In modern high frequency inversion of acoustic scattering data, standard ray theoretic methods play an important role, since the inversion operation is usually formulated in terms of traveltimes and amplitude functions computed along the rays. In this approach one formulates the inversion procedure in terms of a Fourier-integral operator acting on the scattering data. It is well known that this Fourier-integral operator reproduces the most singular part of the scattering potential, provided that there are no multiple ray paths between any two points in the medium. This rules out many practical situations in which caustics in the ray field are present. We show that under a relatively mild condition the inversion technique mentioned above can be extended to allow for caustics. We also present an explicit inversion formula.