## Abstract

A new technique for the fast implementation of Brillouin Optical Time Domain Analysis (BOTDA)
is proposed and demonstrated, carrying the classical BOTDA method to the dynamic sensing
domain. By using a digital signal generator which enables fast switching among 100 scanning
frequencies, we demonstrate a truly distributed and dynamic measurement of a 100m long fiber
with a sampling rate of ~10kHz, limited only by the fiber length and the frequency granularity.
With 10 averages the standard deviation of the measured strain was ~5 µε.

© 2012 OSA

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### Equations (3)

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(1)
$${T}_{scan}={N}_{avg}{N}_{freq}{T}_{round\_trip}$$
(2)
$$\begin{array}{l}{V}_{I}(t)={V}_{0}{\displaystyle \sum _{i=1}^{{N}_{freq}}rect\left(\frac{t}{{T}_{round\_trip}}+\frac{1}{2}-i\right)\mathrm{cos}\left[2\pi ({f}_{i}-{f}_{c})t\right]};\\ {V}_{Q}(t)={V}_{0}{\displaystyle \sum _{i=1}^{{N}_{freq}}rect\left(\frac{t}{{T}_{round\_trip}}+\frac{1}{2}-i\right)\mathrm{sin}\left[2\pi ({f}_{i}-{f}_{c})t\right]};\end{array}$$
(3)
$$\begin{array}{c}{V}_{RF}(t)={V}_{I}(t)\mathrm{cos}(2\pi {f}_{c}t)-{V}_{Q}(t)\mathrm{sin}(2\pi {f}_{c}t)\\ ={V}_{0}{\displaystyle \sum _{i=1}^{{N}_{freq}}rect\left(\frac{t}{{T}_{round\_trip}}+\frac{1}{2}-i\right)\cdot \left[\mathrm{cos}[2\pi ({f}_{i}-{f}_{c})t]\mathrm{cos}(2\pi {f}_{c}t)-\mathrm{sin}[2\pi ({f}_{i}-{f}_{c})t]\mathrm{sin}(2\pi {f}_{c}t)\right]}\\ ={V}_{0}{\displaystyle \sum _{i=1}^{{N}_{freq}}rect\left(\frac{t}{{T}_{round\_trip}}+\frac{1}{2}-i\right)\mathrm{cos}\left[2\pi \left({f}_{start}+\left(i-1\right){f}_{step}\right)\text{\hspace{0.17em}}t\right]}\end{array}$$