Phase Generated Carrier Demodulation Research Articles

High-speed PGC demodulation model and method with subnanometer displacement resolution in a fiber-optic micro-probe laser interferometer

As the key of embedded displacement measurement, a fiber-optic micro-probe laser interferometer (FMI) is of great interest in developing high-end equipment as well as precision metrology. However, conventional phase-generated carrier (PGC) approaches are for low-speed scenes and local error analysis, usually neglecting the global precision analysis and dynamic effect of system parameters under high-speed measurement, thus hindering their broad applications. We present a high-speed PGC demodulation model and method to achieve subnanometer displacement measurement precision in FMI. This model includes a global equivalent resolution analysis and revelation of the demodulation error mechanism. Utilizing this model, the failure issues regarding the PGC demodulation method under high speed and large range are addressed. Furthermore, an ultra-precision PGC demodulation algorithm based on the combination of static and dynamic delay adaptive regulation is proposed to enable high-speed and large-range displacement measurement. In this paper, the proposed model and algorithm are validated through simulation and experimental tests. The results demonstrate a displacement resolution of 0.1 nm with a standard deviation of less than 0.5 nm when measuring at a high velocity of 1.5 m/s—nearly a tenfold increase of the latest study.

Nonlinear error elimination using the fusion of PGC-DCM, geometric fitting, and Atan algorithms.

A phase generated carrier (PGC) demodulation scheme is always accompanied by nonlinear errors. We propose a fusion of PGC differential and cross multiplying (PGC-DCM), geometric fitting, and arctangent (Atan) algorithms for fiber optic interferometric sensors to eliminate nonlinear errors. The output amplitude of the PGC-DCM algorithm is used to judge whether the Lissajous figure of quadrature signals is larger than 1/2 ellipse arc. When the Lissajous figure exceeds 1/2 ellipse arc, the contaminated quadrature signals are corrected by the ellipse correction parameters calculated from the geometric fitting; otherwise, the previous fitting parameters are employed for correction. Geometric fitting is realized by minimizing the Sampson error, and its failure problem under small signals is solved by using the temporary stability of fitting results. Finally, desired signals are extracted from the corrected quadrature signals by the Atan algorithm. Experimental results show that the fusion combines the merits of the three algorithms and expands the application of the geometric fitting in PGC demodulation schemes.

A PGC demodulation scheme based on the Lissajous ellipse fitting for homodyne interferometer without using second harmonic carrier signal

This paper proposes a phase generated carrier (PGC) demodulation scheme for sinusoidal phase modulation interferometer (SPMI) that does not require a second harmonic carrier signal. In this scheme, an in-phase interference signal component with direct current (DC) bias is obtained by low-pass filtering the original interference signal, and a quadrature interference signal component is obtained by conventional means. The Lissajous figure formed by these two quadrature interference signal components is an ellipse whose center deviates from the origin of the I-Q coordinates. By fitting this ellipse, the major and minor axes and the center coordinates can be obtained. These elliptic parameters are then used to eliminate DC bias and normalize the amplitude of the quadrature signal components. Finally, the phase demodulation of the interference signal can be realized by using arctangent algorithm or differential cross multiplication (DCM) algorithm. The results of simulation and experiment have verified the validity and accuracy of the proposed PGC demodulation scheme, and show that it is insensitive to the phase modulation depth C. Compared with conventional PGC demodulation, this scheme requires lower depth of carrier phase modulation. The vibration measurement results indicate that the average signal-to-noise and distortion Ratio (SINAD) and total harmonic distortion (THD) values of demodulation results in the frequency range of 130 Hz to 250 Hz are 34 dB and -33 dB respectively. The proposed PGC demodulation scheme shows good performance in displacement measurement using SPMI.

