Spectroscopic ellipsometry SE in the visible/near-UV spectral range is applied to monitor optical critical dimensions of quartz, Si, and Ta gratings, namely, the depth, linewidth, and period. To analyze the SE measurements, the rigorous coupled-wave theory is applied, whose implementation is described in detail, referred to as the Airy-like internal reflection series with the Fourier factorization rules taken into account. It is demonstrated that the Airy-like series implementation of the coupled-wave theory with the factorization rules provides fast convergence of both the simulated SE parameters and the extracted dimensions. The convergence properties are analyzed with respect to the maximum Fourier harmonics retained inside the periodic media and also with respect to the fineness of slicing imperfect Ta wires with paraboloidally curved edges. © 2006 American Institute of Physics.