Bilateral comparison of traceable two-axis calibrations of an autocollimator between PTB and VTT MIKES

Autocollimators are used in metrology and manufacturing for non-contact angle measurement. They usually have two orthogonal measuring axes and can thus determine the orientation of the surface normals of a reflector in space. Until recently, the calibration possibilities of national metrology institutes were limited to plane angles. Although it was possible to calibrate both measuring axes independently of each other, it was not feasible to determine their cross-talk if angular deflections were present in both axes simultaneously.

To extend autocollimator calibrations from plane to spatial angles, PTB and VTT MIKES have created dedicated calibration devices which are based on different measurement principles and can take on the task of measurand traceability in different ways. PTB’s Spatial Angle Autocollimator Calibrator (SAAC) is based on a Cartesian arrangement of three autocollimators facing three adjacent sides of a reflector cube [1-4]. In parallel, VTT MIKES created the Interferometric 2-directional Small Angle Generator (I2D-SAG) based on an arrangement of angle interferometers [5-6].

Comparing the calibrations of a transfer standard makes it possible to detect systematic errors of the two calibration procedures and to evaluate the validity of their uncertainty budgets. In this context, it is a clear advantage that the uncertainty levels of the two devices are comparable with each other, with an expanded measurement uncertainty U = 0.014 arcsec (95 % coverage probability) over a measuring range of ± 1000 arcsec in the case of PTB, and U = 0.015 arcsec over a range of ± 500 arcsec and U = 0.020 arcsec over ± 1000 arcsec in the case of VTT MIKES. The comparison results have confirmed the uncertainty budgets and thus the calibration capabilities of PTB’s SAAC and of VTT MIKES’ I2D-SAG as stated in the Calibration and Measurement Capabilities (CMC) database of the Bureau International des Poids et Mesures (BIPM KCDB).

When comparing the calibration results, differences in the alignment of the autocollimator relative to the two measuring instruments and to the reference coordinate systems that they define had to be taken into account. To this end, differences in the tilt angles of the autocollimator with respect to both measuring axes as well as differences in the rotation angles with respect to the autocollimator’s optical axis were determined and corrected.

Furthermore, the influence of changing environmental conditions (air pressure, humidity and temperature) on angle measurement using autocollimators cannot be neglected [7-8]. Changes in the air’s refractive index also have to be taken into account, but the influence of the air pressure dominates. The air pressure is not only subject to natural, weather-induced fluctuations, but also depends on the height of the laboratory above sea level. Pressure changes cause changes in the angular response of the autocollimator which are proportional to the tilt angle of the reflector and its distance from the autocollimator lens in relation to its focal length. When calibrating autocollimators, guidelines [9] therefore recommend that the air pressure, humidity ,and temperature, be stated in the calibration certificate while emphasizing the dominant influence of the air pressure. When comparing the calibration results of several laboratories with each other, the differences in the air pressure values have to be taken into account [10].

The figure shows the differences between the calibration results of PTB and of VTT MIKES which were obtained using an autocollimator of the type Elcomat 3000, Möller-Wedel Optical, with a distance of 300 mm between the lens and the reflector. The differences were divided into their x- and y-components, and their values have been colour-coded. The arrangement of the data points that is visible in the figures is designed to characterize the measurement errors more easily, both on small and on large angular scales. The angle measurement errors of autocollimators cover a wide spectrum of angular scales ranging from a few arcseconds (a scale which corresponds to the pixel size of the CCD detector) up to angular scales of hundreds of arcseconds (which are caused by optical aberrations and limits in the alignment of the autocollimator’s optical components).

  
Figure: Visual representation of the differences in the calibrations of an autocollimator performed by PTB and by VTT MIKES. The differences were separated into their x- and y-components (left and right graph), and colours have been used to represent their values [11].

References

[1] Schumann M, et al. 2019 Metrologia 56 (1) 015011 1-14
[2] Schumann M. 2019 Dissertation (Technische Universität Carolo-Wilhelmina, Braunschweig) ISBN 978-3-95606-480-7
[3] Kranz O, et al. 2015 Adv. Opt. Technol. 4 (5-6) 397-411
[4] Geckeler R D, et al. 2012 Adv. Opt. Technol. 1 (6) 427-439
[5] Heikkinen V, et al. 2017 Metrologia 54 (3) 253-261
[6] Heikkinen V, et al. 2019 Proc. SPIE 11109 1110903 1-10
[7] Geckeler R D, et al. 2019 Rev. Sci. Instrum. 90 021705 1-15
[8] Geckeler R D, et al. 2018 Meas. Sci. Technol. 29 075002 1-9
[9] Yandayan T, et al. 2017 EURAMET Calibration Guide No. 22 www.euramet.org
[10] Geckeler R D, et al. 2018 Metrologia 55 4001 1-57
[11] Geckeler R D, et al. 2021 Metrologia, submitted