Improved phase generated carrier demodulation algorithm for eliminating light intensity disturbance and phase modulation amplitude variation

In this paper, we demonstrate an improved dynamic demodulation system for acoustic sensors based on distributed feedback-fiber laser (DFB-FL). The signal is demodulated using the phase-generated carrier (PGC) demodulation technology based on unbalanced Michelson interferometer (MI). An improved PGC demodulation algorithm is introduced, which solves the problems of light intensity disturbance (LID) and phase modulation depth drift in the traditional PGC demodulation algorithm that affect the demodulation results. The acoustic pressure sensitivity test of a packaged DFB-FL acoustic sensor is carried out to evaluate the performances of the demodulation system, a flat acoustic pressure sensitivity and frequency response curve was achieved in the frequency range of 200 Hz~18 kHz, the wavelength-acoustic sensitivity was about -40.22 dB re. pm/Pa. The amplitude changes of demodulation signal with light intensity and modulation depth are also tested, and it shows that the stability of the demodulation system has been significantly improved.

The phase generated carrier (PGC) demodulation technique for phase-sensitive optical time-domain reflectometry (Ф-OTDR) has significant potential in applications involving distributed optical fiber sensing and imaging. An improved PGC demodulation algorithm for a Ф-OTDR combined with an unbalanced Michelson interferometer system is presented in this letter. This modified PGC technique uses the one output signal as a fundamental carrier frequency signal with mathematical transformations, and another output is the modulated signal, which enable the two signals to be output synchronously from the interferometer. Theoretical simulations and experiments demonstrate that the linear and nonlinear distortion caused by phase modulation depth and carrier phase delay are well suppressed by the proposed algorithm with high stability and low distortion. The signal-to-noise-and-distortion ratio of sensors using the proposed method in the same conditions achieve gains of 12.98 dB, 30.82 dB and 6.93 dB over PGC-Arctan, PGC-differential-and-cross-multiplying and PGC-single-path differential division method, respectively. Experimental verification shows that the proposed demodulation system can exactly recover the original signals of multiple vibration positions simultaneously, and the system employing the ameliorated PGC demodulation algorithm has the noise level of about 1.83 × 10−4 rad (√Hz)−1 and a large dynamic range of 65.72 dB @ 800 Hz, which provides a new choice for distributed optical fiber sensing technology.

Phase generated carrier (PGC) demodulation technology has been widely used in fiber-optic interferometric sensors while nonlinearity is always accompanying with the scheme. We propose a highly stable PGC demodulation algorithm combining internal modulation, ellipse fitting algorithm (EFA), phase modulation depth ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> ) self-calibration and differential-cross-multiplying (DCM). A low frequency triangular signal is added to the laser modulation, which ensures the effectiveness of the EFA under small signal condition. And the real-time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> value is calculated by using the ellipse fitting parameters and calibrated to the optimal value of 2.63 rad by a closed loop proportion integration differentiation (PID) module. Furthermore, nonlinear distortions are suppressed by the EFA. Experimental results show that the signal-to-noise and distortion ratio (SINAD) and total harmonic distortion (THD) of the proposed scheme are improved by 13.61 dB and 0.12% than the conventional PGC-DCM algorithm. The standard deviation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> decreased from 0.0178 rad to 0.0058 rad in 1024 seconds. The dynamic range, linearity and phase resolution of the system reach 117.73 dB @ 1 kHz, 99.99% and 4.6 μrad/√Hz, respectively.

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

Phase-generated carrier (PGC) demodulation algorithm is the main demodulation methods in Fiber-optic interferometric sensors (FOISs).The conventional PGC demodulation algorithms are influenced by the carrier phase delay between the interference signal and the carrier signal.In this paper, an automatic carrier phase delay synchronization (CPDS) algorithm based on orthogonal phase-locked technique is proposed.The proposed algorithm can calculate the carrier phase delay value.Then the carrier phase delay can be compensated by adjusting the initial phase of the fundamental carrier and the second-harmonic carrier.The simulation results demonstrate the influence of the carrier phase delay on the demodulation performance.PGC-Arctan demodulation system based on CPDS algorithm is implemented on SoC.The experimental results show that the proposed algorithm is able to obtain and eliminate the carrier phase delay.In comparison to the conventional demodulation algorithm, the signal-to-noise and distortion ratio (SINAD) of the proposed algorithm increases 55.99dB.

