3.2 Extrinsic Fabry-Perot interferometers

Fabry-Perot based sensors are typically extrinsic in nature and used as a point measurement device at the tip of an optical fibre. A common construction of EFPI sensors involves a single mode fibre (SMF) spliced to a capillary with a multi-mode fibre (MMF) which acts as a diaphragm fused to the opposing end of the capillary, creating an air filled cavity between the SMF and MMF. Figure 2 highlights the dimensions relevant to diaphragm deflection and rigidity, with the construction presented in Figure 3. As light reaches the end face of the SMF a portion of the light is reflected, with the remainder transmitted into the air cavity. Similar reflections occur at the air-diaphragm, and diaphragm-external media interfaces. As the light reflected from the inner and outer faces of the diaphragm has travelled a greater distance, than the light reflected at the end face of the SMF, a phase difference between reflections will exist. While FPIs behave similar to FBGs in that they have varying refractive indices along the axial direction, adjustment of the diaphragm thickness can be used as a means of increasing pressure sensitivity by modifying the diaphragm flexural rigidity. Said flexural rigidity is determined by Eq. (4) [33] where h, E and ν are the diaphragm thickness, Young's modulus, and Poisson's ratio respectively. Eq. (5) [33] provides the relationship between diaphragm displacement and uniformly applied pressure, this being fundamental to the temperature sensor presented by Poeggel et al. [34]. From this it becomes apparent that a thinner diaphragm leads to greater maximum deflection, and said maximum deflection occurs at the diaphragm centre.

<sup>D</sup> <sup>¼</sup> Eh<sup>3</sup>

(PVD) to create a 'diaphragm', which was fused directly to an MMF [35]. This construction provides a number of advantages, such as a robust construction, and the ability to custom tune optical path lengths without the uncertainties related to splicing. Eq. (6) presents the relationship between the optical path differences (OPD) with the thermal coefficients of refractive index (αn) and material thickness

<sup>16</sup> � <sup>1</sup> � <sup>ν</sup><sup>2</sup> ð Þ <sup>R</sup><sup>2</sup> � <sup>r</sup><sup>2</sup>

Gao et al. proposed an alternative construction, using particle vapour deposition

Mach-Zehnder interferometers (MZIs) operate by splitting the source light and introducing an optical path difference, before recombining the beams prior to the detector [36]. As a means of sensing in optical fibres, common practice has been to splice a length of photonic crystal fibre (PCF) between two lengths of SMF [37–40]. These operate by allowing the core mode of the SMF to be split into core and cladding modes at the first splice point within the PCF. These are subsequently rejoined at the second splice point with an interference between the two modes becoming apparent in the transmission, this is usually represented by resonant dip (s) in the signal transmitted to the optical spectrum analyser (OSA). Modification to the air holes of the PCF is commonly carried out via collapsing or filling with various fluids, in order to increase sensitivity to the desired measurand. For the purpose of temperature sensing it is common to fill the PCF holes with a fluid which has a high magnitude (as it may be positive or negative) thermo-optic coefficient [37, 39, 41, 42]. Figure 4 below provides a schematic of how a typical MZI sensor setup is presented in literature. In a PCF the two branches of the MZI are the cladding and core modes respectively. A transverse section of a PCF is presented in

z rð Þ¼ <sup>3</sup>

Review of Liquid-Filled Optical Fibre-Based Temperature Sensing

DOI: http://dx.doi.org/10.5772/intechopen.80653

OPD Tð Þ OPD Tð Þ<sup>0</sup>

Figure 5 where the core, and cladding air holes are highlighted.

Sagnac interferometers (SIs) behave similarly to MZIs in that they compare optical path differences of two beams which have been split and subsequently recombined. However, they differ such as the two beams counter-propagate with

(αd) for the PVD diaphragm.

3.4 Sagnac interferometers

Schematic of Mach-Zehnder based sensor.

Figure 4.

