A comparison of traceable spatial angle autocollimator calibrations performed by PTB and VTT MIKES

Abstract

Autocollimators are versatile devices for angle metrology used in a wide range of applications in engineering and manufacturing. A modern electronic autocollimator generally features two measuring axes and can thus fully determine the surface normal of an optical surface relative to it in space. Until recently, however, the calibration capabilities of the 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 crosstalk if angular deflections were present in both axes simultaneously. To expand autocollimator calibrations from plane angles to spatial angles, PTB and VTT MIKES have created dedicated calibration devices which are based on different measurement principles and accomplish the task of measurand traceability in different ways. Comparing calibrations of a transfer standard makes it possible to detect systematic measurement errors of the two devices and to evaluate the validity of their uncertainty budgets. The importance of measurand traceability via calibration for a broad spectrum of autocollimator applications is one of the motivating factors behind the creation of both devices and for this comparison of the calibration capabilities of the two national metrology institutes. The latter is the focus of the work presented here.

Reply to Comment on ‘Angles in the SI: a detailed proposal for solving the problem’

“…Whenever an angle needs measuring, whether for practical or scientific purposes, the degree and its subdivisions have always been perfectly good units. We can see this, for example, in the use of the unit arcsecond in this recent paper on autocollimator calibration [3]. 2 It may initially seem strange, but the radian first appeared in the context of logarithms.…”

“…A small group of mathematicians in the early 18th century were investigating the general properties of logarithms and their inverse, exponentials. In work published posthumously in 1722, 3 Roger Cotes identified the number 2.718 (which we now call e) as the natural base for logarithms, calling this number the ratio modularis (the 'ratio parameter'). Using very similar reasoning, he identified the angle 57.296 (180/π) degrees as the angulus modularis-the 'angle parameter', the natural unit for angle, which we now call the radian.…”

“…Quantity calculus applied to these equations implies that the radian is dimensionless, but this is because the equations are not complete, as explained in [4]. By themselves, arc lengths are of no great practical consequence, as they cannot be accurately measured [3].…”

“…The Introduction of this paper contains a brief discussion of practical problems with the current SI definition of the radian as applied to autocollimators 3. Cotes had died aged 33 in 1716, leaving most of his mathematical work unpublished.…”

Editorial for the Metrologia Focus Issue on Length Metrology

“…The field of angle metrology, which is associated with length metrology, is also pushing the boundaries of achievable resolution as demonstrated by traceable measurement of angles with sub-nanoradian resolution [16] whilst still continuing to deliver high accuracy calibration of angle devices [20]. The need to deliver NMI-level angle metrology in an industrial/research setting was foreseen in the 2018 CCL Strategy Document [21] which saw the need to realise the SI units in situ, where the highest accuracies are required.…”