Imaging principle of a selffocusing lens

Compared with selffocusing cylindrical lens, selffocusing cone lens has its unique features. When paraxial collimated beam goes through a cylindrical lens, its amplitude, phase and period remain the same, but for a conelens, all these parameters are changed. Compared with the light equation for cylindrical lens, the equation for conelens is much more complicated. The paper derived a light equation for conelens. With this equation, the light spot size behind conelens can be designed. It can find application in microillumination systems.