Homodyne Demodulation Research Articles

A Method for Detecting Small Oscillations Based on Homodyne Demodulation with a Tandem Low-Coherence Interferometer

A Method for Detecting Small Oscillations Based on Homodyne Demodulation with a Tandem Low-Coherence Interferometer

Low-coherence interferometry with homodyne demodulation capabilities for distributed fiber-optical sensors

Distributed fiber-optical sensors (DFOS) achieve the best results while interference registration schemes are used when controlled physical field lead to the fiber length and phase difference. DFOS based on fiber-optical phase-amplitude filters (FOPAF) have a simple and reliable design, consisting of distributed sensing elements (DSE) set. However, the main problem is the stabilization of its characteristics in different areas of DSE. On the other hand, the possibilities of low-coherence interferometry with homodyne light demodulation show the possibilities of stabilizing working points, but in the Michelson fiber-optical interferometric tandem scheme. The purpose is to substantiate the option of stabilizing the operation of DSE based on FOPAF, using low-coherence interferometry with homodyne demodulation in monitoring spatially distributed physical fields. The appropriate methods are considered. The analysis of the possible experimental setup based on the low-coherence interferometry with homodyne demodulation in the interferometric tandem scheme in comparison with the variants, based on the low-mode fiber-optical fibers is established. Promising scheme of the experimental installation is presented and the requirements for components are justified. The prospects of using low-coherence interferometry with homodyne demodulation for DFOS based on DSE with FOPAF are shown. The proposed low-coherence interferometry scheme with homodyne demodulation for DFPS on DSE with FOPAF has high sensitivity, is built on affordable equipment and, accordingly, has a low specific cost for the subsequent development of monitoring system.

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.

Distributed dynamic strain measurement with a direct detection scheme by using a three-step-phase-shifted double pulse in a UWFBG array.

We demonstrate a stable homodyne phase demodulation method with a double pulse based on an ultra-weak fiber Bragg grating (UWFBG) array. The technique divides one of the probe pulses into three sections and introduces successive 2π/3 phase differences into each section. By using a simple direct detection scheme, it can achieve distributed and quantitative vibration measurement along the UWFBG array. Compared to the traditional homodyne demodulation technique, the proposed technique is more stable and easier to accomplish. Moreover, the reflected light from the UWFBGs can provide a signal that is modulated uniformly by the dynamic strain and multiple results for averaging, resulting in a higher signal-to-noise ratio (SNR). We experimentally demonstrate the technique's effectiveness by monitoring different vibrations. The SNR for measuring a generic 100 Hz, 0.08 rad vibration in a 3 km UWFBG array with a reflectivity of -40 to -45 dB is estimated to be ∼44.92 dB.

Effect of three-beam interference on phase-generated carrier demodulation of a fiber-optic interferometric sensor.

Homodyne demodulation using a phase-generated carrier (PGC) has been applied in fiber-optic interferometric sensors to overcome the signal fading and distortion due to the drift of the operating point. An assumption needed for the PGC method to be valid is that the sensor output is a sinusoidal function of the phase delay between the arms of the interferometer, which is readily achieved by a two-beam interferometer. In this work, we theoretically and experimentally study the effect of three-beam interference, whose output deviates from a sinusoidal function of the phase delay, on the performance of the PGC scheme. The results show that the deviation could lead to additional undesirable terms in the in-phase and quadrature components in PGC implementation, which may result in significant signal fading with the drift of the operating point. The theoretical analysis leads to two strategies for eliminating these undesirable terms so that the PGC scheme is valid for three-beam interference. The analysis and the strategies were validated experimentally using a fiber-coil Fabry-Perot sensor with two fiber Bragg grating mirrors, each having a reflectivity of 26%.

FPGA-Based Hardware Implementation of Homodyne Demodulation for Optical Fiber Sensors

Homodyne demodulation is a convenient technique for signal detection in interferometric sensors. The demodulation process is typically developed using analog circuits. However, to improve the performance of the demodulator, a digital system must be employed. In this study, we developed an optical fiber sensor by combining: (a) a Michelson interferometer, (b) a micro-electro-mechanical system (MEMS) device, and (c) a field-programmable gate array (FPGA)-based interrogator. Signal processing was integrated into the FPGA-embedded system. The homodyne demodulation algorithm was implemented with hardware modules developed in the hardware description language (HDL) to provide a portable, low-cost, and scalable digital system. The present study successfully demonstrates the development and validation of an FPGA-based interrogator capable of processing interferograms through a homodyne demodulation scheme. The experimental results reveal proper displacement measurements of the proof-mass MEMS and the low amount of hardware resources used. The displacement measurements obtained from the system matched those obtained from a certified characterization system. As the system can be easily reconfigured to the required measured signal, a similar measurement methodology can be developed using other demodulation schemes and optical fiber sensors.

