Scatterometry is an optical technique that has been studied and tested in recent years in semiconductor fabrication metrology for critical dimensions. Previous work presented an iterative linearized method to retrieve surface-relief profile parameters from reflectance measurements upon diffraction. With the iterative linear solution model in this work, rigorous models are developed to represent the random and deterministic or offset errors in scatterometric measurements. The propagation of different types of error from the measurement data to the profile parameter estimates is then presented. The improvement in solution accuracies is then demonstrated with theoretical and experimental data by adjusting for the offset errors. In a companion paper (in process) an improved optimization method is presented to account for unknown offset errors in the measurements based on the offset error model.