Figure 6 presents another set of simulations for the proposed filter, where is an input mask pattern with a size of and a grid resolution of 2.5 nm. This input mask pattern is artificially introduced with some objects that are difficult to manufacture in practice, including some small isolated holes, protrusions, hollows, and irregular features shown inside the red circles. From the perspective of signal processing, these details can be considered as high-frequency noise in the mask and can be evaluated with total variation.11,12 As revealed in Fig. 6, the total variation (denoted as TV in Fig. 6) of reduces from 3080 to 2416 via the Gaussian convolution operation, which removes these small details. Subsequently, by the Sigmoid operation, it leads to a close-to-binary mask with a total variation of 2677, which reduces total variation by 13.1% compared to the original mask . On the other hand, it is interesting to find that the EDE of the output pattern of the mask , the Gaussian filtered mask, and the filtered mask are almost the same. That is because the optical lithography system with a low-pass nature does not deliver high-frequency details to the output pattern on the wafer. Similar to the optical lithography system, the mask filter acts as a low-pass filter to remove these details that are produced in ILT, whereas it does not cause distortions on the output pattern on the wafer. As demonstrated in Figs. 5 and 6, the proposed filter reduces the mask complexity and achieves a close-to-binary mask, so that the filtered mask is reachable in real manufacture.