< back to main site


Dimensional characterisation of a quasispherical resonator by microwave and coordinate measurement techniques..

Underwood, R; Flack, D R; Morantz, P*; Sutton, G; Shore, P*; de Podesta, M (2011) Dimensional characterisation of a quasispherical resonator by microwave and coordinate measurement techniques.. Metrologia, 48 (1). pp. 1-15.

Full text not available from this repository.


We describe the dimensional characterisation of a copper `quasisphere' NPL-Cranfield 2. The quasisphere is assembled from two hemispheres such that the internal shape is a triaxial ellipsoid, the major axes of which have nominal radii 62.000 mm, 62.031 mm, and 62.062 mm. The artefact has been manufactured using diamond-turning technology and shows a deviation from design form of less than ± 1 micrometre over most of its surface. Our characterisation involves both Coordinate Measuring Machine (CMM) experiments and microwave resonance spectroscopy.

We have sought to reduce the dimensional uncertainty below the specified maximum error of the CMM by simultaneous measurements of silicon and Zerodur® spheres of known dimensions. Using these techniques we determined the average radius with an uncertainty of u(k = 1) = 133 nm, a fractional uncertainty of 2.1 parts in 106. However, due to anisotropy of the probe response, we could only determine the eccentricities of the quasi-hemispheres with a fractional uncertainty of approximately 3%.

Our microwave determination of the radius uses the TM11 to TM18 resonances. We find the average radius inferred from analysis of these modes to be consistent within ± 11 nm and with an overall uncertainty of ± 20 nm. We discuss corrections for finite conductivity, probe perturbation, and dielectric surface layers.

Finally, we compare the CMM and microwave analyses, and consider the implications of the current work for attempts to determine the Boltzmann constant with a relative uncertainty below u(k = 1) = 10-6.

Item Type: Article
Keywords: Quasispherical Resonator, Acoustic Resonator, Microwave Resonator, Dimensional Metrology, Boltzmann Constant
Subjects: Engineering Measurements
Engineering Measurements > Thermal
Identification number/DOI: 10.1088/0026-1394/48/1/001
Last Modified: 02 Feb 2018 13:14
URI: http://eprintspublications.npl.co.uk/id/eprint/4912

Actions (login required)

View Item View Item