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A well-rounded sphere

Especially interesting for
  • production measurement technology

Thanks to a new evaluation method, it is now possible to reconstruct the absolute form of spherical measurement objects from the measurement data of PTB's sphere interferometer with an uncertainty of just a few nanometers. This opens up new application possibilities in production measurement technology.

For the determination of the diameter topography, the individually measured surface segments are distributed around the sphere and partly overlap. From these overlaps, the topography of absolute sphere radii can be reconstructed with the aid of an optimization calculation.

Originally, PTB's sphere interferometer had been designed for measuring the volume of spherical standards – especially that of the  silicon spheres of the Avogadro project – via precise diameter determinations with an uncertainty of one nanometer or less. The new  method now also allows an absolute determination of the radius topography and expands the application possibilities of the sphere  interferometer. In addition, the method applied so far for the volume determination of the Avogadro spheres via the determined  diameters was validated. Using the radii instead of the diameters becomes necessary for the volume determination only in the case of spheres with clearly larger roundness deviations.

So-called stitching procedures, where individually measured segments of an (optical) surface are combined to form a total topography,  are already known in the optical industry. For complete sphere topographies, the measurement uncertainty has so far, however, still been larger than the form deviation of the spherical test pieces to be measured. The new evaluation method yields – for the first time – the absolute form of a sphere, exact to a few nanometers, and not the diameter topography (as has been common practice so far) which is point-symmetric to the sphere centre and, thus, does not allow any clear side assignment of the topographic characteristics to the sphere surface.

The associated algorithm was first checked on the basis of simulated data sets. The comparison with the results of real measurements and with independent results from roundness measurements shows very good agreement – and this with a mean deviation of less than 5 nm.

The new evaluation method opens up the possibility of using the sphere interferometer also for the precision form characterization of spherical measurement objects used in production measurement technology. In addition to the established tactile roundness measurements, the new method is characterized by contact-free scanning of the surfaces at a high lateral resolution and achievable measurement uncertainties of just a few nanometers.


Guido Bartl
Department 5.4 Interferometry on Material
Phone: +49 (0) 531 592-5411
E-mail: guido.bartl(at)ptb.de

Scientific publication

Bartl, G.; Krystek, M.; Nicolaus, A.; Giardini, W.: Interferometric determination of topographies of absolute sphere radii using the sphere interferometer of PTB. Meas. Sci. Technol. 21 (2010), 115101