Characteristics of Light Scattering at Small Phase Angles by Surfaces Consisting of Spherical Particles

We present the results of measurements of the phase dependences of brightness and of the polarization and depolarization characteristics for surfaces consisting of spherical glass particles in the phase-angle range from 0.1° to 5.0°. The measurements are performed using the laboratory photometer/polarimeter of Kharkov Astronomical Observatory and the photometer of Jet Propulsion Laboratory. An optically thick layer of transparent-glass spheres with mean size of about 57 m and refractive index of 1.44 exhibits a strong opposition effect due to single scattering. The contribution of interparticle scattering is nearly independent of the phase angle. At an angle of 0.4°, the spheres exhibit a glory ring that manifests itself in the phase behavior of all characteristics investigated. Small details are seen on the curves when a monochromatic radiation source is used for measurements. Their occurrence is confirmed by calculations based on the Mie theory. The unusual behavior of the phase dependences of reflectivity, degree of polarization, and color index for layers composed of spherical particles can be used to search for sites of possible deposits of spherical glass (or ice) particles in regoliths of atmosphereless celestial bodies.     

Light Scattering from Regolith: Intensity Versus Particle Size Behavior

Nature of the photometric phase curves of the regolith like surfaces (like those of the asteroids) are believed to be dependent on the single particle characteristics like particle size, shape, composition etc. and physical characteristics of the surface like porosity and roughness. Most of the phase curves have a rapid surge of intensity at small phase angles (typically below 5^°) known as opposition effect, followed by a linear less decreasing trend at larger phase angles. Average intensity of the linear region has been found to be mostly dependent on the average particle size and its composition, in many laboratory observations. Generally, it is difficult to explain the nature of light scattering by an ensemble of irregular shaped inhomogeneous particles with a theoretical model, just by studying the phase curves. In the present work, we have investigated whether the theoretically expected variation of the scattered light intensity (at a given phase angle) with the average particle size of the grains constituting regoliths, for a given material of the particle is in agreement with the experimental results or not? If yes, this can be a simpler but efficient way to study light scattering by regolith like surfaces. For theoretical analysis, Hapke formula has been used with Mie theory for single particle phase function, where we have neglected the influence of porosity and roughness presently. The data are also fitted with an empirical formula. It has been found that this empirical formula may also be used to estimate the unknown average particle size of a real regolith with known composition.     

The phase dependence of brightness and color of the lunar surface: a study based on integral photometric data

A procedure of an a posteriori correction of the available data on the integral photometry of the Moon is described. This procedure reduces the regular errors of the integral phase curves caused by variations of the libration parameters; the effect due to libration can reach 4%. A method allowing the integral measurements of the Moon to be compared correctly with the photometric measurements of the lunar areas or laboratory samples imitating the lunar soil has been developed. To approximate the phase curves of integral albedo in the phase-angle range from 6° to 120°, we proposed a simple empirical formula A _eq(α) = m _l e ^?ρα + m ₂ e ^?0.7α, where α is the phase angle, ρ is the factor of effective roughness, and m ₁ + m ₂ is the surface albedo at a zero phase angle. An empirical phase dependence of the slope of the lunar spectrum in the 360–1060 nm range has been obtained. The results may be used to test various theoretical models of the light scattering by the lunar surface and to calibrate the data of ground-based and space-borne spectrophotometric observations.     

When are spectral reflectance curves comparable?

Spectral reflectance curves of flat laboratory samples of the carbonaceous chondrite Allende, a basalt, and the ordinary chondrite Bruderheim measured in a bidirectional geometry are shown to differ from those measured using an integrating sphere. In general, reflectance curves obtained by the bidirectional method are redder than those obtained with an integrating sphere. The degree of difference increases with increasing absolute reflectance. When spectral reflectance curves obtained by the two methods are compared to the reflectance curves expected for spherical and aspherical planets covered with the same materials, it is found that in general the integrating sphere measurements provide a better match to a planet at small phase angles. As the phase angle increases, bidirectional reflectance curves provide a closer match.     

