Iterative inversion reconstructs the object from the measured scattered fields by minimizing the cost function defined as the sum of the squared magnitude of the difference between the angular spectrum of the measured fields and that of the fields calculated from the assumed profile of the scatterer. In the conventional iterative inversion using the method of moments the object is discretized into small cells, in which the total field and the permittivity may be assumed to be constant, to linearize the integral representation of the scattered fields. The size of the matrix to calculate the total field inside the scatterer becomes N × N where N is equal to the total number of the discretized cells. The major limitations in the conventional iterative inversions is therefore the computer capability to calculate the forward scattered fields involving the inversion of the fairly large matrix.
The integral equation for the scattered fields may be linearized by expanding the polarization current inside the scatterer in terms of Fourier series in the angular direction and orthogonal and complete eigenfunctions in the radial direction. It may be shown that the eigenfunctions have the resonance characteristics and none of them corresponds to a nonradiating source. The orthogonality of the eigenfunctions makes the unknown coefficients for the polarization current obtainable by arithmetic calculation without matrix inversion when the relative permittivity is assumed to be homogeneous. If the relative profile is -dependent, the coefficients for each angular mode can be calculated separately by the inversion of the matrices of small size. If one choose the resolution of the profile to be reconstructed lower than the highest order of the effective modes of the measured scattered fields, the matrix to be inverted becomes sparse and the computation time for the inversion can be reduced very much even for the profile varying with respect to and radial distance and angle.
In order to find the global minimum of the cost function a hybrid optimization algorithm combining the genetic algorithm and the Levenberg-Marquardt algorithm has been used. High-contrast circular dielectric cylinders having their diameter of 2 wavelengths and 4 wavelengths have been reconstructed with negligible reconstruction errors from multiple incidences of plane waves in the presence of 20 % Gaussian noise in the scattered fields.
