Phase Demodulation Method Research Articles

Fiber-optic distributed acoustic sensor utilizing LiNbO3 straight through waveguide phase modulator.

A novel fiber-optic distributed acoustic sensor (DAS) utilizing a LiNbO3 straight through waveguide phase modulator as phase generation carrier (PGC) modulation module for the detection of acoustic signal is presented. The sensitive principle and the phase demodulation method of the system based on phase-sensitive optical time domain reflectometer (Φ-OTDR) are described. This scheme solves the problems of low modulation frequency and unstable performance of piezoelectric transducer (PZT) in the traditional homodyne detection system and depends only on the pulse repetition frequency. The efficacy of the new approach is demonstrated experimentally, showing that the weak acoustic signal can be demodulated accurately. The noise level of the system is < 4.2×10-3 rad/√Hz, the signal to noise ratio (SNR) is > 16 dB, and the spatial resolution is 10 m, as well as a detection frequency can theoretically achieve 25 kHz at 2 km sensing fiber. It provides a new research idea for DAS and is expected to replace PZT to achieve a high-frequency response, which has good potential in the applications of low cost, long distance and high frequency detection.

Generative adversarial network-based method for the demodulation of coherent signals in laser voice detection

Laser Doppler vibrometry-based voice detection systems can measure voice signals without direct contact by demodulating the Doppler signals caused by sound vibrations. However, in remote voice detection, the coherent signal is significantly affected by noise in the detection environment. This weakens the energy of the signal and reduces the signal-to-noise-ratio (SNR), resulting in the signal being incorrectly demodulated. We present a coherent signal demodulation method based on generative adversarial networks (GANs) called a phase demodulation generative adversarial network (PDGAN) that can overcome this problem. To develop the method, coherent signal and Doppler signal datasets were also established. Demodulation from a coherent signal is accomplished through unsupervised learning within the PDGAN, layer by layer, with global supervised feedback learning for fine-tuning. Experiments confirm that the PDGAN method can demodulate Doppler signals when the SNR is as low as −20 dB, with the demodulation effect being notably better than traditional phase demodulation methods. The PDGAN method is also robust against noise, so it can extend the measurement distance for laser voice detection. Generally, the method’s performance confirms the applicability of deep learning approaches for optical measurement.

Design of a multi-channel micro-capacitor acquisition system

Aiming at the measurement method of electrical capacitance tomography, a set of micro-capacitance acquisition system for planar array capacitance sensor is designed. Using the circuit principle design of high sensitivity and anti-interference, a dual-channel signal generator with adjustable amplitude and phase was designed to excite the capacitance sensor. The core capacitance voltage conversion circuit of the acquisition system adopts an AC excitation type conversion circuit with the ability to resist stray capacitance interference, and analyzes the error influencing factors in combination with the actual circuit components. The array control switch group is designed for multi-channel switching acquisition, and optimized in conjunction with the capacitor voltage conversion circuit. For the phase demodulation method, an orthogonal optimization method based on hardware multiplier is proposed. A micro-capacitor experiment is designed to calibrate the acquisition circuit. The experimental results show that the capacitance acquisition resolution of the micro-capacitor acquisition system within the acquisition range is 2.84fF, the linearity is 0.9998, and the acquisition error is less than 0.12fF.

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.

High-accuracy phase demodulation method compatible to closed fringes in a single-frame interferogram based on deep learning.

Interferogram demodulation is a fundamental problem in optical interferometry. It is still challenging to obtain high-accuracy phases from a single-frame interferogram that contains closed fringes. In this paper, we propose a neural network architecture for single-frame interferogram demodulation. Furthermore, instead of using real experimental data, an interferogram generation model is constructed to generate the dataset for the network's training. A four-stage training strategy adopting appropriate optimizers and loss functions is developed to guarantee the high-accuracy training of the network. The experimental results indicate that the proposed method can achieve a phase demodulation accuracy of 0.01 λ (root mean square error) for actual interferograms containing closed fringes.

