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Innovative Fiber Bragg Grating Sensors for Highly Demanding Applications

Considerations, Concepts, and Designs

Lun-Kai Cheng, and Peter Martijn Toet TNO, Delft, The Netherlands

Abstract

Measurement of physical parameters using mechanical transducers is an important part of fiber optical sensing. Fiber Bragg grating (FBG)–based sensors with dedicated transducers can be designed to measure different physical parameters and can operate in extremely harsh environments. This makes the FBG sensor very suitable for special applications and has advantages over conventional electrical sensors. This chapter discusses the considerations for the development of FBG sensor systems for harsh environments and/or high performance. Applications, considerations, and designs of such sensors for a selected number of physical parameters (pressure, acceleration, and flow) will be discussed.

Keywords

Accelerometer; Fiber Bragg grating; Flowmeter; Harsh environment; Hydrophone; Pressure sensing

7.1. Introduction

The year 2015 was the International Year of Light. Specially for this occasion SPIE published the book Celebrating Light, in which 50 light-based technologies were selected and recognized to be essential to humanity [1]. These 50 applications of light vary from three-dimensional display technology to solar cells and the search for extraterrestrial life by using space telescopes. Among these 50 selected technologies, optical fibers play a key role in the following three revolutionary developments:

• the Internet
• quantum encryption
• structural health monitoring

The first two are related to the application of optical fibers for low-loss and long-distance data transport, for which the optical fiber was originally developed. The third topic is related to the unique properties of an optical fiber for sensing and monitoring. This includes the usage of fiber optic sensors in extreme environments and the possibility of multiplexing fiber optic sensors in a large-scale sensor network system.

Among the different types of fiber optic sensing technologies, the fiber Bragg grating (FBG) is the one most commonly used. The advantages of this technology include a multiplexing capacity for realizing a large sensor network, the flexibility to integrate sensors for different physical parameters into a single system (multiparameter sensing), and the relatively low-cost and high-quality components that are developed for telecom applications.

In this chapter, the basic operation of FBG sensors and the interrogation possibilities are briefly discussed. Thereafter, an overview of the considerations for developing FBG sensors for highly demanding performance or dedicated operational conditions are elaborated. In this, “dedicated conditions” stands for conditions other than the ambient environment. In the last part, the design concepts of a selected number of (mechanical) sensors based on FBG technology will be explored.

7.2. Fiber Bragg Grating Sensor System

In 1978, Hill [2] reported for the first time the change in refractive index in germanium-doped silica fiber by UV exposure. This mechanism was used by Meltz in 1989 to produce an FBG [3].

The FBG has a wavelength-dependent reflection R, which can be calculated using the coupled-wave theory for optical waveguides [4]:

R (λ) = \frac{\sin h^{2} [k L \sqrt{1 - (δ / k)}]}{\cos h^{2} [k L \sqrt{1 - (δ / k)} {(δ / k)}^{2}]}

$R (λ) = \frac{\sin h^{2} [k L \sqrt{1 - (δ / k)}]}{\cos h^{2} [k L \sqrt{1 - (δ / k)} {(δ / k)}^{2}]}$

(7.1)

where k is the coupling constant, L is the length of the grating, and δ is the detuning factor, which is a function of the wavelength. The center reflection wavelength λ_B, also known as the Bragg wavelength, corresponds theoretically to a maximum reflection in Eq. (7.1). This Bragg wavelength can be deduced from Eq. (7.1) and can be calculated as

λ_{B} = 2 n_{e f f} Λ

$λ_{B} = 2 n_{e f f} Λ$

(7.2)

where n_eff is the effective index of the mode propagating in the optical fiber and Λ the period of the refractive index modulation. In an FBG sensor, a change in n_eff and/or Λ will result in a shift in the reflection wavelength λ_B according to Eq. (7.2). The physical parameters that are directly linked to n_eff and/or Λ, and hence the reflection wavelength λ_B, are:

• strain (ε)
• temperature (T)
• hydrostatic pressure (P)

The sensitivity of λ_B to each of these parameters has been described in many papers [5]:

Δ λ_{B} = 2 (Λ \frac{\partial n_{e f f}}{\partial ε} + n_{e f f} \frac{\partial Λ}{\partial ε}) Δ ε + 2 (Λ \frac{\partial n_{e f f}}{\partial T} + n_{e f f} \frac{\partial Λ}{\partial T}) Δ T + 2 (Λ \frac{\partial n_{e f f}}{\partial P} + n_{e f f} \frac{\partial Λ}{\partial P}) Δ P

$Δ λ_{B} = 2 (Λ \frac{\partial n_{e f f}}{\partial ε} + n_{e f f} \frac{\partial Λ}{\partial ε}) Δ ε + 2 (Λ \frac{\partial n_{e f f}}{\partial T} + n_{e f f} \frac{\partial Λ}{\partial T}) Δ T + 2 (Λ \frac{\partial n_{e f f}}{\partial P} + n_{e f f} \frac{\partial Λ}{\partial P}) Δ P$

(7.3)

Strain and temperature are regarded as the primary sensing parameters for an FBG sensor. The sensitivity for strain under standard environmental conditions is typically ∼1.2 pm/με, described by the first term in Eq. (7.3). For temperature this sensitivity is ∼10 pm/K, second term in Eq. (7.3). The sensitivity of an FBG in a bare fiber for hydrostatic pressure has been evaluated by different groups and is found to be about −3 pm/MPa, third term in Eq. (7.3) [6].

In recent years, much research has been done in the field of writing FBGs into fibers. Nowadays two trends can be observed in the manufacturing of FBGs: first, FBGs with “standard” specifications for the high-volume market in which cost reduction or flexible manufacturing is important [7–9], and second, FBGs for nonstandard applications such as stable FBGs for high-temperature applications and FBGs in polarization-maintaining (PM) fibers, photonic crystal fibers, polymer fibers, or active fibers.

For the three primary sensing parameters, the sensitivity of the FBG is determined by the material properties and geometry of the optical fiber. To measure the physical parameter–introduced wavelength shift, an interrogator is used. The sensitivity to the parameters is a combination of the sensitivity of the FBG and the wavelength resolution of the interrogator. Because the sensitivity of the FBG to the primary sensing parameters is fixed, the total sensitivity is determined by the wavelength detection properties of the interrogation system. Most of the commercially available FBG interrogation systems have a wavelength resolution on the order of 1 pm. This system performance corresponds to a resolution in the primary parameters of ∼1 με, ∼0.1K, and ∼0.3 MPa. For most strain or temperature measurements, this resolution is sufficient. Different versions of strain and temperature FBG sensors are commercially available [10–12]. For practical pressure-sensing applications, the resolution of ∼0.3 MPa is in general too low.

