On a problem of inverse scattering in optics: the dielectric inhomogeneous medium

An attempt is made to determine a diffracting object from a diffraction pattern. Specifically the index profile of a dielectric layer backed by a perfectly conducting plane is required. The mathematical difficulties are analysed in a rigorous manner and it is explained why the problem is 'ill posed' in the sense of Hadamard (1932). A weak error on the data can produce on extreme error on the object determination. To overcome this difficulty, recent work by Tikhonov (1976) was consulted. On several examples it is shown that the numerical program used permits the index profile to be determined without hypothesis of their shapes.