High-Speed Mach-Zehnder-OTDR Distributed Optical Fiber Vibration Sensor Using Medium-Coherence Laser
Citation: Yuheng TONG, Zhengying LI, Jiaqi WANG, Honghai WANG, and Haihu YU, ?High-Speed Mach-Zehnder-OTDR
Distributed Optical Fiber Vibration Sensor Using Medium-Coherence Laser,? Photonic Sensors
High-Speed Mach-Zehnder-OTDR Distributed Optical Fiber Vibration Sensor Using Medium-Coherence Laser
Yuheng TONG 0 1
Zhengying LI 0 1
Jiaqi WANG 0 1
Honghai WANG 0 1
Haihu YU 0 1
0 National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology
1 Wuhan 430070 , China
This article presents a high-speed distributed vibration sensing based on Mach-Zehnder-OTDR (optical time-domain reflectometry). Ultra-weak fiber Bragg gratings (UWFBG), whose backward light intensity is 2?4 orders of magnitude higher than that of Rayleigh scattering, are used as the reflection markers. A medium-coherence laser can substitute conventional narrow bandwidth source to achieve an excellent performance of distributed vibration sensing since our unbalanced interferometer matches the interval of UWFBGs. The 3 m of spatial resolution of coherent detection and multiple simultaneous vibration sources locating can be realized based on OTDR. The enhanced signal to noise ratio (SNR) enables fast detection of distributed vibration without averaging. The fastest vibration of 25 kHz and the slowest vibration of 10 Hz can be detected with our system successfully, and the linearity is 0.9896 with a maximum deviation of 3.46 n?.
High-speed; Mach-Zehnder-OTDR; ultra-weak fiber Bragg grating array; medium-coherence laser; optical fiber vibration sensing
Distributed optical fiber vibration sensors have
received great attention over the past decades for
their significant advantages in safety, fully
distributed sensing, and large-scale monitoring [
It is used for a variety of applications including
intruder security , structure health monitoring [
mechanical fault diagnostics [
], and oil pipelines
leakage monitoring [
], where the signal can be
modeled as a spatially resolved temporal
Sagnac and Mach-Zehnder interferometers
(MZIs) have the advantages of high sensitivity and
fast response, but they cannot distinguish multiple
simultaneous vibration sources [
Phase-sensitive optical time-domain
reflectometry (?-OTDR) enables distributed
vibration sensing by analyzing the interference of
the Rayleigh backscattered light from the vicinity of
the coherence length of the pulsed light source when
the pulsed light travels along the fiber. However, the
scattering light is very weak with typical ?80 dB
scattering ratio, and the required high coherence
] causes severe phase noise as well. So its
original signal to noise ratio (SNR) is very poor,
and temporal-spectral averaging is needed to
enhance the SNR [
], which makes this
technique only applicable for low speed vibration
measurement. For improving the accessible
frequency response, Mach-Zehnder interferometer
and ?-OTDR are merged [
]. 5 m of spatial
resolution and several MHz of highest frequency
response are realized but the merged systems have
no capable of restoring signals of multiple points.
Recently, the ultra-weak fiber Bragg grating array is
also utilized for high SNR in an improved ?-OTDR.
The reflection is about 4 orders of magnitude higher
than that of Rayleigh scattering. But these methods
still require a high coherence source: a narrow
linewidth distributed feedback fiber laser (DFB-FL)
with a linewidth of 5 kHz is employed to ensure the
coherence of the reflected light from adjacent FBG
], and in similar system [
], a tunable laser
whose linewidth is 3.7 kHz is selected as the source.
In this paper, we propose a high-speed
Mach-Zehnder-OTDR distributed optical fiber
vibration sensor based on the ultra-weak fiber Bragg
grating (UWFBG). The vibration transducer is a
single-mode fiber, and UWFBGs with reflectivity
around 0.01% is written on the fiber to produce
reflected lights from different positions. Compared
with the previous improved ?-OTDR based on the
UWFBG array, we adjust the optical pulse width to
the appropriate value so that the medium-coherence
optical pulse interferes with passing through our
balanced interference structure. The significant
advantage of the scheme proposed here is its low
cost of DFB laser of which the linewidth is about
10 MHz. In addition, the excellent performances of
distributed optical fiber vibration sensing based on
medium-coherence light are achieved. Our
experimental results show that spatial resolution of
vibration locating is 3 m, and the SNR is up to
6.7 dB without average. Particularly, the detected
frequency response is up to 25 kHz, and the
maximum deviation is about 3.46 n?.
