Illumination uniformity and color mixing results are essential for color vision applications. In this paper, an indirect method is proposed for the uniform illumination, and a mathematically simulated algorithm is developed. We integrate the method of light-emitting diode (LED) array and diffuse reflection surface for uniform illumination system. By considering each single LED as an imperfect Lambertian emitter, we discuss the irradiance distribution over a sphere's inner surface to the three-ring LED array. The sphere's inner surface is a diffuse reflection surface with high hemisphere reflectance. Using the bi-directional reflectance distribution functions (BRDF) of the sphere's inner surface, we simulate the uniformity of the LED illumination at varying distances. Finally, we design a practical LED illumination. The uniformity of practical LED illumination agrees with the simulated result. The results demonstrate the usefulness of this method for uniform illumination design.
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