Scattering and three-dimensional imaging in surface topography measuring interference microscopy.

Surface topography measuring interference microscopy is a three-dimensional (3D) imaging technique that provides quantitative analysis of industrial and biomedical specimens. Many different instrument modalities and configurations exist, but they all share the same theoretical foundation. In this paper, we discuss a unified theoretical framework for 3D image (interferogram) formation in interference microscopy. We show how the scattered amplitude is linearly related to the surface topography according to the Born and the Kirchhoff approximations and highlight the main differences and similarities of each. With reference to the Ewald and McCutchen spheres, the relationship between the spatial frequencies that characterize the illuminating and scattered waves, and those that characterize the object, are defined and formulated as a 3D linear filtering process. It is shown that for the case of near planar surfaces, the 3D filtering process can be reduced to two dimensions under the small height approximation. However, the unified 3D framework provides significant additional insight into the scanning methods used in interference microscopy, effects such as interferometric defocus and ways to mitigate errors introduced by aberrations of the optical system. Furthermore, it is possible to include the nonlinear effects of multiple scattering into the generalized framework. Finally, we consider the inherent nonlinearities introduced when estimating surface topography from the recorded interferogram.