To measure other physical parameters [e.g., (acoustic) pressure, acceleration, electrical current, flow, etc.] a properly designed transducer is used to convert the desired physical parameter into a strain on the FBG. Even an FBG-based chemical sensor can be realized by attaching the FBG to a material that deforms in the presence of the target chemical material, e.g., hydrogen, relative humidity, CO₂, etc. [13–15].

The following sections will give an overview of high-end system performance (Section 7.3), considerations for dedicated operational conditions (Section 7.4), and examples of FBG sensor designs for special physical parameters (Section 7.5).

7.3. High-Demand Fiber Bragg Grating Sensor System Performance

The system performance is the combination of the performance of the FBG sensor(s) and the interrogator. This combination results in a total system with system properties including sensitivity, frequency response, noise level, number of sensors, dynamic range, etc.

The critical properties/characteristics of high-end performance of FBG sensor systems are identified as:

1. high sensitivity
2. high-speed measurement
3. large number of sensors

In this section the influence of the interrogation technology on the three aforementioned properties will be discussed. The development of dedicated interrogators for special applications will be discussed in Section 7.3.4.

Other specifications, e.g., noise level and dynamic range linearity, can be relevant for an application. These system specifications are dedicated to a particular application, and require detailed optimization of all the components and the entire system. These detailed system design optimizations are not included in this chapter.

7.3.1. High Sensitivity

Commercial high-end interrogation systems such as those of Micron Optics [16,17], FAZ Technology [18], and Smart Fibres [19] with improved sensitivity can detect subpicometer wavelength shifts. This corresponds to sub-με strain change sensing or <0.1K temperature change measurement. For several high-end industrial applications of strain and temperature sensing this sensitivity is sufficient. This trend enables high-accuracy measurements using already developed (standard) sensors.

For even more demanding applications, higher sensitivity of the interrogator might be required. This can be realized by using, for example, (fiber) interferometric detection technology with which subfemtometer wavelength changes can be measured. This technology is mostly used for highly sensitive dynamic measurement, e.g., hydrophones. However, no commercial systems based on (fiber) interferometers for generic application are available.

7.3.2. High-Speed Measurement

The required speed of a measurement using an FBG sensor depends on the application and the information to be deduced from the measurement data. A readout speed of tens of hertz is sufficient for almost all temperature measurements and semistatic strain measurements of civil structures. Most of the commercial interrogation systems provide this sampling frequency. For applications such as acoustics (Section 7.5.3), vibration measurement (Section 7.5.4), or detection of pressure pulses or impact-induced shock waves in composite construction, a larger measurement bandwidth is needed.

High-speed commercial interrogators are available [20–23]. Different configurations have been used by different research groups to achieve high speeds even up to 100 MHz [24,25].

7.3.3. Large Number of Sensors

One of the advantages of FBG sensors is the inherent capacity for multiplexing in the wavelength domain. This technology is well known as wavelength domain multiplexing (WDM). For sensor applications, the required reflection optical bandwidth of the FBG depends on the interrogation technology. In general, two FBGs of which the center wavelengths are separated by typically 1–2 nm can be identified and measured without significant cross talk. The number of FBG sensors multiplexed in the wavelength domain depends on the operational wavelength range of the interrogation system and the expected wavelength shift of each FBG sensor. Commercial interrogators operate in general within the C-band and have a range of about 40 nm. For each FBG, a working range of 2 nm is required, with an additional 2 nm to avoid cross talk. As a result, typically 10 FBG sensors can be installed in a single optical fiber and multiplexed in the wavelength domain. An interrogation system with a larger operational wavelength range, up to ∼160 nm, is available to increase the number of sensors on a single fiber [16].

Another multiplexing technology to realize a large FBG sensor network is time domain multiplexing (TDM). This technology is used to expand the number of sensors beyond the capacity of WDM alone. An example of a TDM and WDM configuration is shown in Fig. 7.1.

Although the concept of combining TDM and WDM was already presented decades ago, it is used only for dedicated FBG sensor networks with a very large number of sensors [26].

7.3.4. Development of Dedicated Interrogators

Owing to the increasing acceptance of fiber optic sensor technologies, the number of applications of FBG sensor systems has also grown. A standard interrogator (designed for generic laboratory use) is no longer suitable for many kinds of field applications. The development of dedicated interrogators is desired. The distinct trends for dedicated interrogators that can be identified are low cost, low power consumption, small footprint, and special applications such as space or biomedical:

• Small-size interrogator [27–29]
A small-size interrogator is in general lightweight and enables the development of FBG sensor systems for portable applications. This development can contribute to future wearable sensors [30–32]. One of the technology developments for small interrogators is to fabricate the optical and electronic components with integrated optics technology [33].
• Low cost, low power consumption, and stand-alone system
The application of integrated optics technology to reduce the size and weight of the interrogator is also beneficial to the development of low-cost and low-power interrogators. The manufacture of integrated optic components is based on lithographic technology used in the semiconductor industry: the production of integrated circuits. Using lithographic technologies, even extremely complex components such as computer processors can be manufactured with high yield for a relatively low price. Integrated optical components such as arrayed waveguide gratings [34] for wavelength (de)multiplexing and planar light wave circuits as beam splitter/combiners are standard components for the telecom industry. Incorporating the active electrooptical components such as light source and detector with integrated optics technology will result in a hybrid device with low power consumption.

Figure 7.1 Example of a combination of an array of fiber Bragg gratings with different wavelengths for wavelength domain multiplexing and time separation by a pulsed light source and delay lines for time domain multiplexing.

• Interrogator for space application
Optical fiber sensors can be used under harsh environmental conditions, and by using FBG technology a system for multiparameter sensing can be developed. These properties are interesting for space applications [35]. Using an FBG sensor system in space requires a space-qualified interrogation system. Such developments were demonstrated beginning in 2006 by groups in different space research programs [28,36–39]. The main issues for the components are radiation hardness and vacuum compatibility. For the entire interrogator for space application, the volume, mass, and power consumption are also critical. Furthermore, the interrogator has to be designed to survive the high vibration and shock levels during launching.

