The backscatter from conducting and from dielectric spheres is considered in the time domain. Utilizing rigorously computed values of the amplitude and phase of the continuous wave backscatter, short pulses of electromagnetic waves are synthesized by Fourier series. The resultant response is examined as a function of time, and the individually resolvable returns are compared with some approximate theories.

Backscatter from spheres: A short pulse view

Theoretical calculations using continental, fog, and precipitation aerosol size distribution models are presented here for extinction and backscatter coefficients along horizontal propagation paths at sea level. The coefficients are presented for various atmospheric conditions and for wavelengths between 0.34 micro and 10.6 micro. Finally, the theoretical results are confirmed by comparison with outdoor transmission studies at 10.6 micro and 0.63 micro.

Comparative Studies of Extinction and Backscattering by Aerosols, Fog, and Rain at 10.6 micro and 0.63 micro.

A shooting and bouncing ray (SBR) formulation is presented for treating the electromagnetic scattering from electrically large, inhomogeneous objects. A dense grid of rays representing the incident plane wave is shot toward the inhomogeneous objects. At the scatterer boundary, reflected rays and refracted rays are generated due to the discontinuity of the medium parameters. The trajectory, amplitude, phase and polarization of the rays inside the inhomogeneous object are traced based on geometrical optics. Whenever the rays cross the scatterer surface, additional reflected/refracted rays are generated and are tracked. This is repeated until the intensities of the refracted/reflected rays become negligible. The contributions of the existing rays to the total scattered field are calculated using the equivalence principle in conjunction with a ray-tube integration scheme. The ray formulation is applied to calculate the backscattering from cylinders and spheres and good agreement with the exact series solutions is observed in the high-frequency range. In addition, the backscattering mechanisms in penetrable objects are interpreted in terms of simple ray pictures. >

Electromagnetic scattering from an inhomogeneous object by ray tracing

The complex natural resonances (CNR) for lossless dielectric spheres in a lossless dielectric medium are investigated. Significant differences between the external and internal resonances are presented. The external resonances are related to the external creeping waves and the internal resonances to the internally reflected waves. The internal resonances are more important in practice because of their smaller damping factors. A simple physical interpretation for predicting the resonance behavior of a general dielectric sphere is obtained.

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Electromagnetic resonances of immersed dielectric spheres

An analysis is presented for calculating the backscattered fields of an electromagnetic plane wave by lossless dielectric spheres of arbitrary density. This method involves the Watson transformation which serves to split the exact Mie solution, given as an infinite series, into the geometrical optics fields and the diffracted fields. The former comes from the illuminated region of the sphere and may be obtained from the geometrical optics method. The latter comes from the shadow region and consists of two different types of surface waves. One is a "creeping wave" analogous to that of perfectly conducting spheres. The other is a wave which enters the sphere and emerges as a surface wave in the shadow region. This wave is unique to dielectric spheres and is the stronger of the two surface waves. In the widely used geometric optics methods it is assumed that the optics fields are the dominant contributors even though stationary rays which are not in the direction of backscatter must be added in to give a degree of agreement with the exact Mie series results. In this paper we derive the optics fields and show that they differ in some respects from those obtained by the geometric optics method. They are smaller than heretofore assumed and contribute negligibly to the backscatter in this particular range of ka (4-20). Using our rigorous approach we can show the diffracted fields to be the major contributors to the total backscatter. Numerical results for the backscattering cross sections using diffracted and optics fields, and optics fields alone will be presented for relative index of refraction of 1.6. The agreement between our results (diffracted and optics) and exact results from the Mie series is excellent. A subsequent paper will be concerned with the diffracted fields.

The geometric optics contribution to the scattering from a large dense dielectric sphere

Two approximate methods have been developed for calculating the radar cross sections of nonconducting bodies. The superposition approximation used to obtain the radar cross sections of dielectric clad bodies requires that the scattering properties of the component parts be known. The modified geometrical optics method, which yields the radar cross sections of dielectric bodies, requires no such initial information. These methods can be applied to some bodies with shapes that cannot be treated by means of the classical boundary-value solutions. Furthermore, the computations required are usually considerably simpler than for the boundary-value solutions even when the latter are obtainable.

W.G. Swarner

Papers

Approximations for dielectric or plasma scatterers