Fast convolution method and its application in mask optimization for intensity calculation using basis expansion

Finer grid representation is required for a more accurate description of mask patterns in inverse lithography techniques, thus resulting in a large-size mask representation and heavy computational cost. To mitigate the computation problem caused by intensive convolutions in mask optimization, a new method called convolution using basis expansion (CBE) is discussed in this paper. Matrices defined in fine grid are projected on coarse gird under a base matrix set. The new matrices formed by the expansion coefficients are used to perform convolution on the coarse grid. The convolution on fine grid can be approximated by the sum of a few convolutions on coarse grid following an interpolation procedure. The CBE is verified by random matrix convolutions and intensity calculation in lithography simulation. Results show that the use of the CBE method results in similar image quality with significant running speed enhancement compared with traditional convolution method.