The canonical problem of scattering by a circular cylinder is expressed in integral form. The integrals are evaluated asymptotically to yield the first motion approximations. The geometrical theory of diffraction, developed by Keller, is combined with the first motion approximations to solve the problem of scattering by a smooth convex cylinder. The results are valid for pulses whose durations are short compared to the travel time across the cylinder.
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Freeman Gilbert (1960) studied this question.