The UWFBG Mach-Zehnder-OTDR distributed
vibration sensing system is shown in Fig. 1. The
light source is a DFB laser (LUCENT D2526T31)
with the maximum output power of 1 mW and
linewidth of 10 MHz. The continuous-wave (CW)
light from the laser is modulated into nanosecond
pulse by semiconductor optical amplifier (SOA,
INPHENIX IPSAD1522C) which has an extinction
ratio (ER) higher than 70 dB. The pulse light is
amplified by an erbium-doped fiber amplifier
(EDFA) and then is launched into fiber under test
with uniformly distributed UWFBGs by a circulator.
The reflected pulses from the UWFBGs go through
3? 3 coupler phase demodulation unit which
consists of unbalanced Mach-Zehnder interferometer,
3? 3 coupler, and three detectors. The phase
demodulation unit is used to avoid signal fading and
restore the amplitude of vibration. The serial data
from three detectors are collected by a high-speed
Ultra-weak fiber Bragg grating array
FBG#1 FBG#2 FBG#3 FBG#4
Cylindrical PTZ driver
interferometer 3 m
Fig. 1 Schematic of high-speed Mach-Zehnder-OTDR
distributed optical fiber vibration sensor using
medium-coherence laser. SOA: semiconductor optical amplifier,
EDFA: erbium-doped fiber amplifier, CIR: circulator, PD:
photodetector, and OSC: oscilloscope.
2.1 Theory of vibration source locating
The basic theory locating the position of
vibration source is based on the OTDR technology.
Like any OTDR system, a short light pulse is fed
into the UWFBG array. There is a fixed distance of
L1 between the adjacent gratings, and delay ?T1 of
adjacent pulses can be written as
?T1 = n ? ?L / c = 2nL1 / c (1)
where n is the refractive index of the fiber, c is the
velocity of light in vacuum, and ?L is the optical
path difference (OPD) of pulses reflected by
adjacent gratings. The width ? of optical pulse
should be less than the delay ?T1 to avoid multiple
reflected pulses aliasing. Unbalanced path of the
MZI in phase demodulation unit separates each
reflected pulse to two pulses. Making the OPD of
the MZI equal to 2L1, transmission delay ?T2 of two
arms of MZI can be calculated as
?T2 ? n(L2 ? L3 ) / c ? 2nL1 / c ? ?T1 (2)
where L2 and L3 are the lengths of two interference
As shown in Fig. 2, the slower sub-pulse A2 from
a closer grating will be coincident with the faster
sub-pulse B1 from a further grating and then
interfere. Phase perturbation between the two
adjacent gratings can be demodulated from the
interference signals. Consequently, the
correspondence between interference signals and
sensing position can be established, and the position
of multiple sensing points can be located
simultaneously, as shown in Fig. 3.
?T1 t cOoputUpiclneablralaiInnntcteeerfrdeferMeLr3noacmcehea-trmeZreh ncOdeoprutpiclaelr I ?T1 B1?T2 B2 # 2t
Fig. 2 Principle of vibration source positioning. ?T1 is the
delay of reflection from FBG#1 and FBG#2, and ?T2 is the
delay of optical pulse traveling through the unbalanced MZI. ?
is the width of optical pulse.
2 FBG#1 L1
Interference ar m
Interferential light pulse
I A1 A2
#1 #2 #3 #4 #5 t
Interferential light pulse sequence
Fig. 3 Relationship between the interferential light pulse
sequence and sensing position. The first and last optical pulses
of sequence are useless to record vibration. #1 to #5 are the
serial numbers of sensing fiber segments, respectively.
In contrast to Rayleigh backscattered light of
each fiber section in the conventional ?-OTDR
system, which is attributed by the addition of
random distributed scatters within the section length,
the reflection of the grating can be regarded as a
fixed point reflector. Theoretically, the OPD of each
pair of interferential light pulses can be made zero.
Thus, the system we propose does not require a high
The intensity of interferential light pulse signal
is written as
I = I1 + I2 + 2 I1I2 cos ? ?? + ?0 ? (3)
where I1 and I2 are the intensities of the two optical
pulses arriving at the observation point, respectively,
?? is the dynamic phase shift, and ?0 is the initial
phase. The sensitivity of ?? fades to zero when ?0
is close to multiples of ? [
]. A 3 ? 3 coupler is
chosen to solve this problem. At ideal split ratio, the
output intensity of the three arms of 3 ? 3 coupler
can be expressed as follows:
In ? I1 ? I2 ? 2 I1I2 cos ???? (t) ? (i ? 1) ? ? ,
? 3 ?
i=1, 2, 3. (4)
There is a phase difference of 2? / 3 between
each output port of the 3 ? 3 coupler. Under no
circumstances can the variation ratios of each port
output be 0 simultaneously, so we can detect the
three output signals to demodulate the ?? by
using the algorithm [
When external disturbance is applied on the fiber,
the OPD between the two UWFBGs based on the
demodulated dynamic phase shifts, and the vibration
signal can be restored.