An improved phase generated carrier demodulation algorithm of fiber optic fabry-perot sensor

An improved phase generated carrier demodulation algorithm of fiber optic fabry-perot sensor

Improved Phase Generated Carrier Demodulation Algorithm for Laser Vibration Measurement

Improved Phase Generated Carrier Demodulation Algorithm for Laser Vibration Measurement

A Multi-Phase Phase-Generated Carrier Demodulation Algorithm for Stability Improvement of Noise Transfer Coefficient for Fiber Optic Hydrophone

A Multi-Phase Phase-Generated Carrier Demodulation Algorithm for Stability Improvement of Noise Transfer Coefficient for Fiber Optic Hydrophone

High Precision and Stabilization PGC Demodulation Scheme for Fiber Optic Interferometric Sensors

Ellipse fitting algorithm (EFA) has attracted tremendous interest in phase demodulation schemes to eliminate nonlinear errors, however, there is an inherent drawback that the EFA fails to work when the desired phase signal is small. A high precision and stabilization phase generated carrier (PGC) demodulation scheme using hyper least squares (LS) fitting of ellipse is proposed for the first time, to our best knowledge. The contaminated quadrature signals obtained after mixing and low pass filtering are processed by a hyper LS based EFA to eliminate nonlinear errors. Hyper LS relies on algebraic distance minimization with a carefully chosen scale normalization and statistical bias is eliminated up to second order noise terms, which is far superior to the traditional LS. The temporary stability of the fitting result is used to resolve the drawback of the EFA. A module for judging the ellipse arc of quadrature signals is developed. The EFA is executed when the Lissajous figure is larger than 1/4 ellipse arc, otherwise the fitting result of the previous executed EFA is used to correct the ellipse. Experimental results show that the proposed scheme is highly precise and stable regardless of the desired signal amplitude. It has a high response linearity of 99.997%, a minimum detectable phase of 3.16 μrad and a large dynamic range of 123.52 dB @1 kHz & 1% THD.

Ameliorated PGC demodulation scheme using Taubin least squares fitting of ellipse in fiber optic interferometric sensors

In this paper, we propose an ameliorated phase generated carrier (PGC) demodulation scheme using Taubin least squares (LS) fitting of ellipse to eliminate the nonlinear errors. Taubin LS has carefully chosen a normalization matrix and the ellipse fitting parameters are directly obtained by solving the generalized eigenvector problem, leading to a high accuracy result. Quadrature signals are extracted from the signal fundamental and the sidebands of the fundamental of the carrier, and then corrected by the ellipse fitting algorithm (EFA) based on Taubin LS. A combined internal modulation is used to ensure the proper operation of the EFA under small signals. And the desired phase signal is extracted from the corrected quadrature signals by the differential-cross-multiplying method and evaluated by the total harmonic distortion. Experimental results show that the proposed scheme is superior and highly stable, it has a phase resolution of 3.16 μrad/√Hz, a large dynamic range of 120 dB @ 1 KHz and a good linearity of better than 99.99%.

Absolute distance measurement using frequency sweeping interferometry with large swept range and target drift compensation

Frequency sweeping interferometry (FSI) is an attractive absolute distance measurement (ADM) method because of the advantages of large unambiguity range, simple structure and excellent flexibility. By using a reference interferometer (RI), the calibration of the frequency sweeping range in FSI can be avoided, and the complexity and cost of the system can be further reduced. Then, the measurement accuracy is associated with the accuracy of phase demodulation, the range of frequency sweeping and the compensation of target drift. In this paper, ADM using FSI with large swept range and target drift compensation is presented. A frequency stabilized HeNe laser that travels along the same optical path with the swept source laser was employed to monitor the target drifts of the measurement interferometer and RI. Interference phases of the corresponding interferometers were extracted simultaneously using phase generated carrier demodulation technique, and an accuracy better than 1° was verified by nanometer displacement measurement. Comparative experiments of ADM at a distance of ∼4.5 m with different swept ranges before and after target drift compensation were carried out, and the results demonstrated that larger swept range and target drift compensation could greatly improve the stability and accuracy of measurement.

