Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism

As an important member of optical fiber sensor, fiber optic Extrinsic Fabry-Perot Interferometric (EFPI) sensor has prospects for a wide range of industrial applications due to its small size, compact configuration, good reliability and flexibility. In a white light based fiber optic EFPI sensor system, which has the advantages of large dynamic range and high resolution, spectral analysis equipment is the most important part which takes the major cost of the system. Therefore, multiplexing spectral analysis equipment to measure multiple sensors simultaneously is an effective and necessary way that can save the cost of the whole sensor system. In this paper, a scheme based on the frequency division multiplexing of EFPI optical fiber sensors is proposed. Two EFPI sensors with different gap lengths are parallely connected through the optical fiber coupler. The overlapped interference spectrum of the two EFPI sensors is measured by using an optical spectrum analyzer, which is separated into two individual interference spectrums with a Finite Impuse Response (FIR) band-pass filter. Their envelope components are extracted with Hilbert transform, and then the interference spectrums are normalized by the envelope components. The respective gap lengths of the two EFPI sensors are achieved with the cross correlation calculation. Using this frequency division spectral analysis method, a two-channel multiplexing EFPI sensor system is implemented in the laboratory. The deployment of this frequency division multiplexing technology can greatly reduce the cost of the whole system which has extensive potential applications for distributed fiber optic EFPI sensor system.

Optical fiber Bragg grating (FBG) sensors have significant potential for use as embedded devices to monitor the structural integrity of engineering materials. The main drawback of the FBG strain sensor is its cross-sensitivity to temperature. This paper reports a simple scheme for multiplexing a FBG and an extrinsic Fabry-Perot interferometric (EFPI) sensor to enable the decoupling of strain from temperature. The EFPI sensor was constructed using a precision bore quartz capillary tube which housed two cleaved optical fibers. The gap between the fiber end- faces served as the Fabry-Perot cavity. Since the coefficients of thermal expansion between the optical fiber and the capillary tube were similar, the EFPI sensor has a very low sensitivity towards temperature. Therefore, when both sensors are placed close together, the EFPI sensor can act as the strain sensor, and temperature can be determined from the FBG wavelength shift after taking out the strain effect. The signal processing for the EFPI sensor was based on a channelled spectrum method using a CCD spectrometer. The same CCD spectrometer was also used to determine the wavelength shift of the FBG. The cross-talk between the EFPI and FBG sensors was evaluated. The feasibility of conducting simultaneous strain and temperature measurements was demonstrated.

In this paper we investigate the performance of a SCS-6/Ti-15-3 composite system, a carbon/SiC woven composite system, and an AS4/3501-6 composite system, subjected to long term mechanical fatigue, with an extrinsic Fabry-Perot interferometric (EFPI) fiber optic strain sensor. Both stiffness reduction and the degradation of thermal expansion coefficient (TEC) are monitored. The obtained results show that the EFPI sensor provides reliable data during long term fatigue loading up to 1 million cycles. The results suggest that the EFPI sensor is a viable means to monitor current and proposed characteristic damage metrics for various composite systems. We also monitor the TEC degradation during the thermal fatigue of celion G30-500/PMR-15 woven cross-ply composite system, and present a simple micromechanical model, that employs a shear lag approach, utilized to predict the effect of matrix cracking on the TEC of the composite. Results show that good agreement between experimental data and theoretical results is obtained, and that this parameter changed by as much as 80% over the fatigue life of the composite.

To perform a high temperature strain measurements, the sapphire extrinsic Fabry-Perot interferometer (EFPI) sensor head was attached to a silicon carbide rod and placed in a RF induction heater mounted on an MTS load frame. The high-temperature ceramic adhesive is designed to withstand temperatures up to 4000° F. As a basis for comparison, a gold-coated silica EFPI sensor was attached along side the sapphire EFPI. Initially, strain data was recorded at room temperature as the silicon carbide rod was slowly loaded to 4500 lbs. When the temperature was stabilized at a maximum of 2000° F, the SiC rod was again loaded to determine the effects of temperature on strain. Although the sapphire sensor was capable of measuring strain at higher temperatures, die induction heater, being poorly insulated, was not able to further heat the test material. The purpose of the second experiment was to determine the survivability and repeatability of tiie sapphire EFPI due to high-cycle fatigue loading. The long-term survivability of the sensor, in both static and fatigue loading, has been demonstrated. Although the load frame was shutoff after 200,000 cycles, one would expect to be able to fatigue load tiie sensor for millions of cycles since the components of the EFPI sensing head are free to move inside the alignment tube. This is consistent widi data obtained for similar silica opdcal EFPI sensors diat were fadgue loaded to over 10 million cycles as compared to resistive strain gages that typically can be cycled only to 60,000 at 2000°F.

