Differential Fourier transform technique for the inverse scattering problem

An inversion technique was developed for determining the size distribution of randomly distributed tenuous scatterers from the forward scattering pattern. This technique is applicable for 1-D, 2-D, and 3-D scatterers. It does not require matrix inversion or a priori knowledge of functional forms of the size distribution, and it takes advantage of the fast Fourier transform and digital filtering techniques in spectral analysis. A typical error for 10% noise was within a few percent in the estimation of Gaussian size distribution using 1024-point FFT. The usefulness of this technique in practice was shown in experiments with latex spheres and bacteria.