A closed-loop phase-shifting Fizeau-type interferometer was constructed that uses direct frequency modulation of a laser diode. The interferometer is servo controlled entirely in the phase domain, where optical phases are detected by two-frequency optical heterodyning. A detailed study of stabilization of the interferometer under feedback control was conducted both experimentally and theoretically. The interferometer showed good stability against vibration up to 200 Hz. The stabilization factors obtained experimentally are in good agreement with the theoretical calculations. The phase-shifting experiment was accomplished with high precision as well as with high stability against external disturbances. The profile measurement of a mirror surface was made with a phase-shifting analysis algorithm, and good measurement reproducibility of λ/60 in the root-mean-square value was obtained for ten measurements within a period of 20 min.
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