Phase Demodulation Method Research Articles

Sensitive temperature measurement with composite multicavity Fabry-Perot interferometers (FPIs) and differential phase demodulation

A temperature sensor based on composite multicavity Fabry-Perot interferometers (FPIs) and a sensitivity-enhanced differential phase demodulation method is proposed and demonstrated. The structure was fabricated by partially filled polydimethylsiloxane (PDMS) into a segment of hollow-core fiber (HCF) which is spliced with a single-mode fiber (SMF). In this structure, composite multicavity FPIs are formed, including an air-cavity FPI, a PDMS-cavity FPI and an air-PDMS cavity FPI. The contribution of the different FPIs to the superimposed spectrum is analyzed from the simulated and experimental perspectives. The results demonstrate that the superimposed output spectrum is mainly produced by the air-cavity FPI and the air-PDMS cavity FPI. When the temperature increases, the lengths of the PDMS-cavity and the air-PDMS cavity are enhanced due to the volume expansion of PDMS, and the length of the air-cavity decreases because the air-cavity is compressed by the expanded PDMS. The cavity length variation causes the phase variation in the air-cavity FPI to be the opposite to that in the PDMS-cavity FPI or air-PDMS cavity FPI. Therefore, the phase demodulation sensitivity is enhanced by calculating the differential phase between the air-cavity FPI and the air-PDMS cavity FPI. The experimental results show that the sensitivity amplification factor of differential phase to the single phase of the air-cavity FPI or the air-PDMS cavity FPI is from approximately 1.44–3.25. This phase demodulation method is simpler, faster, more direct, and more convenient than wavelength demodulation from the perspective of demodulating composite interferometers.

Two-step orthogonalization phase demodulation method based on a single differential interferogram.

To reduce the acquisition time of interferogram and provide a dynamic phase retrieval method with arbitrary phase shift using a dual-channel simultaneous polarization phase-shifting system, a two-step orthogonalization phase demodulation method (TOPD) based on a single differential interferogram is proposed in this paper. In this method, the differential interferogram obtained by subtracting two phase-shifting interferograms and one of the Gaussian filtered based-interferograms are used to normalize and orthogonalize, and then the phase related parameters are solved by the Lissajous ellipse fitting method. Finally, the measured phase is obtained with high accuracy. The proposed method further reduces the deviation caused by the filtering operation performed in the two-step phase demodulation method. At the same time, combined it with the Lissajou ellipse fitting method reduces the limitation associated with the approximation conditions of the orthogonalization and normalization method. The experimental and simulation results demonstrate that this method provides a solution with high accuracy, high stability, strong practicability, and few restrictions for phase extraction in quantitative phase imaging.

Robust Phase Reconstruction Using Random Three Step Phase-Shift in Wavelength Tuning Interferometer

The standard stochastic two-step phase shift phase demodulation method analyzes the tangent function of the phase to be measured to extract the phase to be evaluated. It is necessary to eliminate the background light intensity of interference fringes, which has a significant impact on phase reconstruction accuracy. A random three-step phase shift algorithm (RTP) is suggested in this study. The phase shift between two adjacent interference fringes is extracted using the least squares approach in conjunction with a K-order twodimensional polynomial. Additionally, it employs the interference fringe graph’s difference operation to reduce the background light intensity and actualize the restoration of the measurement phase. The experimental and simulations results reveal that phase shift, luminous non-uniformity, and random noise have little effect on the random three-step phase shift method and have strong environmental adaptability.

