Based on the light mapping method of optimal transmission theory,the initial parameters of the free form optical system for zero extension light source are calculated for the design of the optical system for asymmetric illumination,with the distance from the light source to the irradiated surface of 20mm,and the realization of the letter “JL” within the range of 50mm×50mm as the target.The initial parameters of the free form optical system for zero extension light source are calculated,and based on this,the free form optical system for zero extension light source and extended light source is optimally designed and simulated using LightTools software.The results show that for zero extension light source,the free form surface diameter is 86.52mm,the distance between the light source and the free form surface is 34mm,and the illumination distribution control of the letter “JL” can be realized on the irradiated surface；when facing the extended light source with a diameter of 10mm,the diameter of the free surface is 435.16mm,the distance between the light source and the free surface is 242mm,and the illumination distribution control of the letter “JL” can be achieved on the irradiated surface,indicating that the designed system can realize the asymmetric illumination distribution control and effectively improve the efficiency of the design of the free form optical system.