Low-finesse Fabry-Perot Interferometer Research Articles

Multiplexing and passive demodulation of intrinsic low-finesse Fabry-Perot interferometers using free-running DFB diode lasers

This paper presents a novel and simple technique for passive quadrature demodulation of multiplexed low-finesse fiber-optic Fabry-Perot interferometers. The approach proposed here uses two quadrature channels with very close wavelengths generated by two thermostabilized DFB diode lasers operating in continuous-wave mode. A coherent light correlation technique was used to demultiplex the wavelength channels and signals from interferometers at different positions along the fiber. The proposed technique does not require optical filters for spectral channel demultiplexing, making it suitable for demodulating relatively long interferometers with any free spectral range. An in-line array of four identical 13.1 cm long interferometers was used to demonstrate the method's performance. Experimental results demonstrate a phase resolution of 1.38 phase degrees, corresponding to a temperature resolution of 3 × 10−3 °C. Numerical simulations indicate that the main factor limiting the length of the sensing interferometer, and thus the resolution of the system, is the wavelength variation of the temperature-stabilized, independently operating lasers. The number of spectral channels can be easily extended to realize three or four-wavelength demodulation schemes.

A disturbed optical interferometric sensor analyzed on complex s-plane: A new novel vectorial detection technique for the interference patterns

In this work, the interference pattern produced by a disturbed optical interferometer in its optical cavity, is analyzed in the complex s-plane and the new detection technique is called vectorial detection on complex s-plane for the interference patterns (VDCSP_IP). The technique VDCSP_IP requires a complex reference vector s0ref, a complex measurement vector s0med and with their difference a complex detection vector is defined: s0det=s0ref-s0med. Considering the vector s0det four operating conditions are established: first, if s0det=0, then the optical interferometer is not detecting any physical variable; second, if s0det≠0 then the optical interferometer is detecting some physical variable; third, if θ=360o then s0det=0 since the perturbation provokes a complete cycle; fourth, the phase θ must be into the interval 0o<θ<360o. The VDCSP_IP technique was confirmed by simulating the interference pattern of a low-finesse Fabry-Perot interferometer based on two identical Bragg gratings. Based on the numerical results, the theoretical and numerical experiments are in agreement and the four operating conditions were corroborated.The technique VDCSP_IP finds potential application in the signal demodulation of interferometers and in the signal processing of quasi-distributed sensors based on interferometry.

Modified phase-generated carrier demodulation of fiber-optic interferometric ultrasound sensors

We propose and demonstrate a modified phase-generated carrier (PGC) demodulation scheme optimized for detection of ultrasound using interferometric sensors with sinusoidal fringes. The sensor used in demonstration is made from a pair of weak fiber Bragg-gratings at the ends of a coiled fiber that form a low-finesse Fabry-Perot interferometer. The phase of the laser source is modulated using an electro-optic phase modulator to generate the carrier signal and obtain 2 quadrature (the sine and cosine) terms at the first and the second order carrier frequencies. The signal of interest (ultrasound) has much higher frequency than the environmental perturbation but a very small amplitude that causes only small phase shift. Using small-signal approximation, for each of the 2 quadrature terms, we separate the contributions from the environmental perturbations (quasi-DC component) and from the ultrasound (AC component). The AC components that contain the information of the ultrasound signal are then further amplified with a large gain. The signal of interest is constructed by simple algebraic operations on the 2 quasi-DC components and the 2 amplified AC components involving multiplying and summing. This work provides a simple and robust demodulation method with potentially high sensitivity for fiber-optic interferometric ultrasound sensors.

Polarization-insensitive, omnidirectional fiber-optic ultrasonic sensor with quadrature demodulation.

We report an ultrasonic sensor system based on a low-finesse Fabry-Perot interferometer (FPI) formed by two weak chirped fiber Bragg gratings (CFBGs) on a coiled single-mode fiber. The sensor system has several desirable features for practical applications in detecting ultrasound on a solid surface. By controlling the birefringence of the fiber coil during the sensor fabrication, the sensor is made insensitive to the polarization variations of the laser source. The circular symmetric structure of the fiber coil also renders the omnidirectional response of the sensor to ultrasound. While the fiber coil is bonded directly to the structure, the CFBGs are suspended from the structure and free from large background strains with little reduction to the sensitivity of the sensor. The low-finesse FPI features a sinusoidal reflection spectrum. Like the conventional phase-generated carried technique, a phase modulator is utilized to implement quadrature demodulation. Therefore, the sensing system is adaptive to large background perturbations experienced by the fiber coil.

