Efficient empirical determination of maximum permissible error in coordinate metrology. - In: Measurement science and technology, ISSN 1361-6501, Bd. 32 (2021), 10, 105013, insges. 17 S.
Maximum permissible errors (MPEs) are an important measurement system specification and form the basis of periodic verification of a measurement system's performance. However, there is no standard methodology for determining MPEs, so when they are not provided, or not suitable for the measurement procedure performed, it is unclear how to generate an appropriate value with which to verify the system. Whilst a simple approach might be to take many measurements of a calibrated artefact and then use the maximum observed error as the MPE, this method requires a large number of repeat measurements for high confidence in the calculated MPE. Here, we present a statistical method of MPE determination, capable of providing MPEs with high confidence and minimum data collection. The method is presented with 1000 synthetic experiments and is shown to determine an overestimated MPE within 10% of an analytically true value in 99.2% of experiments, while underestimating the MPE with respect to the analytically true value in 0.8% of experiments (overestimating the value, on average, by 1.24%). The method is then applied to a real test case (probing form error for a commercial fringe projection system), where the efficiently determined MPE is overestimated by 0.3% with respect to an MPE determined using an arbitrarily chosen large number of measurements.
https://doi.org/10.1088/1361-6501/ac0c49
Rigorous 3D modeling of confocal microscopy on 2D surface topographies. - In: Measurement science and technology, ISSN 1361-6501, Bd. 32 (2021), 9, 094010, insges. 15 S.
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.
https://doi.org/10.1088/1361-6501/abfd69
Experimental setup for the investigation of reproducibility of novel tool changing systems in nanofabrication machines. - In: Nanomanufacturing and metrology, ISSN 2520-8128, Bd. 4 (2021), 3, S. 181-189
Nanomeasuring machines developed at the Technische Universität Ilmenau enable three-dimensional measurements and manufacturing processes with the lowest uncertainties. Due to the requirements for these processes, a highly reproducible and long-term stable tool changing system is needed. For this purpose, kinematically determined couplings are widely used. The state-of-the-art investigations on those are not sufficient for the highest demands on the reproducibility required for this application. A theoretical determination of the reproducibility based on analytical or numerical methods is possible, however not in the desired nanometer range. Due to this, a measurement setup for the determination of the reproducibility in five degrees of freedom with nanometer uncertainty was developed. First, potential measuring devices are systematically examined and measurement principles were developed out of this. A three-dimensional vector-based uncertainty analysis is performed to prove the feasibility of the measurement principle and provides a basis for further design. As a result, a translatory measurement uncertainty of 10 nm and a rotatory uncertainty of 11 nrad can be reached. Afterwards, the measurement setup is designed, focusing on the metrological frame and the lift-off device. The developed setup exceeds the uncertainties of the measurement setups presented in the state-of-the-art by an order of magnitude, allowing new in-depth investigations of the reproducibility of kinematic couplings.
https://doi.org/10.1007/s41871-021-00103-9
A heterodyne interferometer with separated beam paths for high-precision displacement and angular measurements. - In: Nanomanufacturing and metrology, ISSN 2520-8128, Bd. 4 (2021), 3, S. 200-207
As standard concepts for precision positioning within a machine reach their limits with increasing measurement volumes, inverse concepts are a promising approach for addressing this problem. The inverse principle entails other limitations, as for high-precision positioning of a sensor head within a large measurement volume, three four-beam interferometers are required in order to measure all necessary translations and rotations of the sensor head and reconstruct the topography of the reference system consisting of fixed mirrors in the x-, y-, and z-directions. We present the principle of a passive heterodyne laser interferometer with consequently separated beam paths for the individual heterodyne frequencies. The beam path design is illustrated and described, as well as the design of the signal-processing and evaluation algorithm, which is implemented using a System-On-a-Chip with an integrated FPGA, CPU, and A/D converters. A streamlined bench-top optical assembly was set up and measurements were carried out to investigate the remaining non-linearities. Additionally, reference measurements with a commercial homodyne interferometer were executed.
https://doi.org/10.1007/s41871-021-00101-x
Heterodyne standing-wave interferometer with improved phase stability. - In: Nanomanufacturing and metrology, ISSN 2520-8128, Bd. 4 (2021), 3, S. 190-199
This paper describes a standing-wave interferometer with two laser sources of different wavelengths, diametrically opposed and emitting towards each other. The resulting standing wave has an intensity profile which is moving with a constant velocity, and is directly detected inside the laser beam by two thin and transparent photo sensors. The first sensor is at a fixed position, serving as a phase reference for the second one which is moved along the optical axis, resulting in a frequency shift, proportional to the velocity. The phase difference between both sensors is evaluated for the purpose of interferometric length measurements.
https://doi.org/10.1007/s41871-021-00098-3
Matched coordinates for the analysis of 1D gratings. - In: Journal of the Optical Society of America, ISSN 1520-8532, Bd. 38 (2021), 6, S. 790-798
The Fourier modal method (FMM) is certainly one of the most popular and general methods for the modeling of diffraction gratings. However, for non-lamellar gratings it is associated with a staircase approximation of the profile, leading to poor convergence rate for metallic gratings in TM polarization. One way to overcome this weakness of the FMM is the use of the fast Fourier factorization (FFF) first derived for the differential method. That approach relies on the definition of normal and tangential vectors to the profile. Instead, we introduce a coordinate system that matches laterally the profile and solve the covariant Maxwells equations in the new coordinate system, hence the name matched coordinate method (MCM). Comparison of efficiencies computed with MCM with other data from the literature validates the method.
