Interferometric fiber-optic hydrophones (FOHs) have been widely applied in the exploration and geological surveying of marine resources owing to their high sensitivity, wide dynamic range, and long-term stability. The demodulation scheme is key to the distortion-free restoration of the target signal in FOH systems. Currently, the phase-generated carrier (PGC), 3×3 fiber-coupler, and heterodyne schemes are the most commonly used schemes. The PGC scheme offers advantages such as good linearity and excellent stability; however, nonlinear distortion is unavoidable because of its unstable modulation depth and phase delay. The 3×3 fiber-coupler scheme is widely used owing to its large dynamic range and simple architecture; however, its demodulation performance is limited by the coupler manufacturability. Meanwhile, the heterodyne scheme offers advantages such as good sensitivity and excellent stability; however, noise is inevitable owing to dual-pulse transmission. We previously proposed a frequency-shift quadrature demodulation scheme for FOH systems, which involves constructing a pair of interference pulses via frequency shifting and time-delay processing after bisecting a single pulse, in addition to considering the optical path difference (OPD) between the two arms of the FOH. This scheme, which does not present carrier and manufacturability limitations, offers many advantages, such as low noise floor and large dynamic range. The frequency-shift quadrature demodulation scheme adapts to the calibration algorithm to calculate the direct current (DC)/ alternating current (AC) parameters and then uses them as fixed values. However, in practice, AC/DC values typically fluctuate during long-term operation owing to factors such as temperature variations, which introduces harmonic distortions. In this study, a frequency-shift quadrature-fitting demodulation scheme for an FOH system is proposed, which is improved by introducing a least-squares ellipse-fitting algorithm. The improved scheme solves the AC/DC parameters in real time and eliminates harmonic distortions. The frequency-shift quadrature-fitting demodulation scheme demonstrates satisfactory demodulation performance and long-term operational stability. Additionally, we design the field-programmable gate array (FPGA) architecture of the scheme to increase its flexibility and versatility.

A desirable frequency-shift quadrature-fitting demodulation scheme enables the real-time calculation of AC/DC parameters. In this study, an elliptical-fitting algorithm is introduced to improve the previous scheme. Analysis results show that, because the phase difference between two interference signals remains constant and carries the same target signal, the Lissajous figure formed by the two interference signals is an elliptical arc. Therefore, the corresponding ellipse parameters are calculated via a direct least-squares fitting of the ellipse. Subsequently, based on the correspondence between the interference signal and ellipse formula, the expressions for the AC and DC parameters can be further derived using the ellipse parameters. Next, cos φ and sin φ can be obtained using the AC/DC parameters and interference signals, and the value of phase difference φ can be obtained by performing an arctangent operation on tan φ. Finally, the demodulation results of the two schemes under AC/DC parameter drift are compared experimentally to confirm the performance of the frequency-shift quadrature-fitting demodulation scheme. In the FPGA design of the frequency-shift quadrature-fitting demodulation scheme, performing a direct least-squares fitting on the ellipse in the FPGA is challenging owing to the matrix inverse operation. Thus, we perform the Cholesky decomposition to convert the matrix inverse operation into basic arithmetic and square operations that the FPGA can manage to achieve ellipse fitting.

The experimental setup is constructed based on the schematic illustration shown in Fig. 4. Additionally, a dedicated FOH is constructed for the test, with an OPD of 0.225 m between the two arms, and the piezoelectric ceramics (PZT) is internally integrated with the FOH for target-signal injection. A frequency-shift quadrature demodulation scheme and a frequency-shift quadrature-fitting demodulation scheme are applied using this experimental setup for performance comparison. A 1 kHz, 2.5 rad target signal is applied to the FOH. The experimental results indicate that the time-domain waveforms of the demodulation results using the frequency-shift quadrature demodulation scheme distort under fluctuations (Fig. 6), whereas the distortion-free frequency-shift quadrature-fitting demodulation scheme restores the sinusoidal waveform (Fig. 7). Additionally, the power spectral density, signal-to-noise ratio and distortion (SINAD), and total harmonic distortion (THD) of the demodulation results obtained under the two schemes are analyzed (Fig. 8). The SINAD and THD of the frequency-shift quadrature demodulation scheme are 22.4 dB and 0.12%, respectively, and those of the frequency-shift quadrature-fitting demodulation scheme are 50.6 dB and 0.04%, respectively. The improved scheme exhibits a higher SINAD, a lower THD, and effective harmonic elimination, and performs significantly better than the previous scheme. A Vivado simulation system is used to verify the feasibility of the FPGA design. The simulation proves that the frequency-shift quadrature-fitting demodulation scheme successfully completes the ellipse fitting, arctangent, and unwrapping operations within the FPGA and finally demodulates the 1 kHz, 3 rad sinusoidal target signal (Fig. 11), thus validating the FPGA design.

In this study, a frequency-shift quadrature-fitting demodulation scheme for an FOH system is proposed. In this scheme, a pair of interference pulses is constructed via frequency shifting and time-delay processing after bisecting a single pulse, and the OPD between the two arms of the FOH is considered. Subsequently, the pair is further demodulated using an ellipse-fitting algorithm. Additionally, the FPGA design of the scheme is implemented using the Cholesky decomposition, and its feasibility is verified using the Vivado simulation system. The FPGA design allows the system to perform demodulation without a computer, which increases the flexibility and versatility of the application. Experimental results show that the frequency-shift quadrature-fitting demodulation scheme can accurately demodulate the target signal under AC/DC parameter drifts. The SINAD and THD afforded by the scheme are 50.6 dB and 0.04%, respectively, which are 28.2 dB higher and 0.08% lower than those of the previous scheme, respectively. Thus, the proposed frequency-shift quadrature-fitting demodulation scheme is applicable to underwater acoustic target detection and characteristic measurements.