A Fiber-Optic Gas Sensor and Method for the Measurement of Refractive Index Dispersion in NIR.

This paper presents a method for gas concentration determination based on the measurement of the refractive index dispersion of a gas near the gas resonance in the near-infrared region (NIR). The gas refractive index dispersion line shape is reconstructed from the variation in the spectral interference fringes’ periods, which are generated by a low-finesse Fabry-Perot interferometer during the DFB diode’s linear-over-time optical frequency sweep around the gas resonance frequency. The entire sensing system was modeled and then verified experimentally, for an example of a low concentration methane-air mixture. We demonstrate experimentally a refractive index dispersion measurement resolution of 2 × 10−9 refractive index units (RIU), which corresponds to a change in methane concentration in air of 0.04 vol% at the resonant frequency of 181.285 THz (1653.7 nm). The experimental and modeling results show an excellent agreement. The presented system utilizes a very simple optical design and has good potential for the realization of cost-efficient gas sensors that can be operated remotely through standard telecom optical fibers.

Ultrasensitive refractive index sensor based on enhanced Vernier effect through cascaded fiber core-offset pairs.

An ultrasensitive refractive index (RI) sensor based on enhanced Vernier effect is proposed, which consists of two cascaded fiber core-offset pairs. One pair functions as a Mach-Zehnder interferometer (MZI), the other with larger core offset as a low-finesse Fabry-Perot interferometer (FPI). In traditional Vernier-effect based sensors, an interferometer insensitive to environment change is used as sensing reference. Here in the proposed sensor, interference fringes of the MZI and the FPI shift to opposite directions as ambient RI varies, and to the same direction as surrounding temperature changes. Thus, the envelope of superimposed fringe manifests enhanced Vernier effect for RI sensing while reduced Vernier effect for temperature change. As a result, an ultra-high RI sensitivity of -87261.06 nm/RIU is obtained near the RI of 1.33 with good linearity, while the temperature sensitivity is as low as 204.7 pm/ °C. The proposed structure is robust and of low cost. Furthermore, the proposed scheme of enhanced Vernier effect provides a new perspective and idea in other sensing field.

Highly Sensitive Fabry–Perot Demodulation Based on Coarse Wavelength Sampling and Vernier Effect

A highly sensitive demodulation method for the low-finesse Fabry-Perot interferometer (FPI) sensor is proposed and experimentally demonstrated. To generate the Vernier effect, the sampling interval of a tunable laser source is set close to the free spectral range of the FPI sensor. In order to improve the demodulation precision, the spline fitting process was applied to the sampling data. The dip wavelength of the fitted curve was chosen to measure the spectral shift. In the strain test experiment, the sensitivity of 0.01836 nm/μϵ was obtained. A controllable sensitivity is achieved by changing the sampling interval. It is convenient to balance the sensitivity and the measuring time. The method can be used to enhance the sensitivity of the preexistent low-finesse FPI sensors by changing an optical source in the sensing system. There is no need to make any changes to the FPI sensors and sensing nodes. Furthermore, the method can also be applied for other two-beam interferometry sensors.

A Theoretical Study and Numerical Simulation of a Quasi-Distributed Sensor Based on the Low-Finesse Fabry-Perot Interferometer: Frequency-Division Multiplexing.

The application of the sensor optical fibers in the areas of scientific instrumentation and industrial instrumentation is very attractive due to its numerous advantages. In the industry of civil engineering for example, quasi-distributed sensors made with optical fiber are used for reliable strain and temperature measurements. Here, a quasi-distributed sensor in the frequency domain is discussed. The sensor consists of a series of low-finesse Fabry-Perot interferometers where each Fabry-Perot interferometer acts as a local sensor. Fabry-Perot interferometers are formed by pairs of identical low reflective Bragg gratings imprinted in a single mode fiber. All interferometer sensors have different cavity length, provoking frequency-domain multiplexing. The optical signal represents the superposition of all interference patterns which can be decomposed using the Fourier transform. The frequency spectrum was analyzed and sensor’s properties were defined. Following that, a quasi-distributed sensor was numerically simulated. Our sensor simulation considers sensor properties, signal processing, noise system, and instrumentation. The numerical results show the behavior of resolution vs. signal-to-noise ratio. From our results, the Fabry-Perot sensor has high resolution and low resolution. Both resolutions are conceivable because the Fourier Domain Phase Analysis (FDPA) algorithm elaborates two evaluations of Bragg wavelength shift.

