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1954 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, MAY 15, 2015
An Improved Positioning Algorithm With High
Precision for Dual Mach–Zehnder Interferometry
Disturbance Sensing System
Qinnan Chen, Tiegen Liu, Kun Liu, Junfeng Jiang, Zhe Shen, Zhenyang Ding, Haofeng Hu, Xiangdong Huang,
Liang Pan, and Chunyu Ma
Abstract—An improved positioning algorithm for dual Mach–
Zehnder interferometry (DMZI) disturbance sensing system is pro-
posed. We employ zero-crossing method, which can be computed
easily to extract the disturbance signal segment with maximum
zero-crossing rate. Meanwhile, we use general cross correlation
based on Wiener filtering and Gnn subtraction weighting function
(WG-GCC) to estimate the time delay of the extracted signal, which
is robust to the correlated noise. Finally, we experimentally demon-
strate that the proposed positioning algorithm can greatly improve
the positioning accuracy with positioning error of ±20 m. Com-
pared with the traditional positioning algorithm, the positioning
error has been reduced by an order of magnitude. This algorithm
has a promising potential in real-time fence perimeter applications.
Index Terms—Distributed fiber-optic sensor, fence perimeter ap-
plication, general cross correlation, positioning algorithm, zero-
crossing rate.
I. INTRODUCTION
DUAL Mach–Zehnder interferometry (DMZI) disturbance
sensing system is widely used in perimeter security mon-
itoring, pipeline leakage detection, submarine cable security
monitoring, and other applications [1]–[8] due to advantages of
high sensitivity, fast response, and simple structure [4]–[8]. It
can obtain disturbance position by applying time delay estima-
tion algorithm, which lies at the heart of positioning algorithm.
Currently, the most popular time delay estimation algorithm
is to do cross correlation between the two output signals [1]–[7].
It will bring a huge amount of computation thought it is easily
achieved, which influences real-time performance of the sens-
ing system and its positioning error is easily induced by diverse
noises of output signals [9]. In general, the noise sources which
Manuscript received August 17, 2014; revised November 28, 2014; accepted
January 18, 2015. Date of publication February 15, 2015; date of current version
March 16, 2015. This work was supported in part by the National Basic Research
Program of China under Grant 2010CB327806, in part by National Instrument
Program under Grant 2013YQ030915, in part by the National Natural Science
Foundation of China under Grants 61475114, 61108070, 11004150, 61227011
and 61378043, and in part by the Tianjin Science and Technology Support Key
Project under Grant 11ZCKFGX01900. (Corresponding author: K. Liu.)
Q. Chen, T. Liu, K. Liu, J. Jiang, Z. Ding, H. Hu, L. Pan, and C. Ma are with
the College of Precision Instrument & Opto-electronics Engineering, Tianjin
University, Tianjin 300072, China (e-mail: beiyangkl@tju.edu.cn).
Z. Shen is with the Department of Electrical Engineering and Electronics,
University of Liverpool, Liverpool L69 3GJ, U.K. (e-mail: z.shen3@liv.ac.uk).
X. Huang is with the School of Electronic Information Engineering, Tianjin
University, Tianjin 300072, China (e-mail: xdhuang@tju.edu.cn).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2015.2394494
affect the positioning error include the frequency noise from the
laser source, the polarization noise and the environment noise.
The frequency noise and the polarization noise are ubiquitous
but can be reduced to some extent by compensating the length
difference between interferometer arms and dynamically ad-
justing the polarization state of the light in the interferometer,
respectively [4], [10]. The environment noise is negligible in
some cases such as submarine cable security monitoring, but
it is the major noise source in some applications such as fence
perimeter. Therefore, the main source of noise is not the same
in different applications.
