Independent Real and Imaginary Spectral Analysis for Improving the

Brillouin Frequency Shift Resolution in the Differential

Cross-Spectrum BOTDR (DCS-BOTDR) Fiber Sensor

Ain Nabihah Mohammad Rihan

, Mohd Saiful Dzulkefly Zan

, Yosuke Tanaka

Mohd Hadri Hafiz Mokhtar

, Norhana Arsad

and Ahmad Ashrif A Bakar

Department of Electrical, Electronic & Systems Engineering, Faculty of Engineering & Built Environment,

Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Department of Electrical and Electronic Engineering, Graduate School of Engineering,

Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan

Keywords: Distributed Fiber Sensor, Strain and Temperature Sensor, Brillouin Optical Time Domain Reflectometry,

Spectral Analysis, Fast Fourier Transform.

Abstract: We propose a technique to improve Brillouin gain spectrum (BGS) acquisition in a Brillouin optical time

domain reflectometry (BOTDR) fiber sensor by independently analyzing the real and imaginary components

of the Brillouin backscattered signal through fast Fourier transform (FFT) analysis. This technique aims to

enhance Brillouin frequency shift (BFS) resolution in our previously proposed differential cross-spectrum

BOTDR (DCS-BOTDR) method. Using an intensity modulation scheme to generate a probe pulse pair, we

conducted temperature sensing experiment by heating an 8 m section at the far end of a 1.2 km fiber at 70°C.

The experimental results showed a significant reduction of BGS width from 128 MHz to around 53 MHz with

the real spectrum component. Consequently, this has resulted in the enhancement of the BFS resolution to

1.49 MHz using the real spectrum and 1.51 MHz with the imaginary spectrum. We have also achieved 40 cm

spatial resolution measurement and reduced the processing time from 7.21 s to 7.08 s, demonstrating an

improved efficiency and accuracy for distributed temperature measurement in BOTDR sensor.

1 INTRODUCTION

In recent years, many studies on Brillouin optical time

domain reflectometry (BOTDR) have multiplied due

to its potential applications such as structural health

monitoring of large infrastructures, pipeline

monitoring, and power cable monitoring. The

growing interest was influenced by the ability of

BOTDR systems to detect local variations in

Brillouin frequency shift that are sensitive to

temperature and strain, which allows for distributed

sensing. As a result of the linear dependence of

temperature and strain on the Brillouin frequency

shift (BFS), the Brillouin gain spectrum mapping was

used for distributed temperature and strain sensing in

the BOTDR system (Bao et al., 2021). The BOTDR

system utilized spontaneous Brillouin scattering

(SpBS) to measure the strain distribution. However,

signal-to-noise (SNR) is weak due to the low

amplitude of the SpBS. The SNR can be improved

by increasing the pulse width, but the spatial

resolution will be compromised.

https://orcid.org/0009-0004-8101-1197

https://orcid.org/0000-0002-1440-5434

https://orcid.org/0000-0002-6539-5977

https://orcid.org/0000-0001-5307-073X

https://orcid.org/0000-0003-4543-8383

https://orcid.org/0000-0002-9060-0346

Rihan, A. N. M., Zan, M. S. D., Tanaka, Y., Mokhtar, M. H. H., Arsad, N. and Bakar, A. A. A.

Independent Real and Imaginary Spectral Analysis for Improving the Brillouin Frequency Shift Resolution in the Differential Cross-Spectrum BOTDR (DCS-BOTDR) Fiber Sensor.

DOI: 10.5220/0013167300003902

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2025), pages 35-40

ISBN: 978-989-758-736-8; ISSN: 2184-4364

Figure 1: Time domain Brillouin backscattered (BS) analysis scheme using differential cross spectrum technique.

