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Production sequence of Si-spheres and interferometrical determination of the sphere volume

Investigation of the uncertainty contribution of the alignment accuracy in the double-ended interferometer of PTB


High-accuracy length measurements of prismatic bodies (e.g. gauge blocks) are usually carried out in single-ended interferometers. To perform these measurements, the gauge block must be wrung to a reference plate. However, the quality of the wringing contact influences the measured length and the measurement method is limited to bodies that are suitable for wringing. An alternative is a double-ended interferometer, in which two light beams aligned parallel to each other propagate in opposing directions and illuminate the respective measuring surface of the body, where they are reflected.

Since the beam path in this type of interferometer is complex compared to a single-ended interferometer and the alignment of the system is an essential requirement for accurate length measurements, the alignment procedure had to be further developed. Its influence on the measured length was investigated in cooperation with the working groups 5.41 "Interferometry on Gauge Blocks" and 8.42 "Data Analysis and Measurement Uncertainty" in virtual experiments with the aid of SimOptDevice to estimate the uncertainty contribution [1].

In the study, dependencies of the cosine error on shape deviations of the gauge block geometry have been shown, which do not occur in single-ended interferometer and were generally neglected until now. With the help of virtual experiments, the dependencies have been investigated and mathematical descriptions established have been validated.

Monte Carlo experiments confirmed that the measurement accuracy was improved by the further developed alignment procedure and that the main cause of cosine errors occurring in the double-ended interferometer lies in the shape deviations of the gauge blocks from an ideal cuboid shape. At a coverage probability of 95%, the coverage interval describing the uncertainty contribution is [0.66; 0.63] nm for gauge blocks of calibration class K up to a length of 100 mm and is thus negligibly small compared to other influences.



[1] Fischedick, M., et al. "Investigation of the uncertainty contributions of the alignment of PTB’s double-ended interferometer by virtual experiments." Metrologia 58.6 (2021): 064001. doi.org/10.1088/1681-7575/ac2724



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