**4. Challenges in Brillouin based distributed optical fiber sensors**

#### **4.1. Simultaneous measurement of strain and temperature**

sources are simultaneously modulated also in a sinusoidal function. Subsequently, the optical frequency offset between pump and probe or between scattered Stokes and optical oscillator changes with time as well as position, deviating from the preset constant frequency offset around the BFS νB. Only at some particular locations (called correlation peaks), the frequency offset is maintained as the constant frequency offset because of the in-phase condition so that the local SBS interaction or the beating of the local Stokes and oscillator is **constructive**. At other locations rather than correlation peaks, the frequency offset is always vibrating with time, which leads to a broadened and **destructive** SBS or SpBS. The spatial resolution of

> , <sup>2</sup> n

where *f*m is the modulation frequency of the sinusoidal function, ∆*f* the modulation depth, and ∆νB the Brillouin linewidth defined in Eq. (10). Since the SOCF is naturally realized by an integral or summation signal processing in photonics or electronics, all SBS or SpBS along the entire FUT should be accumulated together (as an example shown in Fig. 6(a), accumulated by a LIA). Consequently, the maximum measurement length (or sensing range, *L*CD) is decided

*m*

. <sup>2</sup> *CD* <sup>=</sup> *m*

Because of the difference of the physical pictures between time domain and correlation domain, their sensing performance is different. For example, the spatial resolution of BOTDA/ BOTDR was typically limited to be ~1 m by the lifetime of acoustic phonons (10 ns) and the nature of intrinsic Brillouin linewidth. However, BOCDA/BOCDR is of CW nature free from this limitation, and their spatial resolution can be ~cm-order [60, 68] or even ~mm-order [69]. Since BOTDA/BOTDR carries out the whole mapping of BGS along the FUT during the time-

*<sup>c</sup> <sup>L</sup>*

<sup>D</sup> D= ×

*<sup>c</sup> <sup>Z</sup>*

*CD*

by the distance between two neighboring correlation peaks [59]:

p

D *B*

*nf f* (34)

*nf* (35)

BOCDA and BOCDR are both determined by[59]

**Figure 12.** Schematic of sensing of location or mapping of BGS.

22 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

As explained in **Section 3**, all Brillouin based distributed optical fiber sensors interrogate the Brillouin frequency shift so as to deduce strain and temperature information based on Eq. (29). It naturally gives a physical challenge, i.e. how to distinguish the response of strain from the response of temperature based on the single parameter of BFS interrogation in a single piece of sensing fiber. In current industrial practices, two individual fibers or two fibers in a fiber cable are used to discriminate the strain and the temperature: the first one is embedded or bonded at the target material/structure to feel the total responses of strain and temperature, while the second fiber is placed beside the first one and kept in loose condition so that it feels the response of temperature only. Another way is to use two distributed sensing systems with two individual fibers [72-75]: one Raman-based or Rayleigh-based sensor is to monitor the temperature; the other Brillouin sensor to monitor the temperature and strain. After distrib‐ uted sensing measurements, the strain and temperature responses can be calculated by mathematics. However, the above practices make the entire sensing system complicated and the calculated responses of strain and temperate change with service time.

Practical applications of Brillouin based distributed optical fiber sensors require a method to effectively discriminate them by use of two intrinsic parameters (denoted by y1 and y2) in one sensing fiber. Their changes (∆y1 and ∆y2) depend on simultaneously the applied strain (∆*ε*) and temperature change (∆*T*), which are governed by the following matrix:

$$
\begin{pmatrix} \Delta \mathbf{y}\_1 \\ \Delta \mathbf{y}\_2 \end{pmatrix} = \begin{pmatrix} A\_1 \ B\_1 \\ A\_2 \ B\_2 \end{pmatrix} \begin{pmatrix} \Delta \mathcal{E} \\ \Delta T \end{pmatrix}, \tag{36}
$$

where *A*<sup>1</sup> (*A*2) and *B*<sup>1</sup> (*B*2) are the strain and temperature coefficients of y1 (y2), respectively. Both ∆*ε* and ∆*T* can be deduced from Eq. (36), given by

$$
\begin{pmatrix} \Delta \mathcal{E} \\ \Delta T \end{pmatrix} = \frac{1}{A\_1 \mathcal{B}\_2 - B\_1 A\_2} \begin{pmatrix} B\_2 & -B\_1 \\ -A\_2 \ A\_1 \end{pmatrix} \begin{pmatrix} \Delta \mathcal{y}\_1 \\ \Delta \mathcal{y}\_2 \end{pmatrix}, \tag{37}
$$

It is obvious to know that the condition that the strain and temperature can be successfully distinguished is determined by

$$A\_1 B\_2 \neq B\_1 A\_2. \tag{38}$$

In fact, the Brillouin-based distributed sensing system always suffer a measurement uncer‐ tainty (∆y1 and ∆y2), which is in a linear proportional relation with the discrimination errors in strain (∆*ε*) and temperature (∆*T*), also given by Eq. (37).

A possible solution using one fiber is to monitor two acoustic resonance peaks at different orders of Brillouin gain spectrum (BGS) in a specially-designed optical fiber [13, 37, 76, 77]. So far, this method cannot ensure accurate discrimination because all the acoustic resonance frequencies exhibit similar behaviors in their dependences on strain and temperature (see Fig. 11) [49]. There is another kind of method reported for discrimination that relies on the possibility that the peak amplitude and BFS of the BGS could have quantitatively different dependences on strain and temperature [78-81]. Its accuracies is not sufficient (e.g., several degrees Celsius and hundreds of micro-strains), which is mainly due to the low signal-to-noise ratio in the BGS peak-amplitude measurement particularly for distributed sensing where troublesome noise from non-sensing locations is accumulated.

#### **4.2. System limitation of time-domain or correlation-domain technique**

There are several system limitations in time-domain BOTDA/BOTDR and correlation-domain BOCDA/BOCDR, which comes from their individual sensing techniques. For example, BOTDA/BOTDR suffers a typical limitation of spatial resolution (~1 m) mainly determined by the linewidth of BGS or the lifetime (~10 ns) of acoustic phonons. Narrower pulse width corresponding to higher spatial resolution according to Eq. (33) weakens the acoustic phonons due to the lifetime of the acoustic phonons and leads to broader BGS as well as lower frequency accuracy due to the convolution between the intrinsic BGS and broader spectrum of the pulse [82, 83]. Moreover, although the time-of-the-flight feature of BOTDA/BOTDR is suitable for long distance sensing, the nature of pump depletion and fiber transmission loss confines the maximum of measurement range within several tens of kilometers [84].

On the other hand, BOCDA/BOCDR can provide extremely high spatial resolution of cm order or mm order with a cost of system complexity. However the correlation-domain sensing nature means that there intrinsically exist periodic correlation peaks in the fiber. Besides, the nominal definitions of spatial resolution and measurement range (see Eq. (34) and Eq. (35)) show that they both depend on the modulation frequency and thus they are in a tradeoff relation with each other [59]. The accumulation of the entire BGS along the FUT corresponding to the measured BGS at the sensing location should include a highmagnitude background of the BGS at the uncorrelated positions, which makes it difficult achieve large range of strain or temperature since higher strain or temperature change shifts the measured BGS closer to the background. As introduced in **Section 3.2**, the access ability of BOCDA/BOCDR is random and the sensing speed in one location is high. However, the sensing speed along the entire FUT is still low and just comparable to BOTDA/BOTDR because the scanning of the sensing location is realized by changing the modulation frequency (see Eq. (35)), which needs quite long time to restart the communication among electronic devices (specially, function generator).
