Conventional phase generation carrier (PGC) demodulation methods include two main approaches of differential and cross multiplying PGC (PGC-DCM) and arctangent PGC (PGC-ARCTAN). Their correct demodulation requires the carrier phase delay and modulation depth to be maintained at specific values. However, in practice, propagation delays in the optical path, analog-to-digital conversion in the signal acquisition system, and interference caused by the PIN photodetector can introduce phase delays between the carrier signal and the modulated carrier signal. Additionally, the modulation depth C is related to the amplitude of the carrier signal and the parameters of the phase modulator, and it changes with the optical wavelength, temperature, and humidity in the actual operating environment, resulting in random drift and fluctuation of C value. These unstable factors directly affect the operation of the entire demodulation system, causing harmonic distortion of the demodulated signal and even demodulation failure. Therefore, solving the instability problems of C value and phase delay is an important task to improve the stability and accuracy of the demodulation system. Nowadays, many scholars have calculated the modulation depth and phase delay by employing different octave carriers compensation to solve this problem and yielded some results. However, the high-order Bessel function and high octave carriers are prone to introduce high-frequency harmonics in the demodulation results, which causes certain nonlinear distortion. Meanwhile, as different multicarriers and different orders of Bessel functions also affect the demodulation results, it is very important to determine the appropriate carrier multiplicity and Bessel order for accurate demodulation.

Considering the influence of different octave carriers and different orders of Bessel functions on the demodulation results, we propose a multistage orthogonal signal fusion (MOSF) computation method that synthesizes the triple-octave carriers and the third-order Bessel functions. Firstly, the phase delay of the interference signal is calculated and compensated, then the modulation depth is calculated based on the compensated signal, and finally, the compensated demodulated signal is obtained. The signal-to-noise-and-distortion (SINAD) and total harmonic distortion (THD) of the MOSF algorithm and the traditional algorithm in demodulating signals with different phase delays and modulation depths are verified by simulation and experimental comparisons. The linear errors and nonlinear distortions of the demodulation results are analyzed in detail, and then the phase delay errors of the demodulated signals of the different algorithms are compared and analyzed to characterize the real-time performance of the different algorithms. Finally, the ground noise level and the maximum detection range of the demodulated signals of the MOSF algorithm are experimentally analyzed.

We conduct controlled experiments to study the stability of different algorithms. Under the different modulation depth changes, the demodulation results are shown in Fig. 8(a), and the SINAD value of the MOSF algorithm fluctuates up and down in the range of 8 dB-15 dB with the center value of 13 dB. Fig. 8(b) shows the THD of the demodulated signals, and the THD of demodulated signals of the MOSF algorithm is stabilized at -96 dB with a very small fluctuation. It is very small, and under different phase delay variations, the demodulation results are shown in Fig. 9(a). The SINAD value of the MOSF algorithm is stabilized between 10 dB-15 dB with the variation of phase delay, and the harmonic distortion THD of different algorithms in Fig. 9(b) also shows that the THD of the MOSF algorithm is stabilized at around -96 dB with the variation of phase delay, possessing very low nonlinear distortion. Fig. 10 shows the phase delay error of the demodulated signal, and Fig. 11 shows the power spectral density plot of the demodulation results of the MOSF algorithm, which indicates the ground noise and the dynamic demodulation range of this algorithm.

We propose a multilevel orthogonal signal synchronization computation method to address the problem of traditional algorithms that are affected by the modulation depth and the phase delay. The algorithm accurately compensates for the carrier phase delay and modulation depth, which makes it more robust and real-time compared with the traditional phase demodulation schemes. An experimental comparison of conventional demodulation algorithms shows that the MOSF algorithm has the lowest noise floor and the largest detection range. The SINAD and THD of the demodulated signal of the MOSF algorithm under different modulation depths and phase delays reach 84 dB and -90 dB respectively. This indicates that the demodulated signal of the MOSF algorithm is little affected by the modulation depth change, which can overcome the nonlinear distortion of the signal well. The higher SINAD means more complete waveform information. Meanwhile, the demodulation results of the phase delay stabilize at 0°, which has a smaller phase difference, and thus the demodulation results are more robust and real-time. Additionally, the phase delay of the demodulation results is stabilized at 0°, with smaller phase difference and better real-time demodulation. In summary, the MOSF algorithm improves the stability, reliability, and real-time performance of the phase demodulation system, which can be widely adopted in weak signal detection in fiber-optic accelerometers, fiber-optic hydrophones, and structural health monitoring of ocean engineering.