This paper presents the design, construction, and characterization of a new optical-fiber-based, low-finesse Fabry-Perot interferometer with a simple cavity formed by two reflecting surfaces (the end of a cleaved optical fiber and a plane, reflecting counter-surface), for the continuous measurement of displacements of several nanometers to several tens of millimeters. No beam collimation or focusing optics are required, resulting in a displacement sensor that is extremely compact (optical fiber diameter 125 μm), is surprisingly tolerant of misalignment (more than 5°), and can be used over a very wide range of temperatures and environmental conditions, including ultra-high-vacuum. The displacement measurement is derived from interferometric phase measurements using an infrared laser source whose wavelength is modulated sinusoidally at a frequency f. The phase signal is in turn derived from changes in the amplitudes of demodulated signals, at both the modulation frequency, f, and its harmonic at 2f, coming from a photodetector that is monitoring light intensity reflected back from the cavity as the cavity length changes. Simple quadrature detection results in phase errors corresponding to displacement errors of up to 25 nm, but by using compensation algorithms discussed in this paper, these inherent non-linearities can be reduced to below 3 nm. In addition, wavelength sweep capability enables measurement of the absolute surface separation. This experimental design creates a unique set of displacement measuring capabilities not previously combined in a single interferometer.