Extension of the 3D analytical transfer function for coherence scanning interferometry

The three-dimensional transfer function (TF) has proven to be particularly suitable for describing measurement processes of depth scanning interference microscopes in the 3D spatial frequency domain. Precise determination of the TF is useful for adequate signal processing and for modeling virtual instruments. However, in its current form, the analytical TF only considers perfectly reflective surfaces and ideal systems. This implies that effects such as aberrations, misalignment, locally varying reflectivity of surfaces and other phenomena that occur in reality, are not taken into account. Therefore, we present an extension of the analytical TF that includes these effects as angle-dependent factors. This extended analytical TF is thoroughly analyzed by several examples. Numerically implemented TFs are used in this paper to validate the results of the analytical TF. In addition, the TF is used to generate image stacks obtained by coherence scanning interferometry (CSI), which are then compared with other models and with experimental results.