Angle metrology at the PTB: current status and developments

Angle metrology at the PTB: current status and developments M. Krause, A. Just, R. D. Geckeler, H. Bosse Physikalisch-Technische Bundesanstalt, Braunschweig und Berlin Bundesallee 100, D-38116 Braunschweig, Germany Tel.: +49-531-592-5200 Fax: +49-531-592-5205 E-mail: Harald.Bosse@ptb.de Abstract In this paper, we will describe the measurement capabilities of the PTB for the highprecision angle calibration over 360 deg, e.g. of angle encoders, and for the calibration over small angle ranges, e.g. of high-resolution electronic autocollimators. As its primary standard for angle measurement, the PTB uses a high-precision angle comparator Heidenhain WMT 220. The systematic angle deviations of the comparator can be determined by independent methods: cross-calibration against a secondary comparison angular measuring system (builtin or external) or self-calibration. Currently, we are able to calibrate the PTB WMT 220 angle comparator with a combined standard uncertainty of 0.001 arcsec. On the basis of these results, we are now able to investigate the limits of the currently applied calibration methods and to develop improved approaches. The WMT 220 comparator is also used for the highly precise calibration of electronic autocollimators (AC). For AC calibrations, combined standard uncertainties below 0.005 arcsec are currently reached. At the moment, the most stringent requirements on AC calibration are given by applications of high-resolution AC in surface topography metrology by deflectometry, e.g., to measure synchrotron beamline optics. We have been investigating factors influencing the angle measurement with AC in deflectometric set-ups. Keywords: Angle metrology, angle encoder, error separation, autocollimator, deflectometry 1. Introduction By definition, the SI unit of the plane angle, radian (rad), is a measurand derived from the unit of length. In practice, however, it is an independent measurand based on the subdivision of the full circle which represents a natural and error-free angular standard of 2 rad. The traceability of angle artefacts (e.g. optical polygons, angle gauge blocks and prisms) or angle measuring instruments (e.g. autocollimators and optical encoders) to the radian is realised at the PTB by the use of the Heidenhain WMT 220 or WMT 905 angle comparators, with the WMT 220 serving as a primary standard for the most accurate calibrations. 2. Angle comparator WMT 220 The main component of the comparator is a rotary table equipped with an air bearing, two measurement systems, and two alternative drive systems, including a non-contact electromagnetic tangential direct drive. The main interferential measuring system consists of a divided circle and eight photoelectric scanning heads distributed at 45 intervals. The radial phase grating with a 400 mm diameter consists of 2 17 grating lines in 360. Each scanning head furnishes sinusoidal signals with twice the graduation frequency and with additional digital interpolation, the final resolution is approx. 0.0012 arcsec per scanning head [1]. The WMT 220 angle comparator is mounted on a massive granite plate which is installed in a clean-room laboratory of the PTB. The laboratory is kept at a high stability of ambient temperature ( T < 0.1 K), constant laminar air flow and the vibration level of the floor is very low. 2-092

Fig. 1. Schematic view of the PTB s WMT 220 angle comparator: (1) air-bearing casing; (2) air-bearing rotor; (3) divided circle of comparator (radial line grating); (4) reading heads; (5) bell-shaped driving element; (6) inner rotor part with ERO 725 angular encoder consisting of (7) divided circle and (8) reading heads; (9), (10) adjustable support plate of rotor; (11) mounting ring; (12) supports and (13) shield. 3. Calibration of angle comparator The comparator itself was calibrated to determine and correct its angular deviations from the true values. Three different independent calibration methods were applied; all based on the error-free standard of 2 rad [2-4]. Table 1. Overview of the applied calibration methods. Comparison measuring system (angular deviation) Number of calibration values in 360 degrees Number of relative angular positions Time for a single calibration + adjustment Cross-calibration EDA calibration Self-calibration ERO 725 ERP 880 Not necessary (0.5 arcsec) (0.04 arcsec) 120 770 128 120 23 1 14 hours + 0 hours 5 hours + 10 hours 2 minutes + 0 minutes Cross-calibration The well-known fundamental cross calibration method [3] is based on a comparison of angular positions 360 /n of two circular divisions in n relative angular positions. This method was realized with n = 120 by using the ERO 725 comparison angle measuring system, which is an integral component of the comparator. Equal Division Average (EDA) method This method by Kajitani and Masuda [4] makes it possible to completely evaluate all harmonic components of the deviations up to the order of (5 7 11) - 1 = 384 by combining measurements obtained at 5, 7 and 11 (5+7+11=23) evenly distributed relative angular positions of the comparator and the external angle measuring system ERP 880 [5]. Both the EDA method and the cross calibration separate the graduation deviations of the angle comparator and the comparison angle systems (ERO 725 or ERP 880). Self-calibration With the WMT 220, the so-called self-calibration method can be applied. It is based on the readout of 16 scanning heads of the comparator's main measuring system during one revolution, without an additional comparison angle measuring system. For this method, in addition to eight scanning heads under 45, eight additional scanning heads are mounted in the comparator, which are arranged in pairs diametrically opposite to one another to form angle intervals of 360 /2 n with 1 n 7, where the smallest interval is about 2.81 [6]. 2-093