Effect of three-beam interference on phase-generated carrier demodulation of a fiber-optic interferometric sensor.

Homodyne demodulation using a phase-generated carrier (PGC) has been applied in fiber-optic interferometric sensors to overcome the signal fading and distortion due to the drift of the operating point. An assumption needed for the PGC method to be valid is that the sensor output is a sinusoidal function of the phase delay between the arms of the interferometer, which is readily achieved by a two-beam interferometer. In this work, we theoretically and experimentally study the effect of three-beam interference, whose output deviates from a sinusoidal function of the phase delay, on the performance of the PGC scheme. The results show that the deviation could lead to additional undesirable terms in the in-phase and quadrature components in PGC implementation, which may result in significant signal fading with the drift of the operating point. The theoretical analysis leads to two strategies for eliminating these undesirable terms so that the PGC scheme is valid for three-beam interference. The analysis and the strategies were validated experimentally using a fiber-coil Fabry-Perot sensor with two fiber Bragg grating mirrors, each having a reflectivity of 26%.

Ameliorated PGC demodulation technique based on the ODR algorithm with insensitivity to phase modulation depth.

For the optical fiber sensing system using phase generated carrier (PGC) technology, it is very important to eliminate the nonlinear effect of phase modulation depth (C) fluctuation on the demodulation results in the actual environment. In this paper, an ameliorated phase generated carrier demodulation technique is presented to calculate the C value and suppress its nonlinear influence on the demodulation results. The value of C is calculated out by the fundamental and third harmonic components with the equation fitted by the orthogonal distance regression algorithm. Then the Bessel recursive formula is used to convert the coefficients of each order of Bessel function contained in demodulation result into C values. Finally, the coefficients in demodulation result are removed by the calculated C values. In the experiment, when the C ranges from 1.0 rad to 3.5 rad, the minimum total harmonic distortion and maximum phase amplitude fluctuation of the ameliorated algorithm are 0.09% and 3.58%, which are far superior to the demodulation results of the traditional arctangent algorithm. The experimental results demonstrate that the proposed method can effectively eliminate the error caused by the fluctuation of the C value, which provides a reference for signal processing in practical applications of fiber-optic interferometric sensors.

High Stability PGC-EFA-DCM Demodulation Algorithm Integrated With a PID Module

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.

Optical fiber distributed vibration sensor based on dual Mach-Zehnder interferometer using an improved phase generated carrier algorithm

Optical fiber distributed vibration sensor based on dual Mach-Zehnder interferometer (DMZI) has been extensively studied for vibration detections. Whereas the accurate signal demodulation technique is still a challenging task for some particular detections, especially for those dynamic vibration sensing with high frequency. In this work, we propose an ameliorated phase generated carrier (PGC) demodulation algorithm for the dynamic vibration sensing in the DMZI based vibration sensing system. A piezoelectric stretcher is firstly cascaded with the reference arm of the DMZI structure. Then a dynamic strain would be produced to change the phase difference of the DMZI structure when the carrier signal and the measured vibration signal are applied on the stretcher and the sensing arm of the DMZI, respectively. Finally, the applied vibration signal can be accurately demodulated by using the improved PGC demodulation algorithm. Theoretical analysis and derivation of the proposed vibration sensing approach are given in detail. Simulation analysis and vibration experiments with different vibration patterns have been implemented to demonstrate the effectiveness of the proposed sensing approach. Experimental results show that the relation between the applied signal and the demodulated signal is approximately linear. Moreover, the high-order harmonic effect and the intensity fluctuation of the demodulated signals have been effectively suppressed in the proposed DMZI based vibration sensing system.