https://doi.org/10.1364/JOSAA.422374
Untersuchungen zur Positioniergenauigkeit der NanoFabrikationsmaschine (NFM-100) :
Investigations on the positioning accuracy of the Nano Fabrication Machine (NFM-100). - In: Technisches Messen, ISSN 2196-7113, Bd. 88 (2021), 9, S. 581-589
This contribution deals with the analysis of the positioning accuracy of a new Nano Fabrication Machine. This machine uses a planar direct drive system and has a positioning range up to 100 mm in diameter. The positioning accuracy was investigated in different movement scenarios, including phases of acceleration and deceleration. Also, the target position error of certain movements at different positions of the machine slider is considered. Currently, the NFM-100 is equipped with a tip-based measuring system. This Atomic Force Microscope (AFM) uses self-actuating and self-sensing microcantilevers, which can be used also for Field-Emission-Scanning-Probe-Lithography (FESPL). This process is capable of fabricating structures in the range of nanometres. In combination with the NFM-100 and its positioning range, nanostructures can be analysed and written in a macroscopic range without any tool change. However, the focus in this article is on the measurement and positioning accuracy of the tip-based measuring system in combination with the NFM-100 and is verified by repeated measurements. Finally, a linescan, realised using both systems, is shown over a long range of motion of 30 mm.
https://doi.org/10.1515/teme-2021-0079
Two-photon direct laser writing beyond the diffraction limit using the nanopositioning and nanomeasuring machine. - In: Nanomanufacturing and metrology, ISSN 2520-8128, Bd. 4 (2021), 3, S. 149-155
Since the first realization of two-photon direct laser writing (DLW) in Maruo et al. (Opt Lett 22:132-134, 1997), the manufacturing using direct laser writing techniques spread out in many laboratories all over the world. Photosensitive materials with different material properties open a new field for micro- and nanofabrication. The achievable structuring resolution using this technique is reported to be sub-100 nm (Paz et al. in J. Laser Appl. 24:042004, 2012), while a smallest linewidth of 25 nm could be shown in Tan et al. (Appl Phys Lett 90:071106, 2007). In our approach, the combination of DLW with the nanopositioning and nanomeasuring machine NMM-1 offers an improvement of the technique from the engineering side regarding the ultra-precise positioning (Weidenfeller et al. in Adv Fabr Technol Micro/Nano Opt Photon XI 10544:105440E, 2018). One big benefit besides the high positioning resolution of 0.1 nm is offered by the positioning range of 25 mm × 25 mm × 5 mm (Jäger et al. in Technisches Messen 67:319-323, 2000; Manske et al. in Meas Sci Technol 18:520-527, 2007). Thus, a trans-scale fabrication without any stitching or combination of different positioning systems is necessary. The immense synergy between the highly precise positioning and the DLW is demonstrated by the realization of resist lines and trenches whose center-to-center distance undergoes the modified diffraction limit for two-photon processes. The precise positioning accuracy enables a defined distance between illuminated lines. Hence, with a comparable huge width of the trenches of 1.655 [my]m due to a low effective numerical aperture of 0.16, a resist line of 30 nm between two written trenches could be achieved. Although the interrelationships for achieving such narrow trenches have not yet been clarified, much smaller resist lines and trench widths are possible with this approach in the near future.
https://doi.org/10.1007/s41871-021-00100-y
Self-heating of resistance thermometers for air temperature measurements with pulsed current supply :
Eigenerwärmung von Widerstandsthermometern für Lufttemperaturmessungen bei Impulstromspeisung. - In: Technisches Messen, ISSN 2196-7113, Bd. 88 (2021), 9, S. 556-561
Sehr präzise Lufttemperaturmessung in der Meteorologie oder in klimatisierten Innenräumen sind herausfordernd, weil Strahlungseinflüsse und die Eigenerwärmung der Widerstandsthermometer teilweise erhebliche Störeinflüsse sind. In unserem Artikel betrachten wir eine spezielle Stromspeisung und weisen nach, dass diese die Eigenerwärmung auf unter ein Millikelvin reduzieren kann. Für einen typischen, für den Außeneinsatz in meteorologischen Wetterstationen geeigneten und üblichen Fühleraufbau erfolgen Simulationen der durch den gepulsten elektrischen Messstrom auftretenden statischen und dynamischen Eigenerwärmung. Der transiente Verlauf der Eigenerwärmung hängt stärker vom inneren Aufbau des Fühlers als vom Wärmeübergangskoeffizienten zur umgebenden ruhenden Luft ab. Die mittlere statische Eigenerwärmung aus einem stark vereinfachten Modell passt gut zum simulierten transienten Verlauf. Die Methode der Impulsstromspeisung hat sich durch die beschriebenen Simulationen als sehr effektiv zur Verringerung der Eigenerwärmung von Widerstandsthermometern erwiesen.
https://doi.org/10.1515/teme-2021-0032
Measurement uncertainty 2020 :
Messunsicherheit 2020. - In: Technisches Messen, ISSN 2196-7113, Bd. 88 (2021), 2, S. 59-60
https://doi.org/10.1515/teme-2021-0003