As the aforementioned noises are difficult to eliminate, re-
searchers pay more attention to the positioning algorithms for
reducing noise. Xie et al. analyzed the positioning error of
DMZI sensor and proposed a positioning error reduction tech-
nique. They used a high-pass filter to reshape the original power
spectrum, and achieve a lower mean square error of the cross-
correlation based positioning algorithm [4], [6]. It is suitable for
submarine cable security application rather than fence perime-
ter application as the environment noise was neglected. Wu
et al. employed endpoint detection technologies such as dis-
crete wavelet to extract the effective signal segment at starting
point of disturbance before applying cross correlation [9], [11],
[12]. However, there is no obvious starting point when intrusion
occurs in fence perimeter application and the positioning error
of cross correlation based algorithm is easily affected by the
environment noise induced by slight vibration along the sensing
cable [10]. Although they obtained a certain degree of accuracy,
there is not enough in practical application.
We theoretically analyze the positioning error of the DMZI
sensing system by taking into account the environment noise.
Based on the theory, we proposed an improved positioning al-
gorithm with high precision for more general applications. As
far as we know, it is the first time to focus on the positioning
algorithm especially for fence perimeter application. Compared
with the traditional positioning algorithm, our method has some
improvements. First, we extract the signal segment with highest
zero-crossing rate, which has higher positioning accuracy in-
stead of endpoint extraction to estimate time delay. Moreover,
the signal extraction is based on zero-crossing technique, which
has advantages of easy implementation and high efficiency [13],
[14]. Furthermore, in order to remove the correlated noise,
general cross correlation based on Wiener filtering and Gnn
subtraction (WG-GCC) weighting function is used to estimate
the time delay [12], [15], [16]. We experimentally demonstrated
0733-8724 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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CHEN et al.: AN IMPROVED POSITIONING ALGORITHM WITH HIGH PRECISION FOR DUAL MACH–ZEHNDER INTERFEROMETRY 1955
Fig. 1. Schematic diagram of DMZI disturbance sensing system. DAQ: Data
Acquisition Card; IPC: Industrial Personal Computer; C1, C4, C5: 3 dB fiber
coupler; C2, C3: Optical circulator; PD1, PD2: Photo-detector.
that the positioning algorithm can improve the positioning ac-
curacy of the sensor in fence perimeter application.
II. THEORY
A DMZI disturbance sensing system is shown in Fig. 1. The
output of the laser with narrow line-width is split equally at cou-
pler C1. The two light beams are launched into a dual Mach–
Zehnder interferometer formed by coupler C4 and coupler C5
after passing through circulator C2 and circulator C3, respec-
tively. The two light beams propagate oppositely in clockwise
and counter-clockwise directions and interfere at peer coupler.
The interference outputs will be detected by PIN diodes PD1
and PD2, respectively. The output signals of the PIN diodes
are acquired by data acquisition card (DAQ) and processed in
industrial personal computer (IPC).
When a disturbance event occurs at point Pwhich has a
distance xfrom the point Aon the fiber, there will be an arrival
time delay dbetween the two channel signals detected by PD1
and PD2. The time delay dcan be expressed as
d=n(L−2x)/c (1)
It indicates that the disturbance position can be deduced from
the time delay d, as the velocity of light in vacuum c, the effective
refractive index of fiber nand the length of interferometer arm
Lare all constants for the system.
For an ideal system, the ac components of the output signals
detected by PD1 and PD2 are
I1(t)=cos(φ(t)) + nc1(t)
I2(t)=cos(φ(t−d)) + nc2(t)(2)
where φ(t) is the phase modulation difference between the two
arms of the interferometer caused by the disturbance event with-
out phase noise induced by polarization, while nc1and nc2are
the additive circuit noise.
The most popular time delay estimation technique is to per-
form cross correlation between two channels, which is based on
the mathematical model [17]
I1(t)=s(t)+n1(t)
I2(t)=s(t−d)+n2(t)(3)
where s(t), n1(t), and n2(t)are real, jointly stationary random
process. Assuming that signal s(t) is uncorrelated with noise
n1(t)and n2(t). We can easily estimate the time delay dby
locating the peak position of the cross correlation function be-
tween the two signals in (3), and then, calculate the vibration
position from (1).
