Coherent Backscatter Enhancement Research Articles

Quantifying the coherent backscatter enhancement of non-spherical particles with discrete dipole approximation.

The prevailing backscattering peak associated with the scattering phase function of large non-absorptive particles can be interpreted with the coherent backscatter enhancement (CBE) theory, but has not been explicitly quantified with numerical simulations based on solving Maxwell's equations. In this paper, representative numerical simulations performed with the discrete-dipole-approximation (DDA) model are used to quantify the effect of CBE on the single-scattering phase function. For each scattering case, the particle volume was divided into multiple thin slices parallel to the incident beam. The dipole polarizations in the j'th slice in response to the incident field of the i'th slice were computed, and then the corresponding contribution to the scattering phase function was calculated. Interference between conjugate terms representing reversible wave paths is constructive at the backscattering direction, which corresponds to the CBE. Subsequently, the contribution of CBE to the scattering phase function was quantified by comparing the electric fields calculated with and without the interference between conjugate terms. Results from these numerical simulations are consistent with conclusions obtained from the CBE theory. The simulations also quantitatively explain why it is difficult to identify a CBE-induced backscattering peak for the phase function of small particles and strong-absorptive particles.

Coherent backscatter enhancement in bistatic Ku- and X-band radar observations of dry snow

Abstract. The coherent backscatter opposition effect (CBOE) enhances the backscatter intensity of electromagnetic waves by up to a factor of 2 in a very narrow cone around the direct return direction when multiple scattering occurs in a weakly absorbing, disordered medium. So far, this effect has not been investigated in terrestrial snow in the microwave spectrum. It has also received little attention in scattering models. We present the first characterization of the CBOE in dry snow using ground-based and spaceborne bistatic radar systems. For a seasonal snowpack in the Ku-band (17.2 GHz), we found backscatter enhancement of 50 %–60 % (+1.8–2.0 dB) at a zero bistatic angle and a peak half-width at half-maximum (HWHM) of 0.25∘. In the X-band (9.65 GHz), we found backscatter enhancement of at least 35 % (+1.3 dB) and an estimated HWHM of 0.12∘ in the accumulation areas of glaciers in the Jungfrau–Aletsch region, Switzerland. Sampling of the peak shape at different bistatic angles allows estimating the scattering and absorption mean free paths, ΛT and ΛA. In the VV polarization, we obtained ΛT=0.4±0.1 m and ΛA=19±12 m at the Ku-band and ΛT=2.1±0.4 m and ΛA=21.8±2.7 m at the X-band, assuming an optically thick medium. The HH polarization yielded similar results. The observed backscatter enhancement is thus significant enough to require consideration in backscatter models describing monostatic and bistatic radar experiments. Enhanced backscattering beyond the Earth, on the surface of solar system bodies, has been interpreted as being caused by the presence of water ice. In agreement with this interpretation, our results confirm the presence of the CBOE at X- and Ku-band frequencies in terrestrial snow.

Coherent backscatter enhancement in single scattering.

Solution of Maxwell's equations to the problem of single scattering can be expanded into iterative series in an order-of-scattering form, where the interference between conjugate terms representing reversible sequences of elementary scatterers is constructive at the backscattering direction, resulting in a coherent backscatter enhancement (CBE). The backscattering phase function of randomly oriented particles is amplified by CBE with an amplification factor between 1 and 2 depending on particle habit and refractive index. The angular width of the CBE-induced backscattering peak line for a specific particle habit is inversely proportional to the particle size parameter. The CBE-induced backscattering peak has been identified in the scattering phase function of a wide range of randomly oriented particles, including non-absorptive spheres, spheroids, and hexagonal particles.

Far-field coherent backscatter enhancement from random aggregations of scatterers and comparisons to backscattering from single isolated spheres.

