Design of axis-symmetrical optical element with two aspherical surfaces for generation of prescribed irradiance distribution

Method of design of axis-symmetrical refractive optical element with two aspherical surfaces for generation of prescribed radially-symmetrical irradiance distribution is presented. The computation problem is reduced to the integration of set of three first-order differential equations solved for the derivatives. The performance of two optical element designs with spherical and aspherical inner surface is compared. The design with aspherical inner surface produces light efficiency of 80-90% for illuminated regions with angular size of 0°-160°.