Wide Measurement Range Distributed Strain Sensing With Phase-Accumulation Optical Frequency Domain Reflectometry

In this paper, a wide measurement range strain sensing method based on phase-accumulation optical frequency domain reflectometry (OFDR) is proposed. Different from the traditional phase demodulation method that analyzes the relative phase between the measurement signal and the reference signal, we achieve large measurement range strain sensing by accumulating the relative phases of adjacent scanning cycles. The proposal can break through the limitation of phase unwrapping in the traditional phase method, and realize the low measurement error in the accumulation process. In the experiments, when the wavelength scanning range is only 0.138 nm, we achieve quasi-static strain measurement with a spatial resolution of 1.8 cm, a maximum strain value of about 14000 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μϵ</i> , and the noise level of about 0.601 rad representing the strain resolution of 0.48 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μϵ.</i> We also analyze the influence of random noise on the method, and verify the good robustness of the phase accumulation method. The research of this paper provides a useful reference for the development of low-cost OFDR system for distributed strain/temperature measurement.

Phase Demodulation Based on K-Space With High Sensitivity for Interferometric Fiber Sensor

This study firstly proposes and experimentally demonstrates a phase demodulation method with high sensitivity for interferometric fiber sensors (IFSs) on the basis of the fast Fourier transform of a wavenumber domain. The phase information of IFSs triggered by changes in environmental parameters is obtained by calculating the initial phase variation of a specific Fourier-transformed spatial frequency. Theoretically, phase sensitivity can be improved by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> times when the optical path difference (OPD) of a spatial frequency peak is increased by a multiple ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> times) of the OPD of other spatial frequency domain peaks. To verify the method experimentally, this study designed a large laterally offset spliced sensor formed by common single-mode fibers on the basis of mode interference. The sensing characteristics of temperature and strain in each set of two-beam interference are analyzed simultaneously by calculating the phase sensitivities of the frequency domain peaks. Furthermore, the highest reported temperature and strain sensitivities of 0.0795 rad/°C and −0.0088 rad/μϵ, respectively, with good repeatability are realized.

High resolution polymer/air double-cavity Fabry–Perot fiber temperature sensor based on exposed core microstructured fiber

This study proposes a high-resolution optical fiber Fabry–Perot (FP) temperature sensor and it is based on an exposed-core microstructured optical fiber (ECF) coated by a ultraviolet curing polymer adhesive. Then, a small piece of multimode fiber (MMF) with large core diameter is spliced in front of ECF to expand the input light beam, and the parallel polymer/air double-cavity FP in such single-mode fiber (SMF)-MMF-ECF-SMF structure is constructed. Additionally, by employing a mobilized demodulation module, the interference signal is analyzed by phase demodulation method. The experimental results show that the temperature sensitivity of the sensor is 30.8 ℃−1 and the resolution is up to 1.6 × 10−4 ℃ in a range of 20 ℃–50 ℃, which can achieve high resolution temperature measurement. Furthermore, to alleviate the wavelength uncertainty of the demodulation device, a double-cavity self-reference differential phase modulation method is explored in the proposed parallel double-cavity FP. It shows that the stability could be improved to five times when system temperature is unstable, which offers an alternative method to further improve the temperature sensing resolution.

Development of a direct phase demodulation method for a Fabry-Pérot interferometer for temperature measurements using frequency scanning

Development of a direct phase demodulation method for a Fabry-Pérot interferometer for temperature measurements using frequency scanning

An improved device and demodulation method for fiber-optic distributed acoustic sensor based on homodyne detection

An improved fiber-optic distributed acoustic sensor (DAS) using a LiNbO3 straight through waveguide electro-optic phase modulator and a novel phase demodulation method based on homodyne detection is proposed in this paper. The principles of the phase-sensitive optical time domain reflectometer (Φ-OTDR) system and the multi-point disturbances phase demodulation algorithm are described in detail. The system structure can solve the problems of large size, difficult integration, low modulation frequency and unstable performance of piezoelectric transducer (PZT), which exists in the traditional homodyne detection system based on Michelson interferometer (MI). Experiments show that it can realize the location and identification of multi-point disturbances, and the acoustic signal can be demodulated accurately. The detectable acoustic frequency depends no longer on the phase modulation frequency. The signal-to-noise ratio (SNR) is above 20 dB, the noise level (NL) is less than 4 × 10−3 rad/√Hz, and the spatial resolution is about 10 m at 5 km sensing fiber. Compared with the heterodyne detection system and traditional homodyne detection system, the system has the advantages of lower cost, higher detection frequency, more stable performance and easier to integrate, which can be applied in some specific fields, such as oil and gas exploration, pipeline detection, border security and so on.