Retrieval of Phase and Temperature Distributions in Axisymmetric Flames From Phase-Modulated Large Lateral Shearing Interferogram

A precise phase modulation and demodulation method was proposed to retrieve temperature distributions in axisymmetric flames by using a single-wavelength large lateral shearing interferometer. A spatial light modulator (SLM) was employed to vary the phases in each pixel continuously in the flame-phase measurement. The uniqueness of the phase extraction was mathematically proved for the first time, and a least square method was applied to recover the profile of flame phase in the interferometer. The ambiguity of the phases at different cycles of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> was eliminated. The phase shift at each pixel was uniquely determined and verified by using simulated data. Further, precise-phase distributions were utilized to retrieve the temperature distribution in a laminar flame. In actual experiments, four axisymmetric laminar flames from diffused to premixed flames were generated by using a Bunsen burner. Profiles of temperature distribution in the flames were extracted and agreed well with the results scanned by using a thermocouple. With the increase of airflow rate, the position of high-temperature zone was observed moving down, and the thermal structure of the premixed flame became more and more obvious. The preheating zone, reaction front, and reaction zone inside the flames were clearly captured.

Optical fiber temperature sensor with insensitive refractive index and strain based on phase demodulation

AbstractWe propose and experimentally demonstrate a temperature sensor based on a suspended‐core microstructure optical fiber (SCMF). The sensor is constructed by fusion splicing a piece of SCMF between two up‐tapers which act as light beam couplers. The Mach‐Zehnder interference (MZI) is formed by the silica core modes and the air cladding modes in the SCMF. The sensitivity of −0.011 rad/°C in the temperature range of 20°C to 90°C is achieved, which is more accurate and stable than conventional wavelength tracking method due to the phase demodulation method can avoid the effects of spectral noise, dip selection, and wavelength sampling rate on the wavelength tracking. In addition, our proposed sensor is inert to external environments such as strain and refractive index, which can well solve the problem of crosstalk during temperature sensing.

Phase demodulation method based on a dual-identical-chirped-pulse and weak fiber Bragg gratings for quasi-distributed acoustic sensing

A phase demodulation method for quasi-distributed acoustic sensing (DAS) systems based on a dual-identical-chirped-pulse and weak fiber Bragg gratings (WFBGs) is proposed. Compared to the use of Rayleigh backscattering light in optical fibers, the implementation of WFBGs can contribute to obtaining an optical signal with a higher signal-to-noise ratio (SNR). The dual-identical-chirped-pulse is generated by a time-delay fiber, and the sinusoidal carrier is generated by the interference between the two chirped pulses reflected by adjacent WFBGs. The phase of the sinusoidal carrier represents the dynamic strain change posed on the sensing fiber. Discrete Fourier transform is used to directly retrieve the phase information. The performance of the phase demodulation from interference signals under different sinusoidal carrier frequencies and SNRs is numerically investigated. The piezoelectric transducer is employed to emulate the sound in the experiment to verify the effectiveness of our method. It is shown that the dynamic strain can be well reconstructed at the end of a 101.64 km fiber when the signal SNR is down to 3.234 dB. Our proposed method enables the application of the long-distance sensing in quasi-DAS systems.

Multiple self-mixing interferometry based on lock-in amplifier analysis for vibration measurement

In this paper, a novel phase demodulation method for multiple self-mixing interferometry (MSMI) is proposed, which can improve the resolution and accuracy of vibration measurement in laser self-mixing interferometry (SMI). The sinusoidal phase modulation of the beam is obtained by an electro-optic modulator (EOM), and phase demodulation is performed by a lock-in amplifier analysis method. The phase equation of MSMI was derived and the theory of the lock-in amplification technique was analyzed in detail. The validity of the proposed method is confirmed by means of simulated signals and then demonstrated by several experimental measurements. The experimental results indicated a good correspondence between theory and experiment.

Fast and accurate two-frame phase demodulation algorithm with statistical averaging

This paper introduces a fast, compact phase demodulation method for two-frame random phase-shifting interferometry. A set of sine and cosine components is obtained with the addition and subtraction of two pre-filtered fringe patterns. Then, using the properties of the trigonometric function, the amount of phase shift is obtained by statistically averaging all the pixels. Finally, the phase distribution of the interferogram is obtained by the arctangent operation. The proposed algorithm has a very low computation burden and does not require iteration, optimization, and orthogonalization while ensuring measurement accuracy; as a result, the consumed time is very short. Simulation and experimental results are presented to verify the accuracy and efficiency of the proposed method.

