Fig. 1. Sketch of the freeform beam transformer.

Fig. 2. Diagram of the IWT method for optical field control.

Fig. 3. (a) Irradiance and (b) phase distributions of the input beam on the z=20  mm plane; the desired (c) irradiance and (d) phase distributions of the output beam on the z=45  mm plane, which is aimed for producing (e) a second output irradiance distribution on the z=75  mm plane. The phase distributions are normalized to have zero average values.

Fig. 4. Evolution of the ϵ value as the iteration increases.

Fig. 5. Designed (a) entrance and (b) exit freeform surfaces.

Fig. 6. Simulated results of the freeform lens designed with the new proposed method: (a) ray-tracing illustration in LightTools, and simulated irradiance distributions on the (b) first and (c) second output planes, respectively. Simulated results of the freeform lens designed with the L2 OT ray mapping method: (d) ray-tracing illustration in LightTools, and simulated irradiance distributions on the (e) first and (f) second output planes, respectively. In each design, the mesh sizes for the two simulated irradiance distributions are 288×288, where the prescribed domains (Γ and Γ′) correspond to the central grids of 256×256 points.

Fig. 7. (a) Final ray mapping of the new proposed method; (b) the L2 OT ray mapping; and (c) their vector differences in the form of arrows originated from the grid points shown in (a). For better visualization, each ray mapping with the grid points of 256 × 256 is interpolated into that with the grid points of 32 × 32.

Fig. 8. Simulated results of the freeform lens designed with the new proposed method: (a) ray-tracing illustration in LightTools, and simulated irradiance distributions on the (b) first and (c) second output planes, respectively. Simulated results of the freeform lens designed with the L2 OT ray mapping method: (d) ray-tracing illustration in LightTools, and simulated irradiance distributions on the (e) first and (f) second output planes, respectively.