Adrian K. Fung

A semi-empirical sea-spectrum model for scattering coefficient estimation

A semi-empirical sea-spectrum model is proposed to be used in a two-scale radar sea scatter model to obtain estimates of radar backscatter over the frequency bandsLtoKu, the incidence angular range20\deg-65\deg, the azimuth angular range0\deg-180\degfrom the wind direction and wind speed range 3.5-30 m/s at 19.5 m above the mean sea level. It is shown that the theoretical estimates obtained are consistent with the existing measurements.

Numerical computation of scattering from a perfectly conducting random surface

A one-dimensionally rough random surface with known statistical properties was generated by digital computer. This surface was divided into many segments of equal length. The moments method was applied to each surface segment assuming perfect conductivity to compute the induced surface current and subsequently the backscattered field due to an impinging plane wave. The return power was then calculated and averaged over different segments. Unlike numerical computations of scattering from deterministic surfaces, problems of stability (as defined by Blackman and Turkey [11]) and convergence of the solution exist for random surface scattering. It is shown that the stability of the numerically computed estimate of the backscattered average power depends on N , the total number of disjoint surface segments averaged; \Delta x , the spacing between surface current points; D , the width of each surface segment; and g , the width of the window function. Relations are obtained which help to make an appropriate choice of these parameters. In general, choices of \Delta x, D , and g are quite sensitive to the incident wavelength and the angular scattering properties of the surface.

A scatter model for vegetation up to Ku-band

Abstract A scatter model is developed based on the matrix doubling method for volume scattering and the Kirchhoff method in rough surface scattering. Scattering from vegetation is assumed to be dominated by leaves and a single leaf is modeled by a thin dielectric disc. In developing the phase matrix for the disc, field within the disc is taken to be constant over the disc thickness, but phase changes across the surface of the disc are accounted for. Comparisons of this scatter model with radar measurements indicate good agreements in polarization, angular trends, and frequency up to Ku-band. This represents a considerable improvement over low-frequency scatter models which are valid up to S-band.

A Scatter Model for Leafy Vegetation

A model for vegetation scatter is developed using the first-order renormalization method. The vegetated medium is taken to be an inhomogeneous medium characterized by a random permittivity function with a cylindrically symmetric fast-decaying correlation function. The permittivity of the vegetation (taken to be a combination of water and some solid material) is estimated by a mixing formula after de Loor [13], and the permittivity of the vegetated medium (taken to be a combination of vegetation and air) is estimated using a formula by Pierce [16]. The backscattering coefficient from such a model is computed as a function of the incidence angle, the frequency, and the moisture content of the vegetation. Comparisons are made with measured data from soybeans, alfalfa, and corn. The agreements obtained in both the absolute levels and the angular trends of the backscattering coefficient appear to justify both the permittivity and the scatter model for vegetation.

Application of a Combined Rough Surface And Volume Scattering Theory to Sea Ice And Snow Backscatter

A radiative transfer theory which combines rough surface and volume scattering effects is applied to interpret backscatter measurements from snow and sea ice. The surface scattering effect is accounted for by the Kirchhoff model evaluated either with or without the deep phase modulation assumption. Hence, the major restriction on the surface model is that the horizontal roughness scale must be large enough to satisfy the large radius of curvature requirement. The inhomogeneous layer for simulating snow or sea ice is modeled by either the Rayleigh phase matrix or a continuous random medium with a cylindrically symmetric correlation function for its permittivity function. It is assumed that for the continuous random medium the Born approximation is applicable for computing the scattering phase functions of this inhomogeneous medium. For simplicity only the top boundary of the inhomogeneous layer is assumed rough. Its bottom interface is a plane separating the layer from a homogeneous semiinfinite medium. Comparisons with snow measurements using Polder and Van Santens mixing formula for the permittivity model show satisfactory agreements at 7.6, 13, and 17 GHz and for sea ice at 9 and 13 GHz. For the cases considered for sea ice, it appears that the Rayleigh phase matrix is an adequate description for volume scattering.

Application of First-Order Renormalization Method to Scattering from a Vegetation-Like Half-Space

A general theory is developed for scattering from an inhomogeneous half-space with strong permittivity fluctuations. Closed form bistatic scattering coefficients are obtained using the method of field renormalization for a vegetation-like medium characterized by a random permittivity function with a large variance and a cylindrically symmetric, fast-decaying correlation function. Multiple-scattering effects are accounted for to the same extent as in the first-order renormalization approach. Behaviors of the scatter model are illustrated by computing sample cases using Carlsons permittivity model for leaves. Cursory comparison between this theory and some recent data shows general agreements in both level and angular trends, indicating promise in the use of the developed scatter model for explaining vegetation scatter.

Scattering from a Vegetation Layer

A plane layer of vegetation separating air and soil is assumed to model dense crops such as alfalfa and soybeans. Backscattering from such a layer is computed by first determining the coherent fields existing in the layer by solving the Dyson equation under bilocal approximation. Then the scattered field is found using the first-order renormalization method. The scatter model is evaluated for different depths to correspond to the changes in height of the crop during its growth period. The behaviors of the scatter model versus moisture content and volume ratio of vegetation and soil permittivity are also illustrated. It was found that while ground effects are, in general, more significant near normal incidence than at large incidence angles, a reversal of this trend is possible for a thin vegetation layer. This offers a possible explanation for the relatively flat angular response observed in some of the measured scattering coefficients around 60-70°, since leaf density is not really uniform in practice. It was also found that any significant peaking of the backscattering coefficient near vertical incidence cannot be explained by volume scattering due to the propagation of the ground reflected field. It is believed that irregular ground is the contributing factor to large returns near vertical incidence.

Theory of cross polarized power returned from a random surface

Cross polarized power resulting from depolarization of electromagnetic waves by a statistically rough surface is calculated. This is done for a circularly polarized incident wave and a homogeneous dielectric surface with either a Gaussian or an exponential correlation function. The polarized return power is also obtained so that comparison between the two could be made.

Method for Retrieving the True Backscattering Coefficient from Measurements with a Real Antenna

Measurements made of the power backscattered by a surface at angles near nornal incidence include contributions due to both coherent and incoherent scattering. Additionally, these contributions are weighted by the antenna pattern. Using a theoretical model to describe the backscattering from a rough soil surface, a procedure is developed for retrieving the true angular pattern of the backscattering coefficient ¿0 from measured estimates of a ¿0 , where the measured estimate is based on the usual assumption that ¿0 is approximately constant over the angular extent of the antenna beam for narrowbeam systems. The retrieved patterns of ¿0 were then used to evaluate the dependence of ¿0 on soil surface roughness at 1.5, 4.25, and 7.25 GHz.

Mechanisms of polarized and depolarized scattering from a rough dielectric surface

Abstract A theory is developed to explain the nature of polarised and depolarized scattering of electromagnetic waves from a slightly rough dielectric surface. The method of small perturbation is used together with the Fourier transformation and results are carried up to and including the second-order. It is shown that first-order fields result from a single scattering process and second order fields result from a two-bounce multiple scattering process. It is also shown that regardless of the dielectric property of the surface, the incident wave number, the incident angle and the direction of the receiver combine to determine exactly the harmonic components of the surface that are responsible for scattering.