LED has numerous advantages, including low energy consumption, high efficiency, compact size, long life. Consequently, it has been widely used in many lighting fields such as road lighting, automotive lighting and indoor lighting [1,2]. Optical free-form surfaces are widely used in non-imaging optical systems, especially in the design of LED non-imaging systems.

In practical design, methods for secondary light distribution based on extended light sources can be roughly categorized into the following three approaches: the Simultaneous multiple surface method (SMS), the generalized function method, the feedback optimization method.

In 1996, Juan C. Minano et al. [3] first proposed simultaneous multiple surface (SMS) method which based on non-imaging optics and edge light principles. This method is particularly valuable when designing optical systems with multiple folds of light. It is important to note that the same light source can have vastly different effects on different optical surfaces. Similar method has been also applied by R. M. Wu et al. [4], where it effectively controlled the directional emission of high-power LEDs. This was achieved by utilizing the light distribution of LEDs and the conservation theorem of optical expansion, with SMS method helping obtain the contour curves of each refraction or total reflection surface. Additionally, C·C.Hsieh et al. [5] studied the design of a multi-module LED headlamp system of vehicle, which used the simultaneous multiple-surface design method to construct a high-focusing multiple-surface reflector and incorporated it into the system, by superposing the light patterns, the designed system satisfied illuminance regulations and has a 70% more energy efficient than conventional 55 W halogen low-beam headlamps. However, the SMS method involves complex principles and calculations and may have limitations in controlling center light distribution.

In 2006, J. Bortz et al. [6] introduced the generalized function method, which is suitable for axisymmetric or translational geometry. This method enables the generation of specific intensity distributions as angle functions or specific illuminance distributions as position functions along freeform surfaces. It allows for the conversion of a given light source distribution into two specified irradiance distributions or a specified irradiance distribution and a specified intensity distribution on a continuous target surface D. Li et al. [7] extended this method to optimize the optical efficiency and uniformity of the lighting system by analyzing the influence of the incident Angle and aberration of the micro-lens array on the micro-projector efficiency. This approach improved the light efficiency loss caused by the large Angle incident, and was more flexible in the control of aberration. However, the design process for the generalized functional method can be intricate, and these systems may not always achieve ideal light efficiency.

In 2014, D. Li et al. [8] proposed a feed-back optimization algorithm based on the partial differential equation method. This approach achieved the secondary surface optimization by reconstructing the target surface partition, which took the illuminance distribution on the target surface in the initial simulation results as feedback, and a uniform illumination of an area with a working distance of 30 m and a diameter of 10 m, was achieved by an extended source with diameter of 3 cm. In addition, Z. H. Ding et al. [9] proposed a direct design method based on the non-Lambertian extended light source to customize a high-performance lens with specified irradiance characteristics This method numerically calculated lens surface profiles while considering the luminous flux and radiation distribution of the extended non-Lambertian light source. It led to the realization of compact and high-performance lighting systems for a moving range of 60∼140 mm light sources. Nevertheless, the Feedback Optimization method's complexity and dependence on initial structures may limit its practical engineering applicability. The direct design method is often tailored to specific light sources and requirements, making it less versatile.

In this study, a hybrid method is proposed to obtain an optimized freeform lens automatically. This method relies on the combination of the weighted superposition method and feedback optimization approach. By using the weighted overlapping of multiple generatrices of point source lens, a new surface generatrix is obtained through a feedback optimization algorithm. Furthermore, the API interface techniques was used to establish a connection between LightTools and Matlab. The integration not only enables the automatic optimization design process but also enhances the upper limit of the optimization effect while maintaining high efficiency in the workflow.