Principle of IFFPIs Based on FBGs

2.1.1.1.2.1 Low-Reflectance IFFPIs Based on FBGs By using a pair of FBGs with a reflective band, IFFPI sensors can be formed. Wan and Taylor proposed an IFFPI sensor based on FBG pairs for temperature measurement [10]. Two short sections, 2 mm in length, were cut from a 2-cm-long FBG and spliced with a SMF in between. The cavity length is 15 mm. The original reflectance of the 2-cm-long FBG is almost 100% and that of the 2-mm FBG mirrors is ~2%. The reflected beams from the FBG pairs interference and fringes can be detected.

Due to the low reflectance of the FBG pairs, the reflection of the IFFPI sensor can be considered by the two-beam interference model, similar as shown light gray curve in Figure 1.6. The reflectance of such an IFFPI sensor can be expressed as

where r1 and r2 are the reflectance of the two FBGs. ф = 4nnL/X is the round-trip phase shift, where n is the effective refractive index of the fiber mode, L is the cavity length of the IFFPI, and X is the wavelength. The use of weak FBGs for forming the IFFPI sensor is beneficial for multiplexing.

By using a wavelength-swept distributed feedback (DFB) laser, the wavelength and the peak intensity of the interference fringes can be determined as a function of the ambient temperature. The temperature was measured in the range of 25-170°C with a resolution of 0.005°C.

  • 2.1.1.1.2.2 High-Reflectance IFFPIs Based on FBG The performance of the IFFPI sensor based on FBG may degrade if there is a mismatch in the spectral profile of the weak FBG pairs. Niu et al. [11] investigated the performance of the IFFPI sensor by using high-reflectance FBGs, that is, strong FBGs. The incident beam was reflected by multiple times between the two strong FBGs, which can amplify the effect of fiber strain on the phase changes of the beam. Therefore, high sensitivity can be achieved by using the high-reflectance IFFPI sensors. Furthermore, the linewidth of the interference fringes becomes narrower and is beneficial for high-resolution spectral measurement. The transmission spectra of the high-finesse IFFPI sensors can be found in Figure 1.8.
  • 2.1.1.1.2.3 Advantages of FBG-IFFPIs: High Mechanical Strength, Multiplexing, Absolute Measurement, and Large Dynamic Range IFFPI sensors based on FBG can stand strain of up to 12,000 RE as the FBG inscription process does not require any cleaving or splicing over the sensor region [12]. IFFPI sensors based on low-reflectance FBG pairs can be used for multiplexing. A total of 50 sensors were experimentally multiplexed by the frequency-division multiplexing method, and the capacity was theoretically estimated to be 500 sensors [13]. Compared with other types of IFFPI sensors, IFFPI sensors based on FBG have the advantages of low insertion loss and small spectral width for each sensor, which greatly enhance the multiplexing capability of IFFPI sensors.

These sensors combine the advantages of both fiber-optic interferometric sensors and FBG sensors. Fiber-optic interferometric sensors often provide high resolution based on the phase-shift detection. However, they suffer from the ambiguity problem that the absolute measurement is not achievable by detecting only one interferometric wavelength, when using the broadband reflections such as the Fresnel reflection or other highly reflective coatings. If the wavelength shift is constrained within a single free spectral range (FSR), the dynamic range is small. On the other hand, FBG sensors have no ambiguity problems by detecting the unique Bragg wavelength, but the measurement resolution is about 1 p,?, which is limited by the wavelength interrogation method and the relatively wide 3 dB linewidth. The ratio of the dynamic range to resolution is around 103:1.

Rao et al. demonstrated an IFFPI sensor based on FBG for absolute strain measurement [14]. The bandwidth of the FBGs for forming the IFFPI cavity was ~0.5 nm and the reflectivity was 10%. The wavelength shift of the FBG versus strain was measured with an optical spectrum analyzer with a resolution of 1 pm. The phase change of the IFFPI cavity was detected by a lock-in amplifier. The Bragg wavelength shift is used for determining the fringe number, N, so that the absolute phase change of the IFFPI, ДФ + 2nN, is determined for the absolute strain sensing. By combining the advantages of both FBG and interferometric sensors, the ratio of the dynamic range to resolution is extended up to 2.4 X 104:1.

Compared with IFFPI with a single pair of Bragg gratings, the identification of the center of the fringe pattern is easier by multiple co-located pairs of FBGs and low-coherence interrogation [15]. FBG-IFFPI sensors can also be designed for dual-parameter measurement [16].

Chirped FBGs (CFBGs) have a wide reflection band of several to tens of nanometers [17], due to the nonuniform refractive index profile in the fiber core. IFFPI sensors can be formed by using two identical CFBGs. There are many transmittance peaks within the reflection band of the sensor. By using a pair of CFBGs with a linewidth of 20 nm and a narrow wavelength sweep range of 0.2 nm, the dynamic range of the sensor can be extended by 100 times compared with that of IFFPI sensors based on FBG. The linewidth and FSR of the IFFPI sensor based on CFBG were 5 and 65 pm, respectively [18].

 
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