Limits of diffractometric reconstruction of line gratings when using scalar diffraction theory

We study errors that occur in geometry and phase reconstruction when using scalar diffraction theory in line gratings with periods below 10 μm. The application of those gratings in so-called computer-generated holograms in high-precision interferometric testing of aspheres and free-form surfaces imposes high demands on the generated phase, leading to error budgets in the range of λ/100. Using rigorous simulations as references, we identify the limits where scalar diffraction theory fails to accurately describe grating geometries and identify the significant error mechanisms.