7.4. Fiber Bragg Grating–Based Sensors for Dedicated Operational Conditions

Fiber optic sensors were first used for defense applications. Following this development, in the 1990s, oil and gas industries recognized the advantages of using optical fiber sensors in harsh environments such as the high temperatures experienced downhole. The lifetime of conventional electrical sensors at such high operating temperatures is limited. Therefore, no permanent monitoring of physical parameters downhole was possible with electrical sensors. The first application of fiber optic sensors for downhole use in the 1990s was distributed temperature sensing (DTS) using Raman scattering–based technology. Soon after the first deployment of a DTS system, the application of using FBGs for pressure and temperature sensing was investigated by many groups [40].

For the development of FBG sensors that can be applied to situations with harsh and exceptional operational conditions, attention must be paid to the individual components, e.g., fiber, FBG, coating, packaging, etc. Some of the operational conditions for the various applications and the corresponding approaches/solutions are summarized in the following paragraphs.

7.4.1. High Temperature

In contrast to electrical sensors, which usually consist of many different materials, the basic material of an optical fiber is silica. Silica can withstand high temperatures up to ∼1000°C, which is regarded as a key advantage for sensor applications such as downhole in oil wells, installations in process industry, energy installations, motors and combustion systems, etc. For high-temperature applications, not only must the optical fiber survive the high temperatures but also the FBG itself, the connectors and bonding, mounting, and packaging materials.

7.4.1.1. Optical Fiber

A bare optical fiber consists of a core and cladding, both of silica. For practical use, a polymer coating is usually applied to the 125-μm-diameter optical fiber. Depending on the application and installation procedures, extra or other coating materials and packaging can be manufactured around the fiber. The operational temperature of the standard optical fiber with acrylate coating is limited to <80°C. For applications at higher temperatures, manufacturers provide polyimide-coated optical fibers, which can be used up to ∼300°C [41]. Metal (copper, aluminum, gold)-coated optical fiber can be manufactured for use at even higher temperatures [42,43]. Depending on the environment, high-temperature fiber is also needed as lead-in and lead-out fiber for realizing the FBG sensor network.

7.4.1.2. Fiber Bragg Grating

The grating pattern of a standard FBG can be erased at high temperatures. To solve this problem, improvements in laser writing technologies and processes have been made since 2012 to extend the operational temperature range. The new-generation chemical composition grating and regenerated FBGs can survive temperatures up to 1000°C using a standard silica fiber [44]. For higher temperatures, the application of sapphire fibers in which an FBG was written using a femtosecond laser was investigated [45].

7.4.1.3. Adhesives

For the measurement of high temperature, a bare optical fiber with the aforementioned FBG for high temperature is sufficient. High-temperature adhesives or welding can be used to fix the lead fiber in between the FBG temperature sensors at the desired location. The bare-fiber FBGs for temperature measurement have only to be isolated from mechanical strain. For the measurement of other physical parameters at high operational temperatures, a mechanical transducer is required to convert the target physical parameter, e.g., pressure, into a strain in the FBG. In this situation the high-temperature FBG has to be mounted onto the mechanical transducer. Care must be taken to select and apply the high-temperature adhesive to the FBG. Inhomogeneous glue distribution over the FBG needs to be avoided. This will affect the local strain transfer and cause inhomogeneous strain along the FBG, which can result in a broader reflection spectrum of the FBG. This is a well-known phenomenon encountered when using FBGs embedded in composite structures for structural health monitoring [46].

7.4.2. Cryogenic Temperature

Different unique advantages of fiber optic sensors are vital for applications at cryogenic temperatures. Applications vary from monitoring of fuel tanks under cryogenic temperatures for space, to LNG installations with a totally passive sensor system without explosion danger, to applications where superconducting magnets are used (e.g., MRI systems or nuclear fusion installations). Other possible applications are temperature, strain, and vibration monitoring of the superconducting magnet construction in MRI or nuclear fusion installations. Optical fibers and FBGs can operate at cryogenic temperatures even down to <4K. The environmental conditions for cryogenic applications determine the selection of the materials and type of fiber and FBG to be used. For space and nuclear fusion applications, the effect of radiation has to be considered, and radiation-hard optical fibers and FBGs will be required. For fuel tank and LNG applications, the packaging of the FBG sensor must be designed and manufactured to resist the chemical compounds of the environment.

7.4.3. High Operational Pressure

The optical fiber including the FBG is made of pure silica and can survive extremely high hydrostatic pressure. This is very useful for applications such as downhole, defense research, deep sea, etc. However, for high-accuracy measurements under high operational pressure, the nonnegligible sensitivity of the FBG to hydrostatic pressure has to be considered and, if necessary, correction has to be applied.

7.4.4. Vacuum

Vacuum compatibility is an issue mainly related to space applications. Silica optical fibers and FBGs can be used under vacuum conditions. Care has to be taken for the practical installation of the fiber optic components. Suitable fiber coating and packaging materials must be used to avoid outgassing and contamination of other highly sensitive instruments such as optical systems in space. Furthermore, special feedthroughs are required to connect optical fiber components in the vacuum part and the pressurized part [47].

7.4.5. Radiation

Radiation-induced attenuation and refractive index change due to radiation in an optical fiber are well-known effects [48]. They are caused by the interaction of radiation with doping materials such as phosphorus (P) and germanium (Ge) in the core of the silica fiber [48]. Especially for applications in space or nuclear fusion installations, this effect must be addressed. The most widely used solutions are either packaging of the optical fiber with proper shielding materials/construction or using a specially developed optical fiber that is less sensitive to radiation. The so-called radiation-hard fibers use a pure silica core without doping materials. The pure silica core optical fiber is available from various suppliers [49,50]. The pure silica core solves the problem of refractive index change under radiation, but because of the stable refractive index, it is difficult to manufacture an FBG using standard UV exposure. New FBG writing technologies have been developed to overcome this issue. Radiation-hard FBGs are commercially available from different suppliers, e.g., TechnicaSA [51] and FemtoFiberTec [52].

7.4.6. Hydrogen

When an optical fiber is exposed to hydrogen, bonding of hydrogen to the germanium doping in the core will result in an increase in the attenuation of the optical fiber [53]. This issue arises, in particular, for optical fibers used for downhole sensing or structural health monitoring of hydrogen fuel tanks [54]. The latter is also relevant for space applications [55]. A solution, widely used in the oil and gas industry, is to put mitigation barriers between the optical fiber and its environment. The barriers vary from hermetically welded metal protection tubes to hydrogen-absorbing gels or carbon coatings around the fiber. A more basic solution that can be applied is the use of a pure silica core as in radiation-hard fibers. The pure silica fibers can also be applied to suppress the hydrogen-darkening effect in fibers. Free hydrogen intrusion into the core can still result in a wavelength-dependent attenuation, but the effect will be reduced significantly in comparison to standard optical fibers.

7.4.7. Low Stiffness Fiber

For an FBG sensor in which a mechanical transducer is used to convert the physical parameter into a strain in the FBG, the total sensitivity depends largely on the design and materials of the transducer. However, the smaller the mechanical transducer is, the more the stiffness of the fiber contributes to the total sensitivity of the transducer. For the development of a small sensor, e.g., for pressure sensing in medical applications, the stiffness of the standard optical fiber in which the FBG is manufactured can be the bottleneck for achieving the required sensitivity, simply because the mechanical force generated by the transducer is not sufficient to elongate the standard silica fiber with a diameter of 125 μm. This problem can be solved by reducing the stiffness of the optical fiber, either by decreasing the amount of material or by decreasing Young's modulus E of the optical fiber.

The first solution is relatively easy to implement. In addition to the standard silica fiber with a diameter of 125 μm for telecom applications, optical fibers with a smaller outer diameter of 80 μm and even down to 40 μm have been developed. FBGs written in a 40-μm fiber are mainly used by Tokyo University for embedding in composites for structural health monitoring of aerospace structures [56].

The second solution of reducing Young's modulus E of the optical fiber can be realized by using polymer optical fibers (POF). The material of the POF is mainly based on polymethyl methacrylate (PMMA). In comparison to Young's modulus of a silica fiber of ∼70 GPa, that of a PMMA-based fiber is a few gigapascals. The stiffness of a POF is about a factor of 20 lower than that of a silica fiber.

7.5. Fiber Bragg Grating–Based Sensors for Special Physical Parameters

In the early 1980s, technology programs of over $100 million were started for the development of acoustic pressure sensors (hydrophones) and gyroscopes for defense applications [57]. The sensing technologies used for the gyroscope and hydrophone were based on fiber interferometer technology. The investments in this technology also enabled the development of other fiber optic key components/technologies and increased the acceptance of fiber optic sensing systems for other applications. This, in turn, benefited other fiber optic sensing technologies, including FBG sensors.

An FBG is primarily sensitive to strain and temperature. For the application of FBG to measure other physical parameters, a transducer is required to convert the physical parameters to be measured into a strain of the FBG. Proper design of the transducer is essential for the performance of the sensor and must be optimized for the target specifications and operational conditions. This requires careful trade-off analysis of different design parameters and the use of dedicated components, as mentioned in Section 7.3. In this section, information about the applications, considerations, concepts, and designs of FBG sensors for the following selected physical parameters will be elaborated:

• high-pressure sensor
• miniaturized pressure sensor
• hydrophone for acoustic measurement
• accelerometer
• flow sensor

Owing to differences in the applications and design considerations, the use of FBGs for pressure sensing is divided into three categories: high-pressure sensors, small pressure sensors, and the hydrophone for acoustic pressure sensing. For each sensor type, the main applications and, when applicable, the typical working range will be discussed.

7.5.1. High-Pressure Sensors

Measuring high pressures of 100 bars or even higher is mainly of interest for oil and gas or process industries to monitor the conditions of the production process. Other applications of high-pressure sensing are the measurement of pressure pulses in explosions for defense research and pressure sensing in industrial installations, e.g., turbines, combustion engines, etc. [58].

In addition to the primary sensing parameters (strain and temperature), a standard FBG in a bare optical fiber is also sensitive to hydrostatic pressure. The hydrostatic pressure sensitivity, for an FBG in a standard telecom fiber, was found to be about −3 pm/MPa = −0.3 pm/bar [59]. To measure a pressure change of 0.1 bar, a wavelength shift of ∼0.03 pm has to be detected. Current high-end interrogation systems, e.g., FAZ Technology FAZT I4, Micron Optics SM130, etc., have a wavelength repeatability approaching the target value. However, owing to the cross-sensitivity of the FBG with temperature, a wavelength shift of 0.03 pm also corresponds to a temperature change of ∼0.003°C. For high-pressure measurement in which only the high-speed pressure changes are relevant, e.g., pressure pulses in pipelines of process industry or explosion pressure measurement for defense research, the slow temperature effects have a longer time scale and can be ignored or filtered out in the frequency domain. The temperature cross-sensitivity effect is considered to be not negligible for absolute or low-frequency pressure measurement.

7.5.1.1. Concepts for Reduced Pressure and Temperature Cross-Sensitivity

The issue of temperature cross-sensitivity of the FBG pressure sensor can be solved by the following sensor design concepts:

1. correction of temperature effects using a second FBG temperature sensor;
2. using common-mode configuration to cancel the temperature effect;
3. using a mechanical transducer (plate, tube);
4. enhanced side-hole fiber pressure sensor.

This will be elaborated briefly in this section.

7.5.1.1.1. Correction of Temperature Effects Using a Second Fiber Bragg Grating Temperature Sensor

In case the temperature can be measured with sufficient accuracy (on the order of 0.001°C), the temperature cross-sensitivity to the pressure measurement using the bare FBG can be corrected by a second FBG, which measures the temperature only (see Fig. 7.2). For practical implementation of this solution, the temperature-sensing FBG has to be isolated from the high pressure, while the temperature of both FBGs has to be equal to within 0.001°C. This solution can be used only for high-pressure sensing in an environment with a homogeneous temperature distribution in the area of the two FBGs. This is expected to be difficult to realize for most applications.

Figure 7.2 Two fiber Bragg gratings (FBGs) with the first FBG for pressure sensing and the second for temperature correction.

As far as is known to the authors, the concept of bare FBGs for pressure sensing is used only for research purposes. No commercial product is available.

7.5.1.1.2. Using Common-Mode Configuration to Cancel the Temperature Effect

This concept is an extension of the aforementioned solution of using a separate FBG temperature reference sensor. The basis of this approach is to obtain a measurement with two FBGs that have different pressure sensitivity but the same temperature sensitivity. This common-mode configuration is achieved by making one single FBG in a special PM fiber, the so-called side-hole fiber. In the side-hole fiber, two holes along the fiber are manufactured next to the core (see Fig. 7.3).

Figure 7.3 Side-hole fiber with the holes aligned in the x direction. The y axis experiences the load from the hydrostatic pressure while the x axis is isolated by the side holes. There is one physical fiber Bragg grating in the core and hence the λ_B,x and λ_B,y will have the same temperature response.