Multi-demodulation phase-shifting and intensity pattern projection profilometry

Phase-shifting is a powerful phase demodulation method for three-dimensional imaging by fringe projection. However, numerous fringe patterns, which encode a single-phase function, are required. In this paper, the use of intensity patterns, which encode multiple phase functions, is proposed. A multi-demodulation phase-shifting algorithm and the intensity pattern projection profilometry approach are developed. A computer simulation and an experimental three-dimensional object measurement are performed to validate the proposal and demonstrate its effectiveness. The results exhibit that a similar accuracy than conventional fringe projection is achieved while using a reduced number of patterns. The proposed approach is a feasible alternative to increase the efficiency of three-dimensional imaging systems based on phase-shifting.

A novel method for simultaneous measurement of temperature and strain based on EFPI/FBG

A modified intensity demodulation method for fiber optic Fabry–Perot cavity and fiber Bragg grating combined sensing system is proposed, through which the cross-sensing error can be reduced effectively and high sensing speed can be realized at the same time. The system is based on an Extrinsic Fabry–Perot Interferometer for strain sensing, and a fiber Bragg grating for temperature sensing. Three-wavelength digital phase demodulation method and passive linear filtering demodulation method are adopted for the demodulation of F–P cavity length and fiber Bragg grating central wavelength, respectively. Meanwhile temperature varied from 25 °C to 105 °C under constant pressure, the demodulation accuracy of strain after correction is ±0.6με, which is improved by 2 times than the direct demodulation result. The demodulation accuracy of temperature is 1.4 °C after correction, with pressure ranging from 0 to 10 MPa at constant temperature. Temperature demodulation error is decreased to 1/3 of its original value. Strain sensing accuracy after correction was ±1με. Experimental studies show that the proposed sensing system has a more compact size and higher measurement accuracy than the previous ones.

Improved unwrapped phase retrieval method of a fringe projection profilometry system based on fewer phase-coding patterns.

In this paper, based on two additional phase-coding patterns, an improved phase demodulation method is proposed. First, six equally spaced coding phases in the interval [$ - \pi $-π, $\pi $π] are embedded in different periods of the coded fringes following a certain sequence. Subsequently, since a group of phase orders can be uniquely determined by the four adjacent coding phases, the phase-order map of the object can be generated. To ensure the accuracy of decoding results, the interference coding numbers should be corrected in advance. In the meantime, the connected regions exhibiting the same orders are classified and then labeled for simplifying the decoding process. The simulation results verify the feasibility of the proposed method. By two groups of 3D imaging experiments, the applicability of this method to multiple objects and discontinuous objects is confirmed.

Highly sensitive gas refractive index sensor based on hollow-core photonic bandgap fiber.

A highly sensitive gas refractive index (RI) sensor based on hollow-core photonic bandgap fiber (HC-PBF) and Fourier transform white-light interferometry was experimentally demonstrated. HC-PBFs with lower loss than hollow silica tubes render a longer air cavity for the Fabry-Perot interferometers (FPIs) without a great deal of compromise to the fringe visibility of interference. Fourier transform phase demodulation method was employed in the experiment and a directly proportional relationship between the phase sensitivity and cavity length was demonstrated. For a cavity length of ∼24.9 mm, the sensor's gas RI sensitivity reaches up to 50775.54 µm/RIU in an air RI range from 1.000 to 1.030. Considering the cavity length demodulation resolution of 0.06 µm achieved by this method, the sensor can detect gas RI change with a resolution of 10-6 RIU, which can meet the sensing demand for almost all the gases. Moreover, the gas RI sensitivity and measurement range can be improved further by lengthening the HC-PBF. The high sensitivity, large dynamic range and good linearity of the proposed sensor make it a good candidate for biosensing, monitoring of modern chemical industry or gas laser systems.

A new method for CE-OFDM phase demodulation

CE-OFDM technology is used to modulate the phase of OFDM signal, and it ensures the range of signal envelope to be constant and overcomes the disadvantage of high OFDM signal peak-to-average ratio. This essay puts forward a kind of phase demodulation mode based on Costas loop for CE-OFDM system, and makes a comparison with the original demodulation modes by MATLAB simulation.

Two-frame fringe pattern phase demodulation using Gram-Schmidt orthonormalization with least squares method.

Gram-Schmidt (GS) orthogonal normalization is a fast and efficient two-frame fringe phase demodulation method. However, the precision of the GS method is limited due to the residual background terms and noise, as well as several approximation operations in the GS method. To obtain a phase map with higher accuracy, we propose an algorithm combining GS orthogonal normalization and least squares iterative (LSI) phase shift algorithm (GS&LSI). In our method, the phase was first obtained using GS method, and then a refinement operation using LSI was adopted to get the final wrapped phase map. Because of the LSI process, the demodulation result is greatly improved in many cases. Simulation and experimental result are presented to validate the potential of the proposed method.

