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F-P (Fabry–Perot) pressure sensors have a wide range of potential applications in high-temperature, high-pressure, and high-dynamic environments. However, existing demodulation methods commonly rely on spectrometers, which limits their application to high-frequency pressure signal acquisition. To solve this problem, this study developed a self-compensated, three-wavelength demodulation system composite with an F-P pressure sensor and a thermocouple to construct a comprehensive sensing system. The system produces accurate pressure measurements in high-temperature, high-pressure, and high-dynamic environments. In static testing at room temperature, the sensing system shows excellent linearity, and the pressure sensitivity is 158.48 nm/MPa. In high-temperature testing, the sensing system maintains high linearity in the range of 100 °C to 700 °C, with a maximum pressure-indication error of about 0.13 MPa (0~5 MPa). In dynamic testing, the sensor exhibits good response characteristics at 1000 Hz and 5000 Hz sinusoidal pressure frequencies, with a signal-to-noise ratio (SNR) greater than 37 dB and 45 dB, respectively. These results indicate that the sensing system proposed in this study has significant competitive advantages in the field of high-temperature, high-speed, and high-precision pressure measurements and provides an important experimental basis and theoretical support for technological progress in related fields. [ABSTRACT FROM AUTHOR]

Pressure sensors prepared from sapphire exhibit excellent characteristics, including high-temperature resistance, high hardness, and resistance to electromagnetic interference. A Fast Fourier Transform and Mean Square Error (FFT-MSE) demodulation algorithm was employed to demodulate a sapphire sandwich-structure Fabry–Perot (F-P) pressure sensor. Through simulation analysis, the experimental results indicated that the demodulation error of the air cavity length in the range of 206 μm to 216 μm was less than 0.0008%. Compared to single demodulation methods and combined demodulation methods based on FFT or Minimum Mean Square Error (MMSE), the method proposed in this work reduced the demodulation error by more than three times and increased accuracy by more than six times. The algorithm was utilized to demodulate the sapphire sandwich-structure F-P pressure sensor, and the test results indicated that the fitting error of the sensor was less than 0.025% within the pressure range of 0 MPa to 10 MPa. The repeatability error was less than 0.066%, the zero-point deviation was 1.26%, and the maximum stability deviation was 0.0063% per 30 min. The algorithm effectively demodulated the actual cavity length variation in the sapphire sandwich-structure F-P pressure sensor, providing a solution for the performance evaluation of the sapphire sandwich-structure F-P pressure sensor. [ABSTRACT FROM AUTHOR]

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A demodulation algorithm is vital for a fiber Bragg grating (FBG) sensing system. In this paper, a novel demodulation algorithm based on the variable-step-size method and crosscorrelation algorithm is proposed to demodulate the wavelength of an FBG. By changing the step size of each calculation, the amount of calculation can be greatly reduced, and pm-level resolution can be achieved over the whole bandwidth. A simulation shows that the demodulation results are not affected by noise, and the algorithm can accurately demodulate the FBG wavelength in a large range. The stability of the algorithm is also tested using three FBG sensors, and the results show that the difference among 25 measurements is only 4 pm. Moreover, the results of temperature calibration experiments show that the sensitivity of the sensor is 41.9 pm/1, which is similar to the value of 45 pm/1 provided by the manufacturer. The R2 value of the fitting curve is 0.9994, which means that the demodulation algorithm can be effectively used in sensing measurement. [ABSTRACT FROM AUTHOR]

In this paper, we propose a distributed optical fiber vibration sensing system based on Φ-OTDR and Michelson interferometer. It can detect multiple vibrations simultaneously along a sensing fiber, and the vibration waveform, frequency, position and amplitude could be demodulated correctly using our proposed PGC demodulation algorithm. The experimental results show, a SNR of 34.86 dB is achieved with the background noise level of − 37 dB at the 1000 m, and the SNR is 28.09 dB with the background noise level of − 32 dB at the 6000 m. [ABSTRACT FROM AUTHOR]

