A method is presented for reconstructing the surface profile of a perfectly conducting rough surface boundary from the measurements of the scattered far-field. The proposed inversion algorithm is based on the use of the Kirchhoff approximation and in order to determine the surface profile, the Fletcher-Powell optimization procedure is applied. A number of numerical results illustrating the method are presented.

A noninvasive method for measuring complex permittivity of biological tissues is proposed. The noninvasive method is based on an inverse scattering technique which employs an iterative procedure. The iterative procedure consists of solving an electric field integral equation using the method of moments and minimizing the square difference between calculated and measured scattered fields. Implementation of the noninvasive method requires the knowledge of the target shape, the incident and measured scattered fields. Based on the noninvasive method, a measuring system of complex permittivity is developed and its reliability is verified.

The inverse problem we consider in this paper seeks, based on the equivalent source method, to determine the shape of perfectly conducting cylinders from the scattered farfield data obtained by using several incident waves. When incident waves of different frequencies are used, the shape of the scatterer can be reconstructed by employing only a few number of observation points. In the reconstruction problem, to determine the shape of the scatterer, the conjugate gradients method is applied. The general approach is applicable to cylindrical scatterers of arbitrary shape. Results of numerical simulations are presented to support the suggested approach.

Reflection mode diffraction tomography is expected to reconstruct a higher resolution image than transmission mode. Its image reconstruction problem, however, in the many cases of practical uses becomes ill-posed one. In this paper, a new reconstruction method of limited angle reflection mode diffraction tomography using maximum entropy method is proposed. Results of simulation showed that the method was able to reconstruct the better quality images than IR method poposed by Kak, et al.

An efficient reconstruction algorithm for diffraction tomography based on the modified Newton-Kantorovich method is presented and numerically studies. With the Fréchet derivative obtained for the Helmholtz equation, one can derive an iterative formula for getting an object function, which is a function of refractive index of a scatterer. Setting an initial guess of the object function to zero, the pth estimate of the function is obtained by performing the inverse Fourier transform of its spectrum. Since the spectrum is bandlimited within a low-frequency band, the algorithm does not require usual regularization techniques to circumvent ill-posedness of the problem. For numerical calculation of the direct scattering problem, the moment method and the FFT-CG method are utilized. Computer simulations are made for lossless and homogeneous dielectric circular cylinders of various radii and refractive indices. In the iteration process of image reconstruction, the imaginary part of the object function is set to zero with a priori knowledge of the lossless scatterer. Then the convergence behavior of the algorithm remarkably gets improved. From the simulated results, it is seen that the algorithm provides high-quality reconstructed images even for cases where the first-order Born approximation breaks down. Furthermore, the results demonstrate fast convergence properties of the iterative procedure. In particular, we can successfully reconstruct the cylinder of radius 1 wavelength and refractive index that differs by 10% from the surrounding medium. The proposed algorithm is also effective for an object of larger radius.