101

3.3 Mach-Zehnder interferometers

12 1 � <sup>ν</sup><sup>2</sup> ð Þ (4)

≈ 1 þ ð Þ α<sup>n</sup> þ α<sup>d</sup> ð Þ T � T<sup>0</sup> (6)

Eh<sup>3</sup> � <sup>P</sup> (5)

Figure 2. Dimensions which influence diaphragm flexural rigidity and deflection.

Figure 3. Schematic of typical EFPI.

Review of Liquid-Filled Optical Fibre-Based Temperature Sensing DOI: http://dx.doi.org/10.5772/intechopen.80653

$$D = \frac{Eh^3}{12(1 - \nu^2)}\tag{4}$$

$$z(r) = \frac{\mathfrak{Z}}{16} \cdot \frac{(\mathfrak{1} - \nu^2) \left(\mathbb{R}^2 - r^2\right)}{Eh^3} \cdot P \tag{5}$$

Gao et al. proposed an alternative construction, using particle vapour deposition (PVD) to create a 'diaphragm', which was fused directly to an MMF [35]. This construction provides a number of advantages, such as a robust construction, and the ability to custom tune optical path lengths without the uncertainties related to splicing. Eq. (6) presents the relationship between the optical path differences (OPD) with the thermal coefficients of refractive index (αn) and material thickness (αd) for the PVD diaphragm.

$$\frac{\text{OPD}(T)}{\text{OPD}(T\_0)} \approx \mathbf{1} + (a\_n + a\_d)(T - T\_0) \tag{6}$$

### 3.3 Mach-Zehnder interferometers

3.2 Extrinsic Fabry-Perot interferometers

Applications of Optical Fibers for Sensing

occurs at the diaphragm centre.

Dimensions which influence diaphragm flexural rigidity and deflection.

Figure 2.

Figure 3.

100

Schematic of typical EFPI.

Fabry-Perot based sensors are typically extrinsic in nature and used as a point measurement device at the tip of an optical fibre. A common construction of EFPI sensors involves a single mode fibre (SMF) spliced to a capillary with a multi-mode fibre (MMF) which acts as a diaphragm fused to the opposing end of the capillary, creating an air filled cavity between the SMF and MMF. Figure 2 highlights the dimensions relevant to diaphragm deflection and rigidity, with the construction presented in Figure 3. As light reaches the end face of the SMF a portion of the light is reflected, with the remainder transmitted into the air cavity. Similar reflections occur at the air-diaphragm, and diaphragm-external media interfaces. As the light reflected from the inner and outer faces of the diaphragm has travelled a greater distance, than the light reflected at the end face of the SMF, a phase difference between reflections will exist. While FPIs behave similar to FBGs in that they have varying refractive indices along the axial direction, adjustment of the diaphragm thickness can be used as a means of increasing pressure sensitivity by modifying the diaphragm flexural rigidity. Said flexural rigidity is determined by Eq. (4) [33] where h, E and ν are the diaphragm thickness, Young's modulus, and Poisson's ratio respectively. Eq. (5) [33] provides the relationship between diaphragm displacement and uniformly applied pressure, this being fundamental to the temperature sensor presented by Poeggel et al. [34]. From this it becomes apparent that a thinner diaphragm leads to greater maximum deflection, and said maximum deflection

Mach-Zehnder interferometers (MZIs) operate by splitting the source light and introducing an optical path difference, before recombining the beams prior to the detector [36]. As a means of sensing in optical fibres, common practice has been to splice a length of photonic crystal fibre (PCF) between two lengths of SMF [37–40]. These operate by allowing the core mode of the SMF to be split into core and cladding modes at the first splice point within the PCF. These are subsequently rejoined at the second splice point with an interference between the two modes becoming apparent in the transmission, this is usually represented by resonant dip (s) in the signal transmitted to the optical spectrum analyser (OSA). Modification to the air holes of the PCF is commonly carried out via collapsing or filling with various fluids, in order to increase sensitivity to the desired measurand. For the purpose of temperature sensing it is common to fill the PCF holes with a fluid which has a high magnitude (as it may be positive or negative) thermo-optic coefficient [37, 39, 41, 42]. Figure 4 below provides a schematic of how a typical MZI sensor setup is presented in literature. In a PCF the two branches of the MZI are the cladding and core modes respectively. A transverse section of a PCF is presented in Figure 5 where the core, and cladding air holes are highlighted.

