik, Vol. 38, No. 6, 2004, pp. 504–512.Original Russian Text Copyright © 2004 by Molodensky 相似文献