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Advances in OptoElectronics
Volume 2009 (2009), Article ID 457549, 9 pages
Research Article

Tensorial Model for Photolithography Aerial Image Simulation

Ecole Centrale Marseille Institut Fresnel, CNRS UMR 6133, 13397 Marseille Cedex 20, France

Received 21 July 2009; Accepted 31 August 2009

Academic Editor: Samir K. Mondal

Copyright © 2009 Caroline Fossati et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we propose to adapt the multilinear algebra tools to the tensor of Transmission Cross-Coefficients (TCC) values for aerial image simulation in order to keep the data tensor as a whole entity. This new approach implicitly extends the singular value decomposition (SVD) to tensors, that is, Higher Order SVD or TUCKER3 tensor decomposition which is used to obtain lower rank- ( 𝐾 1 , 𝐾 2 , 𝐾 3 , 𝐾 4 ) tensor approximation (LRTA ( 𝐾 1 , 𝐾 2 , 𝐾 3 , 𝐾 4 ) ). This model requires an Alternating Least Square (ALS) process known as TUCKALS3 algorithm. The needed number of kernels is estimated using two adapted criteria, well known in signal processing and information theory. For runtime improvement, we use the fixed point algorithm to calculate only the needed eigenvectors. This new approach leads to a fast and accurate algorithm to compute aerial images.