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

In photolithography, aerial image simulation of the mask has become mandatory. To compute aerial images, transmission cross coefficients (TCCs), drawn from Hopkins optical system transmission function, are arranged as a four-way array (four-entry table) called a fourth-order tensor. To estimate the kernels using the linear algebra-based methods, the existing algorithms unfold this tensor into a matrix. To reduce the computational load, this matrix is approximated by lower rank order matrix owing to the singular value decomposition (SVD). We propose to adopt the multilinear algebra tools to the tensor of TCC values in order to keep this data tensor as a whole entity. For runtime improvement, we use a fixed point algorithm to estimate only the needed eigenvectors. To estimate the optimal number of needed eigenvectors, two well-known criteria of signal processing and information theory are adopted. This tensorial approach leads to a fast and accurate algorithm to compute aerial images.