The refractive index distribution of a PM fiber is non–rotationally symmetric. This results in two perpendicular optical axes (fast and slow axes) in a PM fiber. Owing to the non–rotationally symmetric design of the PM fiber, the fundamental modes propagated in each optical axis will have different effective refractive indices: n_eff,x and n_eff,y. An FBG with a period of Λ manufactured in a PM fiber will, according to Eq. (7.2), have different reflection wavelengths, λ_B,x and λ_B,y, for the two optical axes. Both λ_B,x and λ_B,y have the same temperature dependence, which results in the common-mode configuration for temperature. In the late 1980s, different groups [60,61] proposed the application of a side-hole fiber to measure pressure. For the side-hole fiber shown in Fig. 7.3, hydrostatic pressure will cause a direct mechanical load to the y axis while the x axis is isolated from the direct hydrostatic pressure. This results in a configuration with effectively two FBGs for the two polarizations with different pressure sensitivity:

λ_{B, x} = C_{P, x} P + C_{T, x} T

$λ_{B, x} = C_{P, x} P + C_{T, x} T$

(7.4a)

λ_{B, y} = C_{P, y} P + C_{T, y} T

$λ_{B, y} = C_{P, y} P + C_{T, y} T$

(7.4b)

λ_{B, x} - λ_{B, y} = (C_{P, x} - C_{P, y}) P + (C_{T, x} - C_{T, y}) T

$λ_{B, x} - λ_{B, y} = (C_{P, x} - C_{P, y}) P + (C_{T, x} - C_{T, y}) T$

(7.4c)

For the coefficients C_T,x = C_T,y, the wavelength peak separation λ_B,x − λ_B,y between the FBG reflection wavelengths for the two polarization states is a direct measure of the hydrostatic pressure P, while the effect of temperature is compensated for.

Schlumberger Ltd. demonstrated a measurement using this concept up to 10 kpsi (=69 MPa). The sensitivity of peak separation to pressure is measured to be about 470 pm/10 kpsi = 6.8 pm/MPa. According to Schroeder [62] the pressure measurement is nearly independent of the tested temperature range from 25 to 100°C.

7.5.1.1.3. Using a Mechanical Transducer (Plate, Tube)

Using a mechanical transducer to amplify the pressure sensitivity of a fiber optic sensor is the most widely used solution to increase pressure sensitivity. At the beginning of fiber optic sensor development, this approach was used to enable the development of interferometric fiber optic hydrophones for acoustic pressure sensing. This solution relies on the mechanical design and the dimensions of the transducer. The sensitivity and the pressure working range can be optimized for the FBG-based pressure sensor. The most widely used configuration of the transducer is a bending plate (of circular shape). A circular bending plate mounted on the housing of a chamber will deform if the outer pressure differs from the internal pressure of the chamber (Fig. 7.4). The deformation can be used to stretch an FBG and the pressure difference is converted to a strain in the FBG, which results in a wavelength shift. The FBG can either be surface-mounted on the plate or attached through the center of the plate (Fig. 7.4) to have a piston-like configuration.

Figure 7.4 Basic concepts of using a bending plate for a fiber Bragg grating (FBG) pressure sensor. (A) The FBG is surface-mounted to the bending plate and measures the surface strain. (B) The FBG is connected through the center of the sensing plate. The center displacement is converted to a strain in the FBG.

In Fig. 7.4A, the concept of a circular bending plate with simple support and a surface-mounted FBG is sketched. The pressure-induced surface strain is investigated extensively. The sensitivity S_ss, defined as the ratio between the surface strain ε and the pressure difference P, is proportional to

1 / E_{t}^{2}

$1 / E_{t}^{2}$

where E is Young's modulus of the plate material and t is the thickness of the plate. Higher sensitivity can be achieved by a thinner plate. However, the maximum pressure P_m,ss before collapse is proportional to t². There is a trade-off between the sensitivity S_ss and the maximum pressure P_m,ss. The choice of the dimensions and material of the plate has to be optimized according to the application requirements. For high-speed pressure-change measurement, a flat frequency response of the sensor is mostly required. Therefore, the resonance frequency of the bending plate has to be designed to be higher than the required measurement bandwidth.

Another bending plate sensor design is the clamped support in which the edge is fixed to the housing (Fig. 7.4B). The exact expression for the sensitivity S_cl and the maximum pressure P_m,cl differs from that of the simple support design, but the consideration for the trade-off between these two parameters is the same.

7.5.1.1.4. Enhanced Side-Hole Fiber Pressure Sensor

Using an FBG in a side-hole PM fiber to measure high hydrostatic pressure as shown in Section 7.5.1.1.2 can cancel out the temperature effect significantly. The pressure sensitivity is limited by the mechanical properties of the silica fiber but can be enhanced by using an extra mechanical transducer. This was demonstrated by Yamate [63]. The trade-off is a more complex sensor design, as shown in Fig. 7.5.

In contrast to the hydrostatic loading of the side-hole fiber, the concept presented by Yamate generates lateral load to the side-hole PM fiber by a piston. The force to the optical fiber is proportional to the area exposed to the ambient (high) pressure. An extra dummy fiber with the same dimension is used for a stable and well-defined load transfer. The response of the sensor was measured up to 5000 psi (=∼34.5 MPa) for temperatures varying from 20 to 150°C. The pressure sensitivity was measured to be ∼0.33 pm/psi (=∼48 pm/MPa), which is much higher than that of a standard FBG. Using an interrogator with 0.05-pm resolution, a pressure change of about 0.001 MPa (=0.01 bar) can be detected.

7.5.1.2. Examples of Commercial and Special Systems for High Pressure

7.5.1.2.1. Example of Commercial Bending Plate Type of High-Pressure Sensor

FBG pressure sensors are currently commercially available from various suppliers (Micron Optics, FiberSensing, FBGS, Smart Fibres). Most of these pressure sensors were developed for general applications and are not targeted to high pressure. For high-pressure high-temperature (HPHT) applications downhole, an FBG pressure sensor named SmartPort has been developed by Smart Fibres for permanent downhole pressure monitoring. The pressure working range is 1000 bars with a pressure resolution of <1 bar. The sensor is designed to operate at temperatures up to 200°C. Furthermore, several SmartPorts can be connected to realize a multidrop distributed pressure-sensing (DPS) system that can be used for downhole fluid level determination [64]. Up to 24 sensors can be connected with two fibers.

Figure 7.5 Basic concept of a sensor developed by Schlumberger Ltd. to combine a side-hole fiber with FBG to cancel out the temperature sensitivity and a mechanical transducer for increasing the pressure sensitivity. FBG, fiber Bragg grating.

