Common-path dual-wavelength quadrature phase demodulation of EFPI sensors using a broadly tunable MG-Y laser

Highly precise thickness measurement of multilayer films based on the cross-correlation algorithm using a widely tunable MG-Y laser

Inspired by the demodulation algorithm of Fabry-Perot composite sensors in the field of fiber-optic sensing, this paper proposes a method based on a widely tunable modulated grating Y-branch (MG-Y) laser combined with the cross-correlation algorithm to achieve a highly precise measurement of the optical thickness of each layer of a multilayer optical sample. A sample consisting of a double glass stack was selected, and the interference spectrum of the stacked sample was acquired using a widely tunable MG-Y laser. A fast Fourier transform (FFT) algorithm combined with a finite impulse response (FIR) bandpass filter was utilized to separate the different frequency components of the multilayer optical sample. The normalized spectra of each layer were reconstructed using the Hilbert transform. Subsequently, a cross-correlation algorithm was employed to process the normalized spectrum and determine the optical thickness of each layer with high precision. The samples were measured at predetermined locations, with 150 consecutive measurements performed to assess the repetition of the thickness. The standard deviation of these measurements was found to be lower than 1.5 nm. The results show that the cross-correlation algorithm is advantageous in the optical thickness measurement of multilayer films.

Four-wavelength laser interferometry for the demodulation of dual-cavity fiber-optic extrinsic Fabry-Perot interferometric sensors

A four-wavelength passive demodulation algorithm is proposed and experimentally demonstrated for the interrogation of the one cavity in a dual-cavity extrinsic Fabry-Perot interferometric (EFPI) sensor. The lengths of two cavities are adjusted to generate four quadrature signals for each individual cavity. Both simulation and experimental results are presented to validate the performance of this technique. The experimental results demonstrate that dynamic signals at frequencies of 100 Hz, 200 Hz, and 300 Hz with varying amplitude are successfully extracted from a dual-cavity EFPI sensor with initial lengths of 93.4803 µm and 94.0091 µm. The technique shows the potential application to measure dynamic signals in dual-cavity fiber-optic EFPI sensors.

Low-Coherence Homodyne Interferometer for Sub-Megahertz Fiber Optic Sensor Readout

This study proposes a method for interferometric fiber optic sensor readouts. The method utilizes the advantages of the active homodyne demodulation technique and low-coherence interferometry. The usage of the tandem low-coherence interferometer enables modulating the reference interferometer without any changes to the sensor. This achieves high sensitivity, high stability, and a wide frequency band. A sensitivity of up to 0.1 nm (RMS) in the frequency range of 5 kHz is demonstrated by detecting acoustic signals with a fiber Michelson interferometer as a sensor.

Intensity self-compensation method against multi-factors for polarization-based Fabry-Perot interrogation system

Phase interrogation methods for fiber-optic Fabry-Perot (F-P) sensors may inevitably fail in the field due to the influences of irrelevant factors on signal intensity. To address this severe problem, this Letter proposes an intensity self-compensation method (ISCM) to eliminate the consecutive signal fluctuations of a polarization-based F-P interrogation system caused by multiple factors. By providing only the initial intensities of the reference signals, this attempt realizes the real-time intensity compensation of the output signals without affecting their quadrature relationship. Consecutive intensity fluctuations caused by variation of light source power, fiber loss, and polarization state are reduced to 2%-3% by the ISCM. Furthermore, the method performs ideally under dynamic modulation of the sensor. In addition, it can be applied against the inconsistent fluctuations between signals and is suitable for F-P sensors with single or multiple cavities. Owing to the high efficiency, real-time ability, and no moving parts advantage, the proposed method provides an excellent candidate for improving the accuracy and stability of F-P interrogation systems.

