Photometric Model Research Articles

Decimetre-scaled spectrophotometric properties of the nucleus of comet 67P/Churyumov–Gerasimenko from OSIRIS observations

We present the results of the photometric and spectrophotometric properties of the 67P/Churyumov-Gerasimenko nucleus derived with the OSIRIS instrument during the closest fly-by over the comet, which took place on 14 th February 2015 at a distance of {\~} 6 km from the surface. Several images covering the 0{\deg}-33{\deg} phase angle range were acquired, and the spatial resolution achieved was 11 cm/pxl. The flown-by region is located on the big lobe of the comet, near the borders of the Ash, Apis and Imhotep regions. Our analysis shows that this region features local heterogeneities at the decimetre scale. We observed difference of reflectance up to 40{\%} between bright spots and sombre regions, and spectral slope variations up to 50{\%}. The spectral reddening effect observed globally on the comet surface by Fornasier et al. (2015) is also observed locally on this region, but with a less steep behaviour. We note that numerous metre-sized boulders, which exhibit a smaller opposition effect, also appear spectrally redder than their surroundings. In this region, we found no evidence linking observed bright spots to exposed water-ice-rich material. We fitted our dataset using the Hapke 2008 photometric model. The region overflown is globally as dark as the whole nucleus (geometric albedo of 6.8{\%}) and it has a high porosity value in the uppermost-layers (86{\%}). These results of the photometric analysis at a decimetre scale indicate that the photometric properties of the flown-by region are similar to those previously found for the whole nucleus.

An evaluation of the influence of measurement geometry on the uncertainties of photometric model results based on the laboratory measurements of particulate surfaces

Sunlight reflected by particulate surfaces carries important information about its physical properties. Modeling the reflectance of different types of particulate samples is an attractive field of study, so estimating the favorable measurement geometry for accurate inversion of photometric model parameters is necessary. This research examines the distribution of the bidirectional reflectance factor (BRF) with different particle sizes by multi-angular reflectance. Two types of particulate samples (one with low reflectance and the other with moderate reflectance) with particle sizes of 0.3, 0.45 and 0.9mm were measured over a wide viewing range under the assumption of left-to-right symmetry of the BRF. Based on these measurements, we computed the reflectance of particulate surfaces by a photometric model and analyzed the influence of measurement geometry (different combinations of incident zenith angle, viewing zenith angle and azimuth angle) on the inverted parameters and the results modeled by the best-fit parameters. The results show that by using the measurements in the single azimuth (including the principal plane) to invert the model parameters, the difference between the modeled results and measured results will exceed the reflectance change caused by the samples' particle size; this difference is also found when we used the combined measurements at two different incident zenith angles. Including the measurements in the principal plane, an increase in the number of azimuth angles will improve the match between the modeled results and measurements. Our results also confirm that the single-scattering albedo is the only model parameter that could be empirically used to determine the particle sizes of our samples over a wide range of measurement directions. This study proposes several favorable combinations of measurement geometry and also appears to provide a promising empirical reference for the particulate surfaces similar to ours in future laboratory experiments.

Progress on Research of Lunar Photometric Model

Progress on Research of Lunar Photometric Model

Cooperative photometric redshift estimation

AbstractIn the modern galaxy surveys photometric redshifts play a central role in a broad range of studies, from gravitational lensing and dark matter distribution to galaxy evolution. Using a dataset of ~ 25,000 galaxies from the second data release of the Kilo Degree Survey (KiDS) we obtain photometric redshifts with five different methods: (i) Random forest, (ii) Multi Layer Perceptron with Quasi Newton Algorithm, (iii) Multi Layer Perceptron with an optimization network based on the Levenberg-Marquardt learning rule, (iv) the Bayesian Photometric Redshift model (or BPZ) and (v) a classical SED template fitting procedure (Le Phare). We show how SED fitting techniques could provide useful information on the galaxy spectral type which can be used to improve the capability of machine learning methods constraining systematic errors and reduce the occurrence of catastrophic outliers. We use such classification to train specialized regression estimators, by demonstrating that such hybrid approach, involving SED fitting and machine learning in a single collaborative framework, is capable to improve the overall prediction accuracy of photometric redshifts.

