Fig. 1. Diagram of LED illumination system

Fig. 2. Schematic diagram of constructing free-form surface by weighted superposition algorithm

Fig. 3. Center coordinate points of surface after translation

Fig. 4. Diagram of intersection of ray and triangular mesh. (a) Triangle mesh surface; (b) intersection of line and triangle surface

Fig. 5. Diagram of intersection of rays and five free-form surfaces. (a) Single ray intersecting with five free-form surfaces; (b) k rays intersecting with five free-form surfaces

Fig. 6. Free-form surface data points after superposition

Fig. 7. Flow chart of optimization algorithm

Fig. 8. Schematic diagram of LED illumination system with key parameters

Fig. 9. Free-form surface after optimization

Fig. 10. Distributions of target surface illuminance before and after optimization. (a) Distribution of illuminance before optimization; (b) contour distribution of illuminance before optimization; (c) distribution of initial weight illuminance; (d) contour distribution of initial weight illuminance; (e) distribution of illuminance after optimization; (f) contour distribution of illuminance after optimization

Table 1. Design parameters

Table 2. Weight factors before and after optimization

Table 3. Optimization results of different initial weight factors