Метод детектирования малых колебаний на основе гомодинной демодуляции с тандемным низкокогерентным интерферометром

The paper proposes a method for detecting small oscillations in the length of interference fiber-optic sensors, which makes it possible to compensate for the problem of slow drift of the working point with a remote sensor. The result is achieved by combining homodyne demodulation methods with a tandem low-coherence interferometer. Theoretically and experimentally, the possibility of detecting acoustic effects in the operating frequency band of 4 kHz with a sensitivity of up to 0.3 nm has been shown.

High-precision fiber-optic temperature sensor based on Fabry-Perot interferometer with reflective thin-film multilayer structures

An embodiment of a fiber-optic temperature sensor based on a Fabry-Perot interferometer and a scheme for interrogating an experimental sample of the sensor are proposed. The proposed solution makes it possible not to use expensive spectral measuring devices (spectrum analyzer, interrogator). The region of free dispersion and the phase sensitivity of the developed Fabry-Perot interferometer were determined in the temperature range from 20 °C to 590 °C. The accuracy of measuring the ambient temperature is calculated. The long-term stability of the measuring setup at room temperature has been evaluated. The phase shift of the Fabry-Perot interferometer with temperature change was registered. The design of the Fabry-Perot interferometer is implemented using reflective thin-film multilayer structures obtained by stage-by-stage electron-beam deposition in vacuum on polished end cleavages of an optical fiber. The interferometer interrogation method is based on the use of a vertical-cavity surface-emitting laser (VCSEL) operating in a pulsed mode. The principle of registering the phase shift of the interferometer with a change in temperature is based on the use of auxiliary modulation of laser radiation along the wavelength due to modulation (periodic change) of the duration of optical pulses. Auxiliary modulation makes it possible to obtain additional harmonic components in the interferometer signal, which are further used in homodyne demodulation to restore the interferometer phase shift signal proportional to the change in the optical path difference between the interferometer mirrors. The design of the high-temperature sensor is based on a Fabry-Perot interferometer the reflecting mirrors of which are five alternating layers of thin films of TiO2 and Al2O3. Based on the results of the temperature experiment, it was concluded that an increase in the ambient temperature leads to a decrease in the free dispersion region of the Fabry-Perot interferometer. The conclusion made is consistent with the theoretical data. According to the results of the experiment, it is shown that the phase sensitivity of the interferometer to temperature changes is 0.94 rad/K. The accuracy of temperature measurements at the 3σ level was 0.017 K. The results of the study may be of great importance in creating systems for monitoring temperatures above 300 °C. The use of such an interferometer makes it possible to carry out high-precision relative temperature measurements.

High Fidelity MZI-BCG Sensor With Homodyne Demodulation for Unobtrusive HR and BP Monitoring

An all-optical active homodyne detection aided fiber-optic Mach-Zehnder interferometer (MZI) vital signs monitoring system is proposed and investigated. The active homodyne detection is mainly realized by employing a wavelength-tunable vertical-cavity surface-emitting laser (VCSEL) and automatic closed-loop control system (CLCS). It can effectively maintain the MZI sensor to operate around the quadrature point and successfully eliminate the fading effect of output signal induced by low frequency drift. Therefore, high fidelity and high stableness of the ballistocardiograph (BCG) signal is guaranteed. The results show that according to the Bland-Altman and the confidence ellipse analysis, the heart rate (HR) monitoring performance reveals high accuracy and good consistence. What’ more, a multiple linear regression-based blood pressure (BP) estimation model is presented, which shows that the BP is highly correlated with I-J-K complex oriented features, including IJ interval, JK interval and JK amplitude. It indeed offers a potential approach to achieve cuff-less BP estimation merely based on the high-fidelity BCG signal. In conclusion, the proposed MZI-BCG monitoring system is simple to use, and it shows great potential in future unobtrusive cardiac monitoring both in home and hospital.

