Principles of Fiber-Optic Fabry-Perot Interferometric (FFPI) Sensors
The history of FP sensors began at the turn of the nineteenth century with derivatives of the parallel-plate interferometer. Sensors for voltage and pressure measurement were described by Perot and Fabry . After that, Meggers and Peters used FP interference to measure the refractive index . In this book, we focus on FFPI sensors which are based on two-beam, three-beam, and multi-beam interferences, respectively.
The principles of FFPI sensors are mainly explained according to Equation 1.3. When perturbation is introduced to the sensor, the phase difference is influenced with the variation in the OPD of the interferometer. By measuring the shift of the phase or wavelength spectrum, the sensing parameter applied on the FFPI sensor can be quantitatively obtained. The free spectral range (FSR), the spacing between adjacent interference peaks in a spectrum, is also influenced by the OPD variation.
The principle of two-beam interference is the coherent addition of two reflectors with low reflectance. The typical structure is formed by the Fresnel reflections of two fiber ends. As shown in Figure 1.3a, supposing the intensity of the incident light is I, the reflectance of the fiber end is r, that is, ~4%. The transmission t is ~96%. Inr and Int are the reflective intensity and transmitted intensity of the nth reflected beam, respectively. The intensities of the light are shown in Table 1.1. The intensities from the reflected end are I1r, I3t, I5t, and so on.
Table 1.1 Reflective and Transmitted Intensities from a FPI with Low Fresnel Reflection of 4%
Obviously, after the third reflection, the intensity I3r is much lower than the first two, so the influence of I3r can be neglected. It means that it is enough to consider only two reflected beams.
Suppose that the length of the cavity is h, and the refractive indexes of the fiber and the medium between the reflectors are n and n0, respectively. The OPD is A = 2nh + k/2, where k/2 is the half-wave loss because the two beams of the interference occurred by two planes with different properties.
The intensity of the interference, I, can be calculated as
where I1 and I2 represent the intensities of reflected beams from the two fiber end faces. The parameter V is often used to describe the contrast ratio of the interference fringe. When I2/I1 = 1, V = 1, and when I2/Ij = 0 or ^, V = 0. When the interference of the two beams is the same (I1 = I2 = I0), Equation 1.7 can be written as
The typical optical spectrum of the two-beam interference is similar to a sinusoidal function, as shown in Figure 1.3b, according to Equation 1.9. When A = mk, where m = 0, 1, 2, ... , the interference intensity becomes maximum and if A = (m + 1/2)k, where m = 0, 1, 2, ... , the interference intensity becomes minimum. For fiber end faces, the reflectance is nearly 4%, so I1 and I2 are about 4% I- and 3.69% I, and Equation 1.7 can be simplified as
As A relies on the characteristics of the cavity, the changes of the cavity, such as length and refractive index, the optical spectrum will be shifted and can be used for sensing.
These kinds of FFPI sensors have simple structures and low cost. However, as the reflectivity of the FFPI cavity formed by two fiber ends is low, the optical power of reflected interferometric signal is normally small. In order to overcome the drawback of the two-beam FFPI, optical amplification (OA) can be effectively used to enhance the signal level . The operating principle of such an FFPI/OA system is illustrated in Figure 1.4. Light from a broadband amplified spontaneous emission (ASE) source, consisting of an Er-doped fiber (EDF), a 1550/980-nm wavelength-division multiplexer (WDM) coupler, an isolator, and a pump laser, is launched into the FFPI. As shown in the enlarged view of the FFPI, a lead-in fiber and a reflecting
Figure 1.4 Two-beam FFPI sensing system with OA.
fiber are inserted into a hollow quartz tube. A certain air gap of several hundred micrometers between the two flat fiber ends is used to form the FP cavity. The interferometric signal from the FFPI is amplified by the EDF and then detected by an optical spectrum analyzer (OSA).