# Interferometry on Spheres

Working Group 5.41

### Spherical Interferometer

Fig. 1: Photo of spherical interferometer

The spherical interferometer consists of two spherical reference faces set up as a solid etalon, and the sphere to be measured. All spherical faces are carefully centred, and the measurement is carried out by means of concentric spherical waves. Special lenses are used to generate these spherical waves from strongly expanded laser beams with plane wave fronts.

#### Measuring principle

Fig.2:
Schematic diagram of Spherical

The sphere diameter is determined on the basis of a difference measurement: In a first step, with the sphere removed from the optical beam, the interferences are produced by superposition of the waves reflected by the empty etalon, and the distances between opposite points on the two reference faces are measured. Then the sphere is placed between the two faces of the spherical etalon. The interference systems are now produced by the waves which are reflected from the sphere surface and the neighboured reference face. The diameter of the sphere in a particular direction in space is determined from the value of the diameter of the empty etalon minus the two distances between sphere and reference faces.

The interferences are imaged onto an electronic camera, read into a computer in digitized form and evaluated by the method of phase-stepping interferometry. By variation of the air pressure in the interferometer housing by means of motor-actuated edge-welded bellows and measurement of the refractive index of the air with a refractometer, the optical path difference can be varied in such steps as are required for the evaluation of the interferences. The result of the evaluation then is a topography which corresponds to the variation of the distance between the interferometer faces.

Fig: 3: Sphere diameter topography "flying carpet"

By means of a positioning device, the sphere can be rotated about two axes; it can be placed into the spherical etalon in any desired orientation and measured there. An analysis of first measurements of the sphere topography has shown that the accuracy is already below 2 nm. Technical modifications and further developments are under preparation, which will clearly improve the accuracy of the interferential measurement.