Miniature High-Frequency Response, High- Pressure -Range Dynamic Pressure Sensor Based on All-Silica Optical Fiber Fabry-Perot Cavity

A miniature shock-wave pressure sensor based on an optical-fiber tip F-P cavity is described. The basic theory and fabrication process of this sensor are given. The transient interferometric phase of this F-P cavity under the action of a shock pressure wave is demodulated by using the passive homodyne demodulation technique. The static and dynamic calibration test are conducted using piston-type pressure calibration machine and air shock tube. The results indicate that the linearity, repeatability, and hysteresis of the sensor within the 1 MPa pressure range are 4.33%, 1.9%, and 2.8%, respectively, and that the resonant frequency is 8.97 MHz. Pressure sensors in the same package is used to measure the blast wave pressure from pre-charged pneumatic. The pressure probe of the ultra-fine package is used to accurately measure the shock wave pressure produced by the focused electromagnetic shock wave source. The results indicate that different pressure sensors with different diaphragm thickness and different packaging forms can measure shock waves with different ranges and rise times.

Dynamic phase extraction in high-SNR DAS based on UWFBGs without phase unwrapping using scalable homodyne demodulation in direct detection.

We demonstrate a Distributed Acoustic Sensor (DAS) based on Ultra-Weak Fiber Bragg Gratings (UWFBGs) using a scalable homodyne demodulation in direct detection. We show that a distributed interferometric system using delay and mixing of backscattering from consecutive identical gratings can be combined with a Phase-Generated Carrier Differentiate and Cross-Multiply (PGC-DCM) demodulation algorithm to perform dynamic measurements with high SNR, employing a simple narrowband laser and a pin photodiode. The proposed homodyne demodulation technique is suitable for real-time monitoring using distributed measurements, as it does not require computationally costly phase unwrapping common in conventional schemes and is robust against detrimental harmonic distortions, while not requiring additional mechanisms to handle division-by-zero operations. The demodulation scheme is also scalable, as it involves symmetric ordinary differentiation and integration operations suitable for processing with FPGA-based or analogue systems which, thanks to readily realizable schemes for implementing fractional order calculus, are also candidates for small-scale integration. We experimentally demonstrate the effectiveness of the technique by monitoring the dynamic response of a generic 2.5 kHz vibration applied to a PZT placed at the end of a sensing fiber comprised of a 1 km array of 200 UWFBGs each with a reflectivity of ~-43 dB written at a spacing of 5 m, with an SNR of ~34.52 dB.

Study of gain factor effect of erbium doped fiber amplifier on noise floor level of fiber-optic interferometric sensor

Subject of Research. The paper presents experimental study results of the gain factor effect of an erbium doped fiber amplifier on the noise floor level of a fiber-optic interferometric acoustic sensor. Fiber-optic sensor is based on a Michelson interferometer. The optical amplifier is located behind the compensating interferometer which induces the auxiliary phase modulation to the interference signal. The homodyne demodulation algorithm is used to recover the sensor phase signal. Method. During the experiment there were no external acoustical impacts on the sensor. The power control of optical signals from the fiber amplifier was performed. Noise signals from the sensor were written into data files under the different values of the fiber amplifier gain factor. Spectral estimations of the noise floor level of the fiber-optic interferometric sensor were performed by the averaged modified periodogram method under the different values of the fiber amplifier gain factor. Obtained results were used to define the dependence of the noise floor level of the fiber-optic interferometric sensor on the fiber amplifier gain factor. Main Results. Mean noise floor levels were equal to 64 urad/Hz0.5 at 355 Hz, 68 urad/Hz0.5 at 450 Hz and 66 urad/Hz0.5 at 500 Hz. Experimental results showed insignificant increase of the noise floor level of the fiber-optic interferometric sensor with the growth of the optical amplifier gain factor from 14.6 dB to 25.8 dB. The gain factor increase was about several percent and did not exceed inaccuracies of performed measurements. Practical Relevance. The absence of significant changes in the noise floor level of the considered fiber-optic sensor with the changing of the fiber amplifier gain factor is caused by the intensity noise suppression of the used demodulation scheme. The considered fiber amplifier might be used for the amplification of optical signals from the fiber-optic multiplexed array of fiber-optic sensors without the significant deterioration of their noise performance on condition that the homodyne demodulation algorithm with the intensity noise suppression is used.

Dynamic phase extraction in a modulated double-pulse ϕ-OTDR sensor using a stable homodyne demodulation in direct detection.