Diffrence Angle Deviation WMT 220 [arcsec] Angle Deviation WMT 220 [arcsec] Calibration results of angle comparator The results of the calibration of the WMT 220 angle comparator at 128 equidistant angular positions which were attained by self-calibration, are shown in Figure 2. This figure presents the comparator's angle deviation over 360 deg as a function of the nominal angle and as differences from the mean value. The comparator deviation shows a dominating eighth harmonic with an amplitude of approximately 0.01 arcsec, which is characteristic for the comparator s measurement configuration with eight scanning heads, as well as higher harmonic components with smaller amplitudes. 0.020 0.015 0.005-0.005 - -0.015-0.020 0 40 80 120 160 200 240 280 320 360 WMT 220 Angle Measurement [degree] Fig. 2. Calibrated angle deviations of WMT 220 which were attained by the self-calibration method. Figure 3 shows the differences of the other two calibration methods of the WMT 220 from the results of the self-calibration method: (a) the crosscalibration with the ERO 725 and (b) the EDA calibration with the ERP 880. A second harmonic caused by residual contributions from axial run-out is visible in the difference curves, which is superposed by shortperiodic deviations. The decrease in the differences between the calibration methods by a factor of about 2 was mainly reached by the higher accuracy of the ERP 880 in relation to ERO 725 and an optimised self-calibration analysis. 0.008 0.006 0.004 0.002-0.002-0.004-0.006-0.008 - b a 0 40 80 120 160 200 240 280 320 360 WMT 220 Angle Measurement [degree] Fig. 3. Calibration results of the WMT 220: (a) the cross calibration with the ERO 725 and (b) the EDA calibration with the ERP 880, both showing the difference to the result of the self-calibration method. The calibration methods have been investigated and from their results, together with other sources of uncertainty, a combined standard uncertainty of u c = 0.001 arcsec could be determined for the comparator [7]. In comparison to the earlier uncertainty, this is a decrease by a factor of 2.5 [2]. The accuracy of the error separation method depends, amongst other factors, on the stability and accuracy of the angle comparators which are involved, the limits of the experimental realisation of the method, e.g., the relative angular positioning between the comparison angle measurement system and the comparator, and the 2-094

specific implementation of the data analysis. The calibration results presented in this paper demonstrate that with the WMT 220 angle comparator, a high-quality device is available, which allows further investigation into the limits of different calibration methods in detail. This opens up the possibility of investigating factors such as the accuracy of the relative angular positioning of both comparison systems in the case of cross-calibration methods, or the angular location of the scanning heads in the case of self-calibration. Different algorithms for the analysis of the calibration data can be reserved for future examination. 4. Calibration of electronic autocollimators in the PTB Autocollimators are optical devices for the precise and contactless measurement of small angles of tilt of reflecting surfaces. They are well suited for a broad range of applications in metrology and industrial manufacturing, e.g., the calibration of angle measuring tables with the aid of optical polygons, the measurement of straightness and rectangularity of machine tools and CMMs, etc. or scientific applications. Electronic autocollimators have also been successfully applied to the deflectometric topography measurement of challenging optical surfaces with the most stringent requirements on their calibration. One example is the measurement of large flatness standards with sub-nm measurement uncertainty [8, 9]. Another example is the measurement of optics for applications in synchrotron beamlines (featuring large sizes and strong topography gradients) [10]. The calibration of autocollimators is realised by a direct comparison with the WMT 220 angle comparator as the reference standard. In the automatic calibration procedure, the angle measurement values of the autocollimator and of the comparator can be obtained in specified measurement steps in static mode with highly precise positioning [11]. Figure 4 shows the measurement arrangement for the calibration of an Elcomat HR highresolution electronic autocollimator (measurement range ± 300 arcsec, resolution 0.001 arcsec) manufactured by the company Möller-Wedel Optical against the WMT 220 angle comparator. The beam of the autocollimator is reflected by means of a high quality plane mirror located on the adjustable support plate of the comparator rotor. The autocollimator itself is resting on an adjustable granite plate. Fig. 4. Measurement arrangement for the calibration of an Elcomat HR high-resolution autocollimator against the WMT 220 angle comparator. Figure 5 shows the measurement deviations of the Elcomat HR autocollimator, determined from the differences between the value indicated by the autocollimator and the reference values of the comparator in a measurement range of 160 arcsec in steps of 1 arcsec. It shows the mean value and, as grey bars, the standard deviation of a total of six repeat measurements in the forward and backward direction, recorded in three relative positions between the plane mirror and the angle comparator. The total measurement time was approx. 24 hours. The average standard deviation over all 321 calibration values is 0.0014 arcsec. This achieved level of reproducibility allows to correct the small systematic deviations present in the central angular measurement range of the autocollimator. The uncertainty budget of autocollimator calibrations includes, in addition to the uncertainty of the WMT 220 angle comparator, components which depend on the type of autocol- 2-095

