Current commercial interferometers reveal excellent measurement performances, because of its major advantage which enables the displacement measurement with the characterization of the high resolution under the large measuring range. Fabry-Perot interferometer is a compact interferometer with the structure of common optical path. In comparison with the ordinary commercial laser interferometers having non-common optical path, Fabry-Perot interferometer is more insensitive to environmental disturbances. But the disadvantages of Fabry-Perot interferometer are the limited measuring range and the considerable visibility decadence of the interference pattern. To enlarge the measuring range, the folded Fabry-Perot interferometer in which a corner cube reflector severs as the measurement mirror has been proposed in the previous research. However, either the conventional Fabry-Perot interferometer or the folded Fabry-Perot interferometer still have the problem of the considerable visibility decadence of the interference pattern. When the length of optical cavity is changed, the overlapped state of the laser beams will be varied strongly. Hence, it is indispensible to offer a proper signal interpolation algorithm for various signal distributions during the displacement measurement in the whole measuring range. An advanced signal interpolation algorithm for the above-mentioned Fabry-Perot interferometer has been proposed in this investigation. The novel algorithm is able to solve the problem of the displacement measurement due to the considerable visibility decadence of the interference pattern. With this algorithm, a high precision displacement measurement in the large measuring range can be realized by the folded Fabry-Perot interferometer