Due to the trade-off between these parameters,

various studies have been conducted on enhancing

spatial resolution without compromising the SNR

(Almoosa et al., 2022; Horiguchi et al., 2019; Zan et

al., 2018). Almoosa et. al proposed a method to

improve the BFS resolution of the BOTDR system by

using an artificial neural network (ANN) (Almoosa et

al., 2022). This technique demonstrated the

improvement of BFS resolution from 21.13 MHz to

2.88 MHz. Horiguchi et. al reported phase shift pulse

BOTDR (PSP-BOTDR) where a probe pulse pair

modulated by the phase shift keying method and has

obtained 20 cm spatial resolution with this method

(Horiguchi et al., 2019). Differential cross-spectrum

BOTDR (DCS-BOTDR) which has a similar

approach to the PSP-BOTDR was proposed by Zan et

al. (2018), whereby an intensity modulation scheme

is used to generate a long-short probe pulse pair. This

technique has demonstrated 0.2 m spatial resolution

for a 350 m sensing range. Even though all of these

techniques have further improved the spatial

resolution of the BOTDR system, the measurement

time took quite a long period due to high averaging.

In this paper, we introduce a method to acquire the

BGS by independently analysing real and imaginary

parts of the fast Fourier transform (FFT). In the DCS-

BOTDR, the BGS was acquired by analysing power

spectral density (PSD), which is the magnitude of real

and imaginary components. The proposed method

will use a similar intensity modulation scheme of the

DCS-BOTDR to modulate the long-short probe pulse

pair, but use a different approach to extract the BGS.

This experiment will focus on independent analysis to

effectively improve the BFS resolution while also

successfully reducing the measurement time.

2 PRINCIPLES

2.1 Real and Imaginary Spectrum of

DCS-BOTDR

In a conventional BOTDR system, the Brillouin

spectrum was extracted from the backscattered signal

in the frequency domain by applying the FFT.

Fundamentally, the FFT is an algorithm that

calculates fast discrete Fourier transform (DFT)

(Smith, 1997). The DFT converts the time domain

signal into a frequency domain that yields two

components; real and imaginary. Hence, the DCS-

BOTDR method introduces a cross-correlation

method by calculating the complex conjugate of both

components of the FFT to acquire the PSD.

Considering that both real and imaginary parts of the

FFT can work independently, the spectrum analysis

to compare three different spectra; conventional, real,

and imaginary was conducted based on the DCS-

BOTDR method.

Figure 1 provides an overview of the key steps

involved in this method, starting from the generation

of probe pulses to the computation of the differential

Brillouin spectrum. As illustrated, two probe pulses

are utilized which both probes have a long pulse

duration (𝑇



), but only Probe 1 includes a short pulse

duration (𝑇



), separated by an interval duration (𝑇



)

between and Probe 2 serves as a reference. Initially,

the backscattered signal in the time domain can be

expressed as 𝑏





𝑡



,𝑧



, where 𝑧 is the position in the

optical fiber and 𝑡



refers to the reference time. After

converting to the frequency domain by performing

the FFT, the backscattered signal will yield both real

and imaginary components, expressed as:

PHOTOPTICS 2025 - 13th International Conference on Photonics, Optics and Laser Technology

𝐵





𝑓

,𝑧



𝑅𝑒



𝐵





𝑓

,𝑧





𝐼𝑚



𝐵





𝑓

,𝑧





(1)

where 𝐵





𝑓,𝑧



represents the backscattered signal in

the frequency domain at the position 𝑧, 𝑅𝑒 refers to

the real part that corresponds to cosine components,

while 𝐼𝑚 refers to the imaginary part that

corresponds to the sine components. Then, cross-

correlation as depicted in Figure 1 involves

calculating the interaction between the backscattered

signals between Probe 1 ( 𝑏







𝑡



,𝑧



) and Probe 2

𝑏







𝑡



,𝑧



) in the frequency domain. This is computed

and described as follows:

(2)

(3)

Equation 2 and 3 represent the correlation

between real and imaginary components of the

backscattered signals from both probes. They also

signify the interaction of the two signals in the

frequency domain. These equations also yield the real

and imaginary part of the Brillouin spectrum.

“Subtraction” and “Differential Brillouin Spectrum”

columns in Figure 1 depict the subsequent step

computes the magnitude of the cross-spectrum to

determine the PSD of the cross-correlated signal in

the frequency domain. The magnitude of cross-

spectrum is also defined as the conventional spectrum

deployed in the DCS-BOTDR technique and it can be

calculated as:

𝐶







𝜏,𝑡



,𝑧









𝑅𝑒𝐶







𝜏,𝑡



,𝑧







𝐼𝑚𝐶







𝜏,𝑡



,𝑧







(4)

This magnitude combines both real and imaginary

parts and gives the measure of the PSD in the

frequency domain. The steps outlined in Figure 1

ensure that both components are utilized effectively,

leading to an improved understanding and accuracy

of the Brillouin spectrum.