Four-wavelength quadrature phase demodulation technique for extrinsic Fabry-Perot interferometric sensors.

In this Letter, we report a four-wavelength quadrature phase demodulation technique for extrinsic Fabry-Perot interferometric (EFPI) sensors and dynamic signals. Four interferometric signals are obtained from four different laser wavelengths. A wavelength interval of four wavelengths is chosen according to the free spectrum range (FSR) of EFPI sensors to generate two groups of anti-phase signals and two groups of orthogonal signals. The linear fitting (LF) method is applied to two groups of anti-phase signals to eliminate the dc component and ac amplitude to obtain two normalized orthogonal signals. The differential cross multiplication (DCM) method is then used to demodulate the phase signal from these two normalized orthogonal signals. The proposed LF and DCM (LF-DCM) based four-wavelength quadrature phase demodulation overcomes the drawback of the traditional ellipse fitting (EF) and DCM (EF-DCM) based dual-wavelength demodulation method that it is not suitable for weak signal demodulation since the ellipse degenerates into a straight line, which makes the EF algorithm invalid. Moreover, it also avoids the assumption that the dc component and ac amplitude of interferometric signals are identical, which is widely used in three-wavelength demodulation. An EFPI acoustic sensor is tested to prove the four-wavelength quadrature phase demodulation and experimental results show that the proposed phase demodulation method shows advantages of large dynamic range and wide frequency band. Linearity is as high as 0.9999 and a high signal-to-noise ratio (SNR) is observed from 1 Hz to 100 kHz.

Multi-scale and full-field vibration measurement via millimetre-wave sensing

Vibration measurement is of great significance for structural health monitoring (SHM). The emerging microwave vibration measurement technology has distinct advantages over the laser and vision-based approaches, such as long-range, low-power consumption and environmental adaptability. However, it has critical limitations on multi-scale and full-field vibration measurement, especially for SHM of large structures. To overcome these drawbacks, in this paper, we propose mmSHM, a mmWave radar-based vibration measurement approach for SHM. An adaptive segmented phase demodulation (ASPD) method is developed to effectively quantify the displacement variation, allowing accurate displacement measurement spanning from µm to dm scales. What’s more, to eliminate the coupling and aliasing interferences from adjacent targets in full field of view, an improved interferometric phase evolution tracking method is presented to extract the vibration displacement from the range-angle joint dimensions. To be specific, the basic principle of vibration measurement using linear frequency-modulated continuous wave (LFMCW) radar is firstly depicted. Then, the detailed procedures of multi-scale and full-field vibration measurement method are illustrated. Finally, with the built prototype of mmSHM, experimental results under different scenarios show that our method can achieve multi-scale and full-field synchronous vibration measurement with µm-level accuracy. The proposed method can be expected to provide a promising approach for contactless vibration measurement in SHM.

Nano-Displacement Measurement System Using a Modified Orbital Angular Momentum Interferometer

In this study, a nano-displacement measurement system is proposed and demonstrated both theoretically and experimentally, which was based on a modified Mach-Zehnder (M-Z) interferometer using two conjugated orbital angular momentum (OAM) beams. In contrast to the previous M-Z-based OAM interferometer, a reflection module is inserted into the reference arm instead of a simple mirror. As a result, the effect of the transverse position-dependence phase-shift caused by the dove prism can be clearly eliminated and a stable and robust (off-axis insensitive) petal-like interference pattern can be obtained successfully. More importantly, a significant rotation angle of the petal-like pattern vs. the tiny displacement of the tested object can be clearly observed. In accordance with the modified measurement setup, a novel phase-demodulation method enabling to quickly and accurately characterize the rotation angle of the petal-like interference-patterns is proposed and demonstrated also. A tiny displacement ranging from 50 to 800 nm with resolution of <inline-formula> <tex-math notation="LaTeX">$\sim 50$ </tex-math></inline-formula> pm has been measured successfully. The proposed approach may find applications in not only the ultra-high precision displacement sensor, but also the temperature, strain, and refractive index sensors.