A laboratory study of the bidirectional reflectance from particulate samples

The Hapke (Hapke, B. [1981]. J. Geophys. Res. 86, 3039-3054) photometric model and its modifications are widely used to characterize telescopic, spacecraft, and laboratory observations of the bidirectional reflectance of particulate surfaces. Following work and methods laid out in a companion paper (Helfenstein, P., Shepard, M.K. [2011]. Icarus, in press), we deconstruct the Hapke model and, separating all empirical and ad hoc parameters (opposition surge, particle phase function, surface roughness), combine them into a single parameter called the surface phase function, F(α). We illustrate how to extract this function from scattering data sets acquired with the Bloomsburg University Goniometer (BUG). We show how this method can be used to rapidly and accurately characterize bidirectional reflectance data sets from laboratory and spacecraft measurements, often giving better fits to the data. We examine samples with strong color contrasts in different wavelengths. This allows us to examine the exact same surface, changing only the albedo to investigate how the amplitude and the detailed shape of the surface phase function might systematically depend on wavelength and albedo. We also examine the changes in scattering behavior that result when samples are compacted and find the surface phase function and single scattering albedo to be significantly changed. We suggest that these observations support the hypothesis that much of the scattering behavior attributed to the single particle phase function is instead cause by the surface micro-structure.     

The opposition effect in the outer Solar system: A comparative study of the phase function morphology

In this paper, we characterize the morphology of the disk-integrated phase functions of satellites and rings around the giant planets of our solar system. We find that the shape of the phase function is accurately represented by a logarithmic model [Bobrov, M.S., 1970. Physical properties of Saturn's rings. In: Dollfus, A. (Ed.), Surfaces and Interiors of Planets and Satellites. Academic, New York, pp. 376-461]. For practical purposes, we also parametrize the phase curves by a linear-exponential model [Kaasalainen, S., Muinonen, K., Piironen, J., 2001. Comparative study on opposition effect of icy solar system objects. Journal of Quantitative Spectroscopy and Radiative Transfer 70, 529-543] and a simple linear-by-parts model [Lumme, K., Irvine, W.M., 1976. Photometry of Saturn's rings. Astronomical Journal 81, 865-893], which provides three morphological parameters: the amplitude A and the half-width at half-maximum (HWHM) of the opposition surge, and the slope S of the linear part of the phase function at larger phase angles.Our analysis demonstrates that all of these morphological parameters are correlated with the single-scattering albedos of the surfaces.By taking more accurately into consideration the finite angular size of the Sun, we find that the Galilean, Saturnian, Uranian and Neptunian satellites have similar HWHMs (?0.5^°), whereas they have a wide range of amplitudes A. The Moon has the largest HWHM (∼2^°). We interpret that as a consequence of the “solar size bias”, via the finite angular size of the Sun which varies dramatically from the Earth to Neptune. By applying a new method that attempts to morphologically deconvolve the phase function to the solar angular size, we find that icy and young surfaces, with active resurfacing, have the smallest values of A and HWHM, whereas dark objects (and perhaps older surfaces) such as the Moon, Nereid and Saturn's C ring have the largest A and HWHM.Comparison between multiple objects also shows that solar system objects belonging to the same planet have comparable opposition surges. This can be interpreted as a “planetary environmental effect” that acts to locally modify the regolith and the surface properties of objects which are in the same environment.     

Light Scattering by Dust Under Microgravity Conditions

Most of our knowledge on heterogeneous media in the Universe comes from the light they scatter. This light is mainly linearly polarized, and the polarization phase curves contain information about the properties of the scattering dust. In the solar system, the dust seems to be made of irregular aggregates with a size greater than a few microns and a fractal structure. Many constraints appear in the scattering computations, due to the trickiness of the mathematical calculations, and to our ignorance of the precise structure of the dust. This leads to the necessity to perform light scattering measurements on characteristic aggregates, built under low velocity ballistic collisions. Microgravity is a sensible way to achieve such measurements on a cloud of levitating and aggregating dust particles. A first step has been the PROGRA² experiment, which operates during parabolic flights on an aircraft. The instrument is a polar nephelometer measuring successively the light scattered by a dust sample at various angles; it is fully operational, and will provide a data base of polarization phase curves. A second step is the CODAG-SR experiment, which uses the duration of a rocket flight to build up dust aggregates. The instrument measures simultaneously the light scattered at numerous phase angles; it is now space qualified, and should provide in a near future a monitoring of the intensity and polarization phase curves while the aggregation processes are taking place. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scattering in the atmosphere of Venus: III. Line profiles and phase curves for Rayleigh scattering

Spectral line profiles, curves of growth, and curves for the equivalent width of a line as a function of Venus phase angle have been computed for a Rayleigh scattering cloud and compared with those for a cloud of isotropic scatterers. The results are very similar for the two kinds of scattering, with the exception of the curves of equivalent width as a function of Venus phase angle. These latter curves exhibit the “inverse phase effect” and rule out the possibility that the scale height of the clouds can be much less than half the scale height of the gas. The optical depth of the clouds, τ_c, is approximately 100.     