Angle Deviation AC - Ref [arcsec] limator, the calibration parameters and conditions. With highly stable autocollimators, calibrations with standard uncertainties of u c = 0.003 arcsec have been achieved [7]. 0.015 0.005-0.005 - -0.015-160 -120-80 -40 0 40 80 120 160 AC Angle Measurement [arcsec] Fig. 5. Measurement deviations of the Elcomat HR autocollimator in a measurement range of 160 arcsec in steps of 1 arcsec. Mean values and standard deviations (grey bars) of six repeat measurements in both directions and in three relative positions are shown. 5. Conclusion On the basis of these calibration results, investigating the factors influencing the angle response / calibration of electronic autocollimators especially to advance angle metrology for deflectometric applications is a continuing topic of research at the PTB. Influencing factors include the reflectivity of the surface under test, its curvature, the optical path length between it and the autocollimator, the diameter and shape of the aperture stop, and its position both along the autocollimator s optical axis and perpendicular to it. In recent publications, we have examined the effects of the positioning of an aperture stop (used to shape the beam footprint on the surface under test) relative to the autocollimator on its angle response [12] and the influence of the length of the beam path from the autocollimator to the surface under test [13] which can vary greatly in the case of pentaprism-scanning deflectometers. Other fields of research supporting deflectometric applications include the realisation of phase shifting reticles [14, 15] to achieve accurate angle measurement with autocollimators even at small aperture sizes (to increase the lateral resolution), investigations to perform traceable 2D autocollimator calibrations, and research on the influence of dynamic changes in the optical path length, i.e. length changes within a single calibration. References 1. R. Probst, R. Wittekopf, M. Krause, H. Dangschat and A. Ernst. Meas. Sci. Technol. 1998, 9, pp. 1059-66. 2. R. Probst and M. Krause. Proc. 2nd Euspen Int. Conf., Turin Italy. 2001, pp. 326-29. 3. P.J. Sim. Modern Techniques in Metrology. Ed. P.L. Hewitt (Singapore: World Scientific) 1984, pp. 102-121. 4. T. Masuda and M. Kajitani. Precis. Eng. 1989, 11, pp. 95-100. 5. A. Just et al. Submitted to Precision Engineering. 6. A. Ernst. 1994, European Patent 0 440 833 B 1, Patentee: Dr. Johannes Heidenhain GmbH (in German). 7. GUM Guide to the Expression of Uncertainty in Measurement. 1993, Geneva: ISO. 8. R.D. Geckeler. Proc. SPIE. 2006, vol. 6293, 62930O, 12 p. 9. R.D. Geckeler. Meas. Sci. Technol. 2007, 18(1), pp. 115-125. 10. F. Siewert, H. Lammert, T. Zeschke. In: Modern Developments in X-Ray and Neutron Optics, eds. A. Erko, M. Idir, T. Krist, A.G. Michette (Berlin: Springer). pp. 193-200. 11. A. Just, M. Krause, R. Probst, R. Wittekopf. Metrologia. 2003, 40, p. 288-294. 12. R.D. Geckeler and A. Just. Proc. SPIE. 2007, vol. 6704, 670407, 12 p. 13. R.D. Geckeler and A. Just. Proc. SPIE. 2008, vol. 7077, 70770B, 12 p. 14. G. Fütterer. Proc. SPIE. 2005, vol. 5856, pp. 950-959. 15. G. Fütterer. Proc. SPIE. 2007, vol. 6617, 661703, 8 p. 2-096