We propose and experimentally demonstrate a stable homodyne phase demodulation technique in a ϕ-OTDR using a double-pulse probe and a simple direct detection receiver. The technique uses selective phase modulation of one of a pair of pulses to generate a carrier for dynamic phase changes and involves an enhanced phase demodulation scheme suitable for distributed sensing by being robust against light intensity fluctuations, independent of the modulation depth, and convenient for analogue signal processing. The capability of the technique to quantify distributed dynamic phase change due to a generic external impact is experimentally demonstrated by measuring the phase change induced by a nonlinear actuator generating a 2 kHz perturbation at a distance of 1.5 km on a standard singlemode fiber with an SNR of ~24 dB. The demodulated nonlinear response is shown to have a spectrum consistent with one obtained using an FBG sensor and a commercial reading unit.

Performing accelerometer calibration using homodyne laser interferometry with displacements smaller than a quarter wavelength

<p class="Abstract"><span lang="EN-US">Laser interferometry is a preferred method of realizing the National Measurement Standard for vibration by National Metrology Institutes. Laser interferometry is well documented and its detailed implementation described in ISO 16036, part 11. When employing Homodyne demodulation of the quadrature signals, the minimum peak to peak displacement is limited at a quarter of the wavelength, or half a circle when viewed on a lissajous plot. A novel technique is described to extend the vibration calibration frequency range from 10 kHz up to 20 kHz with an applied acceleration of 200 m/s². </span></p>

Experimental comparison of homodyne demodulation algorithms for phase fiber-optic sensor

Subject of Research. The paper presents the results of experimental comparative analysis of homodyne demodulation algorithms based on differential cross multiplying method and on arctangent method under the same conditions. The dependencies of parameters for the output signals on the optical radiation intensity are studied for the considered demodulation algorithms. Method. The prototype of single fiber optic phase interferometric sensor has been used for experimental comparison of signal demodulation algorithms. Main Results. We have found that homodyne demodulation based on arctangent method provides greater (by 7 dB at average) signal-to-noise ratio of output signals over the frequency band of acoustic impact from 100 Hz to 500 Hz as compared to differential cross multiplying algorithms. We have demonstrated that no change in the output signal amplitude occurs for the studied range of values of the optical pulses amplitudes. Obtained results indicate that the homodyne demodulation based on arctangent method is most suitable for application in the phase fiber-optic sensors. It provides higher repeatability of their characteristics than the differential cross multiplying algorithm. Practical Significance. Algorithms of interferometric signals demodulation are widely used in phase fiber-optic sensors. Improvement of their characteristics has a positive effect on the performance of such sensors.

Phase shift influence research of the reference oscillator signal on the output signal in homodyne demodulation scheme

Subject of Research. Important feature of homodyne demodulation method based on the arctangent function approach is the phase shift between the reference oscillator signal and the interference signal. This phenomenon is caused by propagation delays of impulses in the optical interferometric sensor scheme and the analog low-pass filter in front of the phase modulator which produces the reference oscillator signal phase delay. There is multiplying of the reference oscillator signal and the interference signal in this homodyne demodulation scheme during its processing, and the phase shift between these signals leads to a distortion of the output signal. This paper deals with the findings of the phase shift influence of the reference oscillator signal by the output signal of the demodulation scheme at various parameters of the interference signal. Estimation of required accuracy is given of the phase shift compensation for the specified level distortion of the output signal. Method. Mathematical model is proposed in MATLAB. In this model, interference signal with changing parameters by a set of rules is passed through the considered demodulation scheme. This gives the possibility to obtain the dependences of the output signal amplitude from the reference oscillator signal phase shift, the operating point of the interferometer, the depth of phase modulation and amplitude of the measured phase signal. Results obtained during the simulation showed the need to compensate the reference oscillator signal phase shift. To assess this shift in the current homodyne demodulation scheme the original method of its determination has been proposed. The method is based on the transmission of the interference signal and the oscillator signal via one and the same band-pass filter that separates the phase modulation carrier frequency. According to the phase delay between the receiving signals, the value of the reference oscillator signal phase shift can be judged on. This shift can be corrected with knowledge of the value of the reference oscillator signal phase shift. Correction is achieved by making the required delay in reference oscillator signal. Main Results. The results of mathematical modeling show significant nonlinear dependences of the output signal on the reference oscillator signal phase shift at different values of the phase modulation depth, the operating point of the interferometer and the measured phase signal amplitude. It was found out that optimal values of the reference oscillator signal phase shift equal to 0, 180 and 360 provide minimum distortions of the output signal. It was shown that to achieve about 4% distortion level of the output signal phase shift compensation with an accuracy of 3% relative to period of the reference oscillator signal was required. Practical Significance. The original method making it possible to assess the value of the reference oscillator signal phase shift has been proposed. The reference oscillator signal phase shift compensation during considered homodyne demodulation scheme practical implementation provides the correctness of the scheme operation and increases the signal to noise ratio of the output signal.

