Journal of Sensors

Volume 2016, Article ID 3204130, 10 pages

http://dx.doi.org/10.1155/2016/3204130

## Time and Frequency Localized Pulse Shape for Resolution Enhancement in STFT-BOTDR

^{1}Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK^{2}Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK

Received 2 September 2015; Revised 12 November 2015; Accepted 13 December 2015

Academic Editor: Marco Consales

Copyright © 2016 Linqing Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Short-Time Fourier Transform-Brillouin Optical Time-Domain Reflectometry (STFT-BOTDR) implements STFT over the full frequency spectrum to measure the distributed temperature and strain along the optic fiber, providing new research advances in dynamic distributed sensing. The spatial and frequency resolution of the dynamic sensing are limited by the Signal to Noise Ratio (SNR) and the Time-Frequency (*T-F*) localization of the input pulse shape.* T-F* localization is fundamentally important for the communication system, which suppresses interchannel interference (ICI) and intersymbol interference (ISI) to improve the transmission quality in multicarrier modulation (MCM). This paper demonstrates that the* T-F* localized input pulse shape can enhance the SNR and the spatial and frequency resolution in STFT-BOTDR. Simulation and experiments of* T-F* localized different pulses shapes are conducted to compare the limitation of the system resolution. The result indicates that rectangular pulse should be selected to optimize the spatial resolution and Lorentzian pulse could be chosen to optimize the frequency resolution, while Gaussian shape pulse can be used in general applications for its balanced performance in both spatial and frequency resolution. Meanwhile,* T-F* localization is proved to be useful in the pulse shape selection for system resolution optimization.

#### 1. Introduction

Dynamic strain measurement in distributed fiber optic sensing (DFOS) is essential for structural health monitoring (SHM) of the strain changes induced by aging material and seismic or man-made activities [1]. Since the first system was launched in 1999, due to its stability, reliability, and insensitivity to external perturbations, the distributed Brillouin sensor has become one of the most popular diagnostic tools for SHM in bridges, dams, pipelines, and piles [2]. Among the different DFOS systems, BOTDR launches pulsed light into one end of the fiber and detects the scattered spontaneous Brillouin signal at the same end [3, 4]. Single-end detection is convenient for fiber installation and on-site measurement. However, the large averaging number for a good Signal to Noise Ratio (SNR) and the slow frequency scanning method used in classical BOTDR have become obstacles to achieving dynamic measurement [5].

Recently, a fast-speed Short-Time Fourier Transform (STFT) based BOTDR applies a wideband detection architecture to replace the time-consuming frequency scanning method, which provides an opportunity for dynamic measurement. In the literature, the system successfully achieved a 16.7 Hz strain variation on a 12 m fiber section with 4 m spatial resolution and 45 *με* strain uncertainty [6]. The spatial resolution is the minimum detectable length of strain change and has been studied over the past decades to detect small cracks [7], while the strain uncertainty is the strain resolution for the measurement. A longer pulse or a longer rising/falling time will increase the interaction of the light photons and acoustic phonons and lead to a worse spatial resolution along the fiber [1].

BOTDR measures the peak frequency shift of the Brillouin scattering spectrum. SNR is the detective power density at spectrum’s peak divided by the power of the whole spectrum including the sidebands. The SNR of the detected Brillouin scattering spectrum at each point along the fiber reduces when the sideband of the pulse’s spectrum increases. Increased SNR will reduce average time of the measurement to enhance the speed of the analyzer to achieve real-site dynamic measurement [8]. SNR can be affected by the pulse power [9] and the pulse shape, which has significant impact on the spatial resolution, temperature, and strain resolution of the system [10–12].