2.2 Zero-Crossing Point Search

To find the BFS for the imaginary spectrum, a zero-

crossing point search (ZCPS) is applied instead of a

maximum peak search. This is because the frequency

of the zero-crossing point for the imaginary spectrum

is equivalent to the frequency for the real and

conventional spectra (see Figure 2). The ZCPS is

adapted from Nonogaki et al. (2024) which

has proposed this method for a Brillouin optical time

Figure 2: BGS of real, imaginary, and conventional

spectrum.

domain analyzer (BOTDA) system. The BGS of the

imaginary part can be explained as:

𝑓





𝑏



𝑎



(5)

where

𝑎



refers to the slope of the linear regression

between the maximum and minimum values of the

BGS, and

𝑏



is the intercept of the linear

regression. The slope of the linear regression which

can be denoted as a gradient 𝑚 can also determine the

linearity between the BGS of heated and unheated

BGS which will be discussed in the next section.

3 EXPERIMENTAL ANALYSIS

3.1 Experimental Setup

The configuration of the experimental setup is

depicted in Figure 3. Continuous light of 1550 nm

wavelength with 12 dBm input power was upshifted

and downshifted by frequency modulation scheme. A

synthesized signal generator (SSG) supplied a 10

GHz sinusoidal wave to a Mach-Zehnder modulator

(MZM) for frequency shift keying. Arbitrary

waveform generator (AWG) modulates the incoming

optical signal to generate the optical pulses as shown

in Figure 1. By using acousto-optic modulation

(AOM), optical pulses were generated via ON-OFF

keying modulation. Then, the AWG was set to

produce the desired electric pulses such that 𝑇



= 10

ns, 𝑇



= 4 ns, and 𝑇



= 2 ns. Two optical amplifiers

(EDFA 1 and EDFA 2) were incorporated into the

setup to compensate insertion loss, with input

currents of 180 mA and 80 mA respectively. The

overall output power detected by oscilloscope (OSC)

was measured to be 600 mW. The experiment was

carried out using a total fiber length of 1.2 km, with a

heated section placed inside a water bath

approximately 8 meters near the far end of the fiber,

at a fixed temperature of 70°C. The SpBS that

Independent Real and Imaginary Spectral Analysis for Improving the Brillouin Frequency Shift Resolution in the Differential

Cross-Spectrum BOTDR (DCS-BOTDR) Fiber Sensor

consists of both Brillouin gain and loss spectra in the

optical fiber were generated by the optical pulses for

temperature measurement.

Figure 3: Schematic experimental setup of DCS-BOTDR.

LD: laser diode, OC: optical coupler, PC; polarization

controller, MZM: Mach-Zehnder modulator, EDFA:

erbium-doped fiber amplifier, AOM: acousto-optic

modulator, AWG: arbitrary waveform generator, PD:

photodetector, OSC: oscillope, FUT: fiber-under-test,

SpBS: spontaneous Brillouin scattering.

3.2 Results and Analysis

Figure 4 shows three different Brillouin spectra; real,

imaginary, and conventional, acquired using the

proposed technique. The measurement was

monitored at 𝑧 = 1.2 km for both heated and unheated

fiber sections along the FUT. All Brillouin spectra

recorded the same frequency shift at around 46 MHz.

In comparison with the frequency shift, the spectral

bandwidth of the BGS calculated at full-width-half-

maximum (FWHM) shows an improvement

compared to the conventional one. As can be seen in

Figure 4 (a), the conventional spectrum of the heated

section has a broad spectrum width of 128 MHz. In

contrast, a narrower bandwidth of 53 MHz as

depicted in Figure 4 (b), was achieved when only the

real part of the FFT analysis was considered during

the spectral analysis of the time domain signal.

In most cases, the Brillouin spectrum typically

exhibits a Lorentzian line shape with a symmetrical

peak due to lifetime broadening, which makes it

possible to measure the FWHM (Antonacci et al.,

2013). Meanwhile, the imaginary spectrum usually

does not conform to a Lorentzian shape as evident in

Figure 4 (c) because it may exhibit multiple peaks,

unlike the real and conventional spectra.

