This paper presents an in-line, short cavity Fabry-Perot fiber optic strain sensor. A short air cavity inside a single-mode fiber is created by the fusion splicing of appropriately micro machined fiber tips. A precise tuning of the cavity length is introduced and used for the setting of the sensor static characteristics within the quasi-linear range around a quadrature point, which significantly simplifies signal processing. Sensor insertion losses achieved by short cavity design and optimized fusion splicing proved to be below 1 dB. Low insertion loss allows for effective cascading of the proposed strain sensors into a quasi-distributed sensor array. A practical 10-point quasi-distributed strain sensor array was demonstrated in practice, where each in-line sensor was tuned to the same operating point in the static characteristics, thus allowing for simple interrogation of the sensor array by using standard telecommunication OTDR. In addition, precise tuning of the short cavity Fabry Perot sensor was applied for an effective compensation of temperature-induced strain errors and for an increase in the unambiguous measuring range, while improving the overall linearity of the sensor system.
©2007 Optical Society of America
Fiber-optic strain sensors have attracted increasing interest in recent years due to the growing number of applications in various fields of industry.
Various solutions for single point and quasi-distributed fiber-optic strain sensors are presented using Bragg gratings . Bragg gratings are well-established solutions, however they suffer from relatively complex signal processing and temperature dependence. Extrinsic Fabry-Perot (EFP) or intrinsic Fabry-Perot (IFP) interferometer configurations have been developed for a variety of strain sensing applications. EFP uses an air cavity between two cleaved fiber ends and is usually performed by inserting fibers into an alignment ferrule, followed by bonding the fibers and the ferrule by fusing  or epoxy adhesive . Alternatively, IFP uses the semi-reflecting surfaces created inside a fiber that can be performed by sputtering or the electron beam evaporation of TiO2 to form films on the end faces of a short fiber segment followed by splicing the segment in-line with lead fibers [4,5]. While both EFP and IFP configurations show suitable characteristics for single point and quasi-distributed applications such as the possibility of multiplexing and relative high strain resolution, they have specific disadvantages. In the case of EFP, the sensing area is not determined by the air gap between the fibers but by separation of the fixing points on the ferrule. Therefore, each manufactured sensor has a different active length due to epoxy creep into the space between the ferrule and fiber, so individual sensor calibration is required .
The practical design of EFP was presented by Sirkis et al  where the air cavity is created by splicing the hollow-core fiber between two sections of a single-mode fiber. The presented in-line design has several advantages such as simple fabrication, high environmental and mechanical stability due to all-silica design, low temperature dependence and a sensor diameter equals to the fiber diameter. On the other hand the reported interference contrast was relatively low and the transmission losses were not considered. In all reported versions of EPF and IFP relatively complex optical signal processing was applied for determining the strain.
This paper describes an in-line EFP strain sensor. The sensor is similar in design to solution described in , however, it utilizes a simple micromachining process to create a well-controlled short length FP cavity within an optical fiber. The short length FP cavity has several advantages regarding strain sensing applications. The fabrication process, described in Section 3, is optimized for achieving low transmission losses and high repeatability of sensor response characteristics. Application of the short cavity can simplify signal processing considerably and can make FP sensors suitable for multiplexing, based on conventional telecommunication OTDR. Furthermore, we present temperature compensation and quadrature signal generation schemes, that are both the outcome of short cavity design.
2. Sensor description
The strain sensor design is shown on Fig. 1. A short air cavity between the lead-in and lead-out single-mode fibers (SMF) acts as a Fabry-Perot interferometer (FPI), where light waves, reflected from both cavity surfaces, interfere.
