Application of variational calculus to nonimaging optics:: design for small sources in three dimensions

In this work the variational calculus will be applied to the design with axisymetric sequential optical surfaces for small sources directly in 3D. This method is proven to be useful even in the case in which the skewness distributions of output bundle and emitter do not fit. The tool provides both the optimum 3D ray bundles at the exit aperture of a rotational collimator and the best 2D assignation of rays allowing the collimation reach its limit. Once this best assignation has been obtained, the optical profiles can be designed easily using only the central ray of the bundles. Afterwards, the actual device is obtained by rotation As a consequence of the kind of method aforementioned the angular performance of the collimators can be nearly error-free predicted before ray tracing.