Modeling of topography measuring instrument transfer functions by time series models

The transfer function of topography measuring instruments contains important information for an understanding of the metrological characteristics. There are different methods for the estimation of the transfer function. For example, a measurement of the transfer function can be conducted with the aid of material measures that feature defined properties in the frequency domain. Another possibility is to determine the transfer function with the utilization of virtual measurements. However, these methods either require the development of a material measure specifically for this purpose or are only theoretical. We propose an approach that is common in signal processing and time series analysis for the application towards measuring instruments for geometrical product specification (GPS): filter design is used to estimate the instrument's transfer function. With this approach, the transfer function can be determined with the aid of a measuring object with any well-known stochastic surface structure, as long as the manufacturing and measurement of the structures are possible. The general suitability of the approach for both stylus and optical measuring instruments is demonstrated, and the proposed time series model and the required signal pre-processing are optimized. Based on the results, a comparison of the model results with measured transfer functions is conducted and virtual measurements are performed in order to evaluate the accuracy of the determined models. In doing so, it was observed that the surface structure of the measuring object used has an influence on the quality of the results.