A formula for the ray density over a caustic surface for variable index media

Abstract

The acoustic ray density becomes infinite over caustic surfaces and therefore cannot be used as a measure of the concentration of rays at or near the caustic. A finite substitute measure, the density of rays tangent of the caustic, may be obtained by dividing an element of incident flux by the area of the caustic formed by the associated rays. This provides a measure of the energy density over different regions of the caustic. As an example the ray density over the caustic is evaluated for a linear depth dependent index of refraction.