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.

KEYWORDS:

• nonimaging optics
• optical design freeform
• reflector
• faceted reflector
• tailored facet

ORCID

Núria Tomás

http://orcid.org/0000-0001-5799-2870

Additional information

Funding

This study was funded by the Spanish government under contract DPI2012-38647-C02-01 titled “Estrategia para Incluir el Perfil GRIN Inducido en el Proceso de Inyección de las Lentes de Plástico en las Etapas de Diseño de Sistemas Ópticos” (Strategy to Include the GRIN Profile in the Injection Process in Plastic Lenses during Optical Systems Design).

Notes on contributors

Núria Tomás

Núria Tomás is an assistant professor at the Universitat Politècnica de Catalunya. She received her B.S. in optics from Universitat Politècnica de Catalunya in 1990 and M.S. degree in Applied Optics from Reading University in 2001. Her research activity focuses on optical design and she is preparing her Ph.D. degree in physics at UPC. She is currently lecturer of several subjects related with optometric instrumentation in the B.Sc. and M.Sc. of the Terrassa School of Optics and Optometry (UPC).

Josep Arasa

Josep Arasa has been a full professor of the UPC since 1992. His main specialty is the Optical Desing. He received his PhD in physics in 1988 from the University of Barcelona (UB).In 2003 he founded SnellOptics and currently holds the presidency. Since 2000 he is involved in the CD6 (Center for the development of Sensors, Instrumentation and Systems) being scientific responsible for the Research Unit in Plastic Optical Quality (QPO) partnered with ASCAMM, a Catalonian Technology Center. He has also supervised 9 PhD theses in Optical Engineering and is a member of SEDO, SPIE and EOS associations.