Backscatter cross sections of composite random rough surfaces based on the selection of variational parameters to determine the surface height spectral densities of the larger‐ and smaller‐scale surfaces

Bahar, E.; Crittenden, Paul E.

doi:10.1080/01431160701241712

Cited by 4 publications

(12 citation statements)

References 18 publications

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“…The variation technique described above has been examined for Gaussian and Pearson -Moskowitz type surface height spectral density functions. It has been demonstrated that the values for the cross sections are stationary over a very wide range of the variation parameters and E(n) has a very broad minima in this range, usually between n = 2 and n = 8) [13]. Large fluctuations in the values of the cross section occur at the edges near the physical optics and original full wave solutions, with no slope modulation.…”

Section: Scatter Cross Sections Based On a Two Scale Unified Full Wamentioning

confidence: 97%

“…More recently a variation technique was employed to decompose the spectral density function of the composite rough surface, in a smooth and continuous manner [12], into spectral density functions for the larger and smaller scale surfaces. It is shown that the solutions based on this variation method is stationary over a very wide range of the variation parameter, associated with the ratio of the mean square heights or slopes of the larger scale surfaces, and the mean square heights or slopes of the total surface [13].…”

Section: Introductionmentioning

confidence: 98%

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Soil moisture content of composite rough surfaces based on a variational technique to distinguish between the larger and smaller scale surface spectral density functions

Bahar

2007

SPIE Proceedings

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The determination of soil moisture content is often based on the measurements of the ratio of the vertically and horizontally polarized cross sections for large angles of incidence, where the cross sections could be significantly different. Using the high frequency, physical optics model of the earth's surface, this ratio depends primarily on the Fresnel reflection coefficients for the two polarizations, while the impact of surface roughness factors out of the cross section ratio. Thus for highly conducting moisture saturated soils, this ratio approaches one. Using the low frequency, small height-small slope perturbation model of the earth's surface, the vertically and horizontally polarized cross sections are critically dependent on polarization for large angles of incidence, even for the perfectly conducting rough surfaces. However using the standard perturbation model, the ratios of the cross sections are also independent of the surface roughness. Applying the small perturbation approach to highly conducting rough surfaces, the ratio of the horizontally to vertically polarized cross sections approaches zero for grazing angles of incidence, for which the two cross sections differ significantly. There is ample experimental evidence that neither the physical optics nor the small perturbation models are adequate.The standard hybrid two scale physical optics-perturbation approach depends critically upon the decomposition of the composite surface into smaller and larger scale surfaces. The smaller scale surface is restricted to small Rayleigh roughness parameters, proportional to the mean square height, and the larger scale surface is restricted by the large radii of curvature criteria.Using a two scale full wave approach, the cross section are expressed as a weighted sum of a physical optics cross section for the larger scale surface, reduced by a factor equal to the square of the small scale surface characteristic function, and a cross section for the smaller scale surface that is modulated by the slopes of the larger scale surface. A variation technique is used to decompose the surface height spectral density function in a continuous, smooth manner into spectral density functions for the larger and smaller scale surfaces. It is shown that the corresponding polarization dependent rough surface cross sections are stationary over a wide range of the variation parameters. The ratio of the cross sections are dependent of the surface roughness, since the horizontally polarized cross sections are significantly dependent on modulation by the slopes of the larger scale surfaces, for large angles of incidence.

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Section: Scatter Cross Sections Based On a Two Scale Unified Full Wamentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Soil moisture content of composite rough surfaces based on a variational technique to distinguish between the larger and smaller scale surface spectral density functions

Bahar

2007

SPIE Proceedings

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“…This weighted sum is consistent with energy conservation. It also makes the total scatter cross sections stationary over a wide range of the variational parameter (the ratio of the mean square heights of the larger‐scale surface and the total surface) [ Bahar and Lee , 1994; Bahar and Crittenden , 2008].…”

Section: Description Of the Full Wave Variational Techniquementioning

confidence: 99%

“…6. These full wave solutions explain why the cross sections for the horizontally polarized waves are much more sensitive to tilt modulation than the cross sections for vertically polarized waves [ Bahar and Kubik , 1993; Bahar et al , 1983a, 1983b; Bahar and Crittenden , 2008].…”

Section: Description Of the Full Wave Variational Techniquementioning

confidence: 99%

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Like and cross‐polarized scatter cross sections for two‐dimensional, multiscale rough surfaces based on a unified full wave variational technique

Bahar

2011

Radio Science

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[1] A variational method is used to select the specific, smooth decomposition of the total surface height spectral density function into surface height spectral density functions for the larger-and smaller-scale surfaces. Using this decomposition, the total like and crosspolarized scatter cross sections are expressed as weighted sums of physical optics scatter cross sections associated with the larger-scale surfaces and the tilt-modulated scatter cross sections for the smaller-scale surfaces. This variational technique has been shown to be stationary over a wide range of the variational parameter. Since only the slopes of the largerscale surfaces tilt modulate the cross sections of the smaller-scale surfaces, it is necessary to select surface height spectral density functions for the larger-scale surfaces that do not require the introduction of artificial spatial cutoff wave numbers for the spectral density functions. The methods used to smoothly decompose the surface height spectral density functions result in no artificial rapid fluctuations in the corresponding surface height autocorrelation functions for the smaller-and larger-scale surfaces. This method can be applied to the remote sensing of rough sea or land surfaces.Citation: Bahar, E. (2011), Like and cross-polarized scatter cross sections for two-dimensional, multiscale rough surfaces based on a unified full wave variational technique, Radio Sci., 46, RS4002,

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Surface roughness and polarization ratio in microwave remote sensing

Hong

2010

International Journal of Remote Sensing

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Backscatter cross sections of composite random rough surfaces based on the selection of variational parameters to determine the surface height spectral densities of the larger‐ and smaller‐scale surfaces

Cited by 4 publications

References 18 publications

Soil moisture content of composite rough surfaces based on a variational technique to distinguish between the larger and smaller scale surface spectral density functions

Soil moisture content of composite rough surfaces based on a variational technique to distinguish between the larger and smaller scale surface spectral density functions

Like and cross‐polarized scatter cross sections for two‐dimensional, multiscale rough surfaces based on a unified full wave variational technique

Surface roughness and polarization ratio in microwave remote sensing

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