Previous literatures compared time-domain and frequency-domain analysis independently to evaluate the analyzer performance. In 1999, Naruse and Tateda published the relation between the pulse width and the Brillouin backscattered light power and mentioned the trade-off between spatial resolution and frequency resolution [13]. In 2000, the same group announced that different pulse shapes would have different bandwidth of the spectrum and have different frequency-measurement error according to simulations [12]. Hao et al. in 2013 compared three pulse shapes including trapezoidal, triangular, and rectangular pulses and expressed that the Brillouin spectrum power of the triangular pulse shape was higher than the power of other pulse shapes [10, 14]. They also compared other pulse shapes, including Lorentzian, Gaussian, super Gaussian, and triangular shape, and concluded that the Lorentzian shape generated the biggest peak power of Brillouin spectrum and has the measurement accuracy when the Brillouin spectrum peak is set to the same level [11].

In the above previous studies, assumptions were made that the spatial resolution was identical to the pulse width (full width at half maximum (FWHM) of the pulse) and the Brillouin spectrum was affected by frequency-domain information. Spatial resolution can be enhanced by reducing the pulse edges (in time-domain) and frequency resolution can be enhanced by reducing the sideband in pulse spectrum (in frequency-domain). However, time-domain and frequency-domain information are identically important, which should be considered simultaneously to offer the design trade-off analysis between pulse width and frequency linewidth. For instance, when the frequency shifts (due to strain or temperature variation) are narrower than the FWHM, the spectrum will have double peaks and lead to complication in comparison [15], in which time- and frequency-domains’ analysis needs to be considered cooperatively.

The Time-Frequency (*T-F*) localization has been utilized in communication and signal processing [16–18], which generates sharp localization, offers small distortion, and reduces the interference such as intercarrier interference (ICI) and intersymbol interference (ISI) in OFDM communication. The resolution in frequency and time-domain in image processing and computer visions can be enhanced in real applications using *T-F* localization [19–22].

We introduce the* T-F* localization into the design consideration of the BOTDR system. In this paper, Time-Domain Effective-Pulse Width (TEW) and Frequency-Domain Effective-Pulse Linewidth (FEL) are defined to offer a comprehensive view to optimize the analyzer performance. Different pulses with the same FWHM may have different TEW and/or different SNR requirement in the detection and the FEL can be different. In particular, the variance in laser output power, noise level, or averaging number, and so forth, in the same pulse shape, can result in different spatial and frequency resolution. Similarly, the pulses with various effective linewidth can lead to different noise immune ability in the system.

This paper demonstrates the importance for* T-F* localized input pulses to improve the SNR of the Brillouin scattering signal, which leads to a narrower frequency bandwidth and an efficient pulse length to enhance the spatial and frequency resolution. The pulse localization model, based on the physical description of BOTDR and time-frequency analysis of the pulses with the definition of TEW and FEL, has been built to investigate the performance of various pulse shapes, such as Lorentzian, rectangular, Gaussian, and triangular pulses, which are compared theoretically and experimentally according to their performances in the time-domain (spatial resolution) and the frequency-domain (pulse modulated Brillouin spectrum linewidth). The comparison of the four pulse shapes offered matched results in simulation and experiment in the same system and improved the understanding of detection of minimum frequency-change-length and frequency accuracy in different pulse shapes with the same FWHM. Hence the Gaussian pulse can be used in general measurement because of its balanced time and frequency resolution. Practically, the combination of different pulse shapes can be used to obtain accurate measurements in time- and frequency-domain, respectively. To enhance the analyzer performance, the methodology of the* T-F* localization method is a useful tool to design, compare, and implement the pulse and algorithm selection in DFOS.* T-F* localization should be also considered in general to evaluate the power, averaging number settings in DFOS development.

#### 2. Physical and Mathematical Description on BOTDR

In a single mode fiber, 1550 nm light will generate Brillouin scattering signals whose peak frequency shifts about 11 GHz, due to the interaction between the lightwave and acoustic waves in the fiber [23, 24]. The acoustic wave makes the Brillouin gain spectrum (BGS), a Lorentzian shape distribution whose linewidth is determined by the phonon lifetime [25]. Distributed fiber sensing systems detect the frequency shift of the BGS by searching the frequency peaks over time, hence producing distributed sensing information (temperature and strain) along the fiber [26, 27]. The physical and mathematical model has been discussed by several research groups. Minardo et al. [28] constructed the solution of the BOTDA model, while Naruse and Tateda [13] offered a simplified BOTDR model, and Nishiguchi et al. [29] introduced a more general BOTDR model.