Passive quadrature demodulation of multiplexed interferometric sensors using a CW correlation reflectometer with a single DFB diode laser

In this Letter, we report a novel, to the best of our knowledge, and simple approach for passive quadrature-phase demodulation of relatively long multiplexed interferometers based on two-channel coherence correlation reflectometry. Two-wavelength channels are generated using a single unmodulated CW-DFB diode laser and an acousto-optic frequency shifter. The introduced frequency shift determines the optical lengths of the interferometers. In our experiments, all interferometers have the same optical length of 32 cm corresponding to the π/2 phase difference between channel signals. An additional fiber delay line was introduced between channels to destroy coherence between initial and frequency-shifted channels. Demultiplexing of channels and sensors was performed using correlation-based signal processing. Amplitudes of cross correlation peaks obtained for both channels were used to extract the interferometric phase for each interferometer. Phase demodulation of relatively long multiplexed interferometers is experimentally demonstrated. Experimental results prove that the proposed technique is suitable for interrogating a serial array of relatively long interferometers dynamically modulated with phase excursions exceeding 2π. Simultaneous interrogation and phase demodulation were experimentally demonstrated using an in-line array of low-finesse Fabry-Perot interferometric sensors.

Demodulation of Fabry-Perot sensors using random speckles

Random speckles are proposed to demodulate Fabry-Perot (FP) sensors in this study. A piece of multimode fiber is used to interrogate the FP transmission spectrum, and tiny spectral changes lead to significant variations in the generated speckle patterns. In the demonstration experiments, the pressure resolution of 0.001 MPa can be obtained from an open cavity FP sensor based on the convolutional neural network (CNN) demodulation algorithm. It is worth noting that the spectral differences in neighboring orders can be precisely distinguished due to the high sensitivity of speckles. Thus, the fringe-order ambiguity problem is solved and the dynamic measurement range can be greatly improved. The speckle-based demodulation scheme provides a new way to balance resolution, dynamic range, speed, and cost of FP sensors.

Fabry-Perot interferometric sensor demodulation system utilizing multi-peak wavelength tracking and neural network algorithm

For FPI sensor demodulation systems to be used in actual engineering measurement, they must have high performance, low cost, stability, and scalability. Excellent performance, however, necessitates expensive equipment and advanced algorithms. This research provides a new absolute demodulation system for FPI sensors that is high-performance and cost-effective. The reflected light from the sensor was demultiplexed into distinct channels using an array waveguide grating (AWG), with the interference spectrum features change translated as the variation of the transmitted intensity in each AWG channel. This data was fed into an end-to-end neural network model, which was utilized to interrogate multiple interference peaks' absolute peak wavelengths simultaneously. This architecturally simple network model can achieve remarkable generalization capabilities without training large-scale datasets using an appropriate data augmentation strategy. Experiments show that in simultaneous multi-wavelength and cavity length interrogations, the proposed system has the precision of up to ± 14 pm and ± 0.07 µm, respectively. The interrogation resolution can theoretically reach the pm level benefit from the neural network method. Furthermore, the system's outstanding demodulation repeatability and suitability were demonstrated. The system is expected to provide a high-performance and cost-effective, reliable solution for practical engineering applications.

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.

Passive Homodyne Phase Demodulation Technique Based on LF-TIT-DCM Algorithm for Interferometric Sensors

A passive homodyne phase demodulation technique based on a linear-fitting trigonometric-identity-transformation differential cross-multiplication (LF-TIT-DCM) algorithm is proposed. This technique relies on two interferometric signals whose interferometric phase difference is odd times of π. It is able to demodulate phase signals with a large dynamic range and wide frequency band. An anti-phase dual wavelength demodulation system is built to prove the LF-TIT-DCM algorithm. Comparing the traditional quadrature dual wavelength demodulation system with an ellipse fitting DCM (EF-DCM) algorithm, the phase difference of two interferometric signals of the anti-phase dual wavelength demodulation system is set to be π instead of π/2. This technique overcomes the drawback of EF-DCM—that it is not able to demodulate small signals since the ellipse degenerates into a straight line and the ellipse fitting algorithm is invalidated. Experimental results show that the dynamic range of the proposed anti-phase dual wavelength demodulation system is much larger than that of the traditional quadrature dual wavelength demodulation system. Moreover, the proposed anti-phase dual wavelength demodulation system is hardly influenced by optical power, and the laser wavelength should be strictly limited to lower the reference error.

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.

