Fig. 1. Schematic diagram of freeform optical design

Fig. 2. Schematic diagram of the double freeform design of the primary lens

Fig. 3. Schematic diagram of the design of secondary lens

Fig. 4. Plot of the result of curve 1 when iterating over step 619 (the inset showing overfitting at step 619)

Fig. 5. Diagram of the lens group solid model. (a) Double transmission lens set; (b) Combined reflective and transmissive lens set in Ref.14

Fig. 6. Graph of simulation results. (a) LED passing through the secondary lens exit angle of the double transmissive lens set;(b) LED passing through the luminous angle of the double transmissive lens set; (c) Simulation results for double transmission lens set; (d) Simulation results for reflective transmission lens set; (e) Normalized irradiance plot

Fig. 7. Radial distribution of irradiance on the receiving surface

Fig. 8. Schematic diagram of surface tolerance normalized irradiance comparison (the inset shows the effect of surface tolerance on irradiance)

Fig. 9. Simulation diagram of the lens set array. (a) Array ray tracing plot; (b) Effective luminous flux ratio and uniformity of the system at different spacing; (c) Irradiance plot of the receiving surface at a spacing of 0.015 mm