Optimal approximation of transfer cross coefficient for system transmission based on tensorial signal methods

摘要

In photolithography, aerial image simulation of the mask hasnbecome mandatory. To compute aerial images, transmission cross coef-nficients u0001TCCsu0002, drawn from Hopkins optical system transmission func-ntion, are arranged as a four-way array u0001four-entry tableu0002 called a fourth-norder tensor. To estimate the kernels using the linear algebra–basednmethods, the existing algorithms unfold this tensor into a matrix. To re-nduce the computational load, this matrix is approximated by lower ranknorder matrix owing to the singular value decomposition u0001SVDu0002. We pro-npose to adopt the multilinear algebra tools to the tensor of TCC values innorder to keep this data tensor as a whole entity. For runtime improve-nment, we use a fixed point algorithm to estimate only the needed eigen-nvectors. To estimate the optimal number of needed eigenvectors, twonwell-known criteria of signal processing and information theory arenadopted. This tensorial approach leads to a fast and accurate algorithmnto compute aerial images