| Summary: | Laser interferometers can achieve a nanometer-order uncertainty of measurements when their frequencies are locked to the reference frequencies of the atom or molecule transitions. There are three types of displacement-measuring interferometers: homodyne, heterodyne, and frequency modulation (FM) interferometers. Among these types of interferometer, the FM interferometer has many advantageous features. The interference signal is a series of time-dependent harmonics of modulation frequency, so the phase shift can be detected accurately using the synchronous detection method. Moreover, the FM interferometer is the most suitable for combination with a frequency-locked laser because both require frequency modulation. In previous research, low modulation frequencies at some tens of kHz have been used to lock the frequency of laser diodes (LDs). The low modulation frequency for the laser source means that the maximum measurement speed of the FM interferometers is limited. This paper proposes a novel contribution regarding the application of a high-frequency modulation for an LD to improve both the frequency stability of the laser source and the measurement speed of the FM interferometer. The frequency of the LD was locked to an I<sub>2</sub> hyperfine component at 1 MHz modulation frequency. A high bandwidth lock-in amplifier was utilized to detect the saturated absorption signals of the I<sub>2</sub> hyperfine structure and induce the signal to lock the frequency of the LD. The locked LD was then used for an FM displacement measuring interferometer. Moreover, a suitable modulation amplitude that affected the signal-to-noise ratio of both the I<sub>2</sub> absorption signal and the harmonic intensity of the interference signal was determined. In order to verify the measurement resolution of the proposed interferometer, the displacement induced by a piezo electric actuator was concurrently measured by the interferometer and a capacitive sensor. The difference of the displacement results was less than 20 nm. To evaluate the measurement speed, the interferometer was used to measure the axial error of a high-speed spindle at 500 rpm. The main conclusion of this study is that a stable displacement interferometer with high accuracy and a high measurement speed can be achieved using an LD frequency locked to an I<sub>2</sub> hyperfine transition at a high modulation frequency.
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