This paper describes the study of the characteristics of the four-reflection interferometer components, the interferometer realization and the experimental results concerning the vibration measurement by the Minimum-point method and the Sine approximation method. The theoretical study of the beam intensity losses in all the optical components was performed. The comparison between this interferometer and the two-reflection interferometer used in IMGC, by applying the Minimum-point method, has shown comparable results about the sensitivity of the same vibration transducer in the range up to 10 kHz, a higher short term stability and the extension of the frequency range up to 20 kHz with the four reflection interferometer. The basic configuration of the four reflection interferometer was modified in order to get two output quadrature signals, which allow the determination of the amplitude and phase of the displacement by the Sine approximation method. This solution (interferometer and Sine approximation method) makes possible a further extension of the frequency limit to 30 kHz, displacement measurements of the order of nanometers, with a standard uncertainty of 50 pm and the application of a complete and automatic calibration procedure.