When considering the low reflectivities of the cavity surfaces (~4%), the sensor can be described as low-finesse FPI. Therefore, the reflectivity of the sensor RFP (ratio of reflected to incoming light intensity) can be derived using two-beam approximation, which results in the expression:
Φ is the round-trip phase shift, L is cavity length, λ wavelength and R1 and R2 are the reflectivities of cavity interfaces. The effect of beam divergence that causes signal loss with increasing cavity length is considered by the coupling factor ξ. It is defined as the overlap integral of a fiber’s fundamental mode with radius w 0, and a reflected beam with radius w after a completed round-trip. If we assume Gaussian field distribution, it can be described as :
For the Gaussian beam, the radius w can be expressed as a function of cavity length by :
In order to avoid complex signal processing due to the periodic nature of FPI response, represented by Eq. (1), we limited the sensor’s operation to within an unambiguous quasi-linear range around the quadrature point Q, as shown in Fig. 2. In this case the reflectivity of the sensor can be used as a measure of the applied strain.
Since the response is almost linear for a phase change of about π/2 (±π/4 from the quadrature point), the change in cavity length that is caused by the measured strain must not produce phase change larger than π/2. To achieve this, the cavity should be adjusted to cover the desired measuring range of strain and operating wavelength. The change of the phase due to the strain ε can be expressed as:
The required cavity length can be obtained by setting (4) equal to π/2 and ε= εmax:
To assure sensor operation around the quadrature point, the cavity length should be precisely tuned to provide an initial FPI phase of (2m-1)(π/2), where m is an integer. This is achieved by controlled heating and elongating the cavity, as explained later in the text. Another initial phase of the interferometer is also possible in order to provide an arbitrary operating point in the FPI characteristic. This can be advantageous when only positive or only negative strain is expected during measurement, as it allows for expansion of the measurement range.
Short cavity design minimizes the impact of beam divergence and, thereby, provides low transmission loss and well balanced amplitudes of interfering waves. This results in high interference contrast (e.g. good cancellation of back-reflected waves is possible when conditions for destructive interference occur). Low transmission loss and high interference contrast are essential in achieving high signal-to-noise ratio and large sensor count in quasi-distributed array. From the general expression for interference contrast V=(RFPmax-RFPmin)/(RFPmax+ RFPmin), and Eq. (1), we obtain:
Using Eq. (6) we can see that, for cavity lengths of less than 65 μm the interference contrast is above 90 %, but for longer cavities it starts to decrease rapidly (e.g. for L=100 μm, V=75%), as shown in Fig. 3.
3. Sensor fabrication and characterization
As an example, we chose to build a quasi-distributed sensor with a measurement range of ±2500 μm/m, which is typically encountered in various applications such as the monitoring of civil, mechanical and air-space structures. Using Eq. (6), we obtained the required cavity length of 32.5 μm that will assure unambiguous strain sensor operation in the target measurement range under illumination at λ=1300 nm.
The fabrication of a short cavity strain sensor includes three steps: concave cavity formation at the tip of the lead-out fiber, splicing the fibers to perform an in-line sensor and, finally, tuning of the sensor’s length to achieve the desired operating point.
First the short segment of the standard 62.5/125 gradient index multi-mode fiber (MMF) is attached to a standard SMF by splicing and cleaving at the desired distance from the splice, in our case 25 μm, as shown in Fig. 4(a). The appropriate tools were used to achieve repeatable cleaves with 1 μm resolution . This initial 25 μm distance is shorter than the target cavity length, as the fusion splicing process causes the elongation of the cavity. Next, the prepared fiber tip is immersed in 40% HF acid at room temperature [Fig. 4(b)], where the core of the MMF is etched away in the form of a concave cavity, as illustrated in Fig. 4(c). To assure high reflectivity of the structure, it is essential to terminate the etching process at the moment the acid solution reaches the MMF-SMF boundary at the center of the fiber. We, therefore, adopted the etching procedure described in  where the reflectivity is continuously measured during etching using an appropriate optical system. The fiber is removed from the acid at the moment when the reflectivity reaches maximum value. In the following step the prepared fiber is spliced to another flat-cleaved SMF, thus forming the sensor, as shown in Fig. 4(d).
Splicing is performed using a standard fusion splicer (Ericsson FSU 925 PM-A). While the first splice between the MMF and the SMF is achieved using standard parameters for MMF-MMF splicing, the second splice required careful adjustment of fusion parameters to ensure high reflectivity and high interference contrast simultaneously with high tensile strength.