Study of photometric phase curve with new brightness model: refining phase function system parameters of asteroid (107) Camilla

We characterize the morphology of the photometric phase curve model of an asteroid with a three-parameter magnitude phase function H — G1 — G2 system by considering the effect of brightness variation arising from a triaxial ellipsoid representing the asteroid's shape. Applying this new model and a Markov Chain Monte Carlo method, we refine the photometric phase curve of asteroid (107) Camilla and obtain its absolute magnitude H = 7.026−0.054+0.052 mag, and phase function parameters G1 = 0.489−0.044+0.043 and G2 = 0.259−0.023+0.023. Meanwhile, we also determine (107) Camilla's orientation of pole (74.1°−4.5°+4.3°, 50.2°−5.0°+5.4°) with rotational period of 4.843928−0.00001+0.000001 h, and axial ratios a/b = 1.409−0.020+0.020 and b/c = 1.249−0.060+0.063. Furthermore, according to the values of phase function parameters G1 and G2, we infer that asteroid (107) Camilla is an X-type asteroid.

Photometric modelling for laboratory measurements of dark volcanic sand

We have performed laboratory measurements of the bidirectional reflectance factor (BRF) of a sample of dark volcanic sand. The measurements were carried out with three different treatments of the sample to produce different porosity and roughness characteristics. We model the measured BRF with a semi-numerical scattering model for particulate media, meant especially for dark planetary regoliths. We compare the BRF in two different spectral bands, 500–600nm and 800–900nm. The particulate medium (PM) scattering model is found to fit the measured data well, with a phase function representing the differences between the spectral bands. The interpretation of the physical parameters of the PM model is qualitatively sound, but remains somewhat uncertain due in part to the difficulty of characterizing the measured sample.

The XXL Survey

X-ray extragalactic surveys are ideal laboratories for the study of the evolution and clustering of active galactic nuclei (AGN). The XXL Survey spans two fields of a combined 50 $deg^2$ observed for more than 6Ms with XMM-Newton, occupying the parameter space between deep surveys and very wide area surveys; at the same time it benefits from a wealth of ancillary data. This paper marks the first release of the XXL point source catalogue selected in the 2-10 keV energy band with limiting flux $F_{2-10keV}=4.8\cdot10^{-14}\rm{erg\,s^{-1}\,cm^{-2}}$. We use both public and proprietary data sets to identify the counterparts of the X-ray point-like sources and improved upon the photometric redshift determination for AGN by applying a Random Forest classification trained to identify for each object the optimal photometric redshift model library. We also assign a probability to each source to be a star or an outlier. We model with Bayesian analysis the X-ray spectra assuming a power-law model with the presence of an absorbing medium. We find an average unabsorbed photon index of $\Gamma=1.85$ and average hydrogen column density $\log{N_{H}}=21.07 cm^{-2}$. We find no trend of $\Gamma$ or $N_H$ with redshift and a fraction of 26% absorbed sources ($\log N_{H}>22$). We show that the XXL-1000-AGN number counts extended the number counts of the COSMOS survey to higher fluxes and are fully consistent with the Euclidean expectation. We constrain the intrinsic luminosity function of AGN in the 2-10 keV energy band where the unabsorbed X-ray flux is estimated from the X-ray spectral fit up to z=3. Finally, we demonstrate the presence of a supercluster size structure at redshift 0.14, identified by means of percolation analysis of the XXL-1000-AGN sample. The XXL survey, reaching a medium flux limit and covering a wide area is a stepping stone between current deep fields and planned wide area surveys.

Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys

Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometric errors and parameter degeneracies, the redshift and type distributions can be recovered robustly thanks to the hierarchical nature of the model, which is not possible with common photometric redshift estimation techniques. As a result, redshift uncertainties can be fully propagated in cosmological analyses for the first time, fulfilling an essential requirement for the current and future generations of surveys.

Concentrating characteristics of the ellipsoidal concentrator–radiation source system in an optical medium

The features of radiation concentration by an ellipsoidal concentrator are considered for the case in which the concentrator, the radiation source, and the receiver are in the optical medium. Investigations are conducted based on a photometric model that we developed that takes into account the features of the source radiation in the optical medium and change in the radiation indicatrix medium. It is found that, in contrast to direct radiation, in the case of radiation concentration in an optical medium, the irradiance will always increase, since, at the second ellipsoid focus, it increases in proportion to the square of the refractive index of the medium. It is shown that these effects do not depend on the refractive index of the material of the radiation source bulb. Thus, since the radiation source flux is constant both in air and in medium, increasing irradiance leads to a reduction of the source image spot in the medium.

Effects of particle size on bidirectional reflectance factor measurements from particulate surfaces

The bidirectional reflectance factor (BRF) is commonly used to study the structure of a particulate surface based on photometric measurements. In this paper, we describe the bidirectional reflectance factor distribution of natural particulate surfaces with particles sizes varying from 0.15 mm to 0.9 mm. Two types of natural particulate surfaces (one with low reflectance and the other with moderate reflectance) were measured at visible and near-infrared wavelengths using the Northeast Normal University Laboratory Goniospectrometer System (NENULGS). Both the BRFs and anisotropic reflectance factors (ARFs) at selected wavelengths were compared with previously published results to verify the accuracy of our measurements, and we also quantitatively analyzed the effects of particle size on the BRF. It was found that the maximum reflectance difference, which was more distinct for the low-reflectance samples, between particulate surfaces with particle sizes of 0.15 mm and 0.9 mm occurred in the forward scattering direction for all samples, and the value of this maximum difference reached 59% for the low-reflectance samples. Then, we conducted a test of a photometric model to determine which parameters could be confidently linked to the surfaces' reflectance behavior. The inverted parameters were compared with the known physical parameters of our samples, such as the particle size. We found that the single-scattering albedo could be empirically used to determine the particle sizes of our samples when measurements of particulate surfaces with different particle sizes were performed under the same incidence conditions and with wide viewing angles. The potential applications of our results appear very promising for empirically resolving the spatial distribution of particle size within a given particulate sample as well as for deepening our understanding of the scattering properties of particulate media.

Model effectiveness prediction and system adaptation for photometric stereo in murky water

In murky water, the light interaction with the medium particles results in a complex image formation model that is hard to use effectively with a shape estimation framework like Photometric Stereo. All previous approaches have resorted to necessary model simplifications that were though used arbitrarily, without describing how their validity can be estimated in an unknown underwater situation. In this work, we evaluate the effectiveness of such simplified models and we show that this varies strongly with the imaging conditions. For this reason, we propose a novel framework that can predict the effectiveness of a photometric model when the scene is unknown. To achieve this we use a dynamic lighting framework where a robotic platform is able to probe the scene with varying light positions, and the respective change in estimated surface normals serves as a faithful proxy of the true reconstruction error. This creates important benefits over traditional Photometric Stereo frameworks, as our system can adapt some critical factors to an underwater scenario, such as the camera-scene distance and the light position or the photometric model, in order to minimize the reconstruction error. Our work is evaluated through both numerical simulations and real experiments for different distances, underwater visibilities and light source baselines.

