A mathematical model to generate a light reflector that produces a uniform irradiance distribution from a point light source

In this work, we present the development of a mathematical model profile for a light reflector that generates a uniform irradiance distribution from a point light source on a flat region at a fixed distance. The mathematical model is based on the theory of geometric optics, particularly the concepts of reflection, ray tracing, point light sources, spherical caps, and elliptical curvatures. Numerical simulations illustrate that the mathematical model is adequate because its geometry produces a uniform irradiance from a point source. This model allows manufacturers reflectors smaller than parabolic reflectors, which are currently used to generate this type of uniform light irradiance distribution, allowing these devices to be used in smaller optoelectronic systems.