Coherent backscatter enhancement (CBE), a multiple scattering phenomenon, may cause an enhancement of up to a factor of two in the average intensity backscattered from a random aggregation of scatterers. In the ocean, CBE may occur when a fish school or a bubble cloud is remotely illuminated. The research reported here explored the possibility that CBE might be used to remotely discriminate between an aggregation of many scatterers and a single isolated scattering object. For this investigation, the far-field harmonic acoustic pressure backscattered from aggregations of randomly placed omnidirectional point scatterers was determined from numerical solution of the equations from Foldy [(1945) Phys. Rev. 67(3,4), 107-119], and compared to equivalent results from single spherical scatterers having hard surfaces, pressure-release surfaces, or aggregation-matched effective-medium properties. Interestingly, CBE causes a spherical aggregation to backscatter as much or more sound than a single perfectly reflecting sphere of the same size when (ka)1/2(ks)-4/5(kσs1/2)3/4 ≥ 2.3, where k is the acoustic wave number, a is the aggregation radius, s is the average spacing between scatterers, and σs is a scatterer's cross section. And, backscattered intensity samples (in dB) from all simulated aggregations followed an extreme value distribution, a finding that supports the conventional use of backscatter statistics for remote aggregation-versus-single-object discrimination.

Comparisons between a spherical aggregation of scatterers, and hard and soft spheres using single-frequency and pulsed signals

When sound is projected into the ocean, the backscattered signal may provide information about the object(s) from which the sound has scattered. When the backscattered sound comes from an aggregation of strong scatterers, such as a school of fish at their swim-bladder resonance frequency, a phenomenon called Coherent Backscatter Enhancement (CBE) may occur, and this phenomenon could aid in discriminating fish schools from other similar-strength scatterers in the ocean water column. When CBE occurs, the addition of in-phase scattered waves from propagation path pairs produces a scattered field intensity enhancement of as much as two in the direction opposite to that of the incident wave. This presentation describes the results of CBE simulations of spherical aggregations of scatterers based on the Foldy (1945) equations, and provides comparisons to backscattering from single perfectly reflecting spheres. Interestingly, a spherical aggregation of 4200 strong scatterers with wave number scaled radius ka = 32...

Simulating acoustic coherent backscattering enhancement from random aggregations of omnidirectional scatterers.

Coherent backscatter enhancement (CBE) is a multiple scattering phenomenon that can lead to a doubling of the backscattered field intensity from a random aggregation of scatterers. It may be useful for remote sensing of scatterer aggregations, such as fish schools. This paper presents simulations of acoustic CBE from randomly placed omnidirectional point scatterers based on Foldy's field equations. The simulations are verified and validated through comparisons with Bragg scattering and Foldy's effective-medium theory, assessments of acoustic energy conservation, and comparisons with prior optical and acoustical CBE results. To make CBE comparisons with prior optics results, a CBE coherence function was postulated to account for resolution differences between the optics and simulation studies. For the higher-resolution optics studies, the postulated coherence function yields a CBE of 1.68, which matches optical CBE measurements. For the lower-resolution simulations, the same coherence function yields a CBE of 1.034, which agrees with appropriately extrapolated CBE simulation results, 1.030 ± 0.005. Assuming comparable resolution, the acoustics experiment and simulations both produce a CBE of approximately 1.5. The CBE peak is found to increase approximately monotonically with (k(2)σs)(1/4)(ks)(-1), where k is the wave number, s is the average spacing between scatterers, and σs is a scatterer's cross section.

