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Construction Method of Tailored Facets for Use in Freeform Reflectors Design

ABSTRACT A construction method to obtain sets of tailored facets to be used as the initial configuration in the design of freeform reflector surfaces is presented. The construction strategy starts from a collection of flat elementary facets and achieves the initial configuration of the reflector surface by tailoring the facets according to their Bézier surfaces description. The aim of this research is to describe a procedure capable of generating the Bézier surfaces that define elementary tailored facets; these facets could then be used as initial configurations in the design of freeform reflectors. Though beyond the scope of this article, the facets could be used on a subsequent optimization process; that is, the geometry of the elementary facets could be modified through a global optimization process taking into account all facets, in order to further improve the entire illumination system. Ray tracing is used to calculate the facet’s geometry; it applies elementary merit functions to find the parameters defining the Bézier curve that best meets specifications in each elementary facet. This method is based on a sequential 2D projection strategy that employs different strategic planes for calculations. A method to build up the facet’s geometry using a Bézier surface from 2D curves is provided. This approach will successfully generate a set of control points to describe a Bézier surface compatible with any standard optical optimization tool and suitable for use with computer-aided design (CAD) and other tools that represent solids.