Compensation of output signal temperature dependence in homodyne demodulation technique for phase fiber-optic sensors

Modified phase-generated carrier homodyne demodulation technique for fiber-optic sensors is presented. Nowadays phase-generated carrier homodyne demodulation technique is one of the most widespread. One of its drawbacks is the temperature dependence of the output signal because of the modulator scale factor temperature dependence. In order to compensate this dependence an automatic adjustment of the phase modulation depth is necessary. To achieve the result, additional harmonics analysis is used with the help of the Bessel functions. For this purpose the known demodulation scheme is added with the branch, where interferometric signal is multiplied by the third harmonic of the modulation signal. The deviation of optimal ratio of odd harmonics is used as a feedback signal for adjusting the modulation depth. Unwanted emissions arise in the feedback signal, when the third harmonic possesses a value close to zero. To eliminate unwanted emission in the feedback signal, the principle scheme is added with one more branch, where interferometric signal is multiplied by the forth harmonic of the modulation signal. The deviation of optimal ratio of even harmonics is used as a feedback signal alternately with the deviation of optimal ratio of odd harmonics. A mathematical model of the algorithm is designed using the MATLAB package. Results of modeling have confirmed that suggested method gives the possibility for an automatic adjustment of the phase modulation depth and makes it possible to compensate temperature dependence for the modulator scale factor and output signal magnitude.

Detection of Low Frequency Signals using Interferometric Fiber Sensors based on Phase Generated Carrier Demodulation Technique

A fiber-optic sensor is a sensor with high sensitivity, and signal detection technology is one of its key technologies. Phase generated carrier demodulation technology is a homodyne demodulation method widely used for interference fiber-optic sensors. Research reveals that the amplitude of the interference signal and the modulation depth will affect the result of demodulation. The distortion of the demodulated signal can be reduced by the elimination of the effects of the interference signal amplitude and modulation depth. A phase generated carrier demodulation method for interference fiberoptic sensors is proposed to detect weak ELF signals. Theoretical analysis and simulation have been implemented on the demodulation of weak ELF signals using low-level submixer carrier. The results indicate that in the demodulation of weak ELF signals, DC drift occurs in the DCM approach, while the Arctangent approach does not have this problem. Then, an optical fiber sensing system for ELF signals is established based on optical fiber interferometer, indicating the Arctangent approach is able to demodulate the VLF signals accurately.

Application of fiber Bragg grating sensors for the micro-strain measurement of optical components surface

Fiber Bragg Grating Sensors (FBGS) are gaining increasing attention in the fields of micro-stress analysis, showing high accuracy and sensitivity. In this paper, FBGS which wavelength variations can be converted to strains, are used to measure the micro-strain variation of a plane mirror where the forces acting upon. Both the self-gravity and extrusion forces are applied to the surface of the optical elements, generating inevitable deformation and decreasing the test accuracy of the whole optical system. First, a micro-strain model is built using finite element analysis to obtain the qualitative value of the micro-strain variation. Next, a series experiments are performed to validate the model is effective. A detailed analysis of the micro-strain variation is acquired from the phase generated carrier homodyne demodulation and then the three-step phase-shifting algorithm based on an unbalanced Mach-Zehnder interferometer system. The experimental results match well with the theory. Both the modeling and measurement results indicate that the sensitivity of this method in measuring the micro-strain can be reached as small as 10 μϵ

A novel digital active homodyne demodulation scheme based on square‐wave phase modulation for interferometric fiber‐optic sensors

AbstractA novel digital active homodyne demodulation scheme to eliminate the signal fading in interferometric fiber‐optic sensors is proposed. The error signal is obtained by the square‐wave phase modulation and then the digital correlation detection technique is applied to demodulate the low‐frequency environmental phase drift and generate the offset phase, which is then fed back the integrated optical phase modulator to lock the interferometer in quadrature. The high‐frequency signal phase can be read out and recovered from the photodetector output with the interferometer in quadrature. The simulation and experimental results verify the feasibility of the proposed scheme, which obviates the feedback integrator saturation and the system resetting problem encountered in the conventional active homodyne detection schemes. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:20–23, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25640