Design of led TIR-optics producing prescribed illuminance distributions in circle regions

The problem of axis-symmetrical LED TIR-optics design is reduced to the numerical integration of the first-order explicit differential equations. The examples of optical elements producing uniform illuminance distributions with angle size of 40° are computed. The light efficiency of computed optical elements is 90%-92% and the nonuniformity of generated irradiance distribution is less than 4%. The dependence of nonuniformity on the size of light source is obtained. It is shown that the proposed solution provides good performance in case when the size of the light source is 5 (or more) times smaller than the distance from the light source to the inner surface of the optical element.