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Impact expansions and interference patterns in atomic scattering theory for cases of forward scattering, backscatter, inversion problem and screened Coulomb potential approximation
The Hapke (1986) equation is presently fit to ascertain the single-scattering albedo of the icy satellites of Uranus and Neptune and the one-term Henyey-Greenstein particle-phase function g for each of the Middleton and Mungall (1952) goniophotometric data samples. There emerge both very high single-scattering albedos and strongly forward-scattering particle phase functions; while these are in keeping with Mie theory-based theoretical considerations, they contrast with the observed backscattering behavior of icy satellites. It is suggested the icy satellite frost grains are aggregated into particles of complex texture, which produce the unusual backscattering behavior.
Two simple scattering mechanisms are fitted to polarimetric synthetic aperture radar (SAR) observations of forests. The mechanisms are canopy scatter from a reciprocal medium with azimuthal symmetry and a ground scatter term that can represent double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants or Bragg scatter from a moderately rough surface, which is seen through a layer of vertically oriented scatterers. The model is shown to represent the behavior of polarimetric backscatter from a tropical forest and two temperate forest sites by applying it to data from the National Aeronautic and Space Agency/Jet Propulsion Laboratory's Airborne SAR (AIRSAR) system. Scattering contributions from the two basic scattering mechanisms are estimated for clusters of pixels in polarimetric SAR images. The solution involves the estimation of four parameters from four separate equations. This model fit approach is justified as a simplification of more complicated scattering models, which require many inputs to solve the forward scattering problem. The model is used to develop an understanding of the ground-trunk double-bounce scattering that is present in the data, which is seen to vary considerably as a function of incidence angle. Two parameters in the model fit appear to exhibit sensitivity to vegetation canopy structure, which is worth further exploration. Results from the model fit for the ground scattering term are compared with estimates from a forward model and shown to be in good agreement. The behavior of the scattering from the ground-trunk interaction is consistent with the presence of a pseudo-Brewster angle effect for the air-trunk scattering interface. If the Brewster angle is known, it is possible to directly estimate the real part of the dielectric constant of the trunks, a key variable in forward modeling of backscatter from forests. It is also shown how, with a priori knowledge of the forest height, an estimate for the attenuation coefficient of the canopy can be obtained directly from the multi-incidence-angle polarimetric observations. This attenuation coefficient is another key variable in forward models and is generally related to the canopy density.
A knock-on deuteron imager (KoDI) has been implemented to measure the fuel and hotspot asymmetry of cryogenic inertial confinement fusion implosions on OMEGA. Energetic neutrons produced by D–T fusion elastically scatter (“knock on”) deuterons from the fuel layer with a probability that depends on ρR. Deuterons above 10 MeV are produced by near-forward scattering, and imaging them is equivalent to time-integrated neutron imaging of the hotspot. Deuterons below 6 MeV are produced by a combination of side scattering and ranging in the fuel, and encode information about the spatial distribution of the dense fuel. Here, the KoDI instrument consists of a multi-penumbral aperture positioned 10–20 cm from the implosion using a ten-inch manipulator and a detector pack at 350 cm from the implosion to record penumbral images with magnification of up to 35×. Range filters and the intrinsic properties of CR-39 are used to distinguish different charged-particle images by energy along the same line of sight. Image plates fielded behind the CR-39 record a 10 keV x-ray image using the same aperture. A maximum-likelihood reconstruction algorithm has been implemented to infer the source from the projected penumbral images. The effects of scattering and aperture charging on the instrument point-spread function are assessed. Synthetic data are used to validate the reconstruction algorithm and assess an appropriate termination criterion. Significant aperture charging has been observed in the initial experimental dataset, and increases with aperture distance from the implosion, consistent with a simple model of charging by laser-driven EMP.
An apparatus for determining helium to hydrogen ratios in a gaseous sample is presented. The sample is bombarded with alpha particles created by a self contained radioactive source and scattering products falling within a predetermined forward scattering angular range impact a detector assembly. Two detectors are mounted in tandem, the first completely blocking the second with respect to incident scattering products. Alpha particle/hydrogen or alpha particle/helium collisions are identified by whether scattering product impacts occur simultaneously in both detectors or only in the first detector. Relative magnitudes of the two pulses can be used to further discriminate against other effects such as noise and cosmic ray events.
Maps for the prediction of the polarization of light echo arcs are presented. It is noted that the results can be compared with observations in order to test the light-echo model of Katz (1987) and Milgrom (1987) and to determine its parameters. As long as the model assumptions of single scattering and planar geometry remain valid, the polarization is shown to be independent of the geometrical thickness and the optical depth of the dust layer. Cases such as the light source being in the plane of scatterers and arcs consisting of nearly forward scattered light are considered.
