This Letter describes a dual-amplitude modulation technique incorporated into a double reflection extrinsic-type fiber Fabry-Perot interferometer to measure periodic, nonperiodic as well as quasi-static displacements. The modulation scheme simultaneously maintains the interference signal pair in quadrature and provides a reference signal for displacements inferior to a quarter of the source wavelength. The control and phase demodulation of the interferometer carried out via software enable quasi-real-time measurement and facilitates sensor alignment. The sensor system can be exploited in the low frequency range from 10(-3) to ∼500 Hz and has a resolution better than 2.2 nm, targeting applications in geophysics.