Frequency-domain scattering by nonuniform truncated arrays: wave-oriented data processing for inversion and imaging

Abstract

We previously presented an asymptotic diffraction theory for time-harmonic and transient scattering by arbitrarily illuminated truncated nonuniform thin-wire gratings [ J. Opt. Soc. Am. A11, 1291 ( 1994)]. We parameterized and interpreted the results in terms of scattered truncated Floquet modes (FM’s) and Floquet-modulated edge diffraction, which generalize the constructs of the conventional geometric theory of diffraction (GTD). We also demonstrated that numerical implementation of the FM–GTD algorithm yields results that compare very well with data computed from rigorously based numerical reference solutions. We enlarge the previous frequency-domain numerical data base for gratings to scattering by truncated arrays whose elements are arbitrarily oriented strips rather than thin-wire filaments and also to arrays whose element locations depart from truncated periodicity in a random rather than an orderly manner. We show that the FM–GTD parameterization of the scattered field remains applicable under these generalized conditions. With a view toward inversion and imaging, our principal purpose is the application of space-wave-number phase-space processing techniques to extract the footprints of truncated nonuniform periodicity from the scattered-field data. Because the processing is tied to the wave physics, we refer to this procedure as wave-oriented data processing. Implementation involves projection onto appropriate phase-space subdomains and the generation of space–wave-number phase-space distributions by windowed Fourier transforms. It is found that this form of processing in the frequency domain highlights effects of truncation and perturbed periodicity but is not very sensitive to the structure of the array elements (i.e., wires versus strips). In a companion paper [ J. Opt. Soc. Am. A11, 2685 ( 1994)] we perform phase-space processing in the time domain, show how the time-domain FM-GTD phenomenology is revealed through time-frequency distributions, and show also how short-pulse excitation enhances the sensitivity with respect to element structure by means of spatial–temporal resolution.