A low-finesse all-fiber sinusoidal phase modulation interferometer for displacement measurement

We present an all-fiber sinusoidal phase modulation (SPM) interferometer for displacement measurement based on an in-built electro-optical modulator (EOM). The interferometer consists of a fiber-optical Mach–Zehnder interferometer (MZI) and a low-finesse fiber-optic Fabry–Pérot interferometer (FPI) through a circulator. The EOM is combined in one arm of MZI for generating modulating reference beam. Reflected beams from an object and the end of the fiber interfere with the reference beam. The phase differences between the reflected beam from the object and the modulated reference beam are demodulated using an improved phase generated carrier demodulation algorithm which is realized on a field-programmable gate array. Compared with the conventional fiber-optic Fabry–Pérot interferometer, this SPM interferometer effectively expands the working distance. Furthermore, we also demonstrate the effect of the phase difference between the fiber end and the reference arm on the measurement. The displacement can only be extracted correctly when the phase difference deviation between the fiber end and the reference arm is smaller than +/−0.29 rad. The experiment results show that the measurement range of the presented interferometer is up to 20 mm with a nonlinear error of ±53.4 nm. The interferometer has a displacement resolution of 45 pm∕Hz over 20 Hz.