Comparison of near-field acoustic coherent backscattering simulations with optics theory and experiments

Remote discrimination of fish schools from other scatterers in the water column is important for environmental awareness and monitoring, and for a variety of sonar applications. Depending on the school's geometry and number of fish, and the fish's scattering characteristics, there may be preferential backscatter of sound, a phenomenon known as coherent backscatter enhancement (CBE). Thus, the presence and characteristics of CBE could help in discriminating fish schools from other objects. For CBE, the addition of in-phase scattered waves from the propagation path pairs yields a scattered intensity enhancement of a factor of two in the direction opposite to that of the incident wave. However, prior simulations based on the Foldy (1945) equations have suggested the enhancement may be greater than a factor of two for relatively large closely spaced scatterers. This presentation re-examines this topic and provides new CBE simulation results for near field scattering from finite-sized aggregations of point scatterers. Comparisons are made with equivalent results from the optics experiments of Wolf and Maret (1985) and the theory of Akkermans et al. (1986). Extension of this effort to comparisons of CBE from single frequency and broadband pulse illumination is anticipated. [Sponsored by the Office of Naval Research.]

Simulating coherent backscatter enhancement from aggregations of underwater scatterers

Remote classification of scatterers is an enduring priority in active sonar applications. For aggregations of marine life, typically schools or shoals of fish, remote classification may be possible when there is coherent backscattering enhancement (CBE) from the aggregation. CBE is a multiple scattering phenomenon that occurs in optics and acoustics when wave propagation paths within the aggregation are likely to be traversed in both directions. For a plane wave illuminating a half-space of randomly-placed, omnidirectional scatterers, CBE may lead to a doubling of the scattered field intensity in the direction opposite that of the incident wave (Akkermans et al. 1986). This presentation describes acoustic CBE simulations for finite-size spherical aggregations of point scatterers. The results are developed from the classical multiple-scattering equations of Foldy (1945), and are checked to ensure appropriate rotational symmetries and acoustic energy conservation when scatterer locations are random and when they are structured. Variations in the magnitude of the CBE peak and its angular width are presented for different frequencies, aggregation sizes, scatterer densities, and scatterer properties. Extension of these results to sonar-pulse scattering from schools of fish will be discussed. [Supported by the Office of Naval Research.]

Calculations of coherent backscatter enhancement from aggregations of underwater scatterers

Coherent backscattering enhancement (CBE) is a multiple scattering phenomenon that occurs in optics and acoustics. For plane wave illumination of an aggregation of randomly placed omni-directional scatterers, CBE may lead to as much as a doubling of the scattered field intensity in the direction opposite that of the incident wave. This presentation compares different calculation techniques for CBE for plane-wave harmonic incident sound fields scattered from N underwater bubbles. The first calculation technique is based on the classical field theory of Foldy (1945) for point scatterers and is equivalent to a boundary-element calculation that uses one element per scatterer and requires inversion of a fully populated N × N matrix. The second calculation is based on the finite element method and involves inversion of a larger but more sparsely populated matrix, but it allows for the possibility of greater scatterer complexity. Results from both approaches are compared and contrasted for idealized underwater remote sensing scenarios involving different incident-wave frequencies, scatterer cross sections, and ranges from the scatterer aggregation to the receiving array. The eventual goal of this effort is to understand and predict CBE from fish schools. [Work supported by the Office of Naval Research.]

Light backscatter by surfaces composed of small spherical particles

We present measurements of phase angle curves of intensity and degree of linear polarization of powdery surfaces at two spectral bands centered near 0.44 and 0.63 microm. Three powder samples consisting of nonabsorbing spherical particles of sizes comparable with the wavelengths 0.5, 1.0, and 1.5 microm were examined. The particulate surfaces were measured in the phase angle range of 0.2 degrees-50 degrees by two different photometers and/or polarimeters. At small phase angles, powdery samples consisting of spherical particles (having very high albedo that resulted in significant multiple scattering) showed prominent features that corresponded to single-particle scattering. These features became more prominent after compressing the surfaces when we changed the packing density of the powders from 0.29 to 0.48. Noticeable differences were observed between polarimetric curves corresponding to different wavelengths. All the samples demonstrated prominent opposition intensity spikes at phase angles <2 degrees likely caused by the coherent backscatter enhancement due to multiple scattering within the particulate surface. The intensity phase curves at these two wavelengths were similar. The photopolarimetric measurements may have broad applications to the interpretation of photometry, spectroscopy, and polarimetry of the ice regoliths of high albedo satellites.

