Interferometric diameter determination of a silicon sphere using a traceable single laser frequency synthesizer

To determine the absolute diameter of a silicon sphere for the Avogadro constant project, we present a phase-shifting interferometer based on a flat etalon and a traceable single laser frequency synthesizer. By using an optical frequency comb to calibrate a frequency-tunable diode laser, the single laser frequency synthesizer can produce an arbitrary laser frequency with a relative uncertainty of 9.2 × 10^-12 in the range of 4 THz. According to the laser frequency tuning system, the Carré algorithm with arbitrary but equal phase steps is employed to calculate the fractional interference phases. The absolute diameter is obtained by measuring the fractional and integral parts based on the principles of phase-shifting interferometry and frequency-sweeping interferometry, respectively. The uncertainty of a single diameter measurement in air is estimated to be 5 nm, whose uncertainty sources from the laser frequency and the phase-shifting algorithm are negligible.