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.

Ameliorated 3 × 3 coupler-based demodulation algorithm using iteratively reweighted ellipse specific fitting.

Passive demodulation scheme using 3 × 3 coupler has been widely used in phase-sensitive optical time-domain reflectometry (φ-OTDR), interrogation of fiber Bragg gratings or fiber optic interferometric sensors, and sensor multiplexing. However, the asymmetry of the 3 × 3 coupler in real applications affects the demodulation performance seriously. We proposed an ameliorated 3 × 3 coupler-based demodulation algorithm using iteratively reweighted ellipse specific fitting (IRESF) to overcome the drawback. IRESF combines iterative reweight technology with ellipse specific fitting, which decreases the weights of high noise points and always outputs ellipse solutions. Any two output signals from the 3 × 3 coupler-based interferometer are fitted by the IRESF and then corrected as a pair of quadrature signals. The stability of the fitting parameters is utilized to resolve the failures of IRESF under small signals. A real-time 1/4 ellipse arc judging module is designed, if the Lissajous figure is larger than 1/4 ellipse arc, IRESF is executed to offer ellipse correction parameters. Otherwise, the fixed parameters preset in the algorithm are used. The fixed parameters are mean values of the fitting parameters of IRESF under a large stimulus. The desired phase signal is finally extracted from the corrected quadrature signals. Experimental results show that the ameliorated algorithm does not require strict symmetry of the 3 × 3 coupler and can work under small signals. The noise floor of the proposed algorithm is -112 dB re rad/√Hz and the demodulated amplitude is 23.15 dB (14.37 rad) at 1 kHz when THD is 0.0488%. Moreover, the response linearity is as high as 99.999%. Compared to the algorithm using direct least squares, the proposed demodulation algorithm is more robust and precise, which has broad application prospects.

Phase noise suppression technique based on an improved reference interferometer scheme.

The reference interferometer scheme is an effective noise reduction method, but the optical path length difference (OPD) of the two interferometers must be strictly equal, which limits its application in practical environments. In this paper, an improved reference interferometer demodulation technique without strictly equal OPDs is proposed to suppress phase noise. By introducing a reference interferometer, the phase noise can be removed from the demodulation results. The combination of the differential self-multiplication algorithm and the fitted phase modulation depth calculation formula can evaluate the phase modulation depth of both interferometers in real time and simultaneously eliminate the nonlinear distortion caused by phase modulation depth drift and the effect of different OPDs on the reference interferometer scheme. The experimental results show that the technique can obtain highly stable and accurate demodulation results even if the OPDs of the two reference interferometers are different. The phase modulation depth calculation error is less than 0.57%, the maximum phase noise reduction is 15 dB, the average reduction is 9 dB, the minimum total harmonic distortion is 0.17%, and the SINAD reaches 35.90 dB.

Improved topography measurement with a high dynamic range using phase difference sensing technology.

Phase difference sensing technology (PDST) is employed for topography measurement, and two interference structures are proposed to achieve upper-limit adjustment and high resolution in the measurement range: a dual-wavelength system with a single Fabry-Perot (FP) cavity and a single-wavelength system with dual FP cavities. The phase difference between the two interference signals is determined by an elliptic fitting algorithm (EFA), and this change in phase difference is utilized to characterize the step height. Experimental results indicate that the measurement upper-limit can be adjusted to either 410 µm, 187 µm, or 108 µm by varying the wavelength difference in the dual-wavelength system, which gives a measurement error of 2.96%. In contrast, while offering a measurement resolution of 3.47 nm, the single-wavelength system exhibits a measurement error of 5.38%. The proposed method is capable of satisfying the measurement requirements during micro-electromechanical system (MEMS) processing with proficiency.

Fiber optic temperature and strain sensor using dual Mach-Zehnder interferometers.

A fiber optic temperature and strain sensor using dual Mach-Zehnder interferometers (MZIs) is proposed. The dual MZIs were fabricated by fusion splicing of two different fibers between two single-mode fibers. The two fibers of thin-core fiber and small-cladding polarization maintaining fiber were fusion spliced with a core offset. As the responses of the two MZIs are different in terms of temperature and strain, simultaneous temperature and strain measurement were experimentally validated by selecting two resonant dips in the transmission spectrum to construct a matrix. Experimental results show that the proposed sensors had the maximum temperature sensitivity of 66.67 pm/°C and the maximum strain sensitivity of -2.0p m/µÎµ. The minimum discriminated temperature and strain of the two proposed sensors were 0.20°C and 0.71 µÎµ, and 0.33°C and 0.69 µÎµ, respectively. The proposed sensor has promising application prospects due to the merits of ease of fabrication, low costs, and good resolution.

Improved ellipse-fitting phase demodulation technique to suppress the effect of light source intensity noise in interferometric system.

