Rainer Tutsch

The precise calibration of indenter geometries is a critical factor in ensuring reliable instrumented indentation experiments, particularly at the microscale and nanoscale. This study presents the comprehensive and highly accurate calibration of a modified Berkovich indenter using a metrological large-range atomic force microscope, reaching a relative standard uncertainty of less than 1% for the projected area function (PAF) for indentation depths of 200 nm and more. In contrast to previous works, this study specifically focuses on the influence of data evaluation methods on the determination of indenter geometry and the estimation of the measurement uncertainty. A refined uncertainty estimation approach is implemented, overcoming the limitations of both the classical “Guide to the Expression of Uncertainty in Measurement” and the Monte Carlo method, which either require restrictive idealization assumptions on the indenter geometry or entail high computational costs. By leveraging a systematic simulationbased uncertainty assessment, this work provides a robust evaluation of the PAF uncertainty and its dominant contributing factors.

This paper addresses the problem of uncertainty estimation for measurements made with computationally expensive numerical models, which are increasingly applied today. Typically, the Monte Carlo method (MCM) is used for uncertainty propagation in these cases. However, due to its stochastic nature, the MCM is inefficient, requiring a large number of model evaluations and thus resulting in long computation times. In this paper, an efficient alternative to the MCM is introduced. By using systematic samples of the influence quantities which are individually propagated through the measurement model, the overall number of required model evaluations can by drastically reduced. Additionally, the new method offers the possibility to simplify the measurement model for further reduced computational effort. The distributions of the propagated samples are reconstructed using a method specifically designed for systematic samples and combined to the uncertainty distribution of the measurand using convolution. The new method does not only offer increased computational efficiency but also a high information yield, as it estimates the uncertainty distribution of the measurand and the uncertainty contribution of individual influence quantities.

This paper introduces a paradigm shift in atomic force microscope (AFM) scan control, leveraging an artificial intelligence (AI)-based controller. In contrast to conventional control methods, which either show a limited performance, such as proportional integral differential (PID) control, or which purely focus on mathematical optimality as classical optimal control approaches, our proposed AI approach redefines the objective of control for achieving practical optimality. This presented AI controller minimizes the root-mean-square control deviations in routine scans by a factor of about 4 compared to PID control in the presented setup and also showcases a distinctive asymmetric response in complex situations, prioritizing the safety of the AFM tip and sample instead of the lowest possible control deviations. The development and testing of the AI control concept are performed on simulated AFM scans, demonstrating its huge potential.

Zusammenfassung Monte Carlo Verfahren eignen sich zur Bestimmung der Fertigungsgenauigkeit und Messunsicherheit für die Kalibrierung von Massenormalen unter Verwendung von Sorptions-, Duplex- und Auftriebskörpern, hier Transferkörper genannt. Bestimmt werden die aufgabenspezifischen Messunsicherheiten für die Messgrößen Masse, Oberfläche und Volumen. Die Eingangsgrößenen der Simulationen ergeben sich aus den vorgegebenen Fertigungstoleranzen sowie aus den Messunsicherheiten der verwendeten Längenmessgeräte. Das entwickelte Modell erlaubt es, die vorgestellten Transferkörper mit einem einheitlichen Ansatz nach den Vorgaben des GUM zu berechnen. Ergebnisse zu Transferkörpern aus Silizium mit einer Nennmasse von 1 kg werden vorgestellt und diskutiert.

Phase measuring deflectometry is an accepted technique for measuring the shape of specular surfaces. While defloctometry is known to provide high sensitivity in the nanometer range, the absolute form measuring accuracy is typically inferior by several orders of magnitude. The comparatively low accuracy of typical implementations of phase measuring deflectometry is determined by several influencing factors. On the one hand, many system models used do not consider all relevant system parameters, such as refraction in the display substrate or its flatness deviation. On the other hand, due to the complex system geometry, many calibration procedures are susceptible to deviations due to low condition numbers of the mathematical problems. To increase the absolute accuracy of phase measuring deflectometry, the authors have analyzed in detail the calibration procedures, the measurement process, and the evaluation algorithms and have made numerous extensions and optimizations. The present contribution gives an overview of the obtained findings and the applied measures. The performance of the approach is evaluated based on measurements of challengingly curved measurement objects. Based on these selected objects, form measurement deviations of better than 1 μm are documented.

Zusammenfassung: Wenn heute von der Digitalisierung der Produktion gesprochen wird, löst das in der Koordinatenmesstechnik häufig Verwunderung aus, weil die Koordinatenmesstechnik von Anfang an digitale Verfahren genutzt hat. Ohne die Möglichkeiten der Digitalisierung würde es sie gar nicht geben. Erst die rechnergestützte Auswertung ermöglicht eine effiziente Verknüpfung der gemessenen Koordinatenpunkte zu Merkmalen der Produktgeometrie. Heute werden bei optischen Messsystemen Millionen von Koordinatenpunkten in Sekunden aufgenommen und verarbeitet. Die Anwendung der Computertomographie für die Koordinatenmesstechnik wurde erst durch die heute zur Verfügung stehende Rechnerleistung möglich. Aufgrund der vorhandenen digitalen Systeme wurde die Koordinatenmesstechnik bei der Vernetzung schon frühzeitig eingebunden. Während am Anfang die rechnergestützte Übertragung von Ergebnissen im Vordergrund stand, sind heute Koordinatenmesssysteme teilweise vollständig in digital gesteuerte Produktionsprozesse integriert.

In phase-measuring deflectometry for measuring reflecting and transparent surfaces, a high-contrast pattern displayed on a liquid crystal screen is usually optically detected. One of the most important non-idealities of liquid crystal displays with regard to the achievable measurement uncertainty is the refraction in the glass substrate, which leads to an angle-dependent offset between the actual location and the observed location of a feature displayed on the screen. Owing to the typical thicknesses and refractive indices of the glass substrates used, this offset reaches several tenths of a millimeter even at moderate viewing angles. In the approach presented here, the refraction-related offset of features displayed on the screen is determined by simultaneous observation of displayed features and features mounted on the screen. The model used so far was improved, so that apart from a distance of the features to be determined before the evaluation no further previous knowledge is necessary. Within the scope of the investigations carried out, statements on the measurement uncertainty of the method could also be made and verified for the first time.