THE DEMODULATION ALGORITHM OF OPTICAL FIBER FABRY–PEROT SENSOR USING THE NONLINEAR DYNAMIC CHARACTERISTICS OF THE OPTICAL FIBER BROADBAND LIGHT SOURCE

The purpose is to optimize the optical fiber Fabry–Perot (F-P) sensor’s performances to provide a realistic basis for the optical fiber’s development. First, the classification of the optical fiber F-P sensors is summarized. The optical fiber F-P sensors’ fundamental principles are analyzed, focusing on the phase demodulation method that converts the optical fiber F-P sensing system’s input light source into a broadband light source. The broadband light source’s lightwave changes are analyzed, and the Fourier transform method and the fringe counting method are proposed to optimize the phase demodulation method’s function and analyze the light source’s nonlinear dynamic characteristics. According to the proposed demodulation method, the optical fiber F-P sensor with a cavity length change of [Formula: see text][Formula: see text][Formula: see text]m is simulated, and the cavity length selected for the simulation spectrum is the change range’s center value, 185[Formula: see text]um. The wavelength division multiplexer (WDM) decomposes the two optical signals, and an equation directly calculates the wavelength value orthogonal to its phase. The results show that the light intensity’s initial value of the actual spectrum is 0.04, and that of the standard function is 0.06. The light intensities for the maximum peak values are the same, 0.12, with the wavelength in [Formula: see text]–[Formula: see text][Formula: see text]m. When the wavelength exceeds [Formula: see text][Formula: see text]m before the next peak, the light intensity difference between them is large. The two orthogonal optical signals’ peaks change between the cavity length 0.18[Formula: see text]nm and 0.19[Formula: see text]nm after the wavelength selected, and the two signals’ peak values are orthogonal with the cavity length changes. The two signals’ initial and end peak values are different. The curve obtained by the two signals division calculation shows a tangent trend with the highest peak value of 87 and the lowest of [Formula: see text]. The peak curve changes obtained by the two signals’ arctangent calculation are in an orthogonal state, with the maximum peak value of 1.3 and the minimum of [Formula: see text]. The reflected light peak value changes of the optical fiber F-P sensor are in an orthogonal state, with the highest value of [Formula: see text] and the lowest [Formula: see text], and the adjacent peak changes in the wavelengths of 1500–1580 are the same. The curve’s fitting linearity is 1, and the linearity in the dynamic demodulation is 0.9776. The sampling frequency in the phase demodulation is [Formula: see text][Formula: see text]Hz, and the sampling frequency in the dynamic demodulation is [Formula: see text][Formula: see text]Hz, showing that upgrading the interface can increase the dynamic sampling frequency continuously to improve the device performance.

Phase Demodulation Methods for Optical Fiber Vibration Sensing System: A Review

In recent years, phase demodulation methods for optical fiber vibration sensors (OFVS) have attracted more and more attention, aiming to accurately detect vibration signals. The principles of phase modulation and demodulation in OFVS are firstly introduced. Then, three classical phase demodulation methods are described, including phase generated carrier (PGC) demodulation method, <inline-formula> <tex-math notation="LaTeX">${3}\,\,\times \,\,{3}$ </tex-math></inline-formula> coupler demodulation method, and in-phase and quadrature (IQ) demodulation method. Furthermore, the state of art of phase demodulation methods in various OFVS are reviewed. As the results of analysis, different structures of OFVS need appropriate demodulation methods for vibration detection. The Fourier transform method, fringe counting method and PGC demodulation method have strong applicability for Fabry-Perot interference OFVS. The scalability of interferometers provides convenience for PGC demodulation method and <inline-formula> <tex-math notation="LaTeX">${3}\,\,\times \,\,{3}$ </tex-math></inline-formula> coupler demodulation method in the OFVS with composite structure. PGC demodulation method, <inline-formula> <tex-math notation="LaTeX">${3}\,\,\times \,\,{3}$ </tex-math></inline-formula> coupler demodulation method and quadrature demodulation method are good choices for dynamic sensing in FBG-OFVS. The IQ demodulation method is a popular choice for phase sensitive optical time domain reflectometry at present. This paper provides a reference for the OFVS to realize vibration detection with appropriate phase demodulation method.

High-accuracy simultaneous phase extraction and unwrapping method for single interferogram based on convolutional neural network

The high-precision dynamic measurement of optical surfaces in unstable environments is a critical problem in the process of fabrication and application. In order to solve this problem, a high-precision ultra-fast phase demodulation method based on convolutional neural network is proposed in this paper. The wrapped phase and corresponding wrap count map can be obtained from one interferogram at the same time, so the phase extraction and unwrapping are performed simultaneously. It only takes 0.02 seconds to demodulate single-frame interferogram. Simulation and experimental results show that the root-mean-square error between this algorithm and phase-shifting algorithm is better than 0.01λ (λ=632.8nm). It indicates that the proposed method has excellent performance in measurement accuracy and efficiency.

Denoising using 3 × 3 coupler demodulation

A simple and effective phase demodulation method is 3 × 3 coupler demodulation, owing to its simpler structure than phase-generated carrier demodulation. However, it is difficult to obtain ideal demodulation results because of the diversity of noise sources in an optical fiber sensor system, particularly due to polarization fading. We present a noise processing method based on morphological filtering. First, the characteristics of various noises and their effects on the demodulation of a 3 × 3 coupler are analyzed. Subsequently, the polarization fading phenomenon in a single-mode fiber is analyzed, and the effect of polarization fading on the elliptic fitting demodulation of 3 × 3 couplers is described. The method uses morphological filtering based on an elliptic template to overcome the distortion in the demodulation signal due to polarization fading and other factors. Simulation and experimental results show that the proposed method can improve the stability and precision of phase demodulation technology based on the 3 × 3 coupler.

Long-Distance Detection for Periodic Vibration Signal in Φ-OTDR System Using Global Phase Demodulation Method

In order to overcome the limitation of weak intensity of Rayleigh backward scattering signal for long-distance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Phi } $ </tex-math></inline-formula> -OTDR system, a global phase demodulation method is proposed to extend the sensing distance without additional optical amplification. The localization limitation of conventional difference cumulative average algorithm is firstly analyzed. The global phase demodulation is carried out for all the signals on the whole sensing fiber. The autocorrelation processing is then realized to obtain the autocorrelation curves, on which the difference values between two instants can be used to locate the position of vibration signal. Experimental results show that according to the characteristics of autocorrelation curves, the vibration signal and noise signal can be distinguished. The sinusoidal signal with a frequency of 5 Hz and the third harmonic signal with the frequency of 5 Hz, 10 Hz, 15 Hz can be successfully located on the sensing fiber with the length of 90 km, without additional optical amplification. This method can achieve the long-distance detection for periodic vibration signal in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Phi } $ </tex-math></inline-formula> -OTDR system.

A Novel $\phi$-OTDR System With a Phase Demodulation Module Based on Sagnac Balanced Interferometer

At present, a phase demodulation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> -OTDR-based on an unbalanced interferometer is widely used, but its demodulation module is easily affected by external vibration noise. To improve the reliability of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> -OTDR, this paper proposed a phase demodulation method based on a balanced interferometer, which uses the Sagnac interferometer to obtain two Rayleigh scattering intensities and then recovers the phase information using an incoherent phase demodulation algorithm. The experimental results show that the proposed method can recover the disturbance signals on the sensing optical fiber well, even when the demodulation module is in serious external vibration noise including a vibration table shaking with different frequencies, opening and closing a door, and a car honking. These results indicate that the proposed method significantly reduces the influence of environmental vibration noise on the demodulation module, and offers a promising solution for the application of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> -OTDR in a harsh environment.

