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

Interferometry on Spheres

Working Group 5.41

Spherical Interferometer

(Fig.1) Spherical Interferometer 1
(Fig. 2) Spherical Interferometer 2

                         Measuring principle of the spherical interferometer

In WG 5.41, two spherical Fizeau interferometers, sphere interferometers 1 and 2, were set up to determine the volumes of silicon spheres (Fig. 1).


Fig. 2: Differential measurement of the sphere interferometer.

The principle for determining the sphere volume is based on a differential measurement (Fig. 2). In the first step, the sphere is placed between the two surfaces of the spherical etalon. Due to the partially reflecting reference surfaces, multiple reflections occur between the sphere surface and the neighboring reference surface, which superimpose and lead to interference.

In the second step, the sphere is lifted out of the beam path. The interference systems are now generated by the waves created by the multiple reflection between both reference surfaces. Thus, the distances of opposite points of both reference surfaces are measured in the empty etalon.

A diameter value of the sphere in a considered spatial direction


results from the value of the diameter D1,2 of the empty etalon minus the two distances d1 and d2 between the sphere and the respective reference surfaces. With the aid of a positioning device, the sphere can be rotated about two axes and measured at any desired orientation. The aperture angle of the objectives is 60° at sphere interferometer 1 and 45° at sphere interferometer 2 (Fig. 3), so that a complete topographic mapping of the sphere surface can be realized by a few different orientations of the sphere.

Fig. 3: Structure and beam path of spherical interferometer 2.


The divergent beam of the phase passes through the polarizing beam splitter, the λ/4-plate and the collimator and is formed by the Fizeau objectives into a spherical wavefront which is reflected from the sphere.

The interference is imaged onto the chip of a camera and evaluated by the method of phase shift interferometry. The phase steps required for this are achieved by changing the laser wavelength. For this purpose, a laser system specially developed in the laboratory for 633nm is used. On the one hand, it can be tuned over a range of 12 GHz, but on the other hand, it can be stabilized to any frequency with an uncertainty of a few 100 kHz.

As a result of the evaluation, a topography is finally available that reflects the individual diameters in the field of view and the volume of the sphere can be determined: