Scintillation of radio sources: The signature of a caustic

The role of caustics in the scintillation of radio sources due to thin-screen scattering is explored. The classical stationary phase treatment of this type of scattering implies singular behavior at the caustics. Physically, this singularity is resolved by diffractive effects, and a smooth but highly peaked intensity distribution is expected, analogous to what we observe in geometrical optics. However, in a companion paper we showed that the intensity amplification near a caustic can be very mild and is typically swamped by a rapidly oscillating diffractive interference pattern. In this paper we introduce a modified stationary phase method that employs an Airy function approximation near caustics. This modified method provides an accurate estimate of the intensity near the caustic and allows us to show that significant intensity enhancement is only expected to develop for extremely strong scattering screens. In this limit the behavior of the intensity near the caustic depends on only a small number of bulk properties of the scattering screen. As such, not only does it provide a clear signature for when a caustic has been crossed, it also may be used to yield important properties of the scattering medium.