An improved ellipse-fitting algorithm phase demodulation (EFAPD) technique is proposed to reduce the influence of light source intensity noise on a system. In the original EFAPD, the sum of the intensities of coherent light (ICLS) is an important part of the interference signal noise, which makes the demodulation results suffer. The improved EFAPD corrects the ICLS and fringe contrast quantity of the interference signal by an ellipse-fitting algorithm, and then calculates the ICLS based on the structure of pull-cone 3 × 3 coupler, so as to remove it in the algorithm. Experimental results show that the noise of the improved EFAPD system is significantly reduced compared with that of the original EFAPD, with a maximum reduction of 35.57 dB. The improved EFAPD makes up for the deficiency of the original EFAPD in suppressing light source intensity noise, and promotes the application and popularization of EFAPD.

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.

Cardiac damage in autoimmune diseases: Target organ involvement that cannot be ignored.

Autoimmune diseases are diseases that cause damage to the body's own tissues as a result of immune dysfunction, often involving multiple organs and systems. The heart is one of the common target organs of autoimmune diseases. The whole structure of the heart can be affected, causing microcirculatory disorders, arrhythmias, pericardial damage, myocarditis, myocardial fibrosis, and impaired valvular function. However, early clinical manifestations of autoimmune heart damage are often overlooked because they are insidious or have no typical features. The damage is often severe and irreversible when symptoms are apparent, even life-threatening. Therefore, early detection and treatment of heart damage in autoimmune diseases is particularly important. Herein, we review the clinical features and mechanisms of cardiac damage in common rheumatic diseases.

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.

Highly sensitive temperature and strain sensor based on an antiresonant hollow core fiber probe with the Vernier effect.

A highly sensitive temperature and strain sensor based on an antiresonant hollow core fiber (ARHCF) probe with the Vernier effect is proposed and experimentally demonstrated. The ARHCF probe is used as a reference interferometer by sandwiching an ARHCF, which is insensitive to temperature, strain, and refractive index, between a single-mode fiber (SMF) and a polarization-maintaining fiber (PMF). The polarization mode interferometer (PMI), fabricated by splicing a section of PMF with a fiber polarizer at a 45-degree angle, works as a sensing interferometer. The Vernier effect is introduced by connecting the reference interferometer and the PMI in parallel. The experimental results show that by introducing the Vernier effect, the temperature sensitivity is improved from -1.68 to -15.7nm/∘C and the strain sensitivity is improved from 5.09 to 47.65 pm/µÎµ. The magnification is consistent with the theoretical results. The reference segment of the proposed sensor is not affected by ambient factors, which provides a new strategy and idea for the development of multiparameter sensors based on the Vernier effect.

Large-range phase-difference sensing technology for low-frequency strain interrogation.

Phase-difference sensing technology (PDST) has been applied to strain measurement, but its completeness is destroyed by the phase-difference measurement range. A scheme that can realize the completeness of the PDST for low-frequency strain interrogation is proposed. It is built on dual-interferometers and the elliptic-fitting algorithm. To break the measurement range limitation (0, π), a phase compensation setting is applied. The experimental results demonstrate that the method can obtain low-frequency strain signals, and the low-frequency signal whose phase amplitude is greater than π is recovered. The scheme is an efficient and complete method for measuring the strain of low-frequency optical fiber length, which could be applied to low-frequency seismic wave monitoring and rock deformation detection.

Phase-shifted demodulation technique with additional modulation based on a 3 × 3 coupler and EFA for the interrogation of fiber-optic interferometric sensors.

A phase-shifted demodulation technique with a 3×3 coupler and ellipse fitting algorithm (EFA) for the interrogation of interferometric sensors is proposed. To reduce the error of the EFA as to measure small phase signals, additional phase modulation is introduced. The additional modulation provides a walk of the operating point along the Lissajous ellipse large enough to permit calculation of the ellipse parameters at every moment. Experimental result shows that this technique demonstrates high accuracy and stability for measuring small phase signals. The setting of this technology expands the application of the EFA in fiber-optic phase demodulation technology.

Simultaneous measurement of refractive index and temperature or temperature and axial strain based on an inline Mach-Zehnder interferometer with TCF-TF-TCF structure.

A refractive index (RI) and temperature or a temperature and axial strain sensor based on an inline Mach-Zehnder interferometer with thin core fiber (TCF)-thin fiber (TF)-TCF structure is proposed and experimentally demonstrated, requiring only the cleaving and fusion splicing methods. The operation principle depends on the effect that the TF cladding modes interfere with the core mode as an optical coupler. The RI, temperature, or axial strain variations can lead to resonance dip variations in the interferometer spectra, and the RI, temperature, or axial strain sensitivity can be measured by monitoring the wavelength shifts of resonance dips. Then we can measure both RI and temperature, or temperature and axial strain through the demodulation matrix. Four sensors with different TF lengths are fabricated based on numerical simulation. A 15 mm long TF sensor displays an RI sensitivity as high as -174.357nm/RIU, temperature sensitivities in the glycerin solution and the air of 12.47 and 26.19 pm/°C, and axial strain sensitivity of -3.43×10-4nm/µÎµ. Moreover, due to its simple manufacture, high cost-effectiveness and compactness, the proposed sensor has a broad application prospect in physical, chemical, and biological sensing.

Axial strain applied in-fiber Mach-Zehnder interferometer for acceleration measurement.

