O.M. Bucci

Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples

It is shown that the electromagnetic (EM) field, radiated or scattered by bounded sources, can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded. The number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field. This result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain. It is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry. The case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered. For these geometries, precise and fast sampling algorithms of central type are presented, which allow an efficient recovery of EM fields from a nonredundant finite number of samples. Such algorithms are stable with respect to random errors affecting the data.

On the spatial bandwidth of scattered fields

It is shown that the scattered fields are almost space bandlimited functions. The effective bandwidth W is introduced and evaluated for a very general scattering system, as well as the error made using functions bandlimited to w > W for representing the scattered field. The effective bandwidth is very simply related to the maximum dimension of the scattering system; the error drops to negligible values for modest increases of w compared to W , in the case of large scatterers. Important consequences of the above general results are finally stressed.

On the degrees of freedom of scattered fields

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. >

Electromagnetic inverse scattering: Retrievable information and measurement strategies

With reference to inverse scattering from an unknown object of limited extension embedded in a homogeneous background at a fixed frequency, we show that only a finite-dimensional representation of the unknown contrast can be hopefully retrieved. Exploiting the quasi-band-limitedness property of scattered fields, an accurate upper bound to the dimension of such a space is evaluated in both the single incidence and multiview cases. Moreover, effective schemes are given to collect all the information available from the scattering experiments in a nonredundant manner. As a by-product, an optimal (minimally redundant) sampling strategy for the monostatic radar cross section is also provided. Finally, we briefly discuss how the requirement for a globally effective and reliable solution scheme can lead to a reduction of the actually retrievable information.

Reconfigurable arrays by phase-only control

Due to space or cost reasons, a single array antenna can be required to radiate more than one pattern, each pattern being selected by an electronic control, in which only the phase can be modified. A synthesis method for such a problem that is able to determine both the common amplitude and the various phases in an integrated way is presented. Moreover, the approach is flexible enough to take into account additional constraints and allows an efficient implementation. Some test cases showing the effectiveness of the method are presented. >

Optimal interpolation of radiated fields over a sphere

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. >

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

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. >

A hybrid approach for the optimal synthesis of pencil beams through array antennas

A hybrid approach to the synthesis of excitations and locations of nonuniformly spaced arrays in order to achieve optimal focusing in any given direction is proposed and discussed. The approach takes definite advantage from the convexity of the problem with respect to excitation variables, and exploits a Simulated Annealing procedure as far as location variables are concerned. The corresponding synthesized patterns outperform previously known results in standard benchmark problems.

Deterministic Synthesis of Uniform Amplitude Sparse Arrays via New Density Taper Techniques

Uniform amplitude sparse arrays have recently gained a renewed interest and a number of synthesis techniques, mainly based on global optimization algorithms, have been presented. In this paper, after a discussion about the expected characteristics of such arrays, a simple deterministic approach for the case of pencil beams patterns is proposed and discussed. The approach, which outperforms previous synthesis techniques, takes inspiration from existing (not well-known) density taper procedures to develop a two stages synthesis where the first step is solved in a new closed analytical form, while the second one just requires local refinements or fast 1-D optimizations. As a consequence, the proposed approach avoids the need of multidimensional global optimization procedures and the inherent possibly prohibitive computational costs. Notably the first step, which also exhibits an improved flexibility with respect to other analytical techniques, already outperforms previous approaches in a number of cases of interest. Several numerical results confirm the effectiveness and usefulness of the proposed tools.

Subsurface inverse scattering problems: quantifying, qualifying, and achieving the available information

In inverse scattering problems, only a limited amount of independent data is actually available whenever the finite accuracy of the measurement set up is taken into account. In this paper, we deal with the problem of quantifying such an amount in the subsurface sensing case. In particular, an alternative formulation of the problem is given which also allows to understand how to dimensionate the measurement setup in an optimal fashion. Analytical results are reported for the case of a lossless soil, while a numerical study is carried out in the general case. By relying on the same formulation and tools, we also discuss the kind of unknown profiles that can actually be retrieved. In particular, it is shown that the class of retrievable functions exhibits intrinsic multiresolution features. This suggests that adoption of wavelet expansions to represent the unknown function may enhance the reconstruction capabilities. Numerical examples support this conclusion.