The mutual coherence function of a deterministic acoustic field obeying a parabolic equation will be expressed in terms of Fourier representations of the Green functions for the field. In the short wave limit, these representations allow for a uniform treatment of the field near various real space caustics by circumventing apparent singularities. We use the Fourier representation of the Green function to compute, near a caustic, the intensity arising from an extended source and the mutual coherence function arising from a point source. We will show that the asymptotic Green function expression for the coherence function contains interference effects from separated ray paths that are not contained in local radiative transport equations for the coherence function.