This letter reports a high-speed and high-resolution low-coherence interferometric demodulation algorithm without phase jumps. The demodulation algorithm utilizes the restored analytic interference signal and discrete Fourier transform to deduce the Buneman frequency estimation formula and obtain the linear phase. The optical path difference (OPD) is demodulated based on the Buneman frequency estimation and total phase method. Phase jump is eliminated by re-calculating the peak index and phase from the amplitude and phase frequency spectrums when the peak index approximates an integer value. The experimental results verify the phase jumps are eliminated. The proposed demodulation algorithm provides a 0.027-nm cavity length resolution of an extrinsic Fabry-Perot interferometer (EFPI) with 5-kHz demodulation rate and 384 data points number of an optical spectrum. The speed limitation experimental results show the demodulation speed can achieve 300 kHz with 256 data points number of an optical spectrum. The proposed demodulation algorithm is very robust and promising for all kinds of low-coherence interferometers. [ABSTRACT FROM AUTHOR]

This paper presents a fast demodulation algorithm to determine fiber Bragg grating (FBG) from spectra acquired by low wavelength resolution spectrometers. A modified and improved Buneman frequency estimation algorithm is employed in tracking FBG wavelength and eliminating FBG wavelength discontinuities in real-time wavelength demodulation calculations. The FBG demodulation algorithm was tested using a 512-element detector array spectrometer with a 156 pm/element resolution. At a 2-kHz spectrum acquisition rate, the demodulation algorithm achieved a 0.048 pm Bragg wavelength resolution. The computational efficiency and robustness of the new algorithm was compared with a Gaussian FBG peak fitting method. Our method provides a real-time demodulation scheme to track FBG wavelength using low-resolution spectrometers or tunable lasers. It has the potential to significantly reduce the cost of FBG interrogation systems that are employed in high-sensitivity and high-speed sensing applications. [ABSTRACT FROM AUTHOR]

A high-precision wavelength demodulation method based on optical fiber Fabry-Perot tunable (FPT) filter is proposed for the fiber Bragg grating temperature sensing system. This algorithm uses the original sampling data obtained from the data acquisition card to simultaneously calculate the transmission spectrum of the F-P etalon (FPE) and the reflection spectrum of the fiber Bragg grating (FPG) sensors. In each scanning cycle, the transmission spectrum wavelength of the F-P etalon (FPE) is calibrated dynamically in real time, the reflectance spectrum central wavelength of the FPE sensors is calculated by referring to the transmission spectrum wavelength of the FPE that has been calibrated. It effectively weakens the perturbation effect caused by the nonlinear and non-reproducibility of narrowband light source from the fiber FPT filter, reduces the numerical error and effectively eliminates the pseudo peak of the FPE, and greatly improves the measurement accuracy of the system. Most programming languages can implement this algorithm. A temperature sensing experiment for the proposed method has been carried out. Results showed that the demodulation precision by our method could reach up to ±0.2 °C, wavelength demodulation accuracy 3 pm.

Tilted fibre Bragg grating (TFBG) are used as sensors to determine many quantities such as refractive index, temperature, stress, rotation and bending. The TFBG spectrum contains a lot of information and various algorithms are used for its analysis. However, most of these algorithms are dedicated to the analysis of spectral changes under the influence of the refractive index. The most popular algorithm used for this purpose is to calculate the area occupied by cladding modes. Among the remaining algorithms, there are those that use the determination of the cut-off wavelength as a surrounding refractive index (SRI) indicator. Projection on the wavelength axis can also be used to calculate the bending radius of the fibre. However, this is a more difficult task than with SRI, because the mode decay in bending is not so easy to catch. In this article, we propose a multi-step algorithm that allows to determine the impact of bending on mode leakage. At the same time, the place on the wavelength from the side of the Bragg mode and the ghost mode is determined, which represents the cladding mode radiated from the cladding under the influence of bending. The developed algorithm consists of the following operations carried out on the transmission spectrum: Fourier filtering, calculation of the cumulative value of the spectral length, low-pass filtering of the cumulative curve or its corresponding polynomial approximation, determination of the first and second derivative of the approximated curve, and projection of the second derivative of the curve on the wavelength axis. The shift of the wavelength determined in this way indirectly indicates the bending radius of the optical fibre. Based on multiple measurements, we prove that the presented algorithm provides better results when determining the bending radius compared to other algorithms adopted for this purpose and proposed for SRI measurements. Additionally, we analyse the method of determining the shift of a fragment of the spectrum using the phase of the discrete Fourier transform.