2.3 Analysis of frequency response
In a distributed vibration sensing (DVS) system,
the significant factor which limits the frequency
response of the vibration measurement is the highest
External vibration and other environmental
factors can both cause the phase shift ?? .
Nevertheless, compared with the external vibration,
the environmental factors, such as temperature, have
a lower frequency. Thus, ?? can be expressed as
?? (t) ? D cos?st ?? (t) (5)
where D and ?s are the amplitude and angular
frequency of phase shift caused by external vibration,
and ?(t) is the lower frequency phase shift caused by
other environmental factors.
The index i is set to 1. Then substituting (5) into
(4), the alternating component (AC) of (4) is
rewritten as follows:
IAC ? 2 I1I2 cos ??D cos? st ?? ?t ??? . (6)
According to Bessel function, we can acquire (7)
from (6). In order to restore the vibration signal,
enough harmonic information, of which the Bessel
value is greater than 0.1, should be obtained. So, as
for different D, the relationship between IAC and ?s
is appeared clearly in Fig. 4(a).
IAC ? 2 I1I2 ?
?? ? ?
???? J0 ? D ? ? 2? J2k ? D ? cos 2k? st ? cos? ?t ? ?
k ?1 ?
??2 ?? ? ?1?k ?1 J2k ?1 ? D ? cos ? 2k ? 1?? st ?? sin? ?t ???.
? k ?1 ? ?
The value of D is determined by the sensitivity
characteristics of sensor. Here, we do not discuss the
sensitivity enhancement or weakening, so D can be
considered as 1. From Fig. 4(a), it can be got that the
occupied bandwidth of optical intensity variation is
twice of the angular frequency of the vibration. In
accordance with the Nyquist sampling theorem, the
sampling frequency must be more than twice of the
occupied bandwidth of the interference optical
signal to avoid spectrum aliasing. So if the external
vibration has a frequency of fs, the lowest sampling
frequency required is 4fs.
In our DVS system, the repetition rate f? of pulse
light determines the sampling frequency fs. When f?
is fast enough, there are more than one pulse lights
? ad01 80
traveling along the sensor fiber with UWFBG at the
same moment. Hereby, the multiple-pulse crosstalk
will occur. According to Fig. 3, N UWFBGs will
produce N + 2 pulses after MZI in our system. In
consideration of avoiding the spectrum aliasing and
crosstalk, fDVS should satisfy the following equation:
fDVS ? 4 f? ? 4c / ??2n ? N ? 1? L1 ?? .
With an increase in the sensing fiber distance,
fDVS will decrease rapidly, shown as Fig. 4(b). When
the spatial resolution is 3 m and sensing distance is
about 1 km, the sensing bandwidth reaches 25 kHz.
D = 0.25 rad
D = 0.5 rad
D = 1 rad
D = 2 rad
D = 4 rad
Ratio coefficient: 2
2 4 6 8 10 12 14 16 18 20
Angular frequency of dynamic strain (rad ? 1000/s)
L1 = 1 m
L1 = 3 m
L1 = 5 m 27.2
L1 = 7 m 26.8
L1 = 9 m 2266..04
23.6 960 980 1000 1020 1040
600 800 1000 1200 1400 1600
Sensing distance (m)
2.4 Analysis of signal-to-noise ratio
There are 3 main noises in the system: shot noise
?s2 = 2q?(IRBS + In + Id)??B (here q is the charge of
electron, IRBS is the detected current of the Rayleigh
backscattering, Id is the dark current of detector, and
?B is the bandwidth of signal), thermal noise ?T2,
and Rayleigh backscattered noise. Assume the
scattering coefficient for every scattering center is
the same and M scattering centers in each fiber
section with length of L1. The detected current signal
is proportional to the optical intensity, so the
Rayleigh backscattered current noise can be
IRBS ? I0 ?t ? exp ? ?2? LN ? ?k?1 rkN exp ??? s ?t ? ?? s0 ?? (9)
where IRBS(t) is the detected current of the Rayleigh
backscattering at distance LN = NL1, I0(t) is the
intensity of the incident light, ? is the attenuation
coefficient of the fiber, and rkN is the Rayleigh
reflection coefficient of the scatter center in N-th
So the SNR of the detected signal is described as
2R2 PR2BS ? 2q ? PRBSR ? Pr R ? Id ? ?B ?? T2 (10)
where Pr and PRBS are the detected powers of
reflected light and backscattering light, respectively.
