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.

The description of the lateral resolution criterion for profile and areal surface topography measuring instruments is still under discussion in the international standardization. Several studies have examined the different methods proposed in the standardization individually. We describe a comprehensive examination and comparison of the different methods proposed by the standard. In doing so, the star-shaped grooves material measure (type ASG of ISO 25178-70) and the chirped standard are compared by using different measuring instruments and principles. In order to benchmark the results, they are compared to a third method for the transfer function determination which uses an Rk-calibrated material measure and is based on time series modeling. The results illustrate that both described methods have their specific advantages and disadvantages and are wellsuited for individual fields of application.

The fitting of geometric shapes into measurement data is a frequently occurring task in metrology, computer vision or pattern recognition. Least-Squares methods correspond to the state of the art, but do not make use of existing prior knowledge about the measurement system or the measurement object. By using prior knowledge, the uncertainty of a measurement can be reduced. A simple example for prior knowledge is the diameter of a bore hole, which is always greater than zero. The Bayesian approach offers the possibility to include this prior knowledge for the fitting of geometric shapes. In the following, a Bayesian approach for fitting a circle is presented and compared with the established Total-Least-Squares method.

Micro hardness determination on rough surfaces is a topic of interest e.g. in industrial applications where the component surface is of functional relevance. In most approaches, hardness on a rough surface is determined by including profile roughness parameters like R a (e.g., [1][2][3][4][5]) to adjust measured hardness values or to get the minimum indentation depth value where the influence of the surface topography is assumed to become negligibly small. In the present study, local surface topography data were used instead to enable precise micro hardness measurements on a sample with arbitrary surface topography. Samples made of 1.457 1 stainless steel with different surface states were face milled by using an end mill with different feed rates. Instrumented indentation tests were performed on these samples as well as on comparative samples with polished surfaces. From the resulting load-indentation depth (F-d)-curves the averaged indentation hardness was calculated for all surface states. A method was applied to manipulate and to average the F-d-curves to eliminate deviations, occurring at the beginning of the indentation. The indentation hardness was calculated from these modified F-d-curves and compared to the indentation hardness from the actually measured F-d-curves of the polished samples with feasible results. Using surface topography measurements is considered to enable deriving more accurate indentation hardness values directly and to put the investigations to another level. The surface topography of the samples was evaluated by confocal microscope measurements before and after the indentation tests. From the surface topography data at the location of indentation, four parameters were calculated: volume, projected contact area and depth of the indentation mark, as well as the curvature of the surface topography before indentation. These parameters were correlated with the hardness value from the respective indentation and compared to the indentation hardness of the polished sample. The results of the present study are the basis for combining optical imaging techniques like confocal microscopy or white light interferometry and indentation testing equipment to broaden the field of application.

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