The scattering behavior of the Moon at wavelengths of 3.6, 68, and 784 centimeters

Evans, J. V.; Pettengill, G. H.

doi:10.1029/jz068i002p00423

Cited by 111 publications

(69 citation statements)

References 37 publications

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“…For the 13 cm wavelength of the Chandrayaan-1 and LRO radars, the values of s OC-avg () are interpolated from the 3.8 cm and 23 cm average radar cross sections given by [Hagfors, 1970] where 0.32 = ln(23/13)/ln(23/3.8) and 0.68 = ln(13/3.8)/ ln(23/3.8). The data of Evans and Pettengill [1963] indicate that (1) average OC echoes at the highest angles of incidence have a cos() dependence; (2) average SC echoes have a cos() dependence at all angles of incidence; and (3) the ratio of average OC echoes to SC echoes is 2:1 at the highest angles of incidence.…”

Section: Thompson Et Al: Radar Scatter From Icy Lunar Regoliths E010mentioning

confidence: 91%

“…We assume that average diffuse scattering OC and SC components are proportional to cos(). Also, we note that Evans and Pettengill [1963] and have shown that at the highest angles of incidence, the CPR of the average lunar surfaces is near one-half. Thus, we will assume that the ratio s SC-avg…”

Section: A11 Scattering Differences Associated With Rough Surfaces mentioning

confidence: 99%

“…The diffuse component is attributed to scattering from wavelength-sized (one-tenth to 10 wavelengths) rocks, either on the surface or subsurface up to the radar's penetration depth, which is on the order of 10 wavelengths in the maria and up to 40 wavelengths in terra [Campbell and Hawke, 2005]. The SC polarization component at centimeter wavelengths has a cos() dependence for all angles of incidence [Evans and Pettengill, 1963].…”

Section: Overview Of Lunar Radar Scatteringmentioning

confidence: 99%

“…Here = 0°at the center of the lunar disk and = 90°at the limb as viewed from Earth. Hagfors [1970] tabulates s() for wavelengths of 3.8, 23, and 68 cm based on the earlier measurements by Evans and Pettengill [1963]. These radar cross sections were obtained using the conventional Earth-based radar configuration, where circularly polarized waves are transmitted and received to obviate the adverse affects of Faraday rotation in the Earth's ionosphere.…”

Section: Introductionmentioning

confidence: 99%

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Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths

Thompson¹,

Ustinov²,

Heggy³

2011

J. Geophys. Res.

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[1] Two orbital synthetic aperture radars (SARs), the Chandrayaan-1 Mini-SAR (13 cm wavelength) and the Lunar Reconnaissance Orbiter (LRO) Mini-RF (13 and 4.2 cm wavelengths), have been imaging the lunar surface searching for ice deposits in the polar permanently shadowed areas. To understand the radar signatures of lunar polar ices, an empirical two-component model with parametric variations of the specular and diffuse components was developed and validated. This model estimates scattering differences associated with slopes, surface roughness, thin regolith over ice, and patches of ice. Lunar radar backscatter cross sections for the average surface for the Chandrayaan-1 and LRO instruments are estimated from the radar cross sections from the Moon at 3.8, 23, and 68 cm wavelengths measured in the 1960s at the Massachusetts Institute of Technology. This modeling predicts that enhanced diffuse scattering from near-surface ice can be separated from rocks if the scattering is characterized by both the high reflectivity and circular polarization ratios (CPRs) like those observed on Mercury, Mars, and the Galilean satellites. Scattering from near-surface ices covered by a thin regolith can be separated from rocks if the enhancement is twice the average or more. If, however, the lunar ice is dispersed throughout the regolith as ice-filling pores, then scattering differences might be too small to detect. Preliminary validation using LRO radar data for a few polar and midlatitude craters indicate that the observed CPRs are consistent with our models for different regolith ice and roughness conditions. Citation: Thompson, T. W., E. A. Ustinov, and E. Heggy (2011), Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths,

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Section: Thompson Et Al: Radar Scatter From Icy Lunar Regoliths E010mentioning

confidence: 91%

Section: A11 Scattering Differences Associated With Rough Surfaces mentioning

confidence: 99%

Section: Overview Of Lunar Radar Scatteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths

Thompson¹,

Ustinov²,

Heggy³

2011

J. Geophys. Res.

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“…As may be seen in figure 12, the depolarized co mponent of the power obeys the law P(4)) 0: cos 4>, indicating that these signals are scatte red equally from all parts of the proj ec ted di sk. The perce ntage polarization can be expressed in the form [Evans and Pettengill 1963c].…”