In order to demodulate CD3S signals in multipath fading channels, this paper proposed a demodulation algorithm based on KF, UKF and MMSE filter joint estimation. According to the difference and correlation among the chaotic code synchronization, the channel estimation and the data demodulation, the algorithm estimated the chaotic code by UKF, estimated the channel parameters by KF, and reconstructed the data by MMSE filtering. The three filters respectively used one another ' s estimation results as the system parameters and worked alternately to accomplish demodulation by joint estimation. Simulation results demonstrate that the algorithm can overcome the influence of multipath fading and channel noise, no matter whether the channel is time invariant or time-varying,and realizes the demodulation of CD3S signals in multipath channels . [ABSTRACT FROM AUTHOR]

A fiber optic current sensor (FOCS) demodulation algorithm based on differential-self-multiplication (DSM) is proposed, which is insensitive to the variation in phase modulation depth. It is theoretically analyzed and experimentally verified, compared with two traditional demodulation algorithms in this paper. DSM algorithm reduces demodulation errors caused by phase modulation depth variation that will cause harmonic amplitudes to approach zero. And the variation in phase modulation depth can be simulated by changing modulation voltage. In experiments, where the modulation frequency is 350 kHz and the modulation voltage ranges from 0.5 to 9 V, demodulation currents with DSM algorithms are not only more accurate but also more stable than traditional demodulation algorithms. In addition, the robustness of the DSM algorithm is demonstrated by repeating the experiment at different modulation frequency ranges from 100 to 600 kHz. This work provides a stable demodulation algorithm for FOCS, which can be extended to the applications in demodulation for other phase interferometers. • An algorithm that is insensitive to variation in phase modulation depth is proposed. • The proposed algorithm is compared with two traditional demodulation algorithms. • Repeated experiments at different modulation frequencies to demonstrate robustness. [ABSTRACT FROM AUTHOR]

Static strain can be detected by measuring a cross-correlation of reflection spectra from two fiber Bragg gratings (FBGs). However, the static-strain measurement resolution is limited by the dominant Gaussian noise source when using this traditional method. This paper presents a novel static-strain demodulation algorithm for FBG-based Fabry-Perot interferometers (FBG-FPs). The Hilbert transform is proposed for changing the Gaussian distribution of the two FBG-FPs’ reflection spectra, and a cross third-order cumulant is used to use the results of the Hilbert transform and get a group of noise-vanished signals which can be used to accurately calculate the wavelength difference of the two FBG-FPs. The benefit by these processes is that Gaussian noise in the spectra can be suppressed completely in theory and a higher resolution can be reached. In order to verify the precision and flexibility of this algorithm, a detailed theory model and a simulation analysis are given, and an experiment is implemented. As a result, a static-strain resolution of 0.9 nε under laboratory environment condition is achieved, showing a higher resolution than the traditional cross-correlation method.

Highlights • A new phase generated carrier demodulation algorithm is proposed and analyzed. • The proposed PGC-SDD algorithm shows the merits of high stability and low harmonic distortion. • Different traditional PGC demodulation algorithms have been compared. Abstract Phase generation carrier (PGC) demodulation technique is widely adopted in the field of interferometric optical fiber sensors, for its high sensitivity, good linearity and large dynamic range. In this paper, a novel single-path differential divide PGC demodulation algorithm (PGC-SDD) is designed and analyzed. Experimental results show that not only the distortion induced by light intensity but also the harmonic distortion induced by the modulation depth are well suppressed by the PGC-SDD algorithm. The signal-to-noise and distortion ratio of sensors using the proposed algorithm achieved a gain of 28.06 dB and 13.13 dB over that using differential-cross-multiplying (PGC-DCM) algorithm and PGC Arctangent (PGC-Arctan) algorithm, respectively. In addition, the PGC-SDD demodulation algorithm can also demodulate non-periodic signals. [ABSTRACT FROM AUTHOR]