However, in the actual situation, considering the related
noises, the general noise-involved model of interference signal
should be expressed as [4]
I(t)=[1+na(t)] ·cos[φ(t)+ξ(t)+nε(t)+np(t)] + nc(t)
(4)
where ξ(t) is the additional environment noise introduced by
the slight disturbance along the sensing fiber, ncis the additive
circuit noise, na(t)and nε(t)are the visibility and phase noise
induced by polarization effect, and np(t)is the phase noise
coming from the frequency noise of the laser source.
We can neglect the effect of the phase noise coming from
the frequency noise of the laser source, as well as the visibility
variation and phase noise induced by polarization effect. Be-
cause the former can be reduced by compensating the length
difference between interferometer arms, and the latter, can be
compensated by dynamically adjusting polarization state of the
light in the interferometer [4], [10].
Then, the two output signals are simplified as
I1(t)=cos[φ(t)+ξ(t)] + nc1(t)
I2(t)=cos[φ(t−d)+ξ(t)] + nc2(t)(5)
Direct use of model (3) instead of (5) will lead to information
loss of non-additive noises and the wrong estimated result of d
with cross correlations. In order to overcome this issue, we do
a restriction and make two assumptions as follows.
Restriction: The observation time Tis set to a small value to
satisfy that the environment noise is almost constant during the
observation time.
Assumption a: All processes in (5) are stationary random
processes during the short observation time [4].
Assumption b: The cable vibration induced by intrusion is a
simple harmonic oscillation in the short observation time.
The environment noise can be expressed as ξ(t)=ξ(t0)+
Δξ(t),t∈[0,T], where ξ(t0)is a constant value and repre-
sents the environment noise at t0. Under the aforementioned
restriction, Δξ(t)≈0is a small variable changing with time.
Equation (5) can be approximated as
I1(t)=cos[ϕ(t)] + Δξ(t)sin[ϕ(t)] + nc1
I2(t)=cos[ϕ(t−d)] + Δξ(t)sin[ϕ(t−d)] + nc2
(6)
which can be formed by a pure signal and an additive
noise term as the model of (3), where ϕ(t)=φ(t)+ξ(t0),
s(t)=cos[ϕ(t)], and n1(t)=Δξ(t)sin[ϕ(t)] + nc1(t),n
2(t)
=Δξ(t)sin[ϕ(t−d)] + nc2(t).
In terms of the cross-correlation time delay estimation the-
ory under Assumption a, we can estimate dby locating the
peak position of the cross-correlation function between I1(t)
and I2(t). When the received SNR (signal to noise ratio) is high,
the minimum mean square error (MSE) of the positioning er-
1956 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, MAY 15, 2015
ror induced by delay value deviation from the correct peak of
cross-correlation function follows Crammer–Rao lower bound
(CRLB) model [15], [18]:
σ2
CRLB =1
8π2TB(f2
0+B2
12 )1+ 1
SNR2
+1
(7)
where Bis signal bandwidth, f0is center frequency, and Tis the
observation time.
On the basis of Assumption b, the signal segment can be
approximated as the baseband sinusoidal frequency modulation
(SFM) signal with the form of u(t)=cos(βcos(2πft)), where
ϕ(t)=βcos(2πft)is the phase change induced by vibration,
βand fare amplitude and frequency, respectively. For the
baseband SFM signal, the signal bandwidth is B≈2(β+1)f,
and SNR,fare constants in an intrusion event, while f0equals
to 0 [19]–[21]. According to (7), the signal segment with larger
bandwidth Bhas higher positioning precision as SNR,f0and
T are constant. So we should extract the large bandwidth sig-
nal segment for time delay estimation to obtain small MSE of
positioning error.
Meanwhile, the additional environment noise ξ(t) is induced
by the weak disturbance along the sensing cable, and it has
similar character with the disturbance event, which makes the
noises of the two signals (n1(t)=Δξ(t)sin[ϕ(t)] + nc1(t)and
n2(t)=Δξ(t)sin[ϕ(t−d)] + nc2(t)) strongly correlated. The
cross correlation of I1(t)and I2(t)is
RI1I2