Compressed-sensing fiber-optic white light interferometry

In this Letter, we propose a dynamic fiber-optic white light interferometry (WLI) based on the compressed-sensing (CS) principle. The time-varying interference spectra of a Fabry-Perot cavity under vibration are considered as a two-dimensional (2D) signal with respect to both laser wavelength and time, which can be compressively sampled using a programmable semiconductor laser source during the measurement process. After CS reconstruction, the spectrum acquisition rate is equal to the random wavelength modulation rate, up to 10 MHz in this Letter, providing an attractive alternative to laser-based dynamic interferometry. Numerical simulations and nanometer-scale vibration experiments verify the effectiveness of the scheme.

Dual-wavelength demodulation technique for interrogating a shortest cavity in multi-cavity fiber-optic Fabry-Pérot sensors

This paper demonstrates, for the first time, a novel demodulation technique that can be applied for interrogating a shortest cavity in multi-cavity Fabry-Pérot (F-P) sensors. In this demodulation technique, using an amplified spontaneous emission (ASE) light source and two optical fiber broadband filters, the interference only occurs in a shortest F-P cavity that is shorter than the half of the coherence length. Using a signal calibration algorithm, two low-coherence interference optical signals with similar coherence lengths were calibrated to obtain two quadrature signals. Then, the change in the cavity length of the shortest F-P cavity was interrogated by the two quadrature signals and the arctangent algorithm. The experimental results show that the demodulation technique successfully extracted 1 kHz and 500 Hz vibration signals with 39.28 µm and 64.84 µm initial cavity lengths, respectively, in a multi-cavity F-P interferometer. The demodulation speed is up to 500 kHz, and the demodulation technique makes it possible for multi-cavity F-P sensors to measure dynamic and static parameters simultaneously. The results show that the demodulation technique has wide application potential in the dynamic measurement of multi-cavity F-P sensors.

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.

Microwave photonics interrogation for multiplexing fiber Fabry-Perot sensors

A microwave photonics interrogation system for multiplexing fiber Fabry-Perot (FP) sensors is demonstrated in this paper. Different from previous FP demodulation schemes, this system aims at quasi-distributed sensing networks composed of FP sensors with a short effective cavity length less than 1 mm. With the help of a dispersion element, the superimposed reflected spectrum from FP sensors based on a hollow core fiber (HCF) can be converted into separate response passbands in the frequency domain simultaneously, whose center frequency will shift linearly with the variations of environment. The experimental results exhibit high linearity and interrogation ability for both the all-FP multiplexing system and hybrid multiplexing system. A strain interrogation sensitivity of 0.938 kHz/µɛ and temperature sensitivity of -0.699 MHz/°C have been realized, corresponding to a FP cavity length demodulation sensitivity of 1.563 MHz/µm. Furthermore, numerical studies about the impacts of the HCF-FP spectrum envelope on the RF response passband, as well as the theoretical minimum detectable cavity length and multiplexing capacity of the system, are also carried out.

Wideband fiber-optic Fabry-Perot acoustic sensing scheme using high-speed absolute cavity length demodulation

In this paper, we realize a wideband fiber-optic Fabry-Perot (F-P) acoustic sensing (FPAS) scheme by utilizing a high-speed absolute cavity length demodulation with a 70-kHz maximum line rate spectrometer. The wideband FPAS is made of a pre-stress stainless-steel diaphragm based on F-P interferometric structure. The real-time absolute F-P cavity lengths are calculated by a phase demodulation method, which is realized by processing the interference image at a 70-kHz frame rate. Acoustic signal is obtained by extracting the AC component of the demodulated cavity length. The experimental results show that the spectrometer can be running at a 50-kHz line rate, and an acoustic detection wideband of 20 Hz to 20 kHz is obtained. The noise-limited minimum detectable sound pressure level is 18.8 dB, which is sensitive enough for the communication of human voice. The proposed wideband acoustic sensing scheme achieves good robustness, which is promising as a speech-sound microphone for communication during the magnetic resonance imaging procedure.