Highlights • Multimode spectrum simulations. • Improve CCA performance with peak-locking effect. • Experimental and Simulation results. • Fast and easy implementation demodulation algorithm. Abstract In this paper we report on the deployment of Finite Impulse Response (FIR) filters as an extension to the common cross-correlation algorithm (CCA), for accurate peak tracking of multimode and single mode fibre Bragg gratings when dealing with wavelength shifts below the sampling resolution of the demodulator; the well-known peak-locking effect. The performance of the common CCA under these conditions was studied using simulations for single and multiple peak grating spectra and was compared with the performance of proposed, improved CCA method. We studied the cases where fibre Bragg gratings are wavelength-shifted with triangular and sinusoidal manner and how the proposed method behaves under these conditions. We experimentally evaluated our proposed method by utilising strain measurements using a fibre Bragg grating inscribed in a multimode gradient index CYTOP polymer fibre. The method and algorithm showed significant improvement concerning the peak-locking effect, while maintaining the response speed. [ABSTRACT FROM AUTHOR]

An accurate and efficient demodulation algorithm for a fiber Bragg grating (FBG) strain sensor has been proposed and demonstrated. An accurate demodulation can be achieved by scanning only the 0.15-nm reflection spectrum of the FBG sensor instead of scanning the complete reflection spectrum. The proposed algorithm was first used to calculate the integration of 15 regions (10 pm per region) to calculate the wavelength drift. This algorithm is good in that the demodulation time can be greatly reduced without degrading the demodulation accuracy. Hence, the efficient algorithm, which can support a short demodulation time of a low-cost demodulation system, is very suitable for high demodulation rate requirements of the high-speed sensing systems. [ABSTRACT FROM AUTHOR]

In this paper, a strain sensing system based on Distributed-Feedback (DFB) laser array and a high effective demodulate algorithm is proposed. The uniqueness and innovation of the algorithm is in the following two aspects: one is that accurate demodulation can be achieved by scanning only 0.4 nm bandwidth of fiber Bragg grating (FBG) spectrum instead of relying on scanning FBG’s principal power peak; and the other is that the scanned spectrum can be any part of reflected spectrum of FBG sensor, which make it possible of using wavelength-division multiplexing (WDM) for FBG sensing network. In the experiment, DFB laser array with single-channel and four-channel are used to demonstrate the proposed algorithm. Experiments results show that the single-channel’s error is below 5 pm, four-channel’s is below 2 pm, strain and algorithm results show good linearity. [ABSTRACT FROM AUTHOR]

We demonstrate a combined cross correlation and Hilbert transform-based demodulation algorithm for tracking the wavelength shifts of fiber Bragg gratings (FBGs) having a multiple peak reflection spectrum. We show how the Hilbert transform can be employed to convert the task of locating the maximum of the wavelength profile to the one of finding the zero crossing. We observed higher accuracy and fast response compared to other well-known demodulation algorithms such as the centroid detection algorithm and the cross-correlation algorithm. In addition, we show that the multipeak reflection spectrum that occurs in multimode fibers does not greatly affect the algorithm results. Finally, we experimentally recover axial strain measurements using a multipeak reflection spectrum of an FBG inscribed in a multimode gradient index CYTOP fiber using the newly developed algorithm. [ABSTRACT FROM PUBLISHER]