Section: Orthogonal Polarization Observationsmentioning

confidence: 99%

Radar studies of the Moon

Evans¹

1965

J. RES. NATL. BUR. STAN. SECT. D. RAD. SCI.

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Accurate range measurements have been reported only by the group 'working at the Nava l Re· search Laboratory. Their most recent value for the mean center-to-center distance betwee n th e Earth and the Moon is 384,400.2 ± 1.1 km and is based upon a value for the Earth's radius of 6.378,170 m which seemed most cons istent with the observed diurnal variation in range.The absolut e cross section of the Moon has been determined over a wide range of wavelengths to a precision in most cases of ± 3 dB. Unfortunately, this uncertainty is too large to permit any definite conclusions to be drawn concerning the wavelength dependence in the cross section. The observations suggest th at the cross section remains cons tant at about 7 percent of the proj ec ted area of the Moon's disk at wavelengths in the range 1 cm to 1 m, and perhaps rises to 10 percent or higher at wavelengths in the range 1 to 10 m.Short-pulse observations ca n be used to exp lore th e angular dependence in the sca tterin g of radi o waves b y the lunar surface. Usefu l meas urem e nts have bee n tnade at wave le ngth s of 1130, 68,23, 10, and 3.6 em. The angu lar dependence has also been investigated at 8.6 mm , th ough here th e angu lar resolution afforded by a narrow pencil-beam a nte nna was e mployed. At all s ix 'wavele ngth s, it appears that part of th e ec ho arises from a hi ghli ght located at th e ce nt e r of the Moon 's visible disk_ A seco nd com ponent comes almost eq ually from th e re maining parts of th e surface. Th e divi sion of power in th e two compone nts changes mark ed ly as th e wavele ngth is red uced. At 68-cm wavele n gth, 80 percent of th e power is return ed fr om the highli ght , but at 8.6 mm only 15 percent ca n be associated with this co mp one nt. The angu lar power spec trum obse rved for th e power fro m th e highli ght also c ha nges with wavelength, indi cating that th e rm s slope of th e surface in c reases as th e wavelength is red uced. Th ese observations have been interpreted as indicat ing that there is a wid e range of structure sizes on the Moon.The deduced valu es of dielec tric co nstant ran ge from k = 2.79 down to k = 2.13. In view of th e greater experime nt al diffi c ulti es togeth e r with the doubtful validity of th e assumptions at 8.6-mm wavelength, this apparent wavelength dependence should be accepted with caution. If real, it may be ca used by the finit e co ndu ctivity of the mat erial (i.e., s "" a in (6)) or by inh omogeneity in th e surface layers -the den sit y pe rhap s in c reas ing sli ghtly with de pth. These val'ues ce rtainly indi ca te that th e surface is broke n or porous in texture -the material occupying perhaps about 30 percent of the available volume. In short, th e echo inte nsity and angular s pec trum is co mparable to that observed from aircraft over terrestrial des erts.

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Measurements of Electromagnetic Back-scattering from Known, Rough Surfaces*

Renau¹,

Collinson²

1965

Bell System Technical Journal

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We have measured the cross section for backscattering of laser beams from rough aluminum surfaces and a magnesium oxide slab. These surfaces were specially prepared and their statistical properties were measured. The laser wavelengths were Λ = 0.63, 1.15, and 3.39μ, and both parallel and perpendicular polarizations were used. The angle of incidence was varied from 0° to 89°. In these experiments the ratio of the surface rms height h (from the mean surface) to the wavelength Λ is larger than 1/4; for such surfaces the cross section for backscatter at normal incidence is inversely proportional to the square of the rms surface slope, h/l, and is independent of wavelength. At large angles of incidence the cross section increases with increasing slope and also with increasing h/Λ, approaching an upper limit which appears to be predicted by a Lambert scattering law. The angular dependence of the cross section differs for the two polarizations; at grazing incidence the cross section is larger for the parallel polarization. The published characteristics of the angular dependence of the cross section of microwave backscattering from the sea and the moon are in remarkable agreement with the backscattering cross section obtained from the various randomly‐rough laboratory prepared surfaces at all angles of incidence. Comparison of the laboratory results with published moon data yields for the moon surface an rms height of 40 ± 10 cm, a mean correlation distance or mean scale size of 2.8 ± 0.7 meters, an rms slope of 8° ± 4°, and a dielectric constant ε at microwave frequencies of 1.9 ± 0.3 gigacycles.

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The scattering behavior of the Moon at wavelengths of 3.6, 68, and 784 centimeters

Cited by 111 publications

References 37 publications

Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths

Modeling radar scattering from icy lunar regoliths at 13 cm and 4 cm wavelengths

Radar studies of the Moon

Measurements of Electromagnetic Back-scattering from Known, Rough Surfaces*

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