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.
Despite the fact that optical profilers, such as coherence scanning interferometers, are frequently used for fast and contactless topography measurements in various fields of application, measured profiles still suffer from the wave characteristics of light, which leads to systematic deviations that are still not sufficiently investigated. In order to analyze these systematic deviations and their physical relations, we apply a rigorous simulation model considering both the transfer characteristics of the measurement instrument as well as the geometry and material of different measurement objects. Simulation results are compared to measurement results for different polarizations, wavelengths and interferometer types, considering surface structures including edges, slopes and different materials as the main reasons for those deviations. Compared to former publications, a full three-dimensional (3D) modeling of the image formation with regard to two-dimensional (2D) surface structures is provided. The advantages of 3D modeling in contrast to a time efficient 2D approach are discussed. Further, an extract of an atomic force microscope (AFM) measurement result is used as the basis for the FEM simulation in one example in order to achieve most realistic simulation results.
We discuss the height and lateral resolution that can be achieved in vertical scanning white-light interferometry (SWLI). With respect to interferometric height resolution, phase-shifting interferometry (PSI) is assumed to provide the highest accuracy. However, if the noise dependence of SWLI phase evaluation and PSI algorithms is considered, SWLI measurements can be shown to be more precise. With respect to lateral resolution, the determination of the coherence peak position of SWLI signals seems to lead to better results compared to phase based-interferometric measurements. This can be attributed to the well-known batwing effect. Since batwing is a nonlinear effect applying nonlinear filters, e.g. a median filter, it reduces them significantly. If filtering is applied prior to the fringe order determination and phase evaluation, the number of artefacts known as ghost steps can be eliminated without changing the modulus of the phase. Finally, we discuss the dependence of measured height values on surface slope. We show that in interference microscopy there are additional limitations which are more rigid compared to the maximum surface slope angle resulting from the numerical aperture of the objective lens. As a consequence, the measurement precision breaks down at slope changes of steeper flanks even if the modulation depth of the interference signals is still good enough for signal analysis.
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