A Monte Carlo Code to Compute Energy Fluxes in Cometary Nuclei

A Monte Carlo model designed to compute both the input and output radiation fields from spherical-shell cometary atmospheres has been developed. The code is an improved version of that by H. Salo (1988, Icarus76, 253-269); it includes the computation of the full Stokes vector and can compute both the input fluxes impinging on the nucleus surface and the output radiation. This will have specific applications for the near-nucleus photometry, polarimetry, and imaging data collection planned in the near future from space probes. After carrying out some validation tests of the code, we consider here the effects of including the full 4×4 scattering matrix in the calculations of the radiative flux impinging on cometary nuclei. As input to the code we used realistic phase matrices derived by fitting the observed behavior of the linear polarization as a function of phase angle. The observed single scattering linear polarization phase curves of comets are fairly well represented by a mixture of magnesium-rich olivine particles and small carbonaceous particles. The input matrix of the code is thus given by the phase matrix for olivine as obtained in the laboratory plus a variable scattering fraction phase matrix for absorbing carbonaceous particles. These fractions are 3.5% for Comet Halley and 6% for Comet Hale-Bopp, the comet with the highest percentage of all those observed.The errors in the total input flux impinging on the nucleus surface caused by neglecting polarization are found to be within 10% for the full range of solar zenith angles. Additional tests on the resulting linear polarization of the light emerging from cometary nuclei in near-nucleus observation conditions at a variety of coma optical thicknesses show that the polarization phase curves do not experience any significant changes for optical thicknesses τ?0.25 and Halley-like surface albedo, except near 90° phase angle.     

A photometric investigation of the packing state of apollo 11 lunar regolith samples

The angular light scattering properties of an Apollo 11 lunar regolith ‘fines’ sample have been determined experimentally for both flat and undulating sample surface preparations. The light scattering curves, whose shapes are known to be a function of the porosity and slope distribution of the measured surface, have been compared with corresponding Earth-based lunar measurements. The comparison method involves the numerical fitting of theoretical photometric functions to both the astronomical and laboratory data.It is deduced that regolith material can, under favourable circumstances, maintain a very underdense structure (porosity of the surface layer greater than 90 per cent) in air, so that vacuum cold-welding is not essential in the formation of such a structure. Photometric scanning is shown to provide a rapid method of determining the effective porosity of regolith sample surfaces in the laboratory.     

Theoretical polarimetric responses of fractal aggregates,in relation with experimental studies of dust in the solar system

Dust particles in the solar system (e.g. atmospheric hazes, cometary or interplanetary dust, regolith) are likely to be irregular aggregates whose light scattering properties (phase functions of polarization) are drastically different from those of Mie spheres. However, the observation of the light they scatter may provide informations on their physical properties. If the mechanisms which lead to aggregation are invariant with time, the aggregates are likely to be fractal particles made up from individual monomers. Computations, developped in relation with the CODAG experiment, are performed using a Discrete Dipole Approximation, and each monomer is described by one or more dipoles. When the particles are formed from a few monomers made up of numerous dipoles, the polarimetric response of the aggregate is similar to the one of the constituent monomer. When the particles are formed from many monomers made up of individual dipoles, the phase curves are similar to those observed in the solar system. Our calculations suggest that dust particles have a fractal dimension of the order of 2 (Ballistic Cluster-Cluster Aggregation), and that the values of the real and imaginary part of the complex refractive index of the constituent material are high. Those results are in agreement with laboratory measurements on samples representative of astronomical organics and minerals.     

Characterization of terrestrial exoplanets based on the phase curves and albedos of Mercury, Venus and Mars

The empirically derived phase curves of terrestrial planets strongly distinguish between airless Mercury, cloud-covered Venus, and the intermediate case of Mars. The function for Mercury is steeply peaked near phase angle zero due to powerful backscattering from its surface, while that for Venus has 100 times less contrast and exhibits a brightness excess near 170° due to Mie scattering from droplets in the atmosphere. The phase curve of Mars falls between those of Mercury and Venus, and there are variations in luminosity due to the planet’s rotation, seasons, and atmospheric states. The phase function and geometric albedo of the Earth are estimated from published albedos values. The curves for Mercury, Venus and Mars are compared to that of the Earth as well as theoretical phase functions for giant planets. The parameters of these different phase functions can be used to characterize exoplanets.     