Improved calibration of reflectance data from the LRO Lunar Orbiter Laser Altimeter (LOLA) and implications for space weathering

The Lunar Orbiter Laser Altimeter (LOLA) experiment on Lunar Reconnaissance Orbiter (LRO) is a laser altimeter that also measures the strength of the return pulse from the lunar surface. These data have been used to estimate the reflectance of the lunar surface, including regions lacking direct solar illumination. A new calibration of these data is presented that features lower uncertainties overall and more consistent results in the polar regions. We use these data, along with newly available maps of the distribution of lunar maria, also derived from LRO instrument data, to investigate a newly discovered dependence of the albedo of the lunar maria on latitude (Hemingway et al., [2015]). We confirm that there is an increase in albedo with latitude in the lunar maria, and confirm that this variation is not an artifact arising from the distribution of compositions within the lunar maria, using data from the Lunar Prospector Neutron Spectrometer. Radiative transfer modeling of the albedo dependence within the lunar maria is consistent with the very weak to absent dependence of albedo on latitude in the lunar highlands; the lower abundance of the iron source for space weathering products in the lunar highlands weakens the latitude dependence to the extent that it is only weakly detectable in current data. In addition, photometric models and normalization may take into account the fact that the lunar albedo is latitude dependent, but this dependence can cause errors in normalized reflectance of at most 2% for the majority of near-nadir geometries.We also investigate whether the latitude dependent albedo may have obscured detection of small mare deposits at high latitudes. We find that small regions at high latitudes with low roughness similar to the lunar maria are not mare deposits that may have been misclassified owing to high albedos imposed by the latitude dependence. Finally, we suggest that the only modest correlations among space weathering indicators defined for the lunar samples may be due to mixing of soils from distinct latitudes.

Period studies and photometric models for two EB-type binaries EU Hya and AW Vul

New photometry for two Algol-type binaries, EU Hya (P = 0.7782 d) and AW Vul (P = 0.8065 d), was carried out using the 60-cm telescope at Xinglong station of National Astronomical Observatories, Chinese Academy of Sciences. With the updated Wilson-Devinney code, photometric elements were derived from the multi-color light curves. The modeled results indicate that the two systems are near-contact binaries, whose secondary components fill their Roche lobes. The fill-out factors of the primaries are fp = 81.2 (±0.2)% for EU Hya and fp = 82.4 (±0.3)% for AW Vul. Period analysis implies that there exists a downward parabola with a light-time orbit from the (O – C) curve. This kind of periodic oscillation may be attributed to the light-time orbit effect of a third companion. The long-term period decrease may be caused by mass and angular momentum loss. When the orbital period decreases, the fill-out factor of fp will increase. Our results indicate that the primaries will also eventually fill their Roche lobes. EU Hya and AW Vul may possibly evolve from semi-detached binaries into contact ones.

Characterization of a photometric anomaly in lunar Mare Nubium

A novel approach of constructing photometrically seamless mosaics of reflectance, color-ratios, and phase–curve slopes using LROC WAC images has been developed, which can be used to map the photometric parameters of the lunar surface. The approach takes into account both geometric corrections with data on local topography and photometric conjunctions using our simple photometric model. New mosaics obtained with the technique allow more reliable studies of structural and chemical characteristics of the lunar surface. This approach has been applied to analyze the photometric anomaly (21.6S, 17.7W, ~40km in size) in Mare Nubium detected earlier with our Earth-based observations. For each point of the scene the parameters were calculated using the least-square method for several tens of source WAC images. Clementine mosaics also were used in the analysis, e.g., in order to estimate the parameter of maturity degree Is/FeO. The anomaly has low FeO and TiO2 abundance and reveals a higher slope of the phase function than surroundings. Thermal data from LRO Diviner measurements do not show anomalies in this region. We consider this area as a shallow flooding of an elevated formation of highland composition, the material of which could have been excavated and mixed up with upper layers of the lunar surface through meteoroid impacts. The anomalous behavior of the phase function can be explained by the difference of surface structure in the anomaly and surrounding regions on the scale of less than several centimeters. This may be due to larger quantities of small fragments of rocks and clumps on the surface and/or the presence of agglomerates having open structure.