Forward scattering and backscattering play an exceptional role in the physics of two-dimensional interacting fermions. In a Fermi liquid, both give rise to a nonanalytic ω 2 ln (ω) form of the fermionic scattering rate at second order in the interaction. Here we argue that higher powers of ln (ω) show up in the backscattering contribution at higher orders. We show that these terms come from “planar” processes, which are effectively one-dimensional. This is explicitly demonstrated by extending a Fermi liquid to the limit of N >> 1 fermionic flavors, when only planar processes survive. We sum the leading logarithms for the case of a two-dimensional Fermi liquid near a nematic transition, and we obtain an expression for the scattering rate at T = 0 to all orders in the interaction. For a repulsive interaction, the resulting rate is logarithmically suppressed, and the result is valid down to ω = 0. For an attractive interaction, the ground state is an s-wave superconductor with a gap Δ 0 . We show that in this case the scattering rate increases as ω is reduced toward Δ 0 . At ω ≥ Δ 0 , the behavior of the scattering rate is rather unconventional as many pairing channels compete near a nematic critical point, and the s-wave wins only by a narrow margin. We take superconductivity into consideration and obtain the scattering rate also at smaller ω ≃ Δ 0 .
Probability distributions of radio interference on forward scatter of radiation by precipitation
A semianalytic Monte Carlo code originally developed for oceanographic calculations (Poole et al., 1981) has been modified for use in studying multiple scattering of space-based lidar. The approach is very similar to that described by Kunkel and Weinman (1976). The trajectory of each photon is followed from the transmitter through multiple scattering until the photon is either scattered backward out of the atmosphere, scattered forward into the ground and absorbed, or scattered out the sides of the cloud. The probability that the photon will return directly to the detector is computed and summed over all significant scattering events within the field of view of the detector. Multiple scattering of the lidar pulse causes an apparent increase in the transmittance of the medium. Multiple scattering effects for space-based lidar are more significant than for ground-based lidar due to the much larger beam diameter in the atmosphere. These larger diameters are due not only to the greater range between the lidar and the scattering volume, but also the need to maintain relatively large beam divergences to satisfy eye safety restrictions on the laser irradiance at the Earth's surface. The simulations presented here are for a wavelength of 1064 nm and the Deirmendjian C1 phase function, which yields an extinction coefficient of 17.259/km. We have looked at two cases: a space-based lidar at 296 km observing a C1 cloud 293 km from the lidar and, for comparison purposes, a ground-based lidar looking at a C1 cloud with a base height of either 2 km or 5 km. The C1 size distribution roughly approximates that of stratocumulus or altocumulus clouds (aufm Kampe and Weickmann, 1957).
Simple approximations, like the Eddington, are often incapable of coping with the highly asymmetric phase functions typical of particulate scattering. A simple yet accurate method called the delta-Eddington approximation is proposed for determining monochromatic radiative fluxes in an absorbing-scattering atmosphere. In this method, the governing phase function is approximated by a Dirac delta function forward scatter peak and a two-term expansion of the phase function. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. The transmission, reflection, and absorption predicted by the delta-Eddington approximation are compared with doubling method calculations for realistic ranges of optical depth, single-scattering albedo, surface albedo, sun angle and asymmetry factor. The approximation is shown to provide an accurate and analytically simple parameterization of radiation to replace the empirism currently encountered in many general circulation and climate models.
Oceanic low level clouds strongly affect the atmospheric radiation budget. Uncertainties in their microphysical properties and cover currently limit the accuracy of climate predictions. Further, studies quantifying the relative importance of aerosol and dynamics on cloud properties in specific meteorological regimes are poorly constrained by observations in the Western North Atlantic boundary layer. Low level clouds were measured during the Aerosol Cloud meTereology Interactions oVer the western ATlantic Experiment (ACTIVATE) campaign in winter and summer 2020. The two NASA LaRC research aircraft HU-25 Falcon and UC-12 B-200 King Air conducted 35 simultaneous flights to investigate aerosol-cloud interactions of maritime clouds and their impact on radiation. Number concentration, liquid water content, ice water content, and particle size distribution in the size range of 3 µm to 1460 µm in diameter were measured with the fast forward scattering cloud probe (FCDP) and 2-dimensional optical array imaging probe (2D-S) onboard the Falcon. Here, we present an overview of late winter (February-March) and late summer (August-September) oceanic cloud properties in the region 65°W to 80°W and 30°N to 40°N. We compare cloud properties in these two seasons and investigate their dependence on meteorological parameters and aerosol abundance. In a case study, we present cloud observations in a cold air outbreak event on 1 March 2020 with a specific focus on mixed-phase clouds.
The absorption coefficients of stratospheric aerosols are measured using a variation on the integrating plate method. The technique is based on the decrease in the transparency of a substrate when an absorbing aerosol is deposited on it. A Lambert scatterer is placed behind the substrate to integrate forward scattered light and minimize the effect of scattering on the measurement. The low pressure in the stratosphere is used for the direct impaction of particles onto a narrow strip of opal glass. The eight samples collected had a median value of 4 x 10 to the -9th m with an uncertainty of + or - 5 x 10 to the -9th m. If this absorption is due to graphitic carbon, then its concentration is estimated at about 0.4 ng/cu m, or about 0.25% of the total aerosol mass concentration. Estimates of the aerosol scattering coefficients based on satellite extinction inversions result in an aerosol single-scattering albedo in the range of 0.96-1.0.