In this paper, we propose a distributed vibration fiber sensing system based on Polarization Diversity Receiver(PDR). We use Acoustic Optical Modulator(AOM) to generate pulse light and an unbalanced M-Z interferometer to generate two pulse light with a certain time delay in the same period. As the pulse lights propagating in fibers, the Backward Rayleigh scattering lights will interfere with each other. The vibration on the fiber will change the length and refractive index of fiber which results in the change of the phase of the interference signal. Hence, one arm of the M-Z interferometer is modulated by a sinusoidal phase-generated carrier(PGC) signal, and PGC demodulation algorithm has been used to acquire phase information from the Backward Rayleigh scattering lights. In order to overcome the influence of polarization-induced fading and enhance Signal Noise Ratio(SNR), we set a PDR before the photo detector. The Polarization Diversity Receiver segregates the interfere light into two lights with orthogonal states of polarization. Hence, there is always one channel has a better interfere light signal. The experiments are presented to verify the effectiveness of the distributed vibration fiber sensing system proposed.

A novel low-nonlinearity Michelson microprobe fiber interferometer against light intensity disturbance for high-precision embedded displacement measurements is introduced. To analyze the influence of light intensity disturbance on the microprobe and measurement accuracy of the integrated fiber interferometer, an equivalent model of micro-probe sensing with the tilted target is established. The proposed PGC demodulation and nonlinearity correction method with simple principle helps avoid DC component varying with light intensity. The experiments show that residual displacement errors of the micro-probe fiber interferometer are reduced from 4.36 nm to 0.46 nm, thus allowing embedded displacement detection with sub-nanometer accuracy under low frequency light intensity disturbance.

An improved fundamental frequency mixing phase generated carrier demodulation algorithm was proposed.By introducing a direct current filter,the improved algorithm could overcome the limitation that the traditional fundamental frequency mixing phase generated carrier demodulation algorithm was only suitable for small-signal.The improved algorithm retained the useful components of the interference signal and reduced the sampling frequency of the system by introducing an anti-aliasing filter.The up-limit amplitude of the demodulated signal was maximized when the sampling frequency was fixed.And the hardware implementation scheme to realize the improved algorithm was presented.Simulations were carried on the Matlab platform and the digital signal processor simulation platform code composer studio prove the feasibility of the improved algorithm.

In this paper, total harmonic distortion (THD) of phase generated carrier demodulation algorithm by digital arctangent approach (PGC-DAT algorithm) is analyzed. THD due to the deviations of modulation depth and carrier phase delay is investigated both theoretically and experimentally. The analytical expression of THD as the function of carrier modulation depth, signal amplitude, initial phase and deviations of modulation depth and carrier phase delay has been derived. According to our analysis, the maximum THD for different initial phases exists, which reaches the peak value when the signal amplitude is close to 1.2 rad. The best modulation depth to minimize the maximum THD is 2 rad. Finally, an experimental system is set up with the mean THD below -60 dB. The analytical expression of THD derived in this paper agrees well with the experimental results.

Phase generated carrier (PGC) is widely applied in interferometric phase estimation for distance, vibration and velocity measurements. However, traditional PGC methods suffer from nonlinear effects, causing limitations to demodulation of signal. Modified PGC methods, such as ellipse fitting algorithm (EFA), resolves these issues, but usually requires additional phase shift. With our proposed method in this paper, only one period of signal and one test point is required to attain accurate depth of phase modulation and phase. We use a photodiode to calibrate light intensity in data acquisition, and develop a Levenburg-Marquadt algorithm to estimate values of PGC parameters. An improved algorithm is also proposed to avoid local optimization based on prior information to ensure measurement stability. Less than 5 × 10-3 rad phase measurement uncertainty and over 55 dB Signal to Noise and Distortion Ratio (SINAD) is obtained in experiment.