An improved PGC demodulation algorithm for optical fiber interferometers with insensitive to carrier phase delay and modulation depth

Phase generated carrier (PGC) demodulation is widely used in optical fiber interferometers due to its high sensitivity, large dynamic range and high signal fidelity. Based on the traditional PGC DCM demodulation scheme, we propose a algorithm to eliminate the carrier phase delay and compensate the modulation depth of PGC phase demodulation. The proposed algorithm provides real-time compensation for carrier phase delay and modulation depth without additional compensators. Through theoretical analysis and simulation, the performance of the improved demodulation scheme is compared with the traditional PGC-DCM demodulation algorithm. A complete demodulation system hardware is built, and the improved algorithm, the traditional PGC-DCM scheme and the traditional PGC-Arctan algorithm are tested respectively based on the Michelson interferometer. Experimental results show that the proposed algorithm is insensitive to carrier phase delay and modulation depth, its signal-to-noise ratio and distortion rate can reach 56.15 dB, and the total harmonic distortion rate is 0.13 %.

High-Sensitivity Demodulation of Fiber-Optic Acoustic Emission Sensor Using Self-Injection Locked Diode Laser

We demonstrate the use of a self-injection locked distributed feedback (DFB) diode laser for high-sensitivity detection of acoustic emission (AE) using a fiber-coil Fabry-Perot interferometer (FPI) sensor. The FPI AE sensor is formed by two weak fiber Bragg gratings on the ends of a long span of coiled fiber, resulting in dense sinusoidal fringes in its reflection spectrum that allows the use of a modified phase-generated carrier demodulation method. The demodulation method does not require agile tuning capability of the laser, which makes the self-injection locked laser particularly attractive for the application. Experimental results indicate that the self-injection locked laser increases the signal-to-noise ratio by ∼33 dB compared with the free-running DFB laser. We studied the mode-hopping and laser instability of the self-injection locked laser and their effect on the demodulated signal and found that a mode hopping event causes an abrupt change in the laser intensity after the resonator inside the feedback loop. It manifests itself as a short transient signal in the output of the AE sensor system. With the identification of the mode-hopping events, the associated spurious signal can be identified and discarded in the signal processing without causing significant disruption to the sensor system. Experiment shows that the frequency of locked lasers could oscillate during unstable operations. The fundamental frequency is determined by the time delay of the feedback light and is typically much larger than the AE frequency. Therefore, the laser frequency oscillations have no negative effect on the performance of the sensor system. Finally, we show that the frequency of mode-hopping occurrence is related to the length of the feedback loop and reducing the loop length can effectively reduce the frequency of mode-hopping occurrence.

An improved phase generated carrier demodulation algorithm with high stability and low harmonic distortion

In this paper, an improved phase generated carrier (PGC) demodulation algorithm is proposed to eliminate the influence of light intensity disturbance (LID) and reduce harmonic distortion at the same time. The algorithm is theoretically analyzed, numerically simulated, and experimentally verified. The performance of sensor using proposed algorithm is compared with sensor using traditional PGC-differential-cross-multiplying (PGC-DCM) algorithm and PGC algorithm proposed by predecessor, respectively. Experimental results show that the amplitude of the demodulation signal maintains at the true value, and harmonic distortion is well suppressed by the improved algorithm. In experiment, the signal to noise and distortion ratio (SINAD) of the improved algorithm is 28.62 dB, which is 21.2 dB and 5.5 dB higher than the traditional PGC-DCM algorithm and PGC algorithm proposed by predecessor, respectively.

High-stability PGC demodulation technique with an additional sinusoidal modulation based on an auxiliary reference interferometer and EFA.

In the reference interferometer demodulation scheme, it's difficult to guarantee in practice that both interferometers have the same optical path length difference (OPD), which makes the phase modulation depth different in different interferometers with the same laser modulation. The random shift of phase modulation depth also affects the demodulation results. An improved phase-generated carrier (PGC) technique is proposed based on an auxiliary reference interferometer and the ellipse fitting algorithm (EFA). The technique ensures the correct fitting of the EFA for small amplitude signals by introducing a sinusoidal signal as an additional phase modulation. The combination of the reference interferometer and EFA can eliminate the effect of different phase modulation depths of the two interferometers caused by different OPDs, the non-linear distortion caused by phase modulation depth shifts, and improve the accuracy of the demodulation results. The experiment results are consistent with the theoretical analysis, and the method extends the application of the EFA in the reference interferometer phase demodulation technique.

