Direct nonlinear parameter estimation method for a phase generated carrier position sensor.

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.

This paper presented signal demodulation scheme of the laser vibration interferometer system using for measurement of low-frequency vibration. Based on principle of phase generated carrier (PGC) modulation and virtual instrument technology, laser vibration signal demodulation on software and hardware platform were established. Taking the PCI6221 multi-function data acquisition device as the core of hardware circuit, real time data acquisition of reference waveform generation and the signal for measurement was realized. Digital PGC algorithm was established by using LabVIEW software workbench, and then vibration signal real time demodulation was realized. The experiment results indicate that the PGC signal demodulation scheme based on virtual instrument technology reduced drift and noise by traditional analog PGC hardware circuit such as analog multiplier and differentiator, enhanced accuracy of signal demodulation, improved system Signal-to-Noise. High accuracy measurement of the low-frequency vibration signals ranging from 10~200Hz comes true, the measuring resolution is better than 0.5nm, and the dynamic range is 110dB.

We present a novel phase generated carrier (PGC) demodulation technique for homodyne interferometers which is robust to modulation depth variations and source intensity fluctuations. By digitally mixing the waveform with a multitone synthetic function (a linear combination of harmonics of the modulating signal), distortion can become negligible even in presence of large variations of the modulation depth. The technique only requires two mixers and can also provide the DC component of the phase in real time, without needing any previously recorded data or ellipse-fitting algorithms. We validate the technique with simulated waveforms and with experimental data from a wavelength metering experiment using an integrated unbalanced interferometer on-chip, showing that the technique corrects distortion without increasing the noise with respect to the standard PGC technique.

Traditional phase generated carrier (PGC) schemes require that the carrier phase delay be kept zero and the phase modulation depth be maintained at a certain value; otherwise, serious nonlinear errors will be introduced into the phase demodulation of a sinusoidal phase modulation interferometer. Proposed herein is a robust carrier phase delay extraction method for nonlinear errors compensation of PGC demodulation that mitigates the effect of the interference phase shift. The carrier phase delay is directly extracted by adopting the first-, second-, and fourth-order in-phase and quadrature harmonic components generated by quadrature multi-harmonics frequency down conversion. Further, with the extracted phase delay, real-time compensations for the phase delay and phase demodulation depth are realized simultaneously in PGC demodulation. Theoretical analysis and derivation of the proposed method are given in detail. Simulation and displacement measurement experiments with different phase delays and phase modulation depths are performed to verify the effectiveness of the proposed method. The experimental results demonstrate that the proposed method is able to precisely extract the phase delay and efficiently eliminate the effects of the phase delay and modulation depth instability.

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.

In this paper we propose a novel, improved, phase generated carrier (PGC) demodulation algorithm based on the PGC-differential-cross-multiplying approach (PGC-DCM). The influence of phase modulation amplitude variation and light intensity disturbance (LID) on traditional PGC demodulation algorithms is analyzed theoretically and experimentally. An experimental system for remote no-contact microvibration measurement is set up to confirm the stability of the improved PGC algorithm with LID. In the experiment, when the LID with a frequency of 50 Hz and the depth of 0.3 is applied, the signal-to-noise and distortion ratio (SINAD) of the improved PGC algorithm is 19 dB, higher than the SINAD of the PGC-DCM algorithm, which is 8.7 dB.

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.

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.

This paper presents a novel heterodyne demodulation method for nearly-balanced fiber-optic interferometric sensors (FOIS). The proposed approach utilizes a periodically linear frequency-modulated (LFM) sine wave to drive a single acousto-optic modulator (AOM), generating optical pulses that undergo self-mixing interference in a nearly-balanced Michelson interferometer. This process produces a differential frequency carrier term for heterodyne demodulation. To compensate for AOM diffraction efficiency variations induced by driving frequency changes, we introduce a digital pre-deformation compensation (PDC) technique. Additionally, optical path difference (OPD) fluctuations in FOIS cause carrier frequency deviations that lead to nonlinear errors, which are effectively mitigated by phase symmetric orthogonal mixing (PSM) technique. Simulations demonstrate that the proposed heterodyne algorithm (FGH) outperforms conventional phase-generated carrier (PGC) in suppressing OPD fluctuation effects. Experimental results validate FGH’s performance, achieving: a power spectral density (PSD) of -105 dB/ sqrt (Hz) at 500 Hz; a dynamic range upper limit of 36.8 dB at 1 kHz; a maximum total harmonic distortion (THD) of 0.031%; and a signal-to-noise and distortion ratio (SINAD) > 47.4 dB at 1 kHz. These performance metrics fulfill the necessary criteria for practical applications.

When the microprobe sensor is faced with the demand of high-speed biaxial displacement measurement, due to the characteristics of phase generated carrier (PGC) technology, accompanying optical intensity modulation (AOIM) and unfavorable phase modulation depth (PMD) will bring about the tens of nanometer cyclic nonlinear errors, further hindering high-speed and high-precision measurement. Herein, a light source intensity stabilization system based on semiconductor optical amplifier (SOA) feedback control is achieved to eliminate the error caused by AOIM in the presence of high-frequency and large-amplitude laser modulation. Based on this, the reasons for large nonlinear errors in biaxial measurements and the inability to ensure the stability of the accuracy of multiple measurement axes are methodically examined, and an effective nonlinear error elimination methodology based on the normalized amplitude correction of active temperature scanning is proposed. The continuity and linearity of the temperature scanning are also discussed. The performed experiments show that the above approach is capable of reducing the displacement demodulation error from the nanometer scale to the sub-nanometer scale. Further, the nonlinear error is reduced to within 0.1 nm for both measurement axes and the performance becomes consistent. The dual-axis measurement resolution of the microprobe sensor reaches 0.4 nm and the measurement speed is better than 1.2 m/s with the standard deviation of lower than 0.5 nm.

