Ray tracing method in phase space for two-dimensional optical systems

Abstract

Ray tracing is a forward method to calculate the photometric variables at the target of a non-imaging optical system. In this paper, a new ray tracing technique is presented to improve the accuracy and to reduce the computational time of the classical ray tracing approach. The method is based on the phase space representation of the source and the target of the optical system, and it is applied to a two-dimensional TIR-collimator. The strength of the method lies in tracing fewer rays through the system. Only rays that lie in the meridional plane are considered. A procedure that disregards rays in smooth regions in phase space, where the luminance is continuous, is implemented and only the rays close to discontinuities are traced. The efficiency of the method is demonstrated by numerical simulations that compare the new method with Monte Carlo ray tracing. The results show that the phase space approach is faster and more accurate than the already existing ray tracing method; moreover the phase space method converges as one over the number of rays traced unlike Monte Carlo ray tracing in which the speed of convergence is proportional to one over the square root of the number of rays.

Phase Space Ray Tracing for a Two-dimensional Parabolic Reflector

“…Therefore, the finer the triangulation is the more paths are detected. To select the correct parameters, conservation of the energy is employed, see [5] for more details. For the system analyzed in [5] only 5 different paths can occur, while, due to the multiple reflections, for a parabolic reflector many paths can occur.…”

“…In case ∂R 4 (Π) has more than two intersection points with p = constant, that equation should be modified accordingly. This situation occurs when more complicated optical systems are considered and the shape of the regions R 4 (Π) is not very regular (see as an example the case of the TIR collimator described in [5]). …”

“…The averaged PS intensity g PS (p) along a given direction p ∈ P 2 is given by the average of G PS over the bin to which p belongs. Then, the averaged and normalized intensityḡ PS is calculated dividing g PS by the total flux, see [5] for more details.…”

“…In [5] we presented the method for a two-dimensional total internal reflection (TIR) collimator where both the reflection 136 Phase Space Ray Tracing for a Two-dimensional Parabolic Reflector and the refraction law play a role. In this paper we show the method for a two-dimensional parabolic reflector where only the reflection law is considered.…”

“…The method is therefore able to detect most of the relevant paths. The difference between the TIR collimator analyzed in [5] and the parabolic reflector is that for the latter case the refinement procedure has to be very fine to detect many paths. This leads to a large number of path and potentially a long computational time.…”