Abstract. In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge-Ampère type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light, and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software.

Atmospheric pressure plasma jets generated by kHz nanosecond voltage pulses typically consist of guided streamer discharges called plasma bullets. In this work, plasma bullets are generated in a pulsed plasma jet using N 2 as feed gas and their electric field distribution is investigated by polarization-resolved four-wave mixing. The method and its analysis have been extended to resolve radial profiles of non-uniform, but radially symmetric, electric field distributions. In addition, a calibration procedure using an electrode geometry different from the discharge geometry has been developed. A radially resolved profile of the axial electric field component of a plasma bullet in N 2 is presented, as well as the temporal development of the (line-integrated) radial and axial components of the electric field. To verify the results, they are compared to a streamer model adapted to the conditions of the experiment. The peak values obtained from the experiment are in the range expected from streamer literature. However, there are some quantitative differences with the model, which predicts values approximately a factor two lower than those found in the experiment, as well as a faster radial decay. The temporal development shows similar features in both the experiment and the model. Explanations for these differences are provided and further improvements for the method are outlined.

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.