? s2 and ? T2 related to the detector have an
ultra-low magnitude. Since the reflectivity of the
UWFBG is four orders of magnitude greater than
the Rayleigh scattering, Pr is much higher than PRBS.
For this reason, the high SNR of the system could be
3. Experimental results and discussion
In experimental setup, 332 UWFBGs are
distributed over 1-km long fiber with equal interval
of 3 m. The UWFBGs have uniform wavelength of
1550.947 nm, as well as bandwidth of 0.2 nm and
reflectivity of 0.01% (?40 dB). Fiber sections
between UWFBG#100, UWFBG#101,
UWFBG#300, and UWFBG#301 are wound around
two identical cylindrical piezoelectric transducers
(PZTs) to generate strain variation. The
experimental setup includes our proposed DVS
system and a calibration component which is a
standard Mach-Zehnder interferometer, as shown in
Fig. 5. When the DVS system measures, the optical
Switch 1 connects DFB laser (Lucent 2526, 10 MHz
linewidth) to SOA, and the optical Switch 2
connects UWFBG array to circulator. The
wavelength of DFB laser is located at 1550.947 nm
to match the identical UWFBG. The light pulses
have a repetition rate of 100 kHz, with a pulse width
of 20 ns (obey ?< 2nL1 / c). The phase demodulation
unit adopts an imbalance path of 6 m for matching
the interval of gratings. Data are acquired with an
oscilloscope (Keysight DSA 134A) for 50 ms at
200 Msps. The experimental rig is shown as Fig. 6.
Distributed feedback laser Optical switch 1
I Continuo us
C oupler 2
C alibr ation
Ultra-weak FB G array
# 1 #1 00 t
L2 3 ?3
Phase demodu lation un it
Fig. 5 Structure for experiment, all UWFBGs have same reflectivity and central wavelength. When optical switch 2 connects
UWFBG array to coupler 2, a standard Mach-Zehnder interferometer is to calibrate the vibration.
To compare the SNR and the coherent requirement
of light source, on the one hand, a narrow linewidth
laser (NL) and our medium-coherence laser employed
in the conventional ?-OTDR in [
] are compared,
and Fig. 7 shows the comparison of linewidth.
According to Lorenz fitting curve of self-heterodyne of
NL and DFB laser, the full widths at half maximum
(FWHM) are 22.3 kHz and 17.8 MHz, respectively.
Figure 8 shows the results of vibration locating. 20-ns
optical pulses and 1.5-km sensing fiber are used for
testing. With the averaging times of 10, the SNR of
narrow linewidth laser system is 5.31 dB, but the
medium-coherence system cannot locate vibration
source due to the awful SNR.
Lorenz fitting curve of
)Bm??7605 DFFBWsHelMf-h:1e7te.8roMdHynze spectrum
On the other hand, when only PZT1 generates
vibration, the interferential pulse arrays for 100
pulse periods are detected by PD1. In Fig. 9, 6
interferential pulses which correspond to the
distance from 294 m to 312 m are shown. From the
superposition of 100 interferential pulse arrays, it
can be seen that the intensity of the interference
pulse corresponding to the fiber section where PZT1
is located is greatly fluctuated, while the other
pulses do not change much. We extract the peak
value of each pulse in all the 5000 detected
interferential pulse arrays, and Fig. 10 shows the
superposition of intensity fluctuation at each sensing
position. According to (10), we can calculate the
SNR by analyzing the intensity fluctuation
amplitude Asignal in the position with vibration, and
Asignal = 1.12 V
Anoise = 0.24 V
the Anoise in the position without vibration, which is
10lg(Asignal / Anoise). Asignal = 1.12 V and Anoise = 0.24 V,
so SNR is 6.7 dB. Therefore, our system can locate
the vibration clearly without multiple averages.
1.4 Interference segments
?0.2294 Ra2y9le7igh scat3te0r0ing 306 309 312
Fiber length (m)
Fig. 9 Parts of superposition of all 100 output optical pulse
sequence from PD1 when only PZT1 has a vibration.
100 200 300 400 500 600 700 800 900 1000
Fiber length (m)
Fig. 10 Location information without average in our
proposed system by using the medium-coherence.
