This paper presents a method that simultaneously deals with drawbacks of time-average digital holography: limited measurement range, limited spatial resolution, and quantitative analysis of the measured Bessel fringe patterns. When the frequency of the reference wave is shifted by an integer multiple of frequency at which the object oscillates, the measurement range of the method can be shifted either to smaller or to larger vibration amplitudes. In addition, phase modulation of the reference wave is used to obtain a sequence of phase-modulated fringe patterns. Such fringe patterns can be combined by means of phase-shifting algorithms, and amplitudes of vibrations can be straightforwardly computed. This approach independently calculates the amplitude values in every single pixel. The frequency shift and phase modulation are realized by proper control of Bragg cells and therefore no additional hardware is required.