Extensive experimental investigation yielded the next set of fusion parameters (fusion time and current) for the second splice performed on FSU 925: 0.2 s/13.5 mA, 1 s/9.6 mA, and 1.5 s/8 mA, with a pre-heating gap of 50 μm and an overlap of 12 μm. Typical interference contrast achieved under the described conditions was up to 98%, very close to predicted theoretical limit. It is interesting that fusion spliced cavity provided higher interference contrast than the cavity of the same length, formed between two flat-cleaved SM fibers. As a reference we performed a range of tests by inserting flat-cleaved fibers into an alignment tube, where interference contrast was within the range 91% to 94%. Higher interference contras of the proposed fusion spliced cavity can most likely be attributed to the focusing effect achieved by the concave reflective surface and to the fact that the concave surface provides better tolerance to the unparallelism of FP reflective surfaces and other mechanical tolerances encountered in the real cavity production.
The tensile strength of the sensor was better than 3 N, which is roughly the same as in the case of a normal splice (when screen-tested, the sensor broke near the cavity but not at the splice, which is typical for well performed standard splices). The cavity length increased during splicing from an initial 25 μm to about 32.5 μm, which is likely caused by the gas expansion inside cavity during splicing.
The last step in strain sensor fabrication was the tuning of the cavity length (setting the sensor operating point). We used a small electric furnace, initially designed for balancing the optical-fiber Michelson interferometers . The short fiber section, including the sensor cavity, was inserted into the furnace and heated to a temperature that allowed for a permanent change in fiber length. While heating the sensor, we observed a reflected spectrum under the broadband illumination at the optical spectrum analyzer. By stretching the fiber and observing the spectrum, the quadrature point (or any other initial phase) can easily be set for the desired operating wavelength. At this stage it is necessary to take into account the temperatureinduced cavity elongation, which proved to be about 16 nm for 32.5 μm cavity. Therefore, the cavity length needs to be set for 16 nm longer during tuning, in order to ensure the desired length after contraction when cooling to room temperature.
When the strain sensor is applied in quasi-distributed array the transmission loss is of essential importance as it determines the maximum number of sensors that can be integrated into an array. The transmission loss can be attributed to the coupling loss between the lead-in and lead-out fibers that are separated by the air cavity, and of back reflection (return loss) from the sensor. For an incoherent illumination case, which also presents an average loss under coherent illumination, the minimum achievable transmission loss can be estimated as:
where R1 and R2 are the reflectivities of cavity interfaces and ξ is the coupling factor, described by Eq. (2) For a cavity length of 32.5 μm and reflectivities R1=R2=3.75%, the minimum achievable transmission loss is 0.46 dB.
To test the repeatability of the fabrication process and to estimate practically achievable transmission losses, we evaluated 30 produced strain sensor samples. The transmission losses under incoherent illumination were below 1 dB, as shown on the histogram, in Fig. 5 (we used LED source that had a coherence length shorter than the optical-path length of the cavity). The difference between theoretical and predicted loss can be attributed to other imperfections such as fiber core misalignment and scattering at imperfect cavity surfaces.
Furthermore, we observed an average reflectivity of the sensor. These measurements were performed at zero strain and low coherence illumination. The reflectivity of the sensor depended on the direction of the incoming light wave. When the sensor was illuminated from the flat cleaved fiber side, the reflectivity proved to be around 4%. When the sensor was illuminated from the concave side, the reflection was around 2%. This asymmetric behavior is beneficial in the reduction of ghost (multiple) reflections in an OTDR-interrogated array that utilizes equidistantly-spaced sensors.
An enlarged photograph of the produced cavity is shown in Fig. 6.
4. Experimental investigation
Single-point strain sensor performance was investigated by bonding it to the steel cantilever beam close to the resistance strain gauges that served as the strain reference. Figure 7 shows the measured reflectivity of the sensor as a function of strain. The sensor was tuned to quadrature point at zero strain for the peak wavelength of FP laser diode (1307 nm), used as a light source. The sensor exhibits almost linear static characteristics for strain between -2500 to 2500 μm/m, with a corresponding reflectivity change from 1.5% to 6.5%.