Application of multiple photometric models to disk-resolved measurements of Mercury’s surface: Insights into Mercury’s regolith characteristics

Photometric analyses are used to standardize images obtained at a variety of illumination and viewing conditions to a common geometry for the construction of maps or mosaics and for comparison with spectral measurements acquired in the laboratory. Many models exist that can be used to model photometric behavior. Two of the most commonly use models, those of Hapke and Kaasalainen–Shkuratov, are compared for their ability to standardize MESSENGER images of Mercury. Analysis of the modeling results shows that photometric corrections using the Kaasalainen–Shkuratov model provides significantly less contrast between images acquired at large differences in emission angle. The contrast seen between images acquired at large differences in either incidence and phase angle is smaller with the Hapke model based corrections, but not significantly better than that provided by the Kaasalainen–Shkuratov model. Photometric studies are also used to infer scattering properties of the surface regolith. The quantitative correlation between photometric model parameters and surface properties is questionable, but laboratory studies do indicate general correlations and trends between parameters and sample properties that allow for comparisons between surfaces based on photometric modeling. Based on comparisons with the Moon and several asteroids that have been observed by spacecraft, the photometric analyses presented here are interpreted to indicate that Mercury’s regolith is smoother on micrometer scales and has a narrower particle size distribution with a lower mean particle size than lunar regolith. Grain structures of regolith particles from Mercury are inferred to be different than those of the Moon or those asteroids observed to date. Mercury’s regolith may contain a component compositionally distinct from lunar regolith.

OO Aquilae: a solar-type contact binary with intrinsic light curve changes

New multi-color photometry of the solar-type contact binary OO Aql was obtained in 2012 and 2013, using the 60 cm telescope at Xinglong Station of the National Astronomical Observatories, Chinese Academy of Sciences. From two sets of light curves LC1 and LC2, photometric models were performed by using the 2003 version of the Wilson-Devinney code. The overcontact factor of the binary system was determined to be f = 37.0(±0.5)%. The intrinsic variability of this binary occurs in light maxima and minima, which could result from a possible third component and magnetic activity of the late type components. Based on all available light minimum times, the orbital period may change in a complicated mode, i.e., sudden period jumps or continuous period variations. The period of OO Aql may possibly undergo a secular period decrease with a rate of dP/dt = −3.63(±0.30) × 10−8 d yr−1, superimposed by two possible cyclic variations in the O – C curve. The long-term period decrease may be interpreted as conserved mass transfer from the more massive component to the less massive one. The 21.5-yr oscillation may be attributed to cyclic magnetic activity, and the 69.3-yr one may result from the light-time effect of an unseen tertiary body.

CHARACTERIZATION OF KEPLER-91B AND THE INVESTIGATION OF A POTENTIAL TROJAN COMPANION USING EXONEST

Presented here is an independent re-analysis of the Kepler light curve of Kepler-91 (KIC 8219268). Using the EXONEST software package, which provides both Bayesian parameter estimation and Bayesian model testing, we were able to re-confirm the planetary nature of Kepler-91b. In addition to the primary and secondary eclipses of Kepler-91b, a third dimming event appears to occur approximately $60^o$ away (in phase) from the secondary eclipse, leading to the hypothesis that a Trojan planet may be located at the L4 or L5 Lagrange points. Here, we present a comprehensive investigation of four possibilities to explain the observed dimming event using all available photometric data from the Kepler Space Telescope, recently obtained radial velocity measurements, and N-body simulations. We find that the photometric model describing Kepler-91b and a Trojan planet is highly favored over the model involving Kepler-91b alone. However, it predicts an unphysically high temperature for the Trojan companion, leading to the conclusion that the extra dimming event is likely a false-postive.

