Abstract

A geometrical nonlinear inverse solution of the one-dimensional Helmholtz equation is presented, making it possible to deduce the size and strength of a scatterer from the spectrum of the equation. Plotting the real and imaginary parts of the backscattered field as a function of the wave number in the complex plane yields a circle. From the radius and the intercept of this circle, some properties of the scatterer can be deduced without ambiguity and without recourse to any numerical or signal-processing techniques. The method is applied to the complex scattered spectrum but can be adapted to treat the amplitude spectrum alone, thereby extending the experimental conditions for which the inverse problem can be attempted. The inversion procedures are tested on sets of strong inhomogeneous and homogeneous scatterers by using exact solutions to the wave equation and experimental data, respectively.

© 1989 Optical Society of America

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