Fig. 1. Sketch of the design geometry.

Fig. 2. The rectangular (u, v) grid (a) is transformed into a circular (u', v') grid (b) which is used as the stereographic coordinates (c).

Fig. 3. The flow diagram of the new IWT procedure for a curved target.

Fig. 4. The desired curved target. The side length of the target is 240 mm and the z values range from 73.80 mm to 132.42 mm.

Fig. 5. (a) The (u′, v′) grid corresponding to a uniform (u, v) grid on Ω={(u, v)|-0.94≤u≤0.94, -0.94≤v≤0.94} and (b) the final target grid for the first design (only showing 64×64 grid points for better visualization); (c) The final 3D freeform lens model and (d) its simulation results for a point like source (size: 10^-3 mm×10^-3 mm). (The unit of the irradiance: W/mm²)

Fig. 6. (a) The (u′, v′) grid corresponding to a uniform (u, v) grid on Ω={(u, v)|-0.8≤u≤0.8, -0.8≤v≤0.8} and (b) the final target grid for the second design (only showing 64×64 grid points for better visualization); (c) The final 3D freeform lens model and (d) its simulation results for a point like source (size: 10^-3 mm×10^-3 mm). (The unit of the irradiance: W/mm²)

Fig. 7. Simulated irradiance distributions for the first lens design when the source size is changed into (a) 1 mm× 1mm and (b) 2 mm× 2 mm respectively; simulated irradiance distributions for the second lens design when the source size is changed into (c) 1 mm × 1mm and (d) 2 mm × 2 mm respectively. (The unit of the irradiance: W/mm²; the unit of the length: mm)

Fig. 8. Simulated irradiance distributions for the first lens design when the source-lens system is (a) 5 mm and (b) 10 mm closer to the target. Simulated irradiance distributions for the second lens design when the source-lens system is (c) 5 mm and (d) 10 mm closer to the target. (The unit of the irradiance: W/mm²; the unit of the length: mm)