Joint robust principal component analysis and truncated-SVD denoising algorithm for computer-aided alignment of...

To address the limited convergence accuracy in the computer-aided alignment of projection objectives caused by interferometric measurement noise, this study proposes a hierarchical denoising algorithm that integrates non-centered truncated singular value decomposition (SVD) with robust principal component analysis (RPCA). Dense noise is first reduced by applying truncated SVD directly to the repeated-measurement matrix acquired at each field, without row-wise centering or subsequent mean restoration. The field-wise estimates reconstructed from the retained singular components are then concatenated into a multi-field Zernike coefficient matrix, after which RPCA is used to separate the dominant low-rank aberration structure from sparse outliers. The refined matrix is finally embedded into the CAA workflow. The proposed method was numerically validated through Monte Carlo simulations on a DUV lithographic projection-objective design with NA = 1.2, which was used as a numerical proof-of-concept test case. At the nominal noise level, the mean field-averaged RMS wavefront error decreased from 0.020259 ± 0.001285λ without denoising to 0.020013 ± 0.001283λ after denoising, an absolute reduction of 0.000246λ. Relative to the noise-free mean of 0.019997λ, this reduction corresponds to suppression of approximately93.89% of the noise-induced degradation. Across noise levels from 1× to 3× the nominal level, the degradation-suppression ratio remained approximately 66.93%-93.89% for the investigated projection-objective model.