In computational imaging and lithography, it has been a challenge for a numerical model to faithfully preserve symmetries in the physical imaging system. In this Letter, we present a project-to-symmetry-subspace (PTSS) method to prevent symmetry loss during the iterative generation of optical kernels. Essentially, PTSS is to project iterative vectors onto a predefined symmetric subspace when decomposing the transmission cross coefficient (TCC). Simulation results demonstrate the PTSS-generation of a truncated set of optical kernels that are substantially free of symmetry error, regardless of the order of truncation.
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