High-Speed Interrogation of Low-Finesse Fabry–Perot Sensors Using a Telecom DFB Laser Diode

This paper presents a high-speed high-resolution low-finesse Fabry–Perot sensor interrogation system. The system utilizes a standard telecommunication distributed-feedback laser diode and an all-digital high-speed signal processing based on field-programmable-gate-array. The system can resolve multiple Fabry–Perot Interferometers (FPI) simultaneously, which might include multiple sensors, multiparameter sensors, or combinations of sensor(s) and reference FPIs. This opens up possibilities for adopting different measurement system configurations and compensation schemes. The system exhibits white-noise characteristics for a system bandwidth above 100 Hz, with spectral density of about 2 pm/√Hz when interrogating about 1 mm long low-finesse FPI. At an output sampling rate of 10 Hz, a sensor measurement length resolution of less than 50 pm was demonstrated for about a 600 μm long sensing cavity (corresponding to a strain resolution of about 70 nϵ). Proper use of simple all-fiber reference also provided low long-term drift. The system provides an up to 40 KHz sampling rate and was used to demonstrate dynamic measurement of strain variation on a piezo-electric stack and for interrogation of in-cylinder pressure variations within a high-rotation-rate miniature diesel engine. Fabry–Perot sensors with typical lengths between a few hundred and a few mm can be read-out with the current version of the proposed interrogator. The proposed system was built out of a small number of highly cost-efficient optoelectronics and electronics components (all used in FTTH) and thus, opens-up potential for new applications where the cost of interrogation is presently limiting.

Influence of fiber bending on wavelength demodulation of fiber-optic Fabry-Perot interferometric sensors.

In practical applications of fiber optic sensors based on Fabry-Perot interferometers (FPIs), the lead-in optical fiber often experiences dynamic or static bending due to environmental perturbations or limited installation space. Bending introduces wavelength-dependent losses to the sensors, which can cause erroneous readings for sensors based on wavelength demodulation interrogation. Here, we investigate the bending-induced wavelength shift (BIWS) to sensors based on FPIs. Partially explicit expressions of BIWSs for the reflection fringe peaks and valleys have been derived for sensors based on low-finesse FPI. The theoretical model predicts these findings: 1) provided that a fringe peak experiences the same modulation slope by bending losses with a fringe valley, BIWSs for the peak and valley have opposite signs and the BIWS for the valley has a smaller absolute value; 2) BIWS is a linear function of the length of the bending section; 3) a FPI with higher visibility and longer optical path length is more resistant to the influence of bending. Experiments have been carried out and the results agree well with the theoretical predictions.

Highly compact fiber Fabry-Perot interferometer: A new instrument design.

This paper presents the design, construction, and characterization of a new optical-fiber-based, low-finesse Fabry-Perot interferometer with a simple cavity formed by two reflecting surfaces (the end of a cleaved optical fiber and a plane, reflecting counter-surface), for the continuous measurement of displacements of several nanometers to several tens of millimeters. No beam collimation or focusing optics are required, resulting in a displacement sensor that is extremely compact (optical fiber diameter 125 μm), is surprisingly tolerant of misalignment (more than 5°), and can be used over a very wide range of temperatures and environmental conditions, including ultra-high-vacuum. The displacement measurement is derived from interferometric phase measurements using an infrared laser source whose wavelength is modulated sinusoidally at a frequency f. The phase signal is in turn derived from changes in the amplitudes of demodulated signals, at both the modulation frequency, f, and its harmonic at 2f, coming from a photodetector that is monitoring light intensity reflected back from the cavity as the cavity length changes. Simple quadrature detection results in phase errors corresponding to displacement errors of up to 25 nm, but by using compensation algorithms discussed in this paper, these inherent non-linearities can be reduced to below 3 nm. In addition, wavelength sweep capability enables measurement of the absolute surface separation. This experimental design creates a unique set of displacement measuring capabilities not previously combined in a single interferometer.

