Diameter measurement of silicon sphere at nanometer level with laser interferometry in measurement of gravitational constant

Compared with the SS316 stainless steel sphere, the single crystal silicon sphere with more uniform density and smaller nonsphericity is a good candidate for the source mass in measurement of gravitational constant G . This work focuses on the diameter measurement of the silicon sphere with the laser interferometry . The measurement principle is analyzed and the apparatus is built. The silicon sphere to be measured is positioned between two optical wedges, its diameter is determined by measuring the corresponding distances with the laser interferometry . The initial value of each distance is measured by using the optical three coordinate measuring machine , then two lasers with wavelengths of 632.991 nm and 532.202 nm are combined to determine the distance precisely. Various error sources are evaluated and discussed in detail. The combined standard uncertainty of the diameter is 7.1 nm for the measurement at a certain position. When the silicon sphere is placed in different orientations, the average diameter is determined to be 127346 . 317 μ m , with a standard uncertainty of 0 . 052 μ m , which is mainly introduced by the nonsphericity of the sphere. This provides a reliable method for measuring the diameter of the silicon sphere at nanometer level. • Nanometer-level precision measurement of the diameter of silicon spheres. • Laser interferometry method. • Comprehensive error analysis. • Improvement of the precision of the gravitational constant G-value.