Carbon fiber composites (CFRPs) are prone to impact loads during their production, transportation, and service life. These impacts can induce microscopic damage that is always undetectable to the naked eye, thereby posing a significant safety risk to the structural integrity of CFRP structures. In this study, we developed an impact localization system for CFRP structures using extrinsic Fabry-Perot interferometric (EFPI) sensors. The impact signals detected by EFPI sensors are demodulated at high speeds using an intensity modulation method. An impact localization method for the CFRP structure based on the energy-entropy ratio endpoint detection and CNN-BIGRU-Attention is proposed. The time difference of arrival (TDOA) between signals from different EFPI sensors is collected to characterize the impact location. The attention mechanism is integrated into the CNN-BIGRU model to enhance the significance of the TDOA of impact signals detected by proximal EFPI sensors. The model is trained using the training set, with its parameters optimized using the sand cat swarm optimization algorithm and validation set. The localization performance of different models is then evaluated and compared using the test set. The impact localization system based on the CNN-BIGRU-Attention model using EFPI sensors was validated on a CFRP plate with an experimental area of 400 mm × 400 mm. The average error in impact localization is 8.14 mm, and the experimental results demonstrate the effectiveness and satisfactory performance of the proposed method.

In this paper, we proposed an optical fiber extrinsic FabryPerot interferometer (EFPI) sensor for distance detection of ultrasound signal. This optical fiber EFPI sensor was fabricated with a novel and simple technics. In the experiments, both traditional piezoelectric transducer (PZT) and high voltage electrode discharge were used as the ultrasound signal source. The experimental results indicate that strong ultrasound signals can be detected by the fiber EFPI senor in both cases and the maximum detection distance in the air is more than 180 cm.

A three-wavelength passive demodulation technique to interrogate extrinsic Fabry-Perot interferometric (EFPI) sensors with arbitrary cavity length has been developed. The DC component is obtained online, then the applied dynamic signal is recovered by using three new signals without the DC component. The performance of the technique is demonstrated by simulations and experiments. The demodulation technique can extract dynamic signals, regardless of whether the phase modulation is larger than 2π. Theoretically, EFPI sensors with arbitrary cavity length can be demodulated by the demodulation technique, and EFPI sensors with cavity lengths in the 22.96-1002.3 μm range are detected successfully by the same demodulator in experiments. The technique is robust with respect to the bending loss of the leading fiber. The demodulation technique provides a robust and accurate solution to measure dynamic signals for EFPI sensors. It has the properties of high frequency, a large dynamic range, and high sensitivity. The paper demonstrates this technique's potential for measuring dynamic signals.

An extrinsic Fabry-Perot interferometric (EFPI) fiber optic sensor is presented for measurement of strain at high ambient temperatures. The sensor is fabricated using a femto-second (fs) laser. The EFPI sensor is fabricated by micromachining a cavity on the tip of a standard single-mode fiber and is then self-enclosed by fusion splicing another piece of singlemode fiber. The fs-laser based fabrication makes the sensor thermally stable to sustain temperatures as high as 800 °C. The sensor is relatively insensitive towards the temperature as compared to its response towards the applied strain. The sensor can be embedded in Carbon fiber/Bismaleimide (BMI) composite laminates for strain monitoring at high ambient temperatures.

A novel noise suppression method is proposed for the pressure surveillance of heavy oil thermal recovery well using white light extrinsic Fabry-Perot interferometric (EFPI) fiber-optic sensor. The moving grey model GM(1, 1) algorithm is applied to suppress the non-stationary noise and disturbance in downhole environment. Both theoretical analysis and field test results show that there exists a threshold effect for the moving window length selection, the optimized value of window length occurs at the threshold point which best removes the high frequency disturbance as well as retaining the fast change of actual pressure signal. Field test results show that the proposed method can increase the signal to noise ratio (SNR) of pressure profile with 10.4dB, and then can effectively suppress the large deviation in the forecasting result of daily oil production by combining temperature information.

