A Analytical Kernel-Based Stacked Pupil Shift Matrix Decomposition Method for Partially Coherent Imaging

The Sum of Coherence System (SOCS) algorithm is commonly used to calculate the aerial images of partially coherent systems in the lithography simulation. However, computing the kernels of the SOCS algorithm presents significant memory and computational challenges when dealing with the large Transmission Cross Coefficient (TCC) matrix of the Hopkins model. In this paper, we propose a method that utilizes the stacked pupil shift matrix method and analytical circle-sampling functions decomposition to avoid direct computation and storage of the TCC matrix, thereby reducing the computational consumption for obtaining the kernels. Moreover, this method demonstrates flexibility by allowing arbitrary changes to the grid size of the kernels due to its analytical nature and shows adaptability for extension to a vector model. Through numerical simulations, we demonstrate the effectiveness of our method and show that the use of analytical Fourier transforms mitigates many errors associated with discrete Fourier transform processes, further enhancing accuracy.