A novel interferometer for dimensional measurement of a silicon sphere

In order to accurately determine Avogadro´s constant, N_A, the volume of a nearly perfect single-crystal silicon sphere of 1 kg mass and about 90 mm diameter is to be measured with a relative uncertainty less than 10^-7. For this purpose,a new spherical Fizeau interferometer that allows the interference pattern to be evaluated by phase-stepping interferometry has been developed. This technique is based on a special algorithm for Fizeau interferences and requires four phase steps of one quarter of an interference order, which are achieved by changing the air pressure inside the environmental chamber. Uncertainties in the sub-nanometer range can be obtained by this interferometric method. The interferometer´s field of view covers an angle of about 600 imaged onto an electronic camera with about 16000 pixels, so that the variation of the diameter is measured with high angular resolution. For the measurements, the sphere rests on a three-point support. The sphere can be lifted and rotated around two perpendicular axes by means of a motor-driven manipulation device, so that it can be positioned in well-defined orientations