A modified design of the extrinsic Fabry-Perot interferometric (EFPI) optical fiber sensor to allow complete characterization of multicomponent strain fields is proposed. The novel EFPI includes a sensor head with two input fibers such that the respective interference pattern from the end face of the output multimode fiber are in quadrature. Any strain field possessing a component along the line joining the axes of the two fibers causes the initial phase difference to be modulated. The measured change in phase difference is employed to determine this transverse component of the strain field. Absolute, rather than differential measurements of strain are possible using the absolute EFPI sensing system. Applications of the modified sensor-head to smart materials and structures are discussed.

In the present study, real-time measurement of internal and residual strains in GFRP laminates with an optical fiber strain sensor was performed in an autoclave molding. An Extrinsic Fabry-Perot Interferometric (EFPI) type optical fiber strain sensor was embedded into prepreg sheets before the molding. The ion viscosity and the temperature of the epoxy resin matrix were also measured simultaneously with the internal strain measurement. The results of the experiments showed that the internal and residual strain of GFRP laminates during the molding could be monitored by the optical fiber sensor embedded in the parallel direction to the reinforcing fibers. It was also found that the circumstances around the embedded optical fiber strain sensor should be taken into account for the interpretation of the measured internal and residual strain.

In this research program, several optical instruments for high temperature measurement based on single crystal sapphire material are introduced and tested for real-time, reliable, long-term monitoring of temperatures for coal gasifier. These are sapphire fiber extrinsic Fabry-Perot interferometric (EFPI) sensor; intensity-measurement based polarimetric sapphire sensor and broadband polarimetric differential interferometric (BPDI) sapphire sensor. Based on current evaluation and analysis of the experimental results, the broadband polarimetric differential interferometric (BPDI) sensor system was chosen for further prototype instrumentation development. This approach is based on the self-calibrating measurement of optical path differences (OPD) in a single-crystal sapphire disk, which is a function of both the temperature dependent birefringence and the temperature dependent dimensional changes. The BPDI sensor system extracts absolute temperature information by absolute measurement of phase delays. By encoding temperature information in optical spectrum instead of optical intensity, this sensor guarantees its relative immunity to optical source power fluctuations and fiber losses, thus providing a high degree of long-term measurement stability which is highly desired in industrial applications. The entire prototype for BPDI system including the single crystal sapphire probe, zirconia prism, alumina extension tube, optical components and signal processing hardware and software have shown excellent performance in the laboratory experiments shown in this report.

A white-light interferometry based on the Fourier transform method is proposed to measure the optical path difference (OPD) of the high-finesse fiber optic extrinsic Fabry–Pérot interferometric (EFPI) sensor. The Fourier spectrum of the transmission spectrum signal consists of multiple frequency components because of the multiple-beam interference occurring in the high-finesse EFPI sensor. The high-order frequency component of the Fourier spectrum can be extracted by the Fourier transform method to recover the OPD in order to overcome the spectrum overlapping, which happens when the OPD of the EFPI sensor is short. In the experiment, a high-finesse fiber optic EFPI sensor with the cavity length of 120 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(\mu \) </tex-math></inline-formula> m is measured, and the second-order frequency component was extracted to recover the cavity length. The standard deviation of the measurement results was 9.132 nm. The measurement range of the Fourier transform method was effectively extended to the short OPD.

Online phase tracking of an extrinsic Fabry—Perot interferometer (EFPI) and experimental vibration control of a composite beam with a sensing patch are investigated. EFPI sensors have nonlinearity due to their interferometric characteristics. We propose a new sensing patch for compensation of this interferometric nonlinearity. This newly developed sensing patch consists of an EFPI sensor and another sensor that can produce directional information. Therefore, it uses the advantages of their components used in conjuction in order to overcome the disadvantages of the components used separately. A sensing patch that comprises an EFPI sensor and a piezoceramic is fabricated, and the characteristics are experimentally investigated. A simple and practical logic is applied to real-time tracking of the optical phase of an interferometer. The experimental results show that the proposed sensing patch does not suffer from the nonlinear behavior of conventional EFPI sensors and the hysteretic behavior of piezoelectric materials. Moreover, it has excellent strain resolution and a wide dynamic sensing range. The application of a sensing patch has been also investigated: vibration control with this sensing patch has been performed using a fuzzy logic controller (FLC), and the possibility of using a sensing patch as a sensoriactuator is considered.

Fabry-Perot sensors for dynamic studies using spectrally based passive quadrature signal processing