7.5.1.2.2. Other Concepts for Spliceless Distributed Pressure Sensing

For the application of the FBG high-pressure sensor in a harsh environment such as downhole, the connections between the individual pressure sensors need special attention to ensure they are rigid and stable. Therefore, using a tube construction, which can be manufactured in long lengths by available cable production technology, in combination with an FBG array without any splice will result in a spliceless FBG for quasi-DPS. The sensing cable can be manufactured in long lengths and is potentially rigid because the FBG array can be embedded and protected by a protective layer during the production process. Two concepts for high-pressure application are shown in Fig. 7.6.

Figure 7.6 Two spliceless concepts for quasi–distributed pressure sensing based on a pressure tube design. (A) The optical fiber with the fiber Bragg grating (FBG) array is embedded in the tube. (B) Concept with an FBG surface-mounted between two rigid rings attached to the tube.

In the concept of Fig. 7.6A, the optical fiber is embedded in a hollow tube in a helix configuration [65]. A difference in pressure inside and outside the tube will deform the tube and result in a strain in the embedded optical fiber. FBGs incorporated into the fiber are used to measure the strain in the optical fiber to provide information about local pressure differences. In the other concept, in Fig. 7.6B, a simple mechanism is constructed around each pressure-sensing FBG on the hollow tube [66]. This mechanism consists of two rigid rings at the two sides of the pressure-sensing FBG to ensure a constant diameter of the tube at the location of the rings. When the inside pressure P₀ of the tube is higher than the local pressure P outside, the tube wall between the two solid rings will expand. This tube deformation will be accompanied by a strain of the surface on which the FBG is mounted. This pressure-induced strain is picked up by the FBG sensor, which results in a shift in the FBG reflection wavelength. A demonstrator setup has been built to demonstrate the concept. The demonstrator metal pressure tube is 15 mm in diameter (less than the target diameter of 1 in. for downhole application). The inner pressure can be tuned manually, and the response of the proof-of-concept sensor is measured up to 100 bars. The wavelength of the FBG as a function of the pressure was measured and the sensitivity was calculated to be 1.2 pm/bar (=12 pm/MPa).

Using the spliceless concept mentioned earlier combined with an interrogation with large multiplexing capacity, quasi-DPS covering long distances can be realized.

7.5.2. Miniaturized Pressure Sensor

The category of miniaturized pressure sensor with small dimensions is partially covered by using a bare fiber to measure high pressure in the range of megapascals. However, the pressure sensitivity, on the order of 3 pm/MPa, is not sufficient for the major application of small pressure sensors, i.e., for (bio)medical purposes. In vivo pressure measurement with a small sensor is a key asset for cardiology, urology, neurology, pulmonology, gastroenterology, ophthalmology, rheumatology, and cancer treatment [67]. The required pressure resolution for (bio)medical applications can be down to 0.1 mmHg (=13 Pa). In addition to (bio)medical applications, small pressure sensors with high sensitivity can also be used for pressure measurement at locations that are difficult to access and/or environments where electrical pressure sensors are not preferred, e.g., strong electromagnetic interference/radio-frequency interference/MRI environments.

Many in vivo medical instruments are disposable or meant to be used a few times only. Therefore the design of the instrument including the small FBG pressure sensor has to be optimized for low production cost. The market is potentially large but approval for medical applications is subject to strong regulation and requires considerable effort. Various fiber optic-based pressure sensors have been developed and commercialized [67,68]. They are mainly based on Fabry–Perot technology and are commercially available from several suppliers (FISO, Opsens, Samba Sensors, etc.). FBG-based technology provides the possibility of multiplexing a number of pressure sensors in a single fiber to measure in vivo pressure distribution. Designs for the mechanical transducer for pressure sensing are mostly based on the bending plate as mentioned in previous sections. Two configurations of the bending plate concept for a small dimension sensor are shown in Fig. 7.7.

The configuration in Fig. 7.7A was used by Singlehurst [69]. The FBG is mounted through the center of two plates inside the pressure sensor housing. Owing to the opening in the sensor housing, the pressure around the FBG is equal to the environmental hydrostatic pressure. A pressure difference between P and P₀ of the closed chambers will result in a deformation of the two plates and an axial strain in the FBG. A sensor with an outer diameter of 1.07 mm and length of 4.2 mm was fabricated. The sensitivity was measured to be about 0.3 pm/mmHg (=2250 pm/MPa).

Another configuration of bending plates has been demonstrated by different groups using an FBG attached to the surface of the bending plate (Fig. 7.7B) [70–72]. Using a rectangular bending plate/beam results in a thin pressure sensor.

Figure 7.7 Two widely used mechanical concepts for small-dimension pressure sensors. (A) Based on movable/deformable plates to stretch the fiber Bragg grating (FBG). (B) The bending plate concept using a rectangular bending beam.

Figure 7.8 A pressure sensor designed for in vivo vascular pressure measurement [70].

Table 7.1

System Requirements for In Vivo Vascular Pressure Sensor
Requirement	Value
Pressure range	−10 to 300 mmHg
Pressure resolution	<0.35 mmHg
Operational temperature range	20–45°C
Temperature resolution	0.03°C
Diameter of sensor element	≤1 mm
Length of sensor element	≤5 mm
System readout frequency	1000 Hz

The pressure sensor shown in Fig. 7.8 was developed for in vivo vascular pressure sensing. The total sensor also includes temperature measurement using a separate FBG. The corresponding requirements are shown in Table 7.1.

Using a standard silica fiber with a diameter of 125 μm, the mechanical pressure sensitivity was modeled to be 3930 με/MPa. The sensor was tested by a pressure signal of 0.04 MPa (=300 mmHg). The pressure sensitivity was measured to be 4000 pm/MPa. To achieve the target pressure resolution of 0.35 mmHg, a wavelength resolution of 0.187 pm was required. Using an interrogation system with a resolution of 0.1 pm, the target pressure requirement can be met.

For the small-dimension pressure sensor, the stiffness of the silica optical fiber is no longer negligible for the mechanical response of the sensor. The solution of using a thinner silica fiber or POF was mentioned in a previous section. An example of using ultrathin silica fiber with diameter ranges from 20 to 65 μm for pressure sensors was presented by Dennison [73] The hydrostatic pressure sensitivity was measured to be about −60 pm/MPa, which is about a factor of 20 higher than a bare FBG.

