Theoretical background

Ray tracing requires the solution of two system of equations, namely, of the Eikonal equations (to determine ray coordinates), and of the transport equations (to calculate ray amplitudes). Solving the Eikonal is straightforward in most cases, although it requires a correction in phase every time a ray hits a boundary. Solving the transport equation in the classical approach rises singularity problems related to the formation of caustics, which can be eliminated by using alternative approaches, such as the Gaussian beam approximation. With this approach the classical transport equations are substituted with the so-called dynamic equations, which are free of singularities. Both the Eikonal and the dynamical equations are described in the following subsections.