Monte-Carlo simulation of the three dimensional transfer function for coherence scanning interferometry

The optical transfer function TF is an important tool for the characterization of optical instruments and is used mainly for conventional imaging systems. In recent years, however, the concept of three-dimensional (3D) TFs has gained attention in the field of 3D imaging. Calculating the 3D TF is an important step preceding the simulation of scattered fields in measurement systems such as coherence scanning interferometers or confocal microscopes using i.e. numerical methods like FEM or analytical simulations. Here, we propose a statistical approach to the 3D TF employing Monte-Carlo simulations and the inverse sampling method. This verifies previous analytical and numerical computations of the TF and offers an alternative and intuitive way of understanding the 3D image formation in modern optical measurement systems, while it is not limited to assumptions often necessary for analytical derivations.