Lateral resolution and transfer characteristics of vertical scanning white-light interferometers

White-light interferometers are widely used for high-accuracy topography measurement in industrial and scientific applications. A common way to characterize a white-light interferometer is to assume small surface amplitudes resulting in linear transfer characteristics described by the instrument transfer function (ITF). However, the well-known batwing effect gives rise to systematic errors, causing extra nonlinearity to the ITF. In this paper a model to simulate an interference pattern in the image plane as it is obtained by a vertical scanning white-light interferometer is introduced in order to overcome the limitation of small surface amplitudes. Repeating the simulation procedure for different height positions of the object results in an image stack that can be analyzed by the same algorithms as real measurement data. The simulation results agree with experimental observations: the batwing effect occurs in certain situations and the correct amplitude of a rectangular grating structure can be obtained as long as the structure is optically resolved. Both simulation, as well as experimental results, provide transfer characteristics of broader bandwidth than predicted by theoretical approaches based on linear system behavior.