Modeling confocal microscopes using the universal Fourier optics model

Three-dimensional transfer functions (TFs) generally provide a comprehensive description of the transfer behavior of optical surface topography measuring instruments in the spatial frequency domain. Recently, an analytical derivation of the TF has been achieved, and based on this, the so-called universal Fourier optics (UFO) model has been developed for virtual coherence scanning interferometry. Especially for 3D surface topography reconstruction, simulation models usually suffer from long simulation times, even if the scattering process is approximated by the Kirchhoff theory of light scattering. The UFO model reduces the simulation effort to a number of 2D fast Fourier transforms of a phase object, enabling modeling of realistic 3D topographies in a reasonable time for the first time. In contrast to previous models, which are either restricted to 2D or suffer from long computation times, the presented UFO model enables for the first time full 3D simulations of confocal microscopy (CM) with realistic topographies in a reasonable time. Besides coherence scanning interferometry, CM is also a widely used optical profiling technique, and hence, we present a UFO model for CM considering lateral as well as depth scanning. The opportunities provided by the model are demonstrated by simulating confocal image stacks for realistic 3D surface topographies.