The freeform reflector for uniform rectangular illumination

Energy from the source was rearranged through reflection by a freeform reflector, in order to get uniform rectangular illumination. The numerical results of partial differential equation sets were investigated to obtain the freeform reflector and these equations were obtained upon the determination of the characters of source and the desired illumination. As an example, a light emitting diode (LED) with a Lambertian light-emitting surface of 1 x 1 mm(2) and a viewing angle of 120 degrees was applied as the source, and the target plane was a 4 : 3 rectangle with uniform illumination. The projective length of the reflector on x-axis is about 23 mm, and on y-axis is about 21 mm. Thus the illumination system is very compact.