Page 600 - Introduction to Information Optics

584 10. Sensing with Optics

For the purpose of simplicity, assume that the power coupling coefficients
of the two couplers are 0.5 with no optical loss. In this case, the output light
intensity can be written as [13]

2
= / 0 cos | --(n s L s - n rL r) (10.8)

where I 0 represents a constant light intensity; L s and L r represent the sensing
and reference fiber lengths, respectively; n s and n r represent the sensing and
reference fiber refractive indices, respectively; and A is the operating
wavelength. Both n s and L s can change as a function of external perturbations
such as stress or strain. Thus, by detecting the change in the output light
intensity /, external perturbations can be sensed.
To minimize the influence from slowly changing environmental factors such
as temperature and enhance the performance of the fiber sensor, in many cases
the length of the reference arm is periodically modulated [14]. This can be
realized by winding the reference arm fiber on a PZT drum. A sinusoidal
electric signal is added on the PZT drum so that the diameter of the drum is
periodically modulated by the sinusoidal electric signal, which in turn results
in the periodic change in the reference arm fiber length.
Note that interferometric fiber sensors are usually constructed using conven-
tional single mode optical fibers. Conventional single mode fiber can support
two orthogonal polarization modes, owing to such effects as bending, the fiber
becomes birefringent. This effect can result in a change in the interference fringe
visibility. Thus, the signal-to-noise ratio of the sensing signal can be influenced
by this effect [15]. To overcome polarization-induced effects in fiber inter-
ferometry, methods include (1) using polarization-preserving fiber throughout
the entire sensor system; (2) actively controlling the input polarization state;
and (3) employing polarization diversity techniques in which certain output
polarization states are selected to avoid polarization fading [16,17].

10.2.3.2. Fiber-Optic Sensor Based on the Michelson Interferometer

Figure 10.9 shows a kind of Michelson interferometer-based fiber-optic
sensor. In this case, a single directional coupler is used for both splitting and
recombining the light. The light traveling from the source is split into the
sensing and reference arms. After traversing the length of the arms, the light is
reflected back through the same arms by reflectors. The light is then recom-
bined by the initial beam splitter.
There are similarities and differences between Michelson and Mach-Zeh-
nder interferometers. In terms of similarities, the Michelson is often considered
to be a folded Mach-Zehnder, and vice versa. Thus, from this argument one