Consequently, relying on the FWHM analysis for the

imaginary spectrum may increase inaccuracies in the

calculation that potentially affect the reliability of the

result. Another method to evaluate the imaginary

spectrum involves comparing the linearity of

Brillouin spectrum slopes between the heated and

unheated spectra.

Figure 4: Brillouin spectrum at the heated and unheated

section of 1 km for (a) conventional, (b) real, and (c)

imaginary spectrum.

Previously, Peng et al. (2022) conducted a

similar method known as double-slope assisted

BOTDR (DSA-BOTDR) to study the linear

dependence of the Brillouin spectrum on

temperature and evaluate the sensitivity of the

BOTDR system to temperature variations. Based on

Figure 4 (c), the unheated and heated spectra have

small differences in slopes, with values of 0.008 and

0.009 respectively. This difference suggests an

increased sensitivity to temperature changes and the

PHOTOPTICS 2025 - 13th International Conference on Photonics, Optics and Laser Technology

Brillouin spectrum shifted more rapidly under

heated conditions. The small difference in slopes

suggests that the system maintains stability and

consistency across different thermal conditions.

Figures 5 (a) and (b) show the BFS distribution

monitored at the 70°C heated section of the FUT.

From Figure 5 (a), it was found that the spatial

resolution analyzed at the 8 m fiber section was 40

cm and the BFS was approximately 50 MHz. By

calculating the standard deviation, the BFS

resolution can be determined more accurately,

thanks to the narrowed Brillouin spectrum of the real

components and the linear slope from the imaginary

component. The measured BFS resolutions for real,

imaginary, and conventional spectra were 1.49

MHz, 1.51 MHz, and 3.24 MHz, respectively. This

confirms that the BFS resolution can be improved

by employing independent real or imaginary

components for FFT analysis to extract the Brillouin

spectrum. Finally, the time taken to extract the

Brillouin spectrum from the backscattered signal

through FFT analysis was analyzed.

In our experiment, we averaged the data 20,000

times and conducted FFT analysis on a total of 576

BGS spectra, monitored from 1 km to the fiber end

for each type of spectrum (real, imaginary, and

conventional). The processing time required to

compute one BGS for the real, imaginary, and

conventional categories are 7.09s, 7.08s, and 7.21s,

respectively. Concentrating on the independent

computation of either the real or imaginary

components of the BGS for FFT analysis can

significantly reduce processing time. In comparison

with previous works, Table 1 shows the improvement

of the experimental results based on the spatial

resolution and BFS resolution.

Figure 5: BFS distribution comparison of real, imaginary,

and conventional spectrum. (a) Temperature distribution at

8 m heated section. (b) Spatial resolution of the BFS

distribution.

4 CONCLUSIONS

In this paper, we propose a technique to acquire the

Brillouin gain spectrum (BGS) by independently

analyzing the real and imaginary components of the

Brillouin backscattered signal. The experiment was

conducted using DCS-BOTDR intensity modulation

scheme to generate a probe pulse pair. The

Table 1: Performance specifications of different DCS-BOTDR schemes.

Independent Real and Imaginary Spectral Analysis for Improving the Brillouin Frequency Shift Resolution in the Differential

Cross-Spectrum BOTDR (DCS-BOTDR) Fiber Sensor

experiment results show that separating these

components enhanced the Brillouin frequency shift

(BFS) resolution, with the conventional spectrum

width improved from 128 MHz to 53 MHz using the

real spectrum. Additionally, temperature sensitivity

was demonstrated by comparing heated and unheated

imaginary spectra. A 50 MHz BFS shift, 40 cm spatial

resolution, and reduced processing time from 7.21s to

7.08s were achieved.

ACKNOWLEDGEMENTS

This research was supported by the Fundamental

Research Grant Scheme (FRGS) from the Ministry of

Higher Education of Malaysia (MOHE): Grant No.

FRGS/1/2023/TK07/UKM/02/2.

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PHOTOPTICS 2025 - 13th International Conference on Photonics, Optics and Laser Technology