7.5.3. Hydrophone

One of the earliest high-end applications of fiber optic sensors was the hydrophone for underwater acoustic pressure sensing for defense applications [74,75]. The development of this technology was later adapted for seismic applications [76,77], and different systems have been commercialized. Before the discovery of FBGs, the first-generation fiber optic hydrophone was mainly based on a fiber optic interferometer [78,79] and had a complex mechanical mandrel design [80] as well as a complex fiber optic topology [81] to achieve the required sensitivity (Fig. 7.9). The bending plate design has also been investigated [82–84]. The mandrel design is preferred for its small diameter, which can easily be incorporated into an array configuration, which is required for towed array applications [85].

For both defense and seismic applications, extremely low pressure signals must be detected. A system detection limit below the ambient acoustic noise level is desired. This is mostly identified to be the sea-state 0 (SS0), which is about

45 dB μ Pa / \sqrt{Hz}

$45 dB μ Pa / \sqrt{Hz}$

at 1 kHz [86]. Interferometric fiber optic sensor systems with a detection level near SS0 have been developed and demonstrated [87,88].

Owing to the availability of FBGs since around 2005, different concepts and designs have been presented for hydrophones based on FBGs. As for the small-dimension pressure sensors discussed earlier, a piston and bending plate can be used as mechanical transducer concepts. In the literature, the piston-based hydrophone is mostly reported.

7.5.3.1. Frequency Response

In contrast to the high-pressure sensor and the small-dimension pressure sensor, which can be used for measurement of both static and dynamic pressure, a hydrophone is used to sense dynamic acoustic signals. Therefore, the operational frequency range is a key parameter of the hydrophone. This results in extra design constraints. The mechanical construction has to be designed so that the lowest resonance frequency is significantly higher than the highest acoustic frequency of interest in the application. For a given design concept, a higher resonance frequency corresponds in general to a stiffer construction. However, the stiffer the construction is, the smaller the acoustic pressure-induced displacement of the mechanical construction will be. This means a lower strain to the FBG and hence a lower sensitivity. Consequently, for the design of the FBG hydrophone, there is a trade-off between the operational frequency range and the mechanical sensitivity. In publications about FBG hydrophones, the lowest resonance frequency of the sensor is not always reported. Therefore, care is required when comparing the specifications of different FBG hydrophones.

7.5.3.2. Example of Piston Design

In the publication by Zhang [89], the development and tests of a piston type of FBG hydrophone were reported. The effect of the dimensions of the sensor and the materials on the pressure sensitivity were elaborated extensively. For an outer diameter of the cylinder tube of 10 mm the pressure sensitivity was measured to be 7.0 nm/MPa. This is about 2000 times better than the standard bare fiber. Another design reported by Huang [90] demonstrated a sensitivity of 3.64 nm/MPa and had a resonance frequency at 9 kHz.

As mentioned before, the minimum detectable pressure level is determined by the combination of the mechanical pressure sensitivity and the noise level of the FBG interrogation system. To achieve a system noise level equal to the SS0 of

\sim 45 dB μ Pa / \sqrt{Hz}

$\sim 45 dB μ Pa / \sqrt{Hz}$

, extreme performance of the FBG interrogation system will be required. For the FBG hydrophone example reported by Zhang [89], with a mechanical sensitivity of 7.0 nm/MPa, to detect acoustic signals in the range of the SS0, an FBG interrogation technology with a wavelength noise level of

\sim - 118 dB pm / \sqrt{Hz}

$\sim - 118 dB pm / \sqrt{Hz}$

will be needed. The most widely used detection technologies for the FBG wavelength change are interferometers or the use of a laser wavelength at the slope of the FBG reflection peak. In the fiber interferometer technology, the light reflected from the FBG is split into two paths with an optical path difference (OPD). After the light from the two paths is recombined, interference occurs. The phase ϕ of the interference signal is equal to 2πOPD/λ_B. Using a detection interferometer, a shift of the FBG reflection wavelength Δλ_B is converted to a phase change Δϕ with [91]:

Δ ϕ = 2 π OPD \frac{Δ λ_{B}}{λ_{B}^{2}}

$Δ ϕ = 2 π OPD \frac{Δ λ_{B}}{λ_{B}^{2}}$

(7.5)

From the results of the phase change measurement, the change in Δλ_B can be calculated. The sensitivity Δϕ/Δλ_B of the interferometer is proportional to the OPD and can be optimized for the application requirements.

In the solution that uses a laser with the wavelength λ_L on the slope of the FBG reflection peak (Fig. 7.10), the reflected optical power of the laser will change according to the reflection wavelength Δλ_B of the FBG. The sensitivity and the measurement range depend on the slope of the FBG reflection spectrum [92], while the noise level and the detection limit are determined by the stability (wavelength and optical power) of the laser, the detector noise, and the performance of the analog-to-digital converter.

Figure 7.10 Detection of the fiber Bragg grating (FBG) wavelength shift using a small-linewidth laser.

7.5.3.3. Bending Plate Hydrophone Design

The bending plate design is less used in combination with the standard FBG hydrophone. However, the development of a distributed feedback (DFB) fiber laser hydrophone using a rectangular bending beam to realize a slim hydrophone array has been reported by different groups [93,94]. A DFB fiber laser is an FBG technology-based component that has been developed for telecom applications. Stretching the grating structure of the DFB laser will result in a shift of the laser wavelength. This is similar to the operation of an FBG. Because the linewidth of the DFB laser is much smaller in comparison with an FBG, the coherence length is much longer. Owing to this long coherence length, an interferometer with a much longer OPD can be used to achieve a larger scale factor (Δϕ/Δλ_B) in Eq. (7.5). Using the DFB fiber laser with a bending beam mechanical design, a hydrophone with extreme sensitivity can be developed. Foster [93] reported this configuration to achieve SS0 pressure sensitivity. This fiber laser hydrophone system is also proposed for cosmic ray detection [94].

7.5.4. Accelerometer

Accelerometers have many applications varying from monitoring the vibration of civil construction to structural health monitoring of aerospace structures, navigation, and seismic exploration. The development of FBG accelerometers is mainly beneficial to applications in harsh environments or if a large sensor network is required.

The mechanical concept of an FBG accelerometer is based on a mass–spring configuration. The spring can be either a bending beam (cantilever) [95] or the optical fiber itself [96]. In the bending beam concept, the FBG is attached to the bending beam and the acceleration-induced deformation of the bending beam will generate a strain in the FBG. In this concept, the FBG is protected by the bending beam. In the concept of using the FBG as a spring, a higher sensitivity can be achieved. Research development mainly focuses on increasing the sensitivity. Two concepts of a mass–spring system are shown in Fig. 7.11.