The Brillouin scattering process can be expressed by the following equations [25]: where , , and are the amplitudes of the pump light, stokes light, and acoustic wave, respectively. and are the polarization density of the pump and stoke waves, respectively. is the electrostrictive force per unit volume.

By simplifying the equation and assuming that noise is constant along the fiber [28–30],where is the light velocity in a vacuum, is the refractive index of the fiber, is the sum of the damping of the phonon lifetime, and the detuning parameter . is the frequency shift generated by Brillouin scattering, which is proportional to the independent thermodynamic variables of the entropy, , and pressure, :Because Spontaneous Brillouin Scattering (SpBS) does not have a stimulated effect, the SBS terms in (2) and (4) are assumed to be zero to simplify the analysis.

Then the scattered light can be expressed as The spectrum can be described asThis can be written in convolution form as [29]where is the time-nondependent coefficient and is the Fourier transform of the pulse signal .

At a particular time, according to the model given by Naruse and Tateda [13], the spectrum of the Brillouin scattered signal at each point along the fiber can be expressed as where is the power spectrum of a launched pulse in which each frequency component produces a Lorentzian shape Brillouin backscattered light spectrum profile with peak frequency of and full width at half maximum (FWHM) of . The term expresses the frequency changes due to local acoustic waves, where the difference comes from the changes in the properties of the fiber or the changes in strain or temperature.

Based on the equations above, the final scattered back Brillouin spectrum is the integration of all the spectra generated by each frequency component on the pump pulse spectrum. According to (8) and (11), the time-varying Brillouin spectrum is related to the entire pulse shape. In the pulse’s rising and falling edges, the spatial resolution will be reduced because the power in the edges will worsen the spatial resolution by expanding the length of wave interaction. Hence, time localized pulse can enhance the spatial resolution.

The broadened bandwidth and expanded sideband increase the complexity of accurate peak frequency detection. The noise will be increased when the sideband power is comparable with mainlobe power in the pulse modulated SpBS spectrum [12]. In order to remain a good SNR, the sidebands’ power should be minimized. Therefore the frequency localized pulses in BOTDR require the power to be concentrated near the peak frequency to maintain a narrow linewidth.

#### 3. Time-Frequency () Localization

The mean square deviation of the time and frequency distribution of a signal is defined in (12) and (13) [16]. Equation (14) describes the Heisenberg uncertainty principle [17]: where and are the variance of the signal in the time- and frequency-domains, respectively.

In the telecommunication systems, the dispersion of the signal causes intersymbol and interchannel interference when the signal has multicarriers, such as in an Orthogonal Frequency Division Multiplex (OFDM) system [31]. When the signal disperses over time, it may also interfere with subsequent symbols to cause “intersymbol” interference (ISI), reducing the reliability of the communications system [18]. When the signal disperses in the frequency-domains, it may interfere with symbols in other channels, causing “interchannel” interference (ICI), reducing the SNR in each channel [19]. A delta function in the frequency-domain produces a continuous single frequency lightwave with constant power. The uncertainty principle governs that delta functions in both time- and frequency-domains cannot simultaneously exist in the same signal.

*T-F* localization describes the extent to which a pulse signal is restricted in both the time- and frequency-domains. Good localization describes the minimum energy spreading over a certain time span and frequency bandwidth to avoid the power leakage into channels and interfering with neighboring symbols [32]. Besides in telecommunication, the* T-F* localization is also well studied in high resolution geophysical data analysis [20] and in wavelets transform in signal processing [21].

Pulse shapes have different localization characteristic. Rectangular, Lorentzian, Gaussian, and triangular shape pulses were simulated in 3D using STFT. In order to plot the time- and frequency-domain of the pulses simultaneously, the pulses were multiplied with a square STFT window to do the time-frequency analysis of the shapes. The STFT 3D plots and the sideband in both domains are shown in Figures 1 and 2. The pulses all had 50 ns FWHM and 1 *μ*s period and were analyzed using 50 ns window STFT.