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

Concept for a modification of the PTB double-ended interferometer (DEI) for the measurement of small spheres


A stakeholder workshop with experts from industry and science, which took place at PTB in March 2020, came to the conclusion that, in addition to the measurement of "large" spheres for the representation of the unit of mass, there is an important demand from industry for the characterisation of small spheres for the further development of coordinate metrology. Since the existing Fizeau sphere interferometers were built and optimised for the measurement of spheres with a diameter of about 94 mm, are well utilised with corresponding measurements, and can only be modified for measurements on smaller spheres with much effort, an alternative is necessary. According to the industry's suggestions, spheres with diameters of 1 mm to 45 mm should be able to be measured at an uncertainty level of about 10 nm.

In a recent PTB publication [1], an alternative approach for the measurement of spheres is proposed which is based on the extension of the double-ended interferometer (DEI). The DEI was originally set up for the measurement of prismatic bodies in the working group "Interferometry on gauge blocks" for a double-ended optical probing of the end faces. The idea of extending the DEI is to add two lenses that are as similar as possible, arranged symmetrically around a sphere to be measured (see Fig. 1). The analysis of the path lengths in the different arrangements necessary for the measurements of spheres (Fig. 1 shows only one case where the sphere is in the optical path) results in an elegant formula for the determination of a sphere diameter topography from interference phase topographies measured on both sides.

First experimental investigations with common achromatic lenses used in the DEI are shown in Figure 2. The phase topographies shown give reason to hope that radial topographies can be calculated from the measured spherical diameter topographies - similar to what is possible at the Fizeau spherical interferometers, because there is a surprisingly good rotational symmetry. The visible deviations from the ideally constant phase values are due to the spherical aberration of these simple lenses. Simulations carried out with Zemax suggest that this influence is substantially reduced for aspherical lenses.

Schematic of the extended double-ended interferometer
Fig. 1: Schematic of the double-ended interferometer (DEI) extended by two lenses, left and right, for measuring spheres. Shown is the case where the sphere is in the centre of the two lenses. An incident partial beam from the collimated bundle (marked in grey) passes through the points marked with the index "1". The dashed line shows the centre axis of the beam.

Phase topographies on both sides of the double-ended interferometer
Fig. 2: Phase topographies for the wavelength 532 nm obtained on the left and right side of the DEI using simple achromatic lenses.


[1] R Schödel and M Fischedick 2021 “Proposed extension of double-ended gauge block interferometers for measuring spheres” Meas. Sci. Technol. 32 084010 doi.org/10.1088/1361-6501/abfe35



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