Fig. 1. (a) Schematic of forward lithography. (b) Reflection from and transmission through a stratified medium.

Fig. 2. (a) EPE measurement illustration. (b) Numerical superposition region. (c) Pattern edge set (PES). (d) Edges of target pattern I02 in Fig. 4(c).

Fig. 3. PV Band demonstration. (a)–(c) Printed images under different process conditions. (d) Computed PV Band. (e) PV Band of the printed images with I02 in Fig. 4(c) illuminated by the annular source in Fig. 4(a).

Fig. 4. (a) Annular source J0 with σin=0.6 and σout=0.9. (b), (c) The desired target patterns I01, I02.

Fig. 5. Printed wafer images with (a) PE 4494 and (d) PE 5193, EPE images with (b) EPE 1158 and (e) EPE 1512, PV Band images with (c) PV Band 2347 and (f) PV Band 3965 with respect to target patterns I01 and I02 illuminated by the annular source in Fig. 4(a).

Fig. 6. Simulation results with I01 as the target pattern. Columns from left to right: the synthesized source pattern J^, the synthesized mask pattern M^, the EPE images, and the PV Band images illuminating M^ by J^. Rows: proposed approach (a) with γ1 and (b) with γ2, SGD (c) with γ1 and (d) with γ2.

Fig. 7. Randomly initialized masks within the range (0,1); (a) M01 and (b) M02. (c) ω1 and (d) ω2 are the transformed parameters.

Fig. 8. Simulation results with I01 and I02 as the target pattern and weight γ2. Rows: (a) and (c) proposed approach with ω1 and ω2, (b) and (d) SGD with ω1 and ω2 as initial masks.

Fig. 9. Convergence of (a) S, (b) Spe of the simulations in Fig. 8, (c) Spe of the simulations in Figs. 8(a) and 8(b), and (d) Spe of the simulations in Figs. 8(c) and 8(d).