Ray tracing is an integral part of modern imaging and inversion techniques. Several methods have been proposed depending on the requirements of the application. Some algorithms are best applied to fast changing material properties, like an interface between two differing media, while others are well suited to media with gradually changing properties, like composite materials. In this paper, an enhanced numerical algorithm for ray tracing is presented. Focus is given to solutions involving ordinary differential equations with initial-value conditions. The proposed algorithm is the result of a combination of two classical implementations and the authors show that it is well suited for media with both sharp and gradual changes in the index of refraction. Additionally, the authors present an application of ray path computation by using the technique known as the shooting method.

In this work, we present an algorithm capable of emulating ray trajectories that obey the least action principle. The method is based on spectral decomposition of geometric shapes taken from a set of raypaths. As the proposed work relies on shape analysis, it is agnostic on the underlying physics of raypath generation. As such, it is independent of the ray tracing method used to generate the training paths. In cases of mildly heterogeneous media or scenarios with a limited number of geometrical scatters, we show that the algorithm is capable of efficiently populating a given scenario with a dense array of emulated rays whose trajectories are in close agreement with actual rays. We argue that the algorithm also serves as an effective method capable of detecting regions where ray variation is high, such as when possible shadow zones are present.