Multi-harmonic phase demodulation method for instantaneous angular speed estimation using harmonic weighting

Phase demodulation is arguably the most used technique for the estimation of the instantaneous angular speed from vibration signals measured on rotating machinery. Although phase demodulation offers a straightforward approach to determine accurately the rotation speed of a particular shaft in a rotating machine, it does have strict limitations that can hinder the estimation accuracy and its overall reliability. In general, phase demodulation relies on the presence of a single harmonic with a high signal-to-noise ratio for the full duration of the measured vibration signal. Such a precondition hinders its applicability for a generic speed estimation approach for rotating machinery. There are copious real-world scenarios where this requirement is not met, especially given the increasing complexity and dynamic operating range of rotating machines nowadays. In such complex rotating systems, the deterministic signals are not necessarily all harmonically related to a fundamental harmonic. The presence of crossing harmonic orders from non-synchronous rotating components or of lightly damped structural resonances can significantly skew the instantaneous phase demodulation. This paper proposes a novel approach towards phase demodulation by both incorporating multiple harmonics in the demodulation process and also giving the individual harmonic phases time-dependent weighting. This combination of incorporating multiple harmonics and weighting them allows for fully exploiting the information contained within the vibration signal while also promising to be more robust to changing operating regimes. The proposed multi-harmonic demodulation method is investigated thoroughly by assessing its performance on simulated data, on two benchmark experimental data sets, and on a large wind turbine vibration data set consisting of thousands of vibration measurements.

Heterogeneous-frequency-dual-pulse chain and weak FBG array for quasi-distributed acoustic sensing with improved response bandwidth.

By continuously injecting four groups of heterogeneous frequency dual pulses into the sensing fiber with weak fiber Bragg gratings (WFBGs), a quasi-distributed acoustic sensing method based on frequency-division multiplexing is proposed. Each group of pulses generates interference signals with different carrier frequencies after being reflected by the WFBGs. Through the discrete Fourier transform phase demodulation method, each carrier frequency interference signal is demodulated and then the phase is spliced. The feasibility of this method is theoretically analyzed, and a detection with a bandwidth of 2 kHz is realized on a 70 km sensing fiber with a spatial resolution of 10 m.

Phase Demodulation Method for Fringe Projection Measurement Based on Improved Variable-Frequency Coded Patterns.

The phase-to-height imaging model, as a three-dimensional (3D) measurement technology, has been commonly applied in fringe projection to assist surface profile measurement, where the efficient and accurate calculation of phase plays a critical role in precise imaging. To deal with multiple extra coded patterns and 2 jump error caused to the existing absolute phase demodulation methods, a novel method of phase demodulation is proposed based on dual variable-frequency (VF) coded patterns. In this paper, the frequency of coded fringe is defined as the number of coded fringes within a single sinusoidal fringe period. First, the effective wrapped phase (EWP) as calculated using the four-step phase shifting method was split into the wrapped phase region with complete period and the wrapped phase region without complete period. Second, the fringe orders in wrapped phase region with complete period were decoded according to the frequency of the VF coded fringes and the continuous characteristic of the fringe order. Notably, the sampling frequency of fast Fourier transform (FFT) was determined by the length of the decoding interval and can be adjusted automatically with the variation in height of the object. Third, the fringe orders in wrapped phase region without complete period were decoded depending on the consistency of fringe orders in the connected region of wrapped phase. Last, phase demodulation was performed. The experimental results were obtained to confirm the effectiveness of the proposed method in the phase demodulation of both discontinuous objects and highly abrupt objects.