FREQUENCY-DOMAIN SCATTERING BY NONUNIFORM TRUNCATED ARRAYS - WAVE-ORIENTED DATA-PROCESSING FOR INVERSION AND IMAGING

We previously presented an asymptotic diffraction theory for time-harm onic and transient scattering by arbitrarily illuminated truncated non uniform thin-wire gratings [J. Opt. Soc. Am. A 11, 1291 (1994)]. We pa rameterized and interpreted the results in terms of scattered truncate d Floquet modes (FM's) and Floquet-modulated edge diffraction, which g eneralize the constructs of the conventional geometric theory of diffr action (GTD). We also demonstrated that numerical implementation of th e FM-GTD algorithm yields results that compare very well with data com puted from rigorously based numerical reference solutions. We enlarge the previous frequency-domain numerical data base for gratings to scat tering by truncated arrays whose elements are arbitrarily oriented str ips rather than thin-wire filaments and also to arrays whose element l ocations depart from truncated periodicity in a random rather than an orderly manner. We show that the FM-GTD parameterization of the scatte red field remains applicable under these generalized conditions. With a view toward inversion and imaging, our principal purpose is the appl ication of space-wave-number phase-space processing techniques to extr act the footprints of truncated nonuniform periodicity from the scatte red-field data. Because the processing is tied to the wave physics, we refer to this procedure as wave-oriented data processing. Implementat ion involves projection onto appropriate phase-space subdomains and th e generation of space-wave-number phase-space distributions by windowe d Fourier transforms. It is found that this form of processing in the frequency domain highlights effects of truncation and perturbed period icity 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. A 11,2685 (1994)] we perform phase-space processing in the time domain, show how the time-domain FM-GTD phenomenology is revealed through tim e-frequency distributions, and show also how short-pulse excitation en hances the sensitivity with respect to element structure by means of s patial-temporal resolution.