• High-speed demodulation technology cannot maintain high demodulation accuracy. • Self-compensation three-wavelength demodulation algorithm with stable phase difference in large demodulation range. • The demodulation technology has the advantages of fast demodulation speed, high demodulation accuracy, large demodulation range and simple system. This study proposed a self-compensation three-wavelength demodulation method for interrogating fiber-optic extrinsic Fabry–Pérot interferometric (EFPI) sensors. The variation in the EFPI cavity lengths is extracted by the three signals with different wavelengths. The demodulation method uses the demodulated EFPI cavity length to stabilize the phase difference. The phase difference of the calibrated signals is close to π/2 all the time. Thus, the accuracy of the demodulation obtained by using the arctangent method is improved. The experimental results show that the phase difference of the calibrated quadrature signals is always close to π/2 when using the self-compensation demodulation method. The EFPI cavity length varies from 44.885 µm to 83.347 µm, and the vibration signal is not distorted. The sample rate is 500 kHz, which can be used for the interrogation of dynamic signals. This demodulation technique has a high potential for engineering applications owing to its simple design, high robustness, large dynamic range, high sampling rate, and high accuracy. [ABSTRACT FROM AUTHOR]

• A joint demodulation technique with sub nanometer resolution is proposed. • The energy of spectral signal is further concentrated by synchronous squeezing. • The estimated cavity length is obtained by the phase extraction method. • Weighted vector is introduced to reduce the influence of noise on the results. • The final cavity length is obtained by the weighted cosine similarity method. In order to improve the resolution of the demodulation algorithm of the fiber-optic low-finesse extrinsic Fabry-Perot interferometric (EFPI) sensor, this paper presents a joint demodulation algorithm based on the synchronous squeezing wavelet transform phase extraction method and the weighted cosine similarity approach. This algorithm combines the advantages of the synchronous squeezing wavelet transform phase extraction method which can achieve high resolution in dynamic measurement, with the weighted cosine similarity method which can reduce signal interference to obtain high resolution. In the experiment, the joint demodulation algorithm realizes a high-resolution measurement of the EFPI sensor, reaching 0.020 nm and the greatest fluctuation 0.053 nm with an initial cavity length of 60 μm. The resolution of the joint demodulation algorithm has shown promising result at the sub-nanometer level. [ABSTRACT FROM AUTHOR]

• A fast query system of FBG based on swept laser is proposed. • A fast and efficient neighborhood averaging algorithm is proposed. • Experimental results show that the proposed algorithm has strong stability and excellent demodulation accuracy and speed. A fast interrogation scheme for dynamic fiber Bragg grating (FBG) based on a swept laser is presented. A neighborhood average algorithm, meanwhile, is used to real-time and fast demodulate the Bragg wavelength. In this paper, the resolution of the system using neighborhood average algorithm is tested, and the dynamic interrogation of the system is verified using vibration signals. The proposed algorithm achieves a Bragg wavelength resolution of 0.11 pm when the laser scanning frequency is 40 kHz. The stability of the algorithm is compared with Buneman wavelength estimation algorithm. Compared with other commonly used FBG peak search algorithms, the new algorithm has the characteristics of low computational cost, high sensitivity and stability. [ABSTRACT FROM AUTHOR]

This paper presents a demodulation algorithm based on the synchronous integrator circuit for the MEMS tuning fork gyroscope utilizing the digital processing technology. The synchronous integral demodulator (SID) is adopted to demodulate the drive-detection signal and sense-axis output signal separately. Combining with automatic gain control and phase-locked loop technology, the closed-loop control of drive mode has been implemented, and high precision output of the gyroscope has been achieved. The simulation results have verified the effectiveness of the synchronous integrator circuit, which is in good agreement with the theoretical analysis. Compared with other demodulation algorithms, the SID has the advantages of the lower noise level, a better ability to attenuate the harmonics, and the best hardware efficiency. The frequency characteristic of the synchronous integrator is also analyzed, which is vital to the bandwidth of gyroscope. The print circuit board based on field-programmable gate array digital circuit is manufactured and the corresponding experiment is carried out. The experimental results show that the SID algorithm of digital control system for the gyroscope developed in our laboratory has achieved a good performance. The bias instability of tested gyroscope is measured to be 0.2°/h with the angle random walk of 0.14°/ \surd \texth and the nonlinearity of the scale factor is <60 ppm with the measurement range of ±100°/s. [ABSTRACT FROM PUBLISHER]

