METHODS OF ARRANGING MASK PATTERNS RESPONSIVE TO ASSIST FEATURE CONTRIBUTION TO IMAGE INTENSITY AND ASSOCIATED APPARATUS

Methods and apparatus are disclosed that arrange mask patterns in response to the contribution of an assist feature to image intensity. In some methods of arranging mask patterns, a distribution of functions h(ξ−x) is obtained which represents the contribution of an assist feature to image intensity on a main feature. Neighboring regions of the main feature are discretized into finite regions, and the distribution of the functions h(ξ−x) is replaced with representative values h(x,ξ) of the discretized regions. A position of the assist feature is determined using polygonal regions having the same h(x,ξ). As described, the term x is the position of the main feature and the term ξ is the position of the assist.