We present a phase-shifting interferometer based on a frequency-tunable diode laser calibrated by an optical frequency comb and the Carré algorithm. By use of the frequency control strategies of locking the diode laser to different comb modes and scanning the repetition rate, an arbitrary single optical frequency synthesizer is obtained. The relative laser frequency uncertainty is 5.7 × 10(-12) for 1 s averaging time with tracing to an Rb clock and accurate phase steps are achieved by optical frequency tuning. The surface topography of a standard sphere is measured by this phase-shifting interferometer based on a flat reference. The phase measurement repeatability is λ/200. With this technique, phase measurement uncertainties from the laser frequency and phase steps are negligible.