We present an axial strain applied in-fiber Mach-Zehnder interferometer (MZI) for acceleration measurement. A thin core fiber is sandwiched between two single-mode fibers with core offset to form the MZI. A controlled high fringe visibility in the transmission spectrum is obtained by applying an axial strain, leading to a large slope at the quadrature point. The MZI is then clamped to work as an accelerometer. Experimental results show that the resolution achieves 86 ng/√Hz (g is gravity of 9.8 m/s2), the dynamic range reaches as large as 104.1 dB and the linearity of acceleration response is as high as 99.994%. Moreover, the resonance frequency can be tailored by the clamped fiber length and applied axial strain. The proposed sensor is attractive for practical applications due to low temperature crosstalk, compact size and high sensitivity.

Miniaturized Fabry-Perot probe utilizing PMPCF for high temperature measurement.

We propose a miniaturized optical fiber Fabry-Perot probe for high temperature measurement (up to 1000°C). It is simply fabricated by fusion splicing a short section of polarization-maintaining photonic crystal fiber (PMPCF) with a single-mode fiber (SMF). The interface between the core of the SMF and air holes of the PMPCF, and the end face of the PMPCF work as the mirrors. The pure silica core of the PMPCF is employed as the sensing element. Experimental results show that the probe has a high thermal stability and the temperature sensitivity reaches up to 15.34 pm/°C, which is not affected by the length of the PMPCF. The linearity of temperature response is as high as 99.83%. The proposed sensor has promising prospects in practical applications due to simple fabrication process, low cost, compact size, and excellent repeatability.

Thin fiber-based Mach-Zehnder interferometric sensor for measurement of liquid level, refractive index, temperature, and axial strain.

An all-fiber Mach-Zehnder interferometric sensor capable of measuring liquid level, refractive index (RI), temperature, and axial strain is proposed and experimentally demonstrated. The proposed sensor is based on a fiber ball-thin fiber (TF)-core-offset structure sandwiched between two standard single-mode fibers. The variations of ambient liquid level, RI, temperature, and axial strain cause the change of phase difference between the cladding modes and the core mode, which leads to the shift of interference spectrum. The wavelength shifts of three resonant dips in the transmission spectrum are used to investigate the sensing characteristics of the sensor. Experimental results show that the sensor with TF length of 20 mm exhibits high RI and liquid-level sensitivities of $ - {131.7092}\;{\rm nm/RIU}$-131.7092nm/RIU and $ - {120.7}\;{\rm pm/mm}$-120.7pm/mm at a wavelength of 1589.5 nm. Meanwhile, the sensor is insensitive to temperature and axial strain, and the maximum sensitivities are 0.0390 nm/°C and $ - {4}.{84}\; \times \;{{10}^{ - 4}}\;{\rm nm}/\unicode{x00B5} \varepsilon $-4.84×10-4nm/µÎµ, respectively. In addition, the sensor shows superiority in measuring multiple parameters simultaneously.

High temperature Vernier probe utilizing photonic crystal fiber-based Fabry-Perot interferometers.

This study proposes a highly sensitive and stable optical fiber probe based on Vernier effect for high temperature measurement (up to 1000 °C), utilizing photonic crystal fiber (PCF)-based Fabry-Perot interferometers (FPIs). The cascaded FPIs are fabricated by fusion splicing a section of polarization maintaining PCF to a lead-in single-mode fiber, and then a section of temperature-insensitive hollow core PCF is spliced between the PMPCF and a multi-mode fiber. The shift of the spectral envelope is monitored to measure the temperature variation. Experimental results show that the sensitivities of three fabricated probes are as high as 173.43 pm/ °C, 230.53 pm/ °C and 535.16 pm/ °C when operating from room temperature to 1000 °C, which are consistent with theoretical results. The sensitivities are magnified about 13, 19 and 45 times compared with the single FPI. The linearity of the temperature response is as high as 99.73%. The proposed probe has great application prospects due to compactness, high sensitivity and low cost.

Enhanced sensitivity of fiber laser sensor with Brillouin slow light.

We proposed and experimentally demonstrated a new scheme for enhancing the sensitivity of a fiber laser sensor using Brillouin slow light. The Brillouin laser was exposed to environmental vibrations, producing fluctuations at 408 kHz frequency, which were then interrogated using a Mach-Zehnder interferometer. By introducing Brillouin slow light into one arm of the interferometer, the sensitivity increased by 1.57 times that of a device without slow light. We believe this scheme may provide a new way of using Brillouin slow light and that it has some important implications regarding the use of fiber sensors for measuring the vibration, temperature, strain and so on.

Real-time acceleration sensing with an arctan algorithm based on a modal interferometer.

This study proposes a fiber-optic accelerometer for low-frequency vibration signal detection. The phase velocities of the polarization eigenmodes are affected differently by signals, leading to a polarization rotation of the transmitted lights. The orthogonal square roots of the photovoltages are utilized for an arctan demodulation scheme. Experimental results show that it provides a flat response of 75.04 mrad/g, an average resolution of 13.44 µg/√Hz, and a dynamic range of 111.62 dB below 180 Hz. The environmental instability and sensor complexity are significantly reduced, so that the sensor can be further used in the warning of coal and gas outburst.