We propose an effective optimization method for generating smooth freeform surfaces for light-emitting diode(LED)non-rotational illumination based on ray targeting.This method begins with a starting design and goes through two optimization steps.An initial estimate is determined using a partial differential equation(PDE)method and a variable separation mapping.In the first optimization step the merit function is developed with ray targeting to ensure the shape of the illumination pattern.The purpose of the second optimization is to further improve the optical performance by constructing the merit function with uniformity and efficiency.Smooth freeform reflective and refractive surfaces,which can produce a uniform rectangular illumination without rotational symmetry,are designed using this method.The results show that uniform rectangular illumination is achieved and that smooth freeform surfaces are obtained.With ray targeting,the design efficiency can be significantly enhanced,and excellent optical performance can be achieved. We propose an effective optimization method for generating smooth freeform surfaces for light-emitting diode (LED) non-rotational illumination based on ray targeting. This method begins with a starting design and goes through two optimization steps. An initial estimate is determined using a partial differential equation (PDE) method and a variable separation mapping. the first optimization step the merit function is developed with ray targeting to ensure the shape of the illumination pattern. The purpose of the second optimization is to further improve the optical performance by constructing the merit function with uniformity and efficiency. smooth freeform reflective and refractive surfaces. which can produce a uniform rectangular illumination without rotational symmetry, are designed using this method. results show that uniform rectangular illumination is achieved and that smooth freeform surfaces are obtained. targeting, the design efficiency can be significantly enhanced, and exce llent optical performance can be achieved.