Abstract: Instead of constructing a full multi-dimensional look-up-table as a model to find the critical dimension or other parameters in scatterometry, regression or other optimized estimation methods are employed starting from a “best guess” value of the parameter. Eigenvalues of models that are precalculated may be stored and reused later for other structures having certain common characteristics to save time. The scatterometric data that is used to find the value of the one or more parameter can be limited to those at wavelengths that are less sensitive to the underlying film characteristics. A model for a three-dimensional grating may be constructed by slicing a representative structure into a stack of slabs and creating an array of rectangular blocks to approximate each slab. One dimensional boundary problems may be solved for each block which are then matched to find a two-dimensional solution for the slab.