Page 612 - Introduction to Information Optics

596 10. Sensing with Optics

Frequency
Modulation

Fig. 10.18. An optical setup for optical frequency-domain reflectometry.

effects such as Rayleigh scattering) and there is only one perturbation at
location, x, which results in a reflectivity r(x). The returned light signal from
the testing fiber can be written as

ax i2lix
= A Qr(x)e~ e , (10.14)

where A 0 is a constant, and /i is the propagation constant. For the purpose of
simplicity, let

R(x) = A 0r(x)e- (10.15)

Note that R(x) is related to the disturbance distribution. Once this R(x) is
obtained, the disturbance along the fiber can be determined. Due to the
introduction of R(x), Eq. (10.15) can be rewritten as

= R(x)e i2px . (10.16)
However, in real cases, the reflection may not come from one point. The
reflection itself is a distribution. Thus, Eq. (10.16) needs to be written as the
summation from the contributions of different locations. Mathematically, it can
be written as

= R(x)e i2tix dx, (10.1,7)

where L is the total length of the testing fiber.