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.

Three-dimensional transfer functions (3D TFs) are generally assumed to fully describe the transfer behavior of optical topography measuring instruments such as coherence scanning interferometers in the spatial frequency domain. Therefore, 3D TFs are supposed to be independent of the surface under investigation resulting in a clear separation of surface properties and transfer characteristics. In this paper, we show that the 3D TF of an interference microscope differs depending on whether the object is specularly reflecting or consists of point scatterers. In addition to the 3D TF of a point scatterer, we will derive an analytical expression for the 3D TF corresponding to specular surfaces and demonstrate this as being most relevant in practical applications of coherence scanning interferometry (CSI). We additionally study the effects of temporal coherence and disclose that in conventional CSI temporal coherence effects dominate. However, narrowband light sources are advantageous if high spatial frequency components of weak phase objects are to be resolved, whereas, for low-frequency phase objects of higher amplitude, the temporal coherence is less affecting. Finally, we present an approach that explains the different transfer characteristics of coherence peak and phase detection in CSI signal analysis.

Although optical 3D topography measurement instruments are widespread, measured profiles suffer from systematic deviations occurring due to the wave characteristics of light. These deviations can be analyzed by numerical simulations. We present a 3D modeling of the image formation of confocal microscopes. For this, the light-surface interaction is simulated using two different rigorous methods, the finite element method and the rigorous coupled-wave analysis. The image formation in the confocal microscope is simulated using a Fourier optics approach. The model provides high accuracy and advantages with respect to the computational effort as a full 3D model is applied to 2D structures and the lateral scanning process of the confocal microscope is considered without repeating the time consuming rigorous simulation of the scattering process. The accuracy of the model is proved considering different deterministic surface structures, which usually cause strong systematic deviations in measurement results. Further, the influences of apodization and a finite pinhole size are demonstrated.

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Optical measurement systems are an important part of the portfolio of 3D topography sensors. By precise, contactless and rapid measurements these sensors constitute an alternative to tactile instruments. In this contribution the principle of a laser interferometric distance sensor is presented, which in combination with lateral scan axes acts as a topography sensor and also as distance sensor for the compensation of vibrations in a coherence scanning Linnik interferometer. An advantage of this distance sensor is its high acquisition rate of height values, which in case of working as a topography sensor enables high scan velocities as it is demonstrated at a chirp standard measured with a scan velocity of 80 mm/s. This is much higher than the scan velocity of tactile instruments, which are typically limited up to 1 mm/s. In addition, the compensation of vibration disturbances demonstrates the capability of the fast distance measurement.In contrast to other existing high-speed point sensors the relevant components are mass products. This keeps the costs of the sensor setup in a limited range. Furthermore, the sensor shows potential of much higher measurement rates than 116 kHz provided by the sensor used here.