On a special case of the basic problem in diffraction tomagraphy

The basic problem in diffraction tomography is the problem of reconstructing the index of refraction of a scattering object. A new algorithm for its solution in the special case where the index of refraction is assumed to be real and not less than unity is proposed. An estimate of this algorithm’s rate of convergence is given. The limited-view problem has assumed a central place in recent investigations in diffraction tomography. The estimate of our algorithm’s rate of convergence allows one to estimate the degree of uncertainty in the reconstruction of the index of refraction from incomplete data for special directions of wave propagation.