Abstract
Electronic autocollimators are utilised versatilely for non-contact angle measurements in applications like straightness measurements and profilometry. Yet, no calibration of the angle measurement of an autocollimator has been available when both its measurement axes are engaged. Additionally, autocollimators have been calibrated at fixed distances to the reflector, although its distance may vary during the use of an autocollimator. To extend the calibration capabilities of the Physikalisch-Technische Bundesanstalt (PTB) regarding spatial angles and variable distances, a novel calibration device has been set up: the spatial angle autocollimator calibrator (SAAC). In this paper, its concept and its mechanical realisation will be presented. The focus will be on the system’s mathematical modelling and its application in spatial angle calibrations. The model considers the misalignments of the SAAC’s components, including the non-orthogonalities of the measurement axes of the autocollimators and of the rotational axes of the tilting unit. It allows us to derive specific measurement procedures to determine the misalignments in situ and, in turn, to correct the measurements of the autocollimators. Finally, the realisation and the results of a traceable spatial angle calibration of an autocollimator will be presented. This is the first calibration of this type worldwide.
About the authors
Oliver Kranz received his university degree (diploma) in physics from the Leibniz Universität, Hannover, Germany, in 2009. He works as a PhD student in the Length and Angle Graduations Group at PTB. His work focuses on the characterisation of autocollimators in experiments, ray-tracing simulations and mathematical modelling. In addition, he is involved in PTB’s Spatial Angle Autocollimator Calibrator (SAAC), a novel calibration device for autocollimators.
Ralf D. Geckeler received his PhD from the Eberhard-Karls University, Tübingen, Germany. He heads the Length and Angle Graduations Group at PTB, the national metrology institute of Germany. His research focuses on angle measuring devices, such as autocollimators and angle encoders, in international collaboration with industry and research institutes. Current topics include the improvement of autocollimator performance and calibration, the advancement of angle metrology for the characterisation of beamline optics at synchrotron and FEL facilities worldwide, and the development of novel methods and advanced mathematical algorithms for the calibration of angle measuring devices.
Andreas Just received his university degree (diploma) from the Technical University ‘Otto von Guericke’, Magdeburg, Germany, in 1986. He is a member of the Length and Angle Graduations Group at PTB. His work focuses on the calibration of angle standards and instruments, such as autocollimators, and the development of new calibration methods.
Michael Krause received his university degree (diploma) from the University of Applied Sciences, Lübeck, Germany, in 1987. He is a member of the Length and Angle Graduations Group at PTB. His work focuses on angle encoder calibrations and the development of software for analyses of self- and cross-calibration data from these encoders, including PTB’s primary angle standard WMT 220 for the SI unit ‘radian’. He is also responsible for the automatisation of calibration set-ups.
Wolfgang Osten received the Diploma in Physics from the Friedrich-Schiller-University Jena in 1979 and in 1983 the PhD degree from the Martin-Luther-University Halle-Wittenberg for his thesis in the field of holographic interferometry. From 1984 to 1991 he was employed at the Central Institute of Cybernetics and Information Processes in Berlin making investigations in digital image processing and computervision. In 1991 he joined the Bremen Institute of Applied Beam Technology (BIAS) to establish the Department Optical 3D-Metrology. Since September 2002 he has been a full professor at the University of Stuttgart and director of the Institute for Applied Optics. His research work is focused on new concepts for industrial inspection and metrology by combining modern principles of optical metrology, sensor technology and image processing. Special attention is directed to the development of resolution enhanced technologies for the investigation of micro and nano structures.
Acknowledgments
Part of this research was undertaken within the European Metrology Research Programme (EMRP) Joint Research Project (JRP) SIB 58 Angle Metrology. The EMRP is jointly funded by the EMRP participating countries within the European Association of National Metrology Institutes (EURAMET) and the European Union.
Appendix
Method for the determination of the non-orthogonalities of the rotational axes of the tilting unit and the measurement axes of the autocollimator
The non-orthogonalities in this illustration are strongly exaggerated. The autocollimator’s horizontal and vertical measurement directions are regarded as seen from the autocollimator standing upright (roll angle adjustment: 0°). They are co-rotated with the autocollimator. For the presentation of this method, the roll angle adjustments of the autocollimator are assumed to be ideal. See the note below regarding this constraint.
First roll angle adjustment: 0°
The autocollimator is adjusted as depicted in Figure 11: The reticle of the vertical measurement axis (V-Rtc, red line) is aligned parallel to the horizontal deflection direction of the reflected beam (H-Dfl, dashed line). For a horizontal tilting of the mirror, the autocollimator measures the deflection angle of the beam (along the H-Dfl line) with its horizontal CCD (H-CCD, thin black line), while the vertical measurement value is constantly zero. When the mirror is tilted vertically, not only the vertical deflection angle (along the V-Dfl line) is measured by the autocollimator’s vertical CCD (V-CCD) but also the horizontal measurement value is =0 due to the non-orthogonalities of the reticles (v) and the rotational axes of the tilting unit (α).
For this roll angle adjustment, the angle θ1 is calculated by evaluating the measurement values of the autocollimator (using the approximation tan θ1≈sin θ1≈θ1 for small angles θ1):
where H is the horizontal, and V is the vertical measurement value of the autocollimator.
A note on the experimental application of the method: A residual misalignment (non-parallelism) between the reticle of the autocollimator’s vertical measurement axis (V-Rtc) and the horizontal deflection direction of the tilting system (H-Dfl) can be evaluated by the use of autocollimator measurements performed during the horizontal deflection of the tilting system. The resulting angle between V-Rtc and H-Dfl can then be used for correcting the angle θ1 by adding or subtracting it.
Second roll angle adjustment: 90°
For the second roll angle adjustment of the autocollimator, it is rotated by approximately 90° (Figure 12) with respect to its optical axis to align the reticle of its horizontal measurement axis (H-Rtc) parallel to the horizontal deflection direction of the reflected beam (H-Dfl). For a horizontal tilting of the mirror, the autocollimator measures the deflection angle of the beam (along the H-Dfl line) with its vertical CCD (V-CCD), while the horizontal measurement value is constantly zero. The mirror is tilted vertically again. The horizontal CCD (H-CCD) measures the vertical deflection (along the V-Dfl line). The vertical measurement value is ≠0, due to the non-orthogonalities.
For the second roll angle adjustment, the angle θ2 is given by:
With equation (A.1) and (A.2) one obtains
To be compliant with the parameter definitions of the SAAC, α=ryα and v=V0v are valid.
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