Figure 8 presents the quasi-static responses of the optical fiber strain sensor and resistance strain gauges for random positive and negative dynamic strain loads, where a good agreement between both responses is observable.
Ten short cavity FP sensors (with cavity lengths of about 32.5 μm) were produced and arranged into a sensor network. The experiment was realized and evaluated using the setup, presented in Fig. 9.
An entire optical line, built from ten successively connected single-point sensors, separated by 100 m delay lines, was connected to the standard telecommunication OTDR. The OTDR trace is shown in Fig. 10. The red trace represents the system in a relaxed state (zero strain for all sensors) and the green trace represents the loaded system with applied maximum negative strain (-2500 μm/m) to odd sensors, and maximum positive strain (+2500 μm/m) to even sensors. The OTDR vertical scale is in dB and covers a range of over 20 dB. In order to show the entire trace, therefore, changes in the reflectivity, although they are significant, do not appear large at the trace.
Finally, it should be pointed out that stacking of Fabry-Perot sensors does cause mutual interactions (cross-talk) among individual sensors (change of reflectivity in a particular sensor affects optical power transmitted to the next sensor). However cross-talk effects are limited as the transmissions variation at the individual sensors (caused by the change in the applied strain) can not exceed maximum sensor reflectivity (presented air-cavity sensors can reflect back only a few percent of the total incident power, which results in marginal modulation of transmitted optical power). This cross-talk can be further eliminated by measuring Rayleigh back-scattered level just in front of the sensor, which can be used as the reference for calculating the reflectivity of a particular sensor in the network. The alternative method for cross-talk elimination can be summing of the losses on all preceding sensors, while calculating reflectivity of the observed one.
Movie/Fig. 11 shows an expanded view of the OTDR trace (rectangle around 2nd peak on Fig. 11) where the scale of the instrument screen was set to show the response of one sensor in a quasi-distributed network within a range of strain from -2500 μm/m to +2500 μm/m (y-axis range was limited to 4 dB). Since typical contemporary OTDRs achieve resolution of 0.001 dB, strain resolutions up to 1.25 μm/m could be achieved in practice.
The ability to precisely tune the cavity length has two additional applications. First, the sensor with quadrature output signals can be easily designed and produced. Quadrature detection can be used to extend measurement range, increase sensitivity, improve linearity and eliminate the impact of optical power fluctuations on the sensor’s performance. As an example, we produced a sensor with a 65 μm long cavity (twice as long as for single-wavelength interrogation), which resulted in increased sensitivity of the sensor for factor 2 while we preserved initial unambiguous operating range, by the application of quadrature detection.
We used dual-wavelength illumination of the sensor by two laser diode sources (λ1=1307 nm and λ2=1568 nm), as shown in Fig. 12. The separated signals I1 and I2 were provided to photodetectors PD1 and a PD2 through 1300/1550 nm WDM splitter.
The quadrature-shift of the signals on the photodetectors PD1 and PD2 was achieved by tuning the sensor cavity length to the value that set the sensor in quadrature point at λ1 and, simultaneously, to minimum reflectivity at λ2. The tuning process was monitored using two broadband sources (LED) with central wavelengths of 1300 nm and 1550 nm. The reflected spectrum of the tuned sensor is shown in Fig. 13.
The quasi-linear strain sensor response to an applied strain of ±2500 μm/m, using the presented setup, is obtained by calculating the Arctan function of the ratio of normalized light intensities on PD1 and PD2, as demonstrated in Fig. 14. Such a sensor design is also compatible with dual wavelength 1310/1550nm OTDR.
Another application for short-cavity fine tuning is the temperature compensation scheme. This scheme is particularly useful when the strain is measured on surfaces with higher coefficients of thermal expansion (e.g. metals). Figure 15 shows an example of a temperature-compensated strain measuring system that consists of two perpendicularly-oriented strain sensors, successively connected along the same optical fiber.
