The forward-backward method has been shown to be an effective iterative technique for the computation of scattering from one-dimensional rough surfaces, often converging rapidly even for very large surface heights. However, previous studies with this method have computed interactions between widely separated points on the surface exactly, resulting in anO(N2) computational algorithm that becomes intractable for large rough surface sizes, as are required when low grazing incidence angles are approached. An acceleration algorithm for more rapidly computing interactions between widely separated points in the forward-backward method is proposed in this paper and results in an O(N) algorithm with increasing surface size. The approach is based on a spectral domain representation of source currents and the Green's function and is developed for both perfectly conducting and impedance boundary surfaces. The method is applied in a Monte Carlo study of low grazing incidence backscattering from very rough (up to 10 m/s wind speed) ocean-like surfaces at 14 GHz and is found to require only a small fraction of the CPU time required by other competing methods; such as the banded matrix iterative approach/canonical grid and fast multipole methods.

A novel acceleration algorithm for the computation of scattering from rough surfaces with the forward-backward method

In the resonance region, the radar scattering response of any target can be modeled by natural poles, with the formalism of the singularity expansion method. The mapping of poles gives useful information for the discrimination of radar targets. In this paper, we show that a reduced number of natural poles is sufficient to characterize such objects. Furthermore, we propose a procedure for selecting the poles that actually contribute to the scattering response. Results are presented for various perfectly conducting (PC) canonical targets and for a PC complex shape target.

Selection of Contributing Natural Poles for the Characterization of Perfectly Conducting Targets in Resonance Region

In resonance domain, the radar scattering response of any object can be modelled by natural poles of resonance with the formalism of the singularity expansion method. The mapping of these poles in the complex plane gives useful information for the discrimination of a radar target, as its general shape, its characteristic dimension and its constitution. However, the full frequency band corresponding to the resonance domain of a radar target is not always available, thus it is often necessary to look for a compromise. In this paper, we propose to show that it is possible to extract resonance poles one-by-one in tuning a reduced frequency band to the frequency of each wanted pole. This avoids the use of ultra wide band (UWB) data and allows to extract at least some dominant poles of resonance in available narrow frequency bands.

Determination of resonance poles of radar targets in narrow frequency bands

The matrix pencil (MP) method has been utilised for estimating the poles from the IFFT of calculated frequency responses. The novelty is that the optimal choice of pencil parameters in MP is given, and a scheme for adaptive selection of frequency sampling interval is proposed. Lastly, poles of a complex target are calculated by the proposed method and compared with other available data.

Application of matrix pencil method for estimating natural resonances of scatterers

In resonance domain, the radar scattering response of any object can be modelled by natural poles of resonance with the formalism of the Singularity Expansion Method. The mapping of these poles in the complex plane gives useful information for the discrimination of a radar target, as its general shape, its characteristic dimension and its constitution. In this paper, we use an analogy with resonant circuits modelling to define the quality factor Q of each resonance. Therefore, we propose to characterize the resonance behavior of perfectly conducting targets with this quality factor Q and the natural pulsation of resonance ω0. Indeed, this new representation in {ω0; Q} allows to better separate information than the usual mapping of natural poles of resonance in the complex plane. For perfectly conducting canonical and complex shape targets, we present results exhibiting advantages of these two parameters {ω0; Q}.

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Characterization of Perfectly Conducting Targets in Resonance Domain with Their Quality of Resonance

In resonance domain, the radar scattering response can be modeled by natural poles of resonance, with the formalism of the singularity expansion method. The mapping of poles gives useful information for the discrimination of radar targets. In this paper, we show that a reduced number of poles is sufficient to characterize an object. Furthermore, we propose a procedure for selecting poles actually contributing to the scattering response. Results are presented for different canonical targets

Characterization of radar targets in resonance domain with a reduced number of natural poles

In resonance domain, the radar scattering response of any object can be modelled by natural poles of resonance with the formalism of the singularity expansion method. The mapping of these poles in the complex plane, gives useful information for the discrimination of radar targets, as the general shape, the characteristic dimension and the constitution of the target. In this paper, we propose to study the effect on the resonance poles of a dielectric coating on a conducting target. For that, we present results of mapping of poles as a function of the thickness and the permittivity of the coating.

Modification of resonance poles of a conducting target by a dielectric coating

This paper proposes to characterize the resonance behavior of targets with the quality factor, defined by comparison with resonant circuits. Results are presented exhibiting the advantage of using this Q parameter

Study of resonances of scattering objects: comparison with resonant circuits and characterization using Q-factor

In this paper, the bistatic polarimetric signatures of perfectly conducting octahedral and icosahedral reflectors with high dimensions with respect to the wavelength, are considered. A closed form solution for their fast computation is developed and results are compared. These particular faceted polyhedra, both composed by several identical elementary reflectors, should exhibit a large bistatic and monostatic radar cross section (RCS) over a wide angular range. The proposed method is based on coherent summations of the asymptotic solution of the trihedral corner reflector (TCR): the elementary reflector, evaluated for any incidence and observation angles. This can be done with the help of geometrical optics (GO) to take into account shadowing effects. Physical optics (PO) and GO are used to derive the contibution of the TCRs in single, double and triple reflections. First order diffractions are also included in the analysis with the help of method of equivalent currents / incremental length diffraction coefficients (MEC/ILDC).

Comparison of bistatic signatures of octahedral and icosahedral reflectors in high-frequency domain

The problem of electromagnetic wave scattering from a one-step surface is a well-known subject. The reflected power can be evaluated using the widely-used Rayleigh roughness parameter. Here, its extension to the case where the one-step surface overlies a perfectly flat surface, called one-step layer, is studied.

Joseph Saillard

Papers

Characterization of radar targets in resonance domain with a reduced number of natural poles

Modification of resonance poles of a conducting target by a dielectric coating

Study of resonances of scattering objects: comparison with resonant circuits and characterization using Q-factor

Comparison of bistatic signatures of octahedral and icosahedral reflectors in high-frequency domain

Extension of the roughness criterion of a one-step surface to a one-step layer