Degrees of freedom for scatterers with circular cross section

The inverse scattering problem for a scatterer that is independent of one spatial coordinate is considered in the Born approximation. Assuming a circular cross section for the scatterer, the number of degrees of freedom of the field scattered over the full angular range (2π) is evaluated in the presence of noise. This is obtained by making use of the eigenfunction technique and determining the pertinent eigenfunctions and eigenvalues. The finiteness of the number of degrees of freedom leads us to introduce finite sampling techniques. The results also apply to the dual problem of synthesizing wave field structures starting from computer-generated holograms. The evaluation of the number of degrees of freedom for a series of scattering experiments with different illuminating waves is also outlined. Throughout the paper the similarity between the present problems and the problem relating to the degrees of freedom of coherent images formed through thin-ring pupils is exploited.

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