The “measuring” sensor is oriented in the direction of the measured strain εM and operates around a quadrature point with a positive slope. The second, “compensating” sensor operates around a quadrature point with negative slope and is perpendicular to the measured strain direction. The temperature-induced strain εT is the same for both sensors and, therefore, causes an increase in measuring sensor reflectivity, and a decrease in compensating sensor reflectivity. The total reflectivity, which is the sum of both sensor reflectivities (when using OTDR both sensors are separated with a short section of fiber and appear as a single event) remains unaffected by the temperature change. To achieve total temperature compensation, the reflectivities of the measuring and compensating sensors must be properly matched. The reflectivity of the compensating sensor RC should be higher to counterweigh the losses caused by partial reflections from the measuring sensor, and its insertion loss. RC can be calculated from equation:
where tm is the transmission coefficient and RM the reflectivity of the measuring sensor.
In addition, it must be taken into account that measured strain εM produces a lateral strain εμ = -μ∙εM, where μ presents the Poisson’s ratio of measuring object material, which additionally increases the sensitivity of the sensor.
The presented temperature compensation scheme is compatible with the diversity of other possible measurement and reference sensor configurations that are traditionally used to reduce temperature effects in electrical strain gauge measurement systems.
We tested the proposed configuration by bonding the sensors onto a steel plate and heating it up to 175°C. The change in reflectivity of the temperature compensated sensor pair was 0.13%, corresponding to a strain of 160 μm/m (≅1 μm/m/C). The change in reflectivity of the uncompensated sensor was 1.45%, corresponding to a strain of 1815 μm/m (≅11 μm/m/C). Application of the temperature compensating scheme, therefore, resulted in more than a 10 times smaller temperature dependence of the system. We used sensors with RM = 3.9 %, tm = 0.8dB and RC = 4.7%, which was the best match according to Eq. (8), from the produced series of strain sensors. The compensation was not perfect, mostly due to the limited matching achieved between the practically produced sensor pair.
Finally, the temperature-sensitivity (error) of the unmounted single sensor was observed within the temperature range from 20°C to 700°C, which proved to be less than 0.02 nm/°C, and it did not change significantly over the entire test range. This result agrees well with the calculated temperature expansion for silica fiber  with (ΔL/L)/ΔT=5×10-7/°C that yields strain of 0.016 nm/°C for 32.5 μm cavity length.
This paper presented an all-fiber Fabry-Perot strain sensor. The sensor utilizes a short air cavity that is created by a simple micromachining and optimized fusion splicing of two single-mode fibers. After splicing, the sensor is placed in a small furnace and heated to perform a fine tuning of the cavity length. This allows for an arbitrary and precise tuning of the initial phase under zero strain. By adjusting the cavity length, the sensor operates in a half-period linear region of the FP interferometer transfer function that enables simple strain interrogation by measurement of the reflected intensity.
The single-point sensor was evaluated by bonding it to the cantilever beam close to the reference resistive strain gauge. Both responses to the applied quasi-static strain were in good agreement. The sensor characteristic is almost linear within the measuring range of ±2500 μm/m. Other strain ranges are possible by adjusting the cavity length.
The initial sensor phase tuning capability and transmission loss of less than 1 dB makes the sensor suitable for quasi-distributed measurements by the application of standard telecommunication OTDR. Rayleigh backscattering can be used as a reference in order to eliminate amplitude variations of reflected signals caused by source and transmission line fluctuations. The experimental setup of 10-point quasi-distributed sensor was demonstrated in practice.
The ability for precise tuning of the cavity length was also used to achieve further improvements in strain sensor performance. First, fine tuning was applied in the design of a sensor with quadrature shifted output signals that resulted in an extended range, and an improved linearity of the measurement system. The second improvement comprises active compensation of temperature-induced strain using an additional compensating strain sensor. By proper fabrication of the compensating strain sensor we practically decreased the temperature-induced strain error by a factor of more than 10.
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