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The Physical Optics and Exact Inverse Scattering solutions of this author are summarized. For the Physical Optics Inverse Scattering Method, shown are computer-reconstructed images of a sphere and cylinder from computer synthetic scattering data, as well as a sphere from experimentally measured data. For the Exact Inverse Scattering Method, shown are computer-reconstructed source distributions (currents) of a half wave dipole antenna, a point-source, and two point-sources separated by one-half-wavelength, from computer synthetic scattering data., See also AD910661.

Recently developed formulations of the inverse problems in acoustics and electromagnetics are described. There are two types of formulations, one in the geometrical optics limit and the other, an exact formulation for the inverse source problem. Both basic formulations are extended to include the realistic problem of a 'limited aperture' of observations. It is also shown that the inverse source formulation can be applied to the problem of reconstruction of media inhomogeneities from remotely sensed field data. The basic physical optics result is that the characteristic function of the scattering obstacle and the phase and range normalized scattering amplitude are a Fourier transform pair. All other formulations lead to Fredholm integral equations of the first kind.

The extraction of target characteristics from the broad band, impulse-generated echo at a single target aspect is demonstrated for spherical and spheroidal targets. Target recognition by broad band echo-ranging is further compared with CW echo-ranging on theoretical and operational grounds. Even though impulse echo-ranging offers certain advantages, inverse scattering calculations do not appear practical except at short range, and in the absence of overlapping direct and surface-reflected returns. A promising application of broad band echo-ranging not related to inverse scattering proper appears to be the determination of a target's structural characteristics through shock wave excitation of its structural resonances. (Author), See also AD-768 369.

The plane wave representation is generalized in terms of a three- dimensional Fourier transform, to yield an expression, which when combined with the incident field, gives the total electric field everywhere inside and outside non-magnetic scattering bodies. This representation requires the knowledge of the scattering matrix and its analytic continuation in the frequency domain. The use of short pulse data to determine the properties of uniformly coated bodies is considered, where the main attention is applied to the illuminated portion of smooth convex bodies at high frequencies. Computational results are obtained, establishing the conditions that are required to determine the surface of a conducting body from knowledge of the total near field. It is shown for the cases treated (sphere and prolate spheroid), that two separate conditions are required. One of these conditions yields a single surface which is an approximation to the proper surface, whereas, the other condition yields a set of surfaces, among which is the exact surface., See also quarterly report no. 3, AD665857.

The conventional definition of the monostatic monochromatic polarization matrix is first extended to the bistatic case, then to the short pulse case, and finally to the bistatic short pulse case. The transformations and convolutions involved are discussed in some detail. The method of determining the Least Square Best Estimate of the Generalized Polarization matrix from a set of measurements is then developed. It is shown that the Faraday rotation angles introduced by a magneto ionic medium intervening the radar and the target are determinable from measured short pulse monostatic polarization matrix data. It is then shown that the Least Square Best Estimate of the orientation angle of a symmetric target is also determinable from Faraday rotation contaminated short pulse monostatic polarization matrix data.

An inverse scattering method based on geometric acoustics is described and its accuracy investigated numerically as a function of frequency and range for the case of a rigid sphere. (Author)

An effective zero order scattering theory for perfect conductors, consistent with monostatic high range resolution radar concepts, is developed. With the aid of this theory, a basic Inverse Scattering Identity is then developed that states that the characteristic function (in three-dimensional space) of a scatterer is related to the field cross-section (in three-dimensional k-space) by a three-dimensional Fourier Transform. Uniqueness of the inverse for finite sized scatterers is established. A general inverse scattering solution is then developed that permits the determination of an appropriate maximum of information about a scatterer from incomplete scattering data. The specific solution for a finite three-dimensional aperture in the physical optics regime is then developed. The solutions developed in this report can thus be viewed as solutions to the frequency band limited and aspect angle limited short pulse synthetic aperture imaging (and associated data processing) problem; except that the solutions presented are based on rigorous electromagnetic scattering and inverse scattering theory applicable to spatially distributed scatterers, yielding Real Geometrical images; vis-a-vis the conventional heuristic approach based on radar and isolated point scatterers (scattering centers) concepts, yielding Radar images.

The problem in question consists of determining means of solving the inverse scattering problem where the transmitted field is given and the received fields are measured, and this data is used to discover the nature of the target. The problem of what information can be determined about the body if the scattering matrix (phase and amplitude) is known only over an angular sector and measured in the far field, is studied. Some of the results are presented in the second section. In particular, the necessity of using short pulse measurements to separate out the signals from the various scattering centers is pointed out. The study of the short pulse bistatic measurements is under investigation. For smooth convex surface, particular positions of the scattering body can be obtained. (Author)

The problem in question consists of determining means of solving the inverse scattering problem where the transmitted field is given and the received fields are measured, and this data is used to discover the nature of the target. The problem of what information can be determined about the body if the scattering matrix (phase and amplitude) is known only over an angular sector and measured in the far field, is studied further. Asymptotic analysis is used to show that in the high frequency case, portions of a piecewise smooth, convex surface can be found when knowledge of the bistatic scattered field is confined to a small cone. (Author)

This report summarizes research activities of the Division of Electromagnetic Research of the Courant Institute of Mathematical Sciences at New York University under Contract Number AF19 604 3495. The research described is in the field of wave propagation in variable media and mathematical problems related to such studies. (Author)