We present an optical fiber voltage sensor by Michelson interferometer (MI) employing a Fabry–Perot (F–P) tunable optical filter and the phase generated carrier demodulation algorithm. By mounting an MI fabricated by an optical fiber coupler on a piezoelectric transducer, a dynamic strain would be generated to change the phase difference of the interferometer when the measured voltage is applied on the piezoelectric. The phase generated carrier demodulation method was used to obtain the phase variation of the interferometer by applying demodulate signal on an F–P tunable optical filter. The measured voltage can be obtained by the variation of the phase; the random phase shift in the interferometer and the intensity fluctuation of the light source of the sensor can be eliminated. The experiment results show that the relation between the phase variation and the voltage applied on the piezoelectric is approximately linear. The dielectric reliability of the sensor has been verified according to the IEC standard.

一种消除伴生调幅影响的PGC解调方法

Fiber optic inetrferometric sensors have advantages of high sensitivity and can be employed to measure very small disturbance. In this paper, a novel demodulation method of fiber optic interferometer sensor is presented, which is based on the 3 × 3 coupler to demodulate the phase shift. By employing two output signals of the 3 × 3 coupler, it can eliminate the insensitive areas. The optical structure and the demodulation algorithm are easy to deploy, compared with the PGC (phase generated carrier) technique and other 3 × 3 coupler based demodulators. This algorithm can effectively overcome the phase distortion caused by the instability of the light output power. The simulation and experiment demonstrate that the high demodulate precision has been achieved.

High-sensitivity detection of ultra-low-frequency (ULF, <10 Hz) signals is a critical challenge for advanced underwater acoustic monitoring, particularly when scaling to large arrays where performance degradation is a primary bottleneck. This paper demonstrates a time-division multiplexed (TDM) ULF fiber optic hydrophone array whose architecture is specifically designed to overcome this integration challenge. The scheme integrates a push-pull sensing structure to enhance the low-frequency acoustic pressure response, an external triggering synchronization mechanism that ensures precise channel demultiplexing while suppressing timing-jitter-induced phase noise, and the phase-generated carrier differential-cross-multiplication (PGC-DCM) algorithm for stable synchronous demodulation. Experimental results show that the developed array exhibits high element-to-element consistency, with the standard deviation of array response amplitude being better than ±0.35 dB. Critically, the array shows exceptional long-term stability, with phase amplitude fluctuations below 0.043 rad over 12 hours of continuous operation. It demonstrates a flat frequency response from 1 Hz to 2 kHz, with an average acoustic pressure sensitivity of -134.61 dB re rad/μPa. Notably, the time-domain response quality at 1 Hz is significantly superior to that of a standard reference hydrophone. The array's equivalent noise pressure (ENP) at 10 Hz is approximately 1.17 mPa/√Hz, which is nearly 8 dB lower than typical ambient sea noise. At 1 kHz, the ENP is 64.51 µPa/√Hz, below the deep-sea state zero noise level. Furthermore, inter-channel crosstalk is less than -60 dB, and the root-mean-square error (RMSE) of two-dimensional direction-of-arrival (DOA) estimation is 2.37°. These key performance indicators confirm that this scheme provides an effective technical pathway for developing high-performance, practical, large-scale ultra-low-frequency fiber optic hydrophone arrays.

While the development of the optic interferometric sensors achieves great progress, one fact that restricts this development is the demodulation technique. An applicable demodulation method for interferometric sensors is called "The Phase Generated Carrier (PGC) demodulation". Yet this demodulation fails to content the large-scale sensors application for the limitations of the electronic devices. Another arctangent approach based on digital demodulator proves more advantages than the traditional Differentiate and Cross Multiply (DCM) approach which is used in PGC demodulation. In this paper, the arctangent approach based on PGC demodulation is discussed and simulated. Lookup table is used in the arctangent approach. Values equal to the existent data in the lookup table are chosen from the table, and values between two different data in the table are modulated to the linear approximate values. Two primary objects are aimed to demonstrate the advantages of the arctangent approach: (1). the noise analysis of this demodulation, considered two aspects: a. the relativity of the noise amplitude and the size of lookup table. Simulation result indicates that when double the lookup size, the noise amplitude decreases about 6dB; b. the influence to the noise generation which is leaded in by the rank of the polynomial approximate coefficients, the higher this rank is, the better the result comes. An approximate function is proposed about this relationship. (2). the measurement range, operation complexity, quality of operation, and applicability of the arctangent approach are discussed for an effective digital realization.