The optimized source, mask, and resist image at the best focus, 100-nm defocus, and 150-nm defocus positions are all shown in Fig. 6. The red solid line in the figure indicates the target pattern. The PEs are also marked on the top of each resist image. From Fig. 6, one can see that without optimization, the mask can only be printed on the wafer at the best focus position with a large PE of 22,656, whereas no pattern can be printed at the 100-nm and 150-nm defocus positions. When the parametric source and mask have been optimized by using SMO, the mask can be printed at both the best focus and the defocus positions. The resist image is highly faithful to the target pattern with a PE of 5800 at the best focus. However, the PE equals 36,168 at the 150-nm defocus position, which is too large to maintain pattern fidelity. When performing SMNO, we found that the resist image could maintain high pattern fidelity through a large DOF. The PE of SMNO at the best focus, 100-nm defocus, and 150-nm defocus positions are 8038, 7430, and 14,186, respectively. Although the PE of SMNO is larger than that of SMO by 2238 at the best focus position, the PE values at the defocus positions are significantly less. The PE of SMNO at the 150-nm defocus position is 656 and 21,982 smaller than the PE of SMO at the 100-nm and 150-nm defocus positions. Figure 7 shows a comparison of the PEs at various defocus positions, where we found that the PE of SMO increases drastically at a defocus position, but SMNO maintains a low level of PE over a large range of DOF. The comparison of optimization results between the SMO and SMNO demonstrates that SMNO could effectively improve the pattern fidelity and enlarge the DOF, which also reveals that it is necessary to include NA in the optimization.