Low cost, high performance white-light fiber-optic hydrophone system with a trackable working point.

A working-point trackable fiber-optic hydrophone with high acoustic resolution is proposed and experimentally demonstrated. The sensor is based on a polydimethylsiloxane (PDMS) cavity molded at the end of a single-mode fiber, acting as a low-finesse Fabry-Perot (FP) interferometer. The working point tracking is achieved by using a low cost white-light interferometric system with a simple tunable FP filter. By real-time adjusting the optical path difference of the FP filter, the sensor working point can be kept at its highest sensitivity point. This helps address the sensor working point drift due to hydrostatic pressure, water absorption, and/or temperature changes. It is demonstrated that the sensor system has a high resolution with a minimum detectable acoustic pressure of 148 Pa and superior stability compared to a system using a tunable laser.

Nine-point phase demodulation for interferometric measurement

Pure high frequency periodic triangle phase shift is introduced into optical interference, calculates nine data points in each period and obtains discrete phase values. This paper proposes a novel phase demodulation technology analyzing phase information with a symmetric linear method for depressing sampling error. Traditional low finesse Fabry–Perot interferometer produces typical cosine interference signal, performance of which is greatly improved by proposed technology. In experimental configuration we situate an electro-optics crystal to induce phase shift. The variation of Fabry-Perot cavity length is measured with a resolution much higher than the fringe counting or frequency modulation techniques. Simulation and experimentation both demonstrate feasibility and robustness of proposed algorithm. Reconstructed deviation and noise sources are discussed in detail. Various vibration formats are measured as deeper verification.

Analyzing the temperature sensitivity of Fabry-Perot sensor using multilayer graphene diaphragm.

A miniature Fabry-Perot interferometric sensor with an ultra-high temperature sensitivity was constructed by using an approximate 8-layer graphene diaphragm. The extremely thin diaphragm was transferred onto the endface of a ferrule with an inner diameter of 125 μm, and van der Waals interactions between the graphene diaphragm and its substrate created a low finesse Fabry-Perot interferometer with a cavity length of 42.86 μm. Temperature testing demonstrated a temperature-induced cavity length change of 352 nm/°C with a good linearity in the range of 20-60 °C. The result conformed well to the proposed analytical models relating to thermal expansion of trapped gas, thermal-optical property of graphene diaphragm and deflection behavior of bulged graphene blister. However, the ultra-thin diaphragm exhibited a small deflection deformation characteristic due to the applied higher loads.

Analyzing the applicability of miniature ultra-high sensitivity Fabry–Perot acoustic sensor using a nanothick graphene diaphragm

A miniature Fabry–Perot interferometric acoustic sensor with an ultra-high pressure sensitivity was constructed by using approximately 13 layers of graphene film as the diaphragm. The extremely thin diaphragm was transferred onto the endface of a ferrule, which had an inner diameter of 125 μm, and van der Waals interactions between the graphene diaphragm and its substrate created a low finesse Fabry–Perot interferometer with a cavity length of 98 μm. Acoustic testing demonstrated a pressure-induced deflection of 2380 nm kPa−1 and a noise equivalent acoustic signal level of ~2.7 mPa/Hz1/2 for a 3 dB bandwidth with a center frequency of 15 kHz. The sensor also exhibited a dynamic frequency response between 1 and 20 kHz, which conformed well to the result obtained by a reference microphone. The use of a suspended graphene diaphragm has potential applications in highly sensitive pressure/acoustic sensors.

A laser-lock concept to reach cm s-1-precision in Doppler experiments with Fabry-Pérot wavelength calibrators