Online calibration technique for a long-baseline laser interferometer has been studied, which can be used for nanoscale displacement and vibration measurement. The method combined laser interferometer calibration with measurement to meet the needs of online calibration and state detection of long-baseline laser interferometer. Based on Phase Generated Carrier (PGC) demodulation technique, we add a calibration signal which we have already known to phase-modulated carrier, and according to the amplitude variations of calibration signal, we can achieve work condition monitoring of laser interferometer and measurement of environmental changes and the instruction of fluctuations. In the paper, a laser interferometer with 22-meter-long arm, resolution of 20pm and frequency range of DC ~ 200Hz used for displacement and vibration measurement was constructed, completed the online calibration software and hardware design, experimental results show that: by adding a calibration signal with frequency of 400Hz, amplitude 600nm, online condition monitoring of the laser interferometer can be realized. The advantages of this method is,that it can achieve online calibration for laser interferometer without increase burden in hardware, simplify the interferometer debugging process, improve operational efficiency, at the same time, it is of great significance and value to practical application of long-baseline laser interferometer .

An improved demodulation method for the phase-generated carrier (PGC) system by eliminating laser-intensity modulation (LIM) is proposed. The influence of LIM is analyzed theoretically and experimentally. Two parameters are used to describe the effect of LIM: the LIM coefficient (LIMC) and the LIM phase delay (LIMPD). Good stability of the LIMC and LIMPD is confirmed by experimentation with an actual system. The demodulation signal using the traditional method has a much greater higher harmonic component than the improved method due to LIM. The increase of the signal-to-total-harmonic ratio (SHR) using the improved method is >23 dB, and there is a corresponding improvement of 19 dB to the signal to noise and distortion (SINAD) and signal-to-noise ratio (SNR). A new prototype system using the improved PGC method for marine seismic sensing capable of demodulating multiple channels in parallel, simultaneously, is demonstrated. The SHR is stable at 56 dB when the LIMC is <0.5. Similar results are obtained for the SINAD and SNR. The demodulated signal's upper limit is ~100 rad at 100 Hz and 12 rad at 1 kHz, giving a dynamic range reaching 130 dB at 100 Hz. The system's SINAD is stable within 1 dB, whereas the SHR is stable within 2 dB in field application.

Simultaneous phases detection in multi-wavelength interferometry (MWLI) is essential for high-accuracy dynamic absolute distance measurement in high-end equipment manufacturing. To address this problem, a simultaneous phase detection scheme based on frequency-division multiplexing (FDM) technique is proposed in this paper. High-frequency sinusoidal phase modulation with non-overlapping frequencies were applied to multiple lasers individually using electro-optic modulators (EOMs), and interference phases of multiple wavelengths were extracted in parallel using phase generated carrier (PGC) demodulation technique from the FDM interference signal. Principles of FDM multi-wavelength interferometry and simultaneous phase detection scheme were illustrated. A FDM dual-wavelength interferometer was constructed to verify the performance of the proposed phase detection scheme by simulation analysis and experiments. Results of simulations show that the resolution, accuracy and nonlinear error of the two demodulated phases are all better than 0.01°. Experiments of nanometer displacement measurement further verified the good performance of the phase detection scheme and its feasibility in dynamic measurement.

A new highly integrated data acquisition (DAQ) system for a combined, APD-based, dual-modality PET/CT scanner, implementing both analog and digital electronics on the same board, has been fabricated and tested. The DAQ system was designed to achieve high-precision (<1 ns) coincidence detection in PET and high-rate event counting in CT imaging using the same detectors and electronics. One DAQ board holds 64 parallel detector channels that can be sampled directly at the output of the charge-sensitive preamplifiers (CSP) at a rate of 100 MHz with free-running analog-to-digital converters (ADC) from Maxim. Digital signal processing is performed in field programmable gate arrays (FPGAs) from Xilinx. Independent 500 V voltage regulators are mounted on board for optimum biasing of individual APDs coupled to phoswich detectors. The DAQ board has been fabricated on a 12 copper layers printed circuit board (PCB). The low-noise analog front-end is directly interfaced on board through differential CSP outputs to the high-speed digital circuits for optimum coupling and noise immunity. The board shows excellent electrical characteristics with all circuitry powered up, featuring a mean signal to noise and distortion ratio (SINAD) of 47.7 dB over all 64 channels when supplied with a 10 MHz sine waveform at its input. Initial performance characteristics with BGO/LSO phoswich detectors are reported.

A simple lock-in detection technique especially suited for digital phase-generated carrier (PGC) demodulators is proposed in this paper. It mixes the interference signal with rectangular waves whose Fourier expansions contain multiple odd or multiple even harmonics of the carrier to recover the quadrature components needed for interference phase demodulation. In this way, the use of a multiplier is avoided and the efficiency of the algorithm is improved. Noise performance with regard to light intensity variation and circuit noise is analyzed theoretically for both the proposed technique and the traditional lock-in technique, and results show that the former provides a better signal-to-noise ratio than the latter with proper modulation depth and average interference phase. Detailed simulations were conducted and the theoretical analysis was verified. A fiber-optic Michelson interferometer was constructed and the feasibility of the proposed technique is demonstrated.