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

Romuald Sabatier; Caroline Fossati; Salah Bourennane; Antonio Di Giacomo

doi:10.1117/1.3213237

1 July 2009 Optimal approximation of transfer cross coefficient for system transmission based on tensorial signal methods

Romuald Sabatier, Caroline Fossati, Salah Bourennane, Antonio Di Giacomo

Author Affiliations +

Journal of Micro/Nanolithography, MEMS, and MOEMS, Vol. 8, Issue 3, 031407 (July 2009). https://doi.org/10.1117/1.3213237

Abstract

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.

©(2009) Society of Photo-Optical Instrumentation Engineers (SPIE)

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Romuald Sabatier, Caroline Fossati, Salah Bourennane, and Antonio Di Giacomo "Optimal approximation of transfer cross coefficient for system transmission based on tensorial signal methods," Journal of Micro/Nanolithography, MEMS, and MOEMS 8(3), 031407 (1 July 2009). https://doi.org/10.1117/1.3213237

Published: 1 July 2009

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KEYWORDS

Reconstruction algorithms

System on a chip

Projection systems

Matrices

Photomasks

Optical lithography

Image transmission

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