According to the requirement of precision diameter measurement of the single crystal silicon sphere, the principle and characteristics of the measuring system were presented, and mathematical models were established for calculating the ellipticity of concentric interference rings with different beam incident angles. Furthermore, the diameter measuring errors of the fringe center were studied in different incident angle situations. It is shown that the error can be up to 6.6 nm when the original distance between inner face of the etalon plate and the adjacent silicon sphere surface equals 13.2 mm, and the incident angle equals 10-3 rad. A novel method was proposed for accurately adjusting incident angle of laser beam relative to the plate. The experimental results show that the incident angle can be less than 10^-5 rad by applying this method.