Creation of a uniform circular illuminance distribution using faceted reflective NURBS surfaces

Abstract

Non-Uniform-Rational-B-Spline (NURBS) surfaces were investigated as a tool for creating an incoherent uniform circular illuminance distribution on a target plane. Specifically, a superposition solution, employing faceted reflective surfaces was explored. The primary shape of the facets investigated was square, in spherical polar coordinates, mainly due to tiling concerns. An optimization procedure was the primary method for determining the NURBS variables for facet surfaces. For the case of a single square-facet that creates a uniform circular-illuminance distribution, a perfect solution using aim-ray defects proved difficult at best. However, the use of flux tubes in evaluating the illuminance yielded a highly uniform distribution with a very nearly circular shape. Superposition surface-point interpolation NURBS surfaces, constructed with this type of facet, were found to provide an excellent solution to the overall problem. Solutions of this type were shown to be more efficient than a standard algorithmic approach. NURBS surfaces provided excellent boundary control, and while often non-critical in single-aperture systems, boundary control was found to be very important for faceted systems. The techniques developed for creating uniform illuminance distributions with shapes different from the facet aperture were also applied to other problems: such as a square-facet to arcuate-illuminance pattern, and a circular-facet to a square-illuminance pattern.