Here we use two same PZTs to test the locating
and demodulation capability of our DVS system.
They generate vibration at different frequencies and
amplitudes simultaneously, and the parameters of
two sine-wave driven signals are 12 V, 1 kHz, and
6 V, 3 kHz, respectively. The dynamic phase shift can
be demodulated from the intensity variation of
interferential pulse. According to the parameters
used in the experiment [
], the measurement
sensitivity of OPD ?l is 84.2 nm/rad, and the
dynamic strain sensitivity is about 28.06 n?/rad. The
global demodulation result of 1-km fiber is given in
Figs. 11(a) and 11(b). It can be clearly seen that there
exist two magnitude changes located within the
darker frame in Fig. 11(a) at distance of 300 m and
900 m. The two peaks in the Fig. 11(b) correspond to
the two vibration regions in the sensing fiber.
Here for wave shape details we just show the
time response data from ?2.5 ms to 2.5 ms in
Fig. 11(c). The amplitudes of dynamic strains
detected from PZT1 and PZT2 are 59.7 n? and
23.9 n?, respectively. The results from spectral
analysis via fast Fourier transform (FFT) are shown
in Fig. 11(d). It can be found that two clear main
peaks are at 1 kHz and 3 kHz, and the second
harmonic suppression ratios of demodulated signal
are 43.9 dB and 41.13 dB, respectively.
In order to confirm the deviation of amplitude
measurement, linearity and stability experiment
have been also performed. At first, we set the
frequency of sine-wave driving signal of the
vibration source PZT1 to be 1 kHz, and the
amplitude to be increased from 1.2 V to 12 V. The
vibration is measured with the DVS system and the
calibration component respectively, as shown in
Fig. 12. Since the values of MZI do not contain a
round trip, it is divided by 2 to match the values of
DVS. Because the calibration system and our DVS
both exist dithering, the results are averaged for
5 times to compare the detection error. Compared
with the calibrated values from the calibration
component, the maximum measuring error is only
3.46 n?. It can be found that the measured and
calibrated values show a linear relationship, and the
linearity of curving fitting is 0.9896. Secondly, we
drive the PZT1 by a stable sine-wave with voltage of
12 V and frequency of 1 kHz, and the dynamic strain
every 10 minutes for a total of 100 times is collected
by our DVS system. In Fig. 13, the standard
deviation of the system is 3.410 n?. Actually, the
amplitude of vibration source is not absolutely stable,
so it will also introduce dithering.
Further experiment has been made to test the
frequency response of DVS system. In fact, the
frequency response of the vibration transducer can
also influence the frequency response of system, but
the repetition frequency of sampling optical pulse is
(3 kHz, 23.9 n?)
the most important factor in this experiment.
According to the previous theoretical analysis, we
set the frequency of PZT1 to be 10 Hz and 25 kHz,
respectively. And the clear main peaks at 10 Hz and
25 kHz respectively are shown in Fig. 14.
Standard deviation = 3.410 n?
0 200 400 600 800 1000
Fig. 13 Demodulated results of 100 dynamic strains in the
same environment, and an interval of 10 minutes is set between
Frequency: 25 kHz
FFT: 61.26 dB
In this paper, a Mach-Zehnder-OTDR
distributed optical fiber vibration sensing system
using medium-coherence laser is proposed. The
higher reflection generated by UWFBG array is
adopted instead of the Rayleigh backscattering (RBS)
in the sensing fiber, and the position information can
be obtained easily by OTDR. Based on the balanced
Mach-Zehnder structure, the medium-coherence
laser DFB can be used as light source to realize an
excellent SNR. In our experiments, the vibration
sensing signal with a high SNR of 6.7 dB can be
obtained without averaging. The demonstrated setup
has a sampling frequency of 100 kHz for vibration
and improves the highest frequency response to
25 kHz in this monitor system. Spatial resolution of
3 m and simultaneous localization of multiple
vibration sources are achieved in a 1-km long
sensing fiber by detecting the delay of the pulse in
time domain. A 3 ? 3 coupler is used to restore the
amplitude of the vibration signal, and crosstalk
between neighboring sensing position is weak
enough. The maximum measuring error is only
3.46 n? compared with the standard Mach-Zehnder
interferometer, and the linearity of measurement is
This work was supported in part by the National
Natural Science Foundation of China (Grant No.
61735031), Natural Science Foundation of Hubei
Province of China (Grant No. 2018CFA056), and
the Excellent Dissertation Cultivation Funds of
Wuhan University of Technology (Grant No.
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