Smoothing of ellipsoid flow patches in optical design for freeform reflector

The optical design based on foci mapping ellipse flow-patch method has many advantages, such as clear geometric meaning, design flexibility and explicit method of optimization, but there is a drawback that the surface is not smooth. In order to sew up each ellipse flow-patch on the freeform reflector smoothly, the surface of reflector started from one point on the edge and a smooth ellipse flow-patch was built in the direction, then the discontinuity in the direction could be reduced by the energy adjusting method. The time consumption for the surface reconstruction from 40 000 ellipsoid pieces with this method is only about 2 min. The free-form surface cannot only ensure the energy distributed equally, but also improve the smoothness greatly.