Improved PGC demodulation algorithm to eliminate modulation depth and intensity disturbance.

In this paper, an improved phase generated carrier (PGC) demodulation algorithm based on frequency mixing and division difference is proposed. The effects of phase modulation depth variation and light intensity disturbance of the light source on the demodulated phase signal are investigated theoretically and experimentally. Compared to the traditional PGC differential-cross-multiplying (PGC-DCM) and PGC arctangent (PGC-Arctan) demodulation algorithms, the ameliorated demodulation algorithm eliminates the harmonic distortion of the demodulated signal by extracting the carrier modulation depth through frequency mixing. The demodulation error caused by the light intensity disturbance of the light source is suppressed by division difference. The stability of the demodulation system is improved. To verify the algorithm, a PGC demodulation system is built based on a Michelson interferometer. The experimental results show that when the frequency and amplitude of the sensed signal are set to 1 kHz and 0.4 rad, respectively, the signal-to-noise ratio with the proposed algorithm achieves a gain of 35.66 dB over the PGC-Arctan algorithm and 26.26 dB over the PGC-DCM algorithm.

Active linearized PGC demodulation with fusion of PGC-Arctan and PGC-DCM schemes for nonlinear error elimination in SPM interferometer.

To eliminate the nonlinear error of phase generated carrier (PGC) demodulation in sinusoidal phase modulating interferometer (SPMI), an active linearized PGC demodulation with fusion of differential-and-cross-multiplying (PGC-DCM) and the arctangent (PGC-Arctan) schemes is proposed. In this method, the periodic integer multiple of π (π-integer phases) of PGC-Arctan without nonlinear error and the corresponding PGC-DCM results recorded at the same time are fused to obtain a calibration coefficient for PGC-DCM demodulation. Combining the accurate π-integer phases of PGC-Arctan and the calibrated fractional phase in the range of π of PGC-DCM, a linearized PGC demodulation result can be achieved, effectively eliminating the nonlinear error caused by drifts of phase demodulation depth (m) and carrier phase delay (θ). The distinct advantage of the proposed method is that it actively and linearly calibrates the fractional result of PGC-DCM without needing to measure or compensate m and θ. Simulation and displacement measurement experiments with different m and inherent arbitrary θ are performed to validate the proposed method. The experimental results show that nonlinear error of the proposed method can be reduced to about 0.1 nm with real-time linearization.

High noise immunity phase generated carrier demodulation technology for the modulation depth influence elimination

In the traditional phase generated carrier (PGC) demodulation algorithms, the modulation depth is an important factor affecting the demodulation effect, and the demodulated signal can be distorted with the modulation depth variation. To address this limitation, this study proposes a method that introduces the differential self-division operation in the traditional PGC-Arctan algorithm framework to eliminate the influence of the modulation depth of distributed optical fiber acoustic sensor system. The simulation results of signal demodulation at different modulation depths and different SNR values show that the proposed algorithm can eliminate adverse effects of the modulation depth and achieve good demodulation performance. An experimental platform is built to verify the simulation results further. Experimental results show that under different modulation depths, the amplitude error of the proposed algorithm is 0.105%, and the total harmonic distortion is 0.068%. Furthermore, the dynamic range of the proposed algorithm is up to 62.5 dB. The comprehensive analysis results verify that the proposed algorithm can effectively eliminate the modulation depth influence, indicating its good stability and noise resistance. Therefore, the proposed algorithm has a good application prospect in high-performance optical fiber acoustic sensing systems.