### 3.4 Sagnac interferometers

Sagnac interferometers (SIs) behave similarly to MZIs in that they compare optical path differences of two beams which have been split and subsequently recombined. However, they differ such as the two beams counter-propagate with

Figure 4. Schematic of Mach-Zehnder based sensor.

4.1 EFPI type sensors

high temperature resolution.

Figure 7.

103

Schematic of PDMS FPI sensor based on Chen et al. [46].

Chen et al. presented an FPI construction which contained an air micro-bubble encased in cured PDMS [46]. The sensor was manufactured by splicing an SMF to a hollow core fibre (HCF) 282 μm in length. The PDMS was subsequently introduced into the HCF via capillary effect. As PDMS entered the HCF it formed the air microbubble with the SMF, where the length of air micro-bubble was controlled by the period of time PDMS was allowed to enter the HCF. Online monitoring was conducted to establish the free spectral range (FSR) best suited to the desired

The PDMS was cured for 45 min at 338.15 K, fixing the length of the air microbubble. Testing was conducted between 324.35–343.65 K and compared to a PT100 thermometer with a resolution of 0.01 K. Results indicated sensitivity was quite high with a value of 2.7035 nm/K and a highly linear response where R2 = 0.992. In addition to the reported sensitivity, reference was made to the benefit of using a double FPI in the sensor. This consisted of a thin FPI (air micro-bubble) and thick FPI (PDMS filling). The thin FPI allowed for a large FSR and the thick FPI offered

Poeggel et al. [34] presented a novel ultra-high resolution temperature sensor (UHRTS). The sensor was comprised of an existing optical fibre pressure temperature sensor (OFPTS) [47] which was further encased in an outer oil-filled capillary. The sensor was noted to have an external diameter of less than 1 mm lending to its capability to be used in volume restricted areas, a schematic of the sensor is provided in Figure 8. By combining an FBG with the highly sensitive EFPI, the UHRTS behaved similar to that of Chen et al. [46] in that the FBG and air cavity allowed for a wide spectral range to be utilised with the diaphragm element providing high resolution. Dissimilar to Chen et al. however, the construction of the OFTS was reliant on the thin diaphragm element to transduce volume changes in the oil to a temperature measurement. This being in demonstrated by Eqs. (4) and (5) in Section 3. It was claimed that the high ratio of oil in the outer capillary compared to air in the EFPI cavity was what resulted in high sensitivity. The sensor presented had a reported, theoretical, sensitivity of 52.7 <sup>10</sup><sup>3</sup> nm/K. Comparison of the UHRTS to a Bosch BMP085 [48] was carried out over a temperature range of 7 K. While both sensors detected the 7 K variation, measured EFPI sensitivity was much lower than predicted, at 8.77 nm/K. It was suggested that the error was likely caused by inconsistencies in the manufacturing process of the sensor, and the presence of micro air bubbles in the oil which resulted in response damping. Considering oil was introduced into the capillary via a micro-syringe rather than by capillary effect as utilised by several authors such as Chen et al. [46] and Xu et al. [39] this may have

application. A schematic of the sensor is presented in Figure 7.

Review of Liquid-Filled Optical Fibre-Based Temperature Sensing

DOI: http://dx.doi.org/10.5772/intechopen.80653

Figure 6. Schematic of potential Sagnac interferometer based sensor.

respect to each other before being recombined at the detector. This type of interferometer is the basis of fibre-optic gyroscopes [43]. While it has been utilised in thermometry [44, 45] the sensors reported have not seen a similar level of research compared to their MZI counterparts. Reported sensors used a source beam counterpropagated by a 3 coupler. Birefringence in the PCF resulted in the optical path difference which was detected by the OSA [44, 45]. Figure 6 above highlights how an SI based sensor may be constructed using optical fibre equipment.