Enhancing single-shot fringe pattern phase demodulation using advanced variational image decomposition

In many full-field optical metrology techniques, i.e. interferometry, moiré, and structured light, the information about the measurand, e.g. displacement, strain, or 3D shape, is stored in the phase distribution of a recorded two-dimensional intensity pattern—the fringe pattern. Its analysis (phase demodulation) therefore plays a crucial role in the measurement procedure, significantly affecting the total accuracy of the optical system. Phase demodulation methods based on just a single fringe pattern are especially interesting, due to their robustness to environmental disturbances and ability to examine dynamic events. However, the calculated phase map is easily spoiled by errors, which appear mainly because of fringe pattern imperfections, i.e. random noise, parasitic interferences, a nonsinusoidal fringe pattern profile or a non-uniform image background. In this contribution, an advanced variational image decomposition scheme is proposed to reduce these phase demodulation errors. The reported purely phase domain method can be easily adopted to aid virtually any fringe analysis method, including single-frame and multi-frame phase-shifting, possibly enhancing retrieved phase distribution without the need for hardware manipulation. We employed it to improve single-frame Hilbert–Huang transform-based fringe analysis. The remarkable efficiency and versatility of the developed algorithm are verified by processing synthetic and experimental fringe patterns and phase maps. The demonstrated approach compares favorably with the very capable 2D empirical mode decomposition reference method.

Absolute distance measurement based on spectral interferometry using femtosecond optical frequency comb

We demonstrated an absolute distance measurement method based on the frequency folding effect using the spectral interferometry of femtosecond optical frequency comb. And the investigation was carried out on the ranging accuracy influence of the phase noise in the traditional complicated phase unwrapping method via band-pass filter and Fourier Transform. To reduce the effects of the phase noise, we proposed the non-filtered and differential envelop phase demodulation method, and its robustness was illustrated with a standard deviation of 75 nm for the stability of single point measurements. Further, through the extension of the non-ambiguity range, we achieved a resolution of better than 30 µm in a long distance measurements range of 70 m, yielding a relative precision of 3.1 × 10−7.

108-km Distributed Acoustic Sensor With 220-p$\varepsilon /\surd$Hz Strain Resolution and 5-m Spatial Resolution

The measurement distance is one of the most important parameters for distributed acoustic sensor (DAS). In this paper, we report a long-distance and high-sensitivity DAS system based on time-gated digital optical frequency domain reflectometry. The bi-directional distributed Raman amplification is adopted to realize long measurement distance. The shape of optical pulse is pre-distorted to be a standard Hanning window, which provides a theoretical peak-side lobe ratio of 46 dB to suppress the crosstalk. The interference fading and polarization fading are well suppressed, and hence phase-demodulation method is adopted, instead of intensity demodulation method. As a result, the sensitivity is enhanced and the full information (amplitude, phase, and frequency) of the vibration can be obtained. In experiments, the fiber length is about 108 km, whereas the spatial resolution is 5 m. A weak vibration with peak-peak amplitude of 14.7 nε is correctly located at the distance of 98 km with a high SNR of 30 dB. It is the first time that 220-pε/√Hz strain sensitivity is realized over 100-km-level fiber and the vibration waveform is retrieved linearly without harmonics.

An optical fiber Fabry–Pérot micro-pressure sensor based on beam-membrane structure

In this paper, an optical fiber Fabry–Pérot (FP) sensor for micro-pressure measurement is proposed. The FP interferometric cavity is composed of an end face of the incident optical fiber and a sensitive silicon diaphragm. The sensitive silicon diaphragm creatively utilizes a beam-membrane structure which is fabricated by micro-electro-mechanical system manufacturing technology. The finite element method simulation results show that the beam-membrane structure can achieve higher sensitivity and better linearity. The sensor performance test platform is built by a ASE-wide spectrum light source, optical spectrum analyzer, micro-pressure gas source and so on. The phase demodulation method is employed to demodulate the cavity length signal from the spectrum. The measure range of the sensor is 0–10 KPa, and the experimental sensitivity of the cavity length can reach to 242 nm KPa−1.