Starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities, the degrees of freedom of the scattered field are introduced and then computed. The degrees of freedom are shown to be practically equal to the Nyquist number appropriate to the effective (spatial) bandwidth of the scattered field and to the extension of the observation domain. Accordingly, a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error. It is also shown that the field representation can be made in terms of field values and simple sampling functions, provided that a marginal increase in the approximation error is tolerated. The results not only completely justify the use of sampling interpolation for representing scattering fields, but also demonstrate that such representation is practically an optimal one. An algorithm for the reconstruction of scattered fields, given the maximum allowed error, is then produced. >

On the degrees of freedom of scattered fields

A new method to numerically solve time-domain integral equations pertinent to electromagnetic surface scattering phenomena is presented. The method uses approximate prolate spheroidal wave functions and standard Rao-Wilton-Glisson basis functions to effect the temporal and spatial discretization of the integral equations, respectively. Because the temporal basis functions are noncausal, an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time. Numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time-bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency-domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time-domain solver.

A novel scheme for the solution of the time-domain integral equations of electromagnetics

The computational complexity of classical marching-on-in-time (MOT) methods for solving time domain integral equations (TDIEs) pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as O(N/sub t/N/sub s//sup 2/) (N/sub t/ and N/sub s/ denote the number of temporal and spatial degrees of freedom (DOF) of the electric current on the target). This scaling law impedes the application of these schemes to the analysis of large-scale scattering phenomena. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based TDIE solvers. Previously, we described a two-level PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting targets; the computational complexity of this algorithm scales as O(N/sub t/N/sub s//sup 1.5/logN/sub s/). Here, a multilevel PWTD scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described. In addition, a multilevel PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting scatterers using O(N/sub t/N/sub s/log/sup 2/N/sub s/) CPU resources is outlined. Last, the accuracy and CPU/memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies.

Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm

An optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples. Using the concept of the field equivalent (spatial) bandwidth, a central interpolation scheme is developed to compute the field in theta , phi coordinates, starting from its samples. The maximum allowable sample spacing and error upper bounds are also rigorously derived. Several simulated examples of pattern reconstruction are presented, for both the cases of field and power pattern interpolation. The interpolation error, as a function of the retained sample number, has been also evaluated and compared with the theoretical upper bounds. The algorithm stability versus randomly distributed errors added to the exact samples is demonstrated. >

Optimal interpolation of radiated fields over a sphere

An optimal sampling interpolation algorithm which allows the accurate recovery of plane-rectangular near-field samples from the knowledge of the plane-polar ones is developed. This enables the standard near-field-far-field (NF-FF) transformation, which takes full advantage of the fast Fourier transform (FFT) algorithm, to be applied to plane-polar scanning. The maximum allowable sample spacing is also rigorously derived, and it is shown that it can be significantly greater than lambda /2 as the measurement place moves away from the source. This allows a remarkable reduction of both measurement time and memory storage requirements. The sampling approach is compared with that based on the bivariate Lagrange interpolation (BLI) method. The sampling reconstruction agrees with the exact results significantly better than the BLI, in spite of the significantly lower number of required measurements. >

Fast and accurate near-field-far-field transformation by sampling interpolation of plane-polar measurements

A new series for the interpolation of band-limited functions is found by using an approximation to tho prolate spheroidal wave function as a convergence factor. A truncation error bound is found for the central interpolation of band-limited functions using the new series. It is shown that this bound is lower than other known bounds in many cases of interest.

Interpolation of band-limited functions using the approximate prolate series (Corresp.)

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Interpolation of band-limited functions using the approximate prolate series (Corresp.)