Scattering of plane sound waves by a compressible vortex is investigated by direct computation of the two-dimensional Navier-Stokes equations. Nonreflecting boundary conditions are utilized, and their accuracy is established by comparing results on different sized domains. Scattered waves are directly measured from the computations. The resulting amplitude and directivity pattern of the scattered waves is discussed, and compared to various theoretical predictions. For compact vortices (zero circulation), the scattered waves directly computed are in good agreement with predictions based on an acoustic analogy. Strong scattering at about + or - 30 degrees from the direction of incident wave propagation is observed. Back scattering is an order of magnitude smaller than forward scattering. For vortices with finite circulation refraction of the sound by the mean flow field outside the vortex core is found to be important in determining the amplitude and directivity of the scattered wave field.
Solar phase curves for Rhea are presented using new telescopic opposition data along with Voyager imaging observations. Two viable solutions were found to Hapke's model which was used to describe this phase curve. The porosity derived from the model's opposition parameters show that the optically active portion of Rhea's regolith has a porosity between 80 and 95 percent, which is slightly lower than the porosity seen on Europa and higher than the porosity measured for the Moon using similar methods. The macroscopic roughness is comparable to that measured by Vebiscer and Veverka for Rhea. The single particle scattering functions found in this study are predominantly forward scattering, which contradicts the results of Vebiscer and Veverka.
The Mie formulation for homogeneous spheres is generalized to handle core/shell systems and multiple concentric layers in a manner that exploits an analogy with stratified planar systems, thereby allowing concentric multi-layered structures to be treated as photonic bandgap materials. Representative results from a Mie code employing this analogy demonstrate that photonic bands are present for periodic concentric spheres, though not readily apparent in extinction spectra. Rather, the periodicity simply alters the scattering profile, enhancing the ratio of backscattering to forward scattering inside the bandgap, whereas modification of the interference structure is evident in extinction spectra in accordance with the optical theorem
This talk will focus on photonic bandgaps that arise due to nearly free photon and tight-binding effects in coupled microparticle and ring-resonator systems. The Mie formulation for homogeneous spheres is generalized to handle core/shell systems and multiple concentric layers in a manner that exploits an analogy with stratified planar systems, thereby allowing concentric multi-layered structures to be treated as photonic bandgap (PBG) materials. Representative results from a Mie code employing this analogy demonstrate that photonic bands arising from nearly free photon effects are easily observed in the backscattering, asymmetry parameter, and albedo for periodic quarter-wave concentric layers, though are not readily apparent in extinction spectra. Rather, the periodicity simply alters the scattering profile, enhancing the ratio of backscattering to forward scattering inside the bandgap, in direct analogy with planar quarter-wave multilayers. PBGs arising from tight-binding may also be observed when the layers (or rings) are designed such that the coupling between them is weak. We demonstrate that for a structure consisting of N coupled micro-resonators, the morphology dependent resonances split into N higher-Q modes, in direct analogy with other types of oscillators, and that this splitting ultimately results in PBGs which can lead to enhanced nonlinear optical effects.
New multi-roll coronagraphic images of the HD181327 debris disk obtained using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope reveal the debris ring in its entirety at high signal-to-noise ratio and unprecedented spatial resolution. We present and apply a new multi-roll image processing routine to identify and further remove quasi-static point-spread function-subtraction residuals and quantify systematic uncertainties. We also use a new iterative image deprojection technique to constrain the true disk geometry and aggressively remove any surface brightness asymmetries that can be explained without invoking dust density enhancements/ deficits. The measured empirical scattering phase function for the disk is more forward scattering than previously thought and is not well-fit by a Henyey-Greenstein function. The empirical scattering phase function varies with stellocentric distance, consistent with the expected radiation pressured-induced size segregation exterior to the belt. Within the belt, the empirical scattering phase function contradicts unperturbed debris ring models, suggesting the presence of an unseen planet. The radial profile of the flux density is degenerate with a radially varying scattering phase function; therefore estimates of the ring's true width and edge slope may be highly uncertain.We detect large scale asymmetries in the disk, consistent with either the recent catastrophic disruption of a body with mass greater than 1% the mass of Pluto, or disk warping due to strong interactions with the interstellar medium.
The paper discusses an analytical solution for the nadir radiance as measured from a satellite, based on a simplified single-scattering approximation in which the scattered radiation is not subject to extinction. In the solution, terms can be identified as due to a reflection from the vicinity of the object pixel, and respectively, (1) upward scattering to zenith above the object pixel (cross radiance), and (2) downward scattering from the entire atmosphere to the object pixel (cross irradiance). It is shown that the cross radiance is proportional to the forward scattering optical thickness, as defined, and the cross irradiance to the backscattering optical thickness. In addition, explicit expressions and computer solutions for the cross radiance from annular or from rectangular reflecting areas are presented. It is concluded that the effect depends on the height distribution and on the sharpness of the forward peak of the scattering particles.