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582                       10. Sensing with Optics
          10.2.2.2. Polarization-Based Fiber-Optic Sensors

          Optical fiber is made of glass. The refractive index of the fiber can be
       changed due to the application of stress or strain. This phenomenon is called
       the photoelastic effect. In addition, in many cases, the stress or strain in
       different directions is different so that the induced refractive index change is
       also different in different directions. Thus, there is an induced phase difference
       among different polarization directions. In other words, under external pertur-
       bation, such as stress or strain, the optical fiber works like a linear retarder, as
       described in Sec. 10.2.2.1. Therefore, by detecting the change in the output
       polarization state, the external perturbation can be sensed.
          Figure 10.7 shows the optical setup for the polarization-based fiber-optic sensor
       [12]. It is formed by polarizing the light from a light source via a polarizer that
       could be a length of polarization-preserving fiber. The polarized light is launched
       at 45° to the preferred axes of a length of birefringent polarization-preserving fiber.
       This section of fiber serves as a sensing fiber. As mentioned earlier, under external
       perturbation such as stress or strain, the phase difference between two polarization
       states is changed. Mathematically speaking, d is a function of external perturba-
       tion; i.e., <5 = 6(p) where p represents the amount of possible perturbations. Then,
       based on Eq. (10.6), the output polarization state is changed according to the
       perturbation. Therefore, by analyzing the output polarization state by using an
       analyzer as the exit end of the fiber, as shown in Fig. 10.7, the external perturbation
       can be sensed. One of the major advantages of polarization-based fiber-optic-
       sensors is the capability of optical common mode rejection.
         To make the fiber-optic sensor practical, it must be sensitive to the
       phenomena it is designed to measure and insensitive to changes in other
       environmental parameters. For the strain or stress measurement, environ-
       mental temperature is an unwanted environmental parameter. For the polar-
       ization-based fiber-optic sensor, environmentally induced refractive index
       changes in the two polarization directions are almost the same. There is almost
       no induced phase difference between two polarization states; in other words,
       d x 0. Thus, environmental temperature fluctuation will not substantially
       deteriorate the performance of the sensor.



                           Polarization preserving fiber
                             \
                                         external stress or strain




       Light source                                              photodetecter
                       Polarizer                  analyzer
                        Fig. 10.7. Polarization-based fiber-optic sensor.
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