Ray tracing in a finite-element domain using nodal basis functions.

A method is presented for tracing rays through a medium discretized as finite-element volumes. The ray-trajectory equations are cast into the local element coordinate frame, and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The finite-element methodology is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The procedure is applied to a finite-element model of an optic with a severe refractive-index gradient, and the results are compared to the closed-form gradient ray-path integral approach.