Synthesis of specular reflectors for a finite size light source

Abstract

Finding a reflector shape to provide a required light distribution is a major problem in the design of luminaires. Most methods for solving the problem assume the light source is a point. However, this assumption leads to great discrepancies between the required and calculated luminous intensity. In addition, it gives no answer to the question of whether it is possible to provide any arbitrary light distribution. A method for computing the shape of a specular reflector, with cylindrical or axial symmetry, operating with a finite size light source and providing a required light distribution, is presented in this study. The luminance distribution of the surface of the light source is specified very close to reality. The method is based on solving a system of first-order differential equations that describe a pro-file curve of a reflector under specified initial conditions (Cauchy problem). The study defines under what conditions a required light distribution of a reflector can be realized. The mechanism (image transformation function) for finding the optimum geometrical parameters of a reflector for a given light distribution and for given initial conditions is described.

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