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Finite Light Source – Mathematical Description

Calculating the reflector shape for required light distribution is the critical focus for optical design of lighting fittings.

Most calculation methods deal with a point light source. However, this approximation does not always lead to agreement between calculated and actual parameters. The main principle of the optical design with a real source is that luminance values are averaged at each point of reflected field within the output pupil of the reflector that reflects light to this point. The optical design SHAPE software allows one to calculate the light distribution of the systems with a finite source for rotational and cylindrical symmetries. Luminous characteristics of the light source surface, specified as a uniform light source of finite dimensions, are widely applied in design.

The SHAPE mathematical methods of optical design for a light source of finite dimensions are based on solving a system of first-order differential equations, which describe the reflector profile under specified initial conditions (Cauchy problem). The algorithm for determining the optimal geometric parameters of reflector for a specified light distribution is described in the publications "Synthesis of specular reflectors for a finite size light source" (A.A. Korobko, O.K. Kusch — Lighting Research and Technology , 2004  — 36: 13-29) and "Computer-Aided Optical Design of Illuminating and Irradiating Devices" (O.K. Kusch).