Differential-pressure fiber-optic airflow sensor for wind tunnel testing

A differential-pressure fiber-optic airflow (DPFA) sensor based on Fabry-Perot (FP) interferometry for wind tunnel testing is proposed and demonstrated. The DPFA sensor can be well coupled with a Pitot tube, similar to the operation of the differential diaphragm capsule in the airspeed indicator on the aircraft. For differential pressure sensing between total pressure and static pressure in the airflow, an FP cavity is formed between the sensing diaphragm and a fiber end-face, and a tubule is inserted into the FP cavity. According to the principle of differential pressure derived from Bernoulli's equation, the airflow velocity can be determined by monitoring the change of the FP cavity length. The experimental results demonstrate that a DPFA sensor with 0∼11 kPa measurable range, 826.975 nm/kPa sensitivity, and 0.008% (0.89 Pa) resolution can be realized. Combined with a 100 Hz-sweep frequency self-developed white light interferometric (WLI) interrogator and a Pitot tube, the DPFA sensor can be used for measuring the airflow velocity of 2.0∼119.24 m/s with an accuracy of 0.61%. The system is applied to the analysis of the flat-plate boundary layer, a wind tunnel experimental model, where the results are consistent with those of the theoretical analysis and from the standard electronic pressure transducer. With the large measurable range, high sweep frequency, and high precision, the system has potential application value for wind tunnel experimental investigation and in-flight measurement of airspeed.

Simultaneous measurement of acoustic pressure and temperature using a Fabry-Perot interferometric fiber-optic cantilever sensor

A Fabry-Perot (F-P) interferometric fiber-optic cantilever sensor is presented for simultaneous measurement of acoustic pressure and temperature, which are demodulated by a single high-speed spectrometer. The acoustic pressure wave pushes the cantilever to produce periodic deflection, while the temperature deforms the sensor and causes the F-P cavity length to change slowly. The absolute length of the F-P cavity of the fiber-optic cantilever sensor is calculated rapidly by using a spectral demodulation method. The acoustic pressure and temperature are obtained by high-pass filtering and averaging the continuously measured absolute cavity length value, respectively. The experimental results show that the acoustic pressure can be detected with an ultra-high sensitivity of 198.3 nm/Pa at 1 kHz. In addition, an increase in temperature reduces the resonant frequency of the acoustic response and increases the static F-P cavity length. The temperature coefficient of the resonance frequency shift and the temperature response of the sensor are -0.49 Hz/°C and 83 nm/°C, respectively. Furthermore, through temperature compensation, the measurement error of acoustic pressure reaches ± 3%. The proposed dual parameter measurement scheme greatly simplifies the system structure and reduces the system cost.

Multiplexing fiber-optic Fabry-Perot acoustic sensors using self-calibrating wavelength shifting interferometry

Flexible and stable demodulation techniques of large-scale fiber-optic Fabry-Perot (FP) acoustic sensors are highly desirable for accelerating their industrial applications. In this paper, we report a novel self-calibrating wavelength shifting interferometry (WSI) technique that enables simultaneous multi-point acoustic detection using diaphragm based fiber-optic FP acoustic sensors. A widely tunable modulated grating Y-branch (MG-Y) laser (1527∼1567 nm) performs high-speed wavelength switching, introducing phase-shifts in the wavelength domain for real-time phase retrieval. The proposed self-calibrating WSI is easily extended for multiplexing FP acoustic sensors by calibrating the corresponding phase-shift step of each sensor probe. Based on a modified Hariharan 5-step phase shifting algorithm, the phase-shift step for each channel can be calibrated in real-time, making the system robust in applications involving large environmental perturbations. An all-optical multi-point acoustic detection system based on WSI is proposed and experimentally demonstrated for the first time. Sound source localization experiments show that the multi-point acoustic detection system works stably and the positioning accuracy is about 2.42 cm.

Quadrature phase-stabilized three-wavelength interrogation of a fiber-optic Fabry-Perot acoustic sensor

In this Letter, we propose a quadrature phase-stabilized three-wavelength demodulation technique for the interrogation of fiber-optic Fabry-Perot acoustic sensors. It is based on accurate and fast tuning of a monolithic modulated grating Y-branch laser. Three quadrature wavelengths are chosen to perform high-speed cavity length demodulation by wavelength switching, thereby avoiding imbalances and disturbances between the three optical paths in conventional three-wavelength quadrature phase-demodulation systems. A feedback-stabilization scheme for maintaining the quadrature phase condition is proposed for the first time, to the best of our knowledge, providing potential for long-term monitoring in harsh environments.