Figure 7.11 Concepts for using a mass–spring system for acceleration measurement. (A) The simplest concept, using the optical fiber as the spring. (B) An advanced setup demonstrated by Mita [96] to improve sensitivity and stability. FBG, fiber Bragg grating.

As for the fiber optic hydrophone, the operational frequency range is an important parameter for the FBG accelerometer. There is also a trade-off between the sensitivity and the resonance frequency of the accelerometer. For comparisons between FBG accelerometers, this has to be taken into account. The results of two publications about FBG accelerometers for different frequency ranges are shown in this section. Liu [97] designed and reported an accelerometer with a resonance frequency of ∼1200 Hz and a sensitivity of 23.8 pm/g. Li [98] demonstrated a sensor for a lower frequency range. The resonance frequency was 25 Hz. Owing to the lower stiffness of the mechanical transducer, a higher sensitivity of 1333 pm/g can be realized.

FBG accelerometers are already commercially available from several suppliers, e.g., Alxenses, FiberSensing, Smart Fibres, Micron Optics, Brüel & Kjær, etc. Information about the mechanical design is rarely provided. The accelerometer from Brüel & Kjær has a special design [99](Fig. 7.12). The design is based on two symmetrical balanced cantilevers with identical mass. Owing to the design, an acceleration in the indicated direction will result in a rotation of the two cantilevers in opposite directions, which causes a strain in the FBG mounted between them. This concept minimizes the cross-sensitivity from acceleration in other directions. A sensitivity of 20 pm/g was demonstrated in combination with a resonance frequency of 3.1 kHz. A commercial version including housing and fiber optic connectors was developed to multiplex an array of FBG accelerometers for measurement in industrial environments.

Figure 7.12 The Brüel & Kjær fiber Bragg grating accelerometer. (A) The mechanical design. (B) The commercial version including housing and fiber connection.

7.5.5. Flowmeter

High-accuracy flow sensing is vital for the process and oil and gas industries. In this section, two concepts to measure flow speed are discussed.

The first concept is based on flow-induced vortex pressure fluctuation to generate a strain signal that is detected by an FBG [100]. The second concept uses hot-wire anemometry and converts the flow speed into a temperature that is measured by the FBG. The hot wire is the optical fiber itself. This concept was presented by Gao [101]. The small diameter of the fiber makes flow measurement in small pipeline systems possible.

7.5.5.1. Vortex Flowmeter

In this section, the concept of an FBG vortex flow sensor for HPHT application is described. Vortices are a well-known physical phenomenon in fluid dynamics. Behind an object (bluff body) placed in a flow, an alternating pressure is generated (see Fig. 7.13). The frequency f_V of vortex shedding is proportional to the flow velocity U, according to [102]

f_{V} = S t \frac{U}{W}

$f_{V} = S t \frac{U}{W}$

(7.6)

where St is the Strouhal number and W is the width of the bluff body.

Figure 7.13 Vortex shedding behind a bluff body in a flow [103].

Figure 7.14 (Left) Sensor concept design. (Right) Three-dimensional model of a fiber Bragg grating (FBG) vortex flow sensor.

Vortex shedding has been used to construct an FBG vortex flow sensor. The design concept of this sensor is shown in Fig. 7.14. The sensor is realized by a triangle bluff body combined with a thin tail section: the sensor plate. The sensor plate vibrates in response to the vortex shedding pressure fluctuation. The FBG is integrated into the sensor plate and measures the vibration-induced strain variation of the plate (Fig. 7.14).

According to Eq. (7.6), the relevant parameter for the measurement is the vortex shedding frequency f_V. The measurement is to a large extent insensitive to variation in both the amplitude (intensity) of the FBG reflection and the amplitude of the strain.

7.5.5.1.1. Design and Optimization of High-Temperature and High-Pressure Vortex Flow Sensor

For downhole application, an HPHT vortex flow sensor has been developed. The target operational specifications are >300°C and >100 bars. The relation between the applied flow speed and the vortex shedding frequency f_V measured by the FBG sensor is shown in Fig. 7.15. A linear relation is observed for flow speed ranges from 0.5 to ∼25 m/s.

Figure 7.15 Results from a fiber Bragg grating vortex flow sensor.

This FBG vortex flow sensor for high temperature and high pressure is currently commercialized by Smart Fibres [104].

7.5.5.2. Hot-Wire Anemometry-Based Fiber Bragg Grating Flow Sensor

Anemometry using electrical heating wire is a widely used technology for flow-speed measurement [105]. When a heated wire is placed in a flowing environment, the flow will abduct the heat and cool down the wire. For a constant energy supply, the temperature of the heated wire is a function of the flow speed of the medium. Using a combination of a cobalt-doped fiber and an FBG, an all optical fiber–based hot-wire anemometer can be realized [101]. In this concept, an FBG is manufactured in a short piece of cobalt-doped fiber, which is spliced to a standard optical fiber. The Co-doped fiber has an absorption coefficient of about 5 dB/cm at 1480 nm. Pumping the fiber with this wavelength will convert the optical power into heat to realize an optically heated fiber. The FBG manufactured in this fiber operates in the 1550-nm wavelength window (C-band) and is used to monitor the temperature of the heated fiber. Flow around the optically heated fiber will remove the heat and lower the temperature of the fiber. The application of this flow sensor is demonstrated both in air [101] and in liquid [106]. The relation between the FBG wavelength and the air flow speed for different pump powers has been investigated and reported [101]. The wavelength change as a function of the flow speed is similar to the response of the electrical hot-wire anemometer. The same model, data processing, and data analysis can be applied to the FBG-based concept. For sufficient pump power and sensitivity of the interrogation system, a series of the Co-doped optical heated fiber can be realized in an array configuration for distributed flow sensing (see Figs. 7.16 and 7.17).

Figure 7.16 Fiber Bragg grating (FBG)-based anemometer test setup using a heated Co-doped fiber in combination with an FBG for temperature measurement.

Figure 7.17 Test results for the anemometry-based fiber Bragg grating (FBG) flow sensor in water. The FBG temperature is measured as a function of the water flow speed.

Acknowledgments

The authors would like to thank Wim de Jong, Ernst-Jan Buis, and James Day for fruitful discussions; the TNO Optics Department for preparing this chapter; and Smart Fibres, Brüel & Kjær, and Hong Kong Polytechnic University for granting their permission to use information about their technologies and products.

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Table of Contents for 7. Innovative Fiber Bragg Grating Sensors for Highly Demanding Applications: Considerations, Concepts, and Designs

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