This article presents the novel FPGA-based 1 Gb/s near-Shannon-limit ACM modem developed within the MHOMS program with particular focus on the advanced modem algorithm solutions devised. A number of powerful FEC schemes have been analyzed as possible candidates for the MHOMS modem, and the final selection is justified in terms of the best tradeoff between complexity and performance. State-of-the-art modulation and demodulation algorithms are also presented, including nonlinearity dynamic precompensation techniques and innovative synchronization strategies required by the selected powerful modulation and coding schemes. Overall modem performances are also shown for a variety of spectral efficiencies. [ABSTRACT FROM PUBLISHER]

Tilted fibre Bragg grating (TFBG) are used as sensors to determine many quantities such as refractive index, temperature, stress, rotation and bending. The TFBG spectrum contains a lot of information and various algorithms are used for its analysis. However, most of these algorithms are dedicated to the analysis of spectral changes under the influence of the refractive index. The most popular algorithm used for this purpose is to calculate the area occupied by cladding modes. Among the remaining algorithms, there are those that use the determination of the cut-off wavelength as a surrounding refractive index (SRI) indicator. Projection on the wavelength axis can also be used to calculate the bending radius of the fibre. However, this is a more difficult task than with SRI, because the mode decay in bending is not so easy to catch. In this article, we propose a multi-step algorithm that allows to determine the impact of bending on mode leakage. At the same time, the place on the wavelength from the side of the Bragg mode and the ghost mode is determined, which represents the cladding mode radiated from the cladding under the influence of bending. The developed algorithm consists of the following operations carried out on the transmission spectrum: Fourier filtering, calculation of the cumulative value of the spectral length, low-pass filtering of the cumulative curve or its corresponding polynomial approximation, determination of the first and second derivative of the approximated curve, and projection of the second derivative of the curve on the wavelength axis. The shift of the wavelength determined in this way indirectly indicates the bending radius of the optical fibre. Based on multiple measurements, we prove that the presented algorithm provides better results when determining the bending radius compared to other algorithms adopted for this purpose and proposed for SRI measurements. Additionally, we analyse the method of determining the shift of a fragment of the spectrum using the phase of the discrete Fourier transform. [ABSTRACT FROM AUTHOR]

In this letter, a demodulation algorithm for fiber Bragg grating (FBG) sensor is presented. The proposed demodulation algorithm evaluates the wavelength shift in the reflected spectrum of an FBG sensor. It computes the cross-correlation between the perturbed spectrum and the undisturbed spectrum. We compare the proposed algorithm with another three reported algorithms and then discuss the experimental results in respect of the reflective index of FBGs and other factors that may influence the sensing resolution. We report strain resolutions of 0.4 and 1.5 muepsiv in high reflective gratings and low reflective gratings, respectively [ABSTRACT FROM PUBLISHER]

• A novel demodulation algorithm based on IMR is developed for FBG sensor network. • The proposed algorithm based on IMR of FBG's spectrum instead of peak detection. • Only 9 points of 0.16 nm bandwidth are need to be sampled by detector for each FBG. • The proposed algorithm has high precision with respect to micro-strain measurement. A multi-peak fiber Bragg grating (FBG) sensor demodulation algorithm is proposed. To the best of authors' knowledge, this is the first multi-peak FBG demodulation algorithm based on invariant moments retrieval (IMR) instead of FBG peak detection. Based on the proposed method, 36 data points of FBG spectra are only need to be sampled for accurate demodulation of four FBG sensor network. Besides, the sampled spectrum can be any part of whole spectrum. In comparison with other algorithm based on data processing of FBG's whole spectrum or detection of FBG's peak, the proposed method has high precision with respect to measurement and lower requirement with respect to the data sampling resolution, which is valuable for micro-strain demodulation. [ABSTRACT FROM AUTHOR]