The SMART-1 AMIE experiment: implication to the lunar opposition effect

The lunar surface reveals a sharp opposition effect, which is to be explained by the shadowing and coherent backscattering mechanisms. Generalizing the radiative transfer theory via Monte Carlo methods, we are carrying out studies of backscattering in regolith-like scattering media. We have also started systematic laboratory measurements of structural simulators of lunar regolith. The SMART-1 AMIE and D-CIXS/XSM experiments provide us a unique opportunity for a simultaneous multiwavelength study of the lunar regolith close to opposition, since the SMART-1 spacecraft will pass over several different types of lunar surface at zero phase angles. Results of our theoretical and laboratory investigations can be used as a basis to interpret the SMART-1 AMIE and D-CIXS/XSM experiments. In particular, it seems to be possible to estimate regional variations of regolith particle volume fraction and their size. A short review of observational, experimental and theoretical works is also presented here.     

Light scattering by fluffy Mg-Fe-SiO and C mixtures as cometary analogs (PROGRA experiment)

Cometary particles mainly consist of silicates and carbon compounds; they seem to be fluffy aggregates of tiny grains, as found in some IDPs. The linear polarization of the scattered light is an efficient method to characterize their physical properties. Laboratory simulations of light scattering by cometary analog particles help to disentangle different physical parameters by comparison with observational data. We present here polarization laboratory results with nine samples levitating particles: five samples of vapor-condensed magnesiosilica, one ferrosilica smoke, a mixture of magnesio-ferrosilica smokes, one mixture of ferrosilica with carbon and one mixture of magnesio-ferrosilica with carbon. The phase curves are bell-shaped with a maximum polarization at a phase range of (80°-100°). A shallow negative branch can be present at phase angles smaller than 20°. The different characteristics of the phase curves are discussed considering the size and the structure of the constituent grains and the size of the particles. For the five magnesiosilica samples, the maximum in polarization is in the 40% range (close to cometary values), and no wavelength dependence is detected; the negative branch, whose presence seems to be linked to the presence of large aggregates of fine silica (SiO₂) grains, does not always exist. For the ferrosilica smoke, the maximum in polarization is about 30% in red light (632.8 nm) and 40% in green light (543.5 nm); the negative branch occurs for phase angles smaller than 20°. For the two mixtures with carbon black, the polarization spectral gradient is positive, as expected for cometary analog particles. Finally, the phase curves obtained for agglomerates of magnesio-ferrosilica and carbon (expected to be the main components of cometary particles) are comparable to those obtained by remote observations of dust in cometary comae.     

Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan's atmosphere

New low-temperature methane absorption coefficients pertinent to the Titan environment are presented as derived from the Huygens DISR spectral measurements combined with the in-situ measurements of the methane gas abundance profile measured by the Huygens Gas Chromatograph/Mass Spectrometer (GCMS). The visible and near-infrared spectrometers of the descent imager/spectral radiometer (DISR) instrument on the Huygens probe looked upward and downward covering wavelengths from 480 to 1620 nm at altitudes from 150 km to the surface during the descent to Titan's surface. The measurements at continuum wavelengths were used to determine the vertical distribution, single-scattering albedos, and phase functions of the aerosols. The gas chromatograph/mass spectrometer (GCMS) instrument on the probe measured the methane mixing ratio throughout the descent. The DISR measurements are the first direct measurements of the absorbing properties of methane gas made in the atmosphere of Titan at the pathlengths, pressures, and temperatures that occur there. Here we use the DISR spectral measurements to determine the relative methane absorptions at different wavelengths along the path from the probe to the sun throughout the descent. These transmissions as functions of methane path length are fit by exponential sums and used in a haze radiative transfer model to compare the results to the spectra measured by DISR. We also compare the recent laboratory measurements of methane absorption at low temperatures [Irwin et al., 2006. Improved near-infrared methane band models and k-distribution parameters from 2000 to 9500 cm⁻¹ and implications for interpretation of outer planet spectra. Icarus 181, 309-319] with the DISR measurements. We find that the strong bands formed at low pressures on Titan act as if they have roughly half the absorption predicted by the laboratory measurements, while the weak absorption regions absorb considerably more than suggested by some extrapolations of warm measurements to the cold Titan temperatures. We give factors as a function of wavelength that can be used with the published methane coefficients between 830 and 1620 nm to give agreement with the DISR measurements. We also give exponential sum coefficients for methane absorptions that fit the DISR observations. We find the DISR observations of the weaker methane bands shortward of 830 nm agree with the methane coefficients given by Karkoschka [1994. Spectrophotometry of the jovian planets and Titan at 300- to 1000-nm wavelength: the methane spectrum. Icarus 111, 174-192]. Finally, we discuss the implications of our results for computations of methane absorption in the atmospheres of the outer planets.     