A full photometric and geometric model for attached webcam/matte screen devices

We present a thorough photometric and geometric study of the multimedia devices composed of both a matte screen and an attached camera, where it is shown that the light emitted by an image displayed on the monitor can be expressed in closed-form at any point facing the screen, and that the geometric calibration of the camera attached to the screen can be simplified by introducing simple geometric constraints. These theoretical contributions are experimentally validated in a photometric stereo application with extended sources, where a colored scene is reconstructed while watching a collection of graylevel images displayed on the screen, providing a cheap and entertaining way to acquire realistic 3D-representations for, e.g., augmented reality.

Experimental characterization of the opposition surge in fine-grained water–ice and high albedo ice analogs

We measured the bidirectional reflectance in the VIS–NIR spectral range of different surfaces prepared from small-grained spherical water–ice particles over a wide range of incidence and emission geometries, including opposition. We show that coherent backscattering is dominating the opposition effect on fresh sample material, but its contribution decreases when particles become more irregularly shaped and the bulk porosity increases. Strong temporal evolution of the photometric properties of icy samples, caused by particle sintering and resulting in a decrease of backscattering, is shown. The sintering of the ice particles is documented using cryo-SEM micrographs of fresh and evolved samples. To complement the photometric characterization of ices, multiple high albedo laboratory analogs were investigated to study the effects of shape, grain size distribution, wavelength and surface roughness. In addition to the main backscattering peak, the phase curves also display the effect of glory in the case of surfaces of granular surfaces formed by either spherical ice or glass particles. We show that the angular position of the glory can be used to determine accurately the average size of the particles. Reflectance data are fitted by the Hapke photometric model, the Minnaert model and three morphological models. The resulting parameters can be used to reproduce our data and compare them to the results of other laboratory experiments and astronomical observations.

Spectral calibration for deriving surface mineralogy of Asteroid (25143) Itokawa from Hayabusa Near-Infrared Spectrometer (NIRS) data

We present spectral calibration equations for determining mafic silicate composition of near-Earth asteroid (25143) Itokawa from visible/near-infrared (VNIR) spectra (0.85–2.1μm) measured using the Near Infrared Spectrometer (NIRS) on board the Japanese Hayabusa spacecraft. Itokawa was the target of the Hayabusa sample return mission and has a surface composition similar to LL chondrites. Existing laboratory spectral calibrations (e.g., Dunn, T.L. et al. [2010]. Icarus 208, 789–797) use a spectral wavelength range that is wider (0.75–2.5μm) than that of the NIRS instrument (0.85–2.1μm), making them unfit for interpreting the Hayabusa spectral data currently archived in the Planetary Data System (PDS). We used laboratory near-infrared (NIR) reflectance spectra of ordinary chondrites (H, L and LL) from the study of Dunn et al. (Dunn, T.L. et al. [2010]. Icarus 208, 789–797), which we resampled to the NIRS wavelength range. Using spectral parameters extracted from these resampled spectra we established a relationship between band parameters and mafic silicate compositions (olivine and low-Ca pyroxene). We found a correlation >90% between mafic silicate compositions (fayalite and ferrosilite mol.%) estimated by our spectral method, and electron microprobe measured values from Dunn et al. (Dunn, T.L. et al. [2010]. Icarus 208, 789–797). The standard deviation between the measured and estimated values is 1.5 and 1.1mol.% for fayalite and ferrosilite, respectively. To test the validity of the new equations we blind tested them using nine laboratory spectra of L and LL chondrites with well-known compositions. We found that the absolute difference between the measured and computed values is in the range 0.1–1.6mol.%. Our study demonstrates that this new calibration is robust and can be applied to Hayabusa NIRS data despite its limited spectral range (0.85–2.1μm). We applied the equations to a subset of uncalibrated (no photometric corrections) NIRS spectra and we obtained fayalite and ferrosilite values that are consistent with Itokawa having a LL chondrite surface composition. We intend to develop a photometric model to calibrate the NIRS spectra to standard viewing geometry and apply the new equations to create a global mineralogical map of Itokawa.