Particle size effect on the opposition spike and negative polarization

We report results of experiments designed to increase our understanding of the influence of particle size on the photometric opposition spike and negative polarization observed in the reflectance and polarization phase curves of particulate surfaces. We concentrate our studies on particle-size separates of alumina (bright powders) and boron carbide (absorbing powders). We use two photopolarimeters that span small (0.2–17°) and large (2–160°) phase-angle ranges. The results suggest that the negative polarization has two dominant mechanisms: (1) the coherent-backscatter enhancement and (2) single-particle scatter, and that the contributions of the mechanisms are a function of particle size. The measured photometric and polarimetric phase functions can be applied to evaluate models used to calculate scattering properties of particulate surfaces.

The Opposition Effect and Negative Polarization of Structural Analogs for Planetary Regoliths

To better understand the negative polarization and brightness opposition effects observed on airless celestial bodies, we carried out simultaneous photometric and polarimetric measurements of laboratory samples that simulate the structure of planetary regoliths. Computer modeling of shadow-hiding and coherent backscatter in regolith-like media are also presented. The laboratory investigations were carried out with a photometer/polarimeter at phase angles covering 0.2°–4° and wavelengths of 0.63 and 0.45 μm. We studied samples that characterize a variety of microscopic structures and albedos. A particle-size dependence of the negative branch of polarization for powdered dielectric surfaces was found. Colored samples such as a powder Fe 2O 3 exhibit a very prominent wavelength dependence of the photometric and polarimetric opposition phenomena. Metallic powders usually exhibit a wide branch of the negative polarization independent of the size of particles. For fine dielectric powders, both opposition phenomena become more prominent when the samples were compressed. Our computer modeling based on ray tracing in particulate media shows that shadow-hiding affects the negative polarization only in combination with the coherent backscatter enhancement. Modeling reveals that scattering orders higher than second contribute to negative polarization even in dark particulate surfaces. Our model qualitatively reproduces the effects of varying sample-compression that we observed in the laboratory. Our experimental and computer modeling studies mutually confirm that the degree of polarization for highly reflective dielectric surfaces depends not only on phase angle but also on surface tilt. Even at exactly zero phase the degree of polarization for tilted surfaces can be nonzero. A tilt of the surface normal to the scattering plane gives a parallel shift of the negative polarization branch to large values of | P|. The tilt in the perpendicular plane gives the same shift in the direction of positive polarization. At exactly zero phase angle, a celestial body of irregular shape can exhibit nonzero polarization even in integral polarimetric observations.

A Study of Saturn's Ring Phase Curves from HST Observations

Solar phase curves between 0.3° and 6.0° and color ratios at wavelengths λ=0.336 μm and λ=0.555 μm for Saturn's rings are presented using recent Hubble Space Telescope observations. We test the hypothesis that the phase reddening of the rings is less due to collective properties of the ring particles than to the individual properties of the ring particles. We use a modified Drossart model, the Hapke model, and the Shkuratov model to model reddening by either intraparticle shadow-hiding on fractal and normal surfaces, multiple scattering, or some combination. The modified Drossart model (including only shadowing) failed to reproduce the data. The Hapke model gives fair fits, except for the color ratios. A detailed study of the opposition effect suggests that coherent backscattering is the principal cause of the opposition surge at very small phase angles. The shape of the phase curve and color ratios of each main ring regions are accurately represented by the Shkuratov model, which includes both a shadow-hiding effect and coherent backscatter enhancement. Our analysis demonstrates that in terms of particle roughness, the C ring particles are comparable to the Moon, but the Cassini division and especially the A and B ring particles are significantly rougher, suggesting lumpy particles such as often seen in models. Another conspicuous difference between ring regions is in the effective size d of regolith grains ( d∼λ for the C ring particles, d∼1–10 μm for the other rings).