The composition of liquid methane-nitrogen aerosols in Titan’s lower atmosphere from Monte Carlo simulations

Molecular level Monte Carlo simulations have been performed with various model potentials for the CH₄-N₂ vapor-liquid equilibrium at conditions prevalent in the atmosphere of Saturn’s moon Titan. With a single potential parameter adjustment to reproduce the vapor-liquid equilibrium at a higher temperature, Monte Carlo simulations are in excellent agreement with available laboratory measurements. The results demonstrate the ability of simple pair potential models to describe phase equilibria with the requisite accuracy for atmospheric modeling, while keeping the number of adjustable parameters at a minimum. This allows for stable extrapolation beyond the range of available laboratory measurements into the supercooled region of the phase diagram, so that Monte Carlo simulations can serve as a reference to validate phenomenological models commonly used in atmospheric modeling. This is most important when the relevant region of the phase diagram lies outside the range of laboratory measurements as in the case of Titan. The present Monte Carlo simulations confirm the validity of phenomenological thermodynamic equations of state specifically designed for application to Titan. The validity extends well into the supercooled region of the phase diagram. The possible range of saturation levels of Titan’s troposphere above altitudes of 7 km is found to be completely determined by the remaining uncertainty of the most recent revision of the Cassini-Huygens data, yielding a saturation of 100 ± 6% with respect to CH₄-N₂ condensation up to an altitude of about 20 km.     

基于精密光程差调制的时域干涉信号闭合相位检测方法研究

闭合相位法是实现长基线恒星光干涉高分辨成像的重要技术手段之一,获得精确的闭合相位信息是进行光干涉图像重构的先决条件.提出一种基于精密光程差调制的时域干涉信号闭合相位检测方法,在3路干涉臂上进行非冗余精密光程调制,并通过多次干涉测量结合数据拟合的方法消除光程差调制中存在的正弦误差,使得光程调制的精度达到20 nm以内.引入高速探测器件提升时域干涉信号的采样频率,对探测器上获得的时域干涉信号进行傅立叶变换处理,获得3路干涉臂精确的闭合相位信息.室内实验结果表明,基于精密光程调制的时域信号闭合相位计算精度可以达到1/50波长以内.     

Peculiar shapes of asteroids: Implications for light curves and periods of rotation

This paper presents some simple geometrical models of asteroids with theoretical light curves similar to the observed ones. In some cases the results suggest rotation periods to be double those one can obtain adopting two- or three-axial ellipsoids as models.A possible model, not in terms of a binary system, for asteroids with light curves like those of eclipsing binary stars, is also given.It should be stressed that the models studied in this paper are probably not very similar to real asteroids, but the principal conclusions should not be changed when more sophisticated models are considered.The work is to be a starting point for future researches on laboratory models of asteroids, in order to define, in a quantitative way, how the light curves are affected by the surface roughness and/or the large scale irregularities of the shape of an asteroid.     

High-order expansion of the solution of preliminary orbit determination problem

A method for high-order treatment of uncertainties in preliminary orbit determination is presented. The observations consist in three couples of topocentric right ascensions and declinations at three observation epochs. The goal of preliminary orbit determination is to compute a trajectory that fits with the observations in two-body dynamics. The uncertainties of the observations are usually mapped to the phase space only when additional observations are available and a least squares fitting problem is set up. A method based on Taylor differential algebra for the analytical treatment of observation uncertainties is implemented. Taylor differential algebra allows for the efficient computation of the arbitrary order Taylor expansion of a sufficiently continuous multivariate function. This enables the mapping of the uncertainties from the observation space to the phase space as high-order multivariate Taylor polynomials. These maps can then be propagated forward in time to predict the observable set at successive epochs. This method can be suitably used to recover newly discovered objects when a scarce number of measurements is available. Simulated topocentric observations of asteroids on realistic orbits are used to assess the performances of the method.     

Possible application of circular polarization for remote sensing of cosmic bodies

Phase dependences of circular polarization were obtained with a precision Stokes polarimeter designed and constructed at the Main Astronomical Observatory of AS Ukraine. A study was made of dielectric and metallic powders with grains of diameter 10–100 m. Metallic powders were found to produce an essential circular polarization - up to 3%, just as dielectric powders did not show circular polarization values more than 0.05% Change of circular polarization with phase angle V is greatly depended on surface structure. Loose powders give phase curves with the same sign of circular polarization everywhere and with maximum at large phase angles V > 120 . Measurements of compacted powders show curves which change the sign repeatedly and have additional maxima, including a maximum at small phase angles V < 40 . A theory was created which considers a circular polarization as a result of multiple reflections of light from particulate surface. The theory provides reasonable good fit to the experimental data. It was concluded that measurements of circular polarization can be used to find metals in surface material of cosmic bodies (especially asteroids) and to determine characteristics of surface structure, in particular, to establish presence of regolith on metal-rich bodies.