The range of validity and the accuracy of scalar analysis with renormalization for periodic diffractive phase elements is evaluated by a comparison with the Fourier modal method. It is found that the error of renormalized scalar diffraction theory is small for normal incident light with wavelengths in the range from 350 nm to 1000 nm and for height pitch ratios less than 1. The scalar method is implemented in a hybrid scalar-vector diffraction method that reduces the solving time for one-dimensional gratings by a factor up to 100. The scatterometry parameters, such as height, fill factor and wall angles, are obtained using a generalized least square method. The input to this least squares method is 1) best estimates and the associated covariance matrix of all measured quantities, including influence quantities, and 2) a measurement model describing all known physical relations between the measured quantities and the scatterometry parameters. The output includes best estimates and the associated covariance matrix of the scatterometry parameters.

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