Nonimaging optics is focused on the study of techniques to design optical systems for the purpose of energy transfer instead of image forming. The flowline optical design method, based on the definition of the geometrical flux vector J
, is one of these techniques. The main advantage of the flowline method is its capability to visualize and estimate how radiant energy is transferred by the optical systems using the concepts of vector field theory, such as field line or flux tube, which overcomes traditional raytrace methods. The main objective this paper is to extend the flowline method to analyze and design real 3D concentration and illumination systems by the development of new simulation techniques. In this paper, analyzed real 3D refractive and reflective systems using the flowline vector potential method. A new constant term of optical path length is introduced, similar and comparable to the gauge invariant, which produces a correction to enable the agreement between raytrace- and flowline-based computations. This new optical simulation methodology provides traditional raytrace results, such as irradiance maps, but opens new perspectives to obtaining higher precision with lower computation time. It can also provide new information for the vector field maps of 3D refractive/reflective systems.
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