A concept of the Young interference experiment has been applied in the design of a fiber optic homodyne phase demodulator. The system is based on a bicell-photodetector in the Fourier plane. The above system has been designed, described, and verified together with an estimation of the minimization of phase measurement error in connection with the distance between photodetectors, wavelength, and focal length of the Fourier lens. The fundamental investigation concerning the choice of a distance between photodetectors and its influence on the demodulator's linearity has been presented and discussed as well.