State-of-the-art Doppler experiments require wavelength calibration with precision at the cm/s level. A low-finesse Fabry-Perot interferometer (FPI) can provide a wavelength comb with a very large bandwidth as required for astronomical experiments, but unavoidable spectral drifts are difficult to control. Instead of actively controlling the FPI cavity, we propose to passively stabilize the interferometer and track the time-dependent cavity length drift externally. A dual-finesse cavity allows drift tracking during observation. The drift of the cavity length is monitored in the high-finesse range relative to an external standard: a single narrow transmission peak is locked to an external cavity diode laser and compared to an atomic frequency. Following standard locking schemes, tracking at sub-mm/s precision can be achieved. This is several orders of magnitude better than currently planned high-precision Doppler experiments. It allows freedom for relaxed designs rendering this approach particularly interesting for upcoming Doppler experiments. We also show that the large number of interference modes used in an FPI allows us to unambiguously identify the interference mode of each FPI transmission peak defining its absolute wavelength solution. The accuracy reached in each resonance with the laser concept is then defined by the cavity length that is determined from the one locked peak and by the group velocity dispersion. The latter can vary by several 100m/s over the relevant frequency range and severely limits the accuracy of individual peak locations. A potential way to determine the absolute peak positions is to externally measure the frequency of each individual peak with a laser frequency comb (LFC). Thus, the concept of laser-locked FPIs may be useful for applying the absolute accuracy of an LFC to astronomical spectrographs without the need for an LFC at the observatory.

Spatially continuous distributed fiber optic sensing using optical carrier based microwave interferometry.

This paper reports a spatially continuous distributed fiber optic sensing technique using optical carrier based microwave interferometry (OCMI), in which many optical interferometers with the same or different optical path differences are interrogated in the microwave domain and their locations can be unambiguously determined. The concept is demonstrated using cascaded weak optical reflectors along a single optical fiber, where any two arbitrary reflectors are paired to define a low-finesse Fabry-Perot interferometer. While spatially continuous (i.e., no dark zone), fully distributed strain measurement was used as an example to demonstrate the capability, the proposed concept may also be implemented on other types of waveguide or free-space interferometers and used for distributed measurement of various physical, chemical and biological quantities.

Characterisation of a Nafion film by optical fibre Fabry–Perot interferometry for humidity sensing

Nafion has been evaluated as a sensing phase of an optical fibre humidity sensor based on a low-finesse Fabry–Perot interferometer. The sensor was constructed by manual deposition of a drop of a Nafion solution on the tip of a single mode optical fibre, forming a Fabry–Perot resonant cavity. The absorption of water by the Nafion film makes it swells, changing its refractive index and the length of the cavity, which produces a phase shift in the interference signal. The sensitivity, stability and response time of the sensor were evaluated in the RH range from 22 to 80% by analysing the correspondent reflection spectra of the interference fringes. As a result, it was obtained that Nafion can be used as sensing phase of an optical fibre humidity sensor based on optical fibre Fabry–Perot interferometry, presenting a response time of 242ms (3% RH variation) and a sensitivity of 3.5nm/%RH.

High-sensitivity fiber-tip pressure sensor with graphene diaphragm

A miniature fiber-tip pressure sensor was built by using an extremely thin graphene film as the diaphragm. The graphene also acts as a light reflector, which, in conjunction with the reflection at the fiber end-air interface, forms a low finesse Fabry-Perot interferometer. The graphene based sensor demonstrated pressure sensitivity over 39.4 nm/kPa with a diaphragm diameter of 25 μm. The use of graphene as diaphragm material would allow highly sensitive and compact fiber-tip sensors.

Spheroidal Fabry-Perot microcavities in optical fibers for high-sensitivity sensing

All-optical-fiber Fabry-Perot interferometers (FPIs) with microcavities of different shapes were investigated. It was found that the size and shape of the cavity plays an important role on the performance of these interferometers. To corroborate the analysis, FPIs with spheroidal cavities were fabricated by splicing a photonic crystal fiber (PCF) with large voids and a conventional single mode fiber (SMF), using an ad hoc splicing program. It was found that the strain sensitivity of FPIs with spheroidal cavities can be controlled through the dimensions of the spheroid. For example, a FPI whose cavity had a size of ~10x60 μm exhibited strain sensitivity of ~10.3 pm/με and fringe contrast of ~38 dB. Such strain sensitivity is ~10 times larger than that of the popular fiber Bragg gratings (~1.2 pm/με) and higher than that of most low-finesse FPIs. The thermal sensitivity of our FPIs is extremely low (~1pm/°C) due to the air cavities. Thus, a number of temperature-independent ultra-sensitive microscopic sensors can be devised with the interferometers here proposed since many parameters can be converted to strain. To this end, simple vibration sensors are demonstrated.