Two types of DAS system

Intensity-based system
- first gen
- not quantitive
- cheaper & robustness
- Amplitude of Rayleigh backscattered energy
Phase-based system
- second gen
- quantitative
- expansive

Intensity based system

The perturbed fiber will have a different intensity image:

2-m fiber -> non-linear and random. Not easy to use.

Complicated, but could provide quantitative result.

The first pulse: \(\delta\phi_1(z,t_1)=\phi(z+\delta z, t_1)-\phi(z,t_1)=2k\Delta z+c_0\)

The second pluse: because of the strain in fiber, there will be a distortion \(\delta z\).

\[\delta\phi_2(z,t_1)=\phi(z+\delta z, t_2)-\phi(z,t_2)=2k\Delta z+2k\delta z+c_0\]

The differential phase: \(d\phi(z, t_1) = \delta \phi_2-\delta \phi_1=2k\delta z\)

Note that \(\delta z\) is much smaller than \(\Delta z\). Change in length will change in refractive index(assume it’s linear).

Then, \(\delta \phi = \frac{4\pi nL_G}{\lambda}[\frac{\Delta x}{x}+\frac{\Delta n }{n}]\)

–> \(\delta \varepsilon_{xx}(t, x_j)\approx 1.16\times 10^{-10}\delta \Phi(rad)\)

Note that this is happened in one time and one channel.