Design of TIR optics generating the prescribed irradiance distribution in the circle region

We present the method for computation of highly effective total internal reflection (TIR) optics for LED-based illumination systems. The computation problem is reduced to the integration of several explicit independent first-order differential equations. Two designs of TIR optics are considered and compared: with flat and with aspherical upper surface. The dependence of nonuniformity of generated irradiance distribution on the size of the light source is studied for both designs numerically. It is shown that point source approximation is acceptable in cases when the size of the light source is 5 (or more) times less than the distance to the inner surface of the optical element.