摘要:

The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high‐frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration dat

ISSN:0048-6604    

DOI:10.1029/93RS00278

年代:1993

数据来源: WILEY

摘要:

The modified radiative transfer theory is used to obtain the backscattering coefficients of a two‐layer random medium. Since exact solutions to the MRT equations are not available certain approximations are used. First, a first‐order approximation is made to obtain the backscattering coefficients. In an attempt to investigate the appropriateness of the first‐order approximation, higher‐order solutions are obtained. It is observed that the second‐order solution is important because it is the primary source of depolarization (cross‐polarized backscatter); besides it also helps one to estimate the error involved in settling for a first‐order approximation. Hence the second‐order backscattering coefficients are calculated and cast in a form suitable for physical interpretation. It is noticed that certain “phase” terms are absent. After exploring the reasons for this, it is suggested that the present MRT theory be further modified to accommodate these terms. Finally, with the help of numerical examples, characteristics of the second‐order solutions are studied by comparing them with the corresponding Born results and also with the

ISSN:0048-6604    

DOI:10.1029/92RS02883

年代:1993

数据来源: WILEY

摘要:

In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation‐dissipation theory for media with a temperature profile. Both finite‐size objects and half‐space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation‐dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation‐dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchh

ISSN:0048-6604    

DOI:10.1029/93RS01078

年代:1993

数据来源: WILEY

摘要:

An extension of the continuous aperture Woodward‐Lawson sampling theorem has been developed for a finite linear array of equidistant identical elements with arbitrary excitations. It is shown that by sampling the array factor at a finite number of specified points in the far field, the exact array factor over all space can be efficiently reconstructed in closed form. The specified sample points lie in real space and hence are measurable provided that the interelement spacing is greater than approximately one half of a wavelength. This paper provides insight as to why the length parameter used in the sampling formulas for discrete arrays is larger than the physical span of the lattice points in contrast with the continuous aperture case where the length parameter is precisely the physical aperture lengt

ISSN:0048-6604    

DOI:10.1029/93RS00591

年代:1993

数据来源: WILEY

摘要:

The multiple knife edge model for terrain diffraction problems is extended to apply to solid terrain. The model is constructed by bridging over the spaces between diffracting screens with perfectly reflecting plane surfaces that connect the tops of the diffracting screens. In this way the diffracting screens are hidden from view, and the plane surfaces become a solid, reflecting, model of terrain. Nevertheless, there remains a mathematical similarity with multiple knife edges, and a series solution already known for multiple knife edges can be adapted to the new model. Although bridging over the knife edges adds new modes of propagation, many of these modes make identical contributions to the field, and the final series contains no more terms than for knife edges only. As with knife edges, computing time increses rapidly as a function of the number of knife edges, and the series may not converge if the terrain profile contains valleys. However, valleys can always be removed by means of Babinet's principle. Sample results show that bridging over knife edges results in increased attenuation and a smoother variation with terrain height. A round hill can be approximated, and the resulting attenuation approaches the known attenuation for a round hill, as the number of bridged knife edges increases.

ISSN:0048-6604    

DOI:10.1029/93RS00898

年代:1993

数据来源: WILEY

摘要:

The well‐known along‐track resolution loss in synthetic aperture radar (SAR) ocean wave image spectra is investigated comparing simulations based on Hasselmann's nonlinear integral transform and measurements from the Norwegian Continental Shelf Experiment 1988 experiment. In the literature the resolution loss has often been modeled as a low‐pass filter process, described by the rms azimuth shift width σx, acting within a quasi‐linear SAR transformation. Estimates from real data of σx, as a function the range‐to‐platform velocity (R/V) and incidence angle, are compared to Hasselmann's new nonlinear spectral transformation and the widely used quasi‐linear model. Simulations correlated with real wave data show that the quasi‐linear model, with contributions to σxfrom the entire spectrum, overestimates σxby roughly 30–40%. The conformity between Hasselmann's model and real data is excellent, however. The numerics also indicate that the degree of nonlinearity in Hasselmann's transform is explicitly related to the surface truth parameters' significant wave height and peak wavelength. Furthermore, the spectral bandwidth, including the subresolution part of the ocean wave spectrum, seems to be of minor importance. It is also shown that the resultant smearing (due to imaging nonlinearities) cannot explicitly be separated from the coherent linear velocity bunching part of the transform. This point is especially discussed since it has led previously to some dissension regarding which ocean spectral components are most essential in

ISSN:0048-6604    

DOI:10.1029/93RS00415

年代:1993

数据来源: WILEY

摘要:

In this paper the time domain scattering problem of a stratified dissipative half‐space excited by a point source is considered. Both the direct and inverse scattering problem are treated. The dissipative wave equation is reduced to an equation in one spatial dimension by spatial Fourier series and a Hankel transform. The transformed wave equation is then solved by a combination of a time domain wave‐splitting technique and a Green function technique. The Green functions represent the internal fields inside the stratified medium. The splitting is expressed in terms of a Neumann operatorKwhich has an explicit expression as a convolution integral with a Bessel function kernel. Based upon this wave splitting, Green functions can be defined and a set of first order partial differential equations for Green functions are derived. The equations are well suited for a numerical treatment and a number of numerical examples for both the direct and inverse problems are presented. A brief discussion of the invariant imbedding method applied to the direct and inverse scattering problem is also given. It is shown that one‐sided reflection data are sufficient to reconstruct the phase velocity and the dissipation coefficient simultaneously by using two different values of the Hankel transform para

ISSN:0048-6604    

DOI:10.1029/93RS00590

年代:1993

数据来源: WILEY

摘要:

We examine the question of satisfaction of the reciprocity theorem in the context of geometrical theory of diffraction. To this end, we consider two sets of scattering problems involving a smooth, convex, perfectly conducting obstacleS, related by the reciprocity theorem. Initially, we find that the satisfaction of reciprocity conditions by the results derived from the use of the geometric theory of diffraction formulas is not obvious. We then proceed to show that they may be recast in forms that are indeed reciprocal in nature.

ISSN:0048-6604    

DOI:10.1029/93RS00942

年代:1993

数据来源: WILEY

摘要:

We present experimental results on the scattering of electromagnetic waves at millimeter‐wave frequencies from one‐dimensional very rough conducting surfaces with controlled surface roughness statistics. Very rough surfaces are defined as surfaces with rms height and correlation length of the order of a wavelength such that the rms slope is at least unity. It is expected that scattering experiments using these surfaces can provide useful insights since their statistics lie outside the range of validity of the present theories, namely, the Kirchhoff and perturbation theories. Strong backscattering enhancement at different incident angles, both in the transverse electric and transverse magnetic polarizations, are observed experimentally. Numerical calculations based on the exact integral equation method for cylindrical beam wave illumination compare favorably with the experimental results. The agreement between measurements and numerical calculations is good over a wide range of incident angles and for all scattering angles. The close agreement between the experimental results and numerical simulations indicates that this controlled experimental setup can be used to study scattering phenomena from one‐dimensional very rough surfaces with different roughness statistics as well as from two‐dimensional rough s

ISSN:0048-6604    

DOI:10.1029/93RS00362

年代:1993

数据来源: WILEY

摘要:

An equivalent‐medium model is developed for vegetation media to relate the propagation constant γ, associated with propagation of the mean field through a vegetation canopy, to the geometrical and dielectric parameters of the canopy constituents at high frequencies. The model is intended for media containing vertical dielectric cylinders, representing the stalks, and randomly oriented, arbitrary shaped thin dielectric disks, representing the leaves. The formulation accounts for absorption and scattering losses by both stalks and leaves. A resistive sheet model in conjunction with the physical optics approximation is used to model scattering by the canopy leaves, which is valid when the leaf dimensions are larger than a wavelength. The model is found to be in good agreement with experimental results at 10.2 GHz. The experimental component of the study included measurements of the attenuation loss for horizontally polarized and vertically polarized waves transmitted through a fully grown corn canopy. The measurements were made at incidence angles of 20°, 40°, 60°, and 90° relative to normal incidence. The proposed model is suitable for cornlike canopies, provided the leaves are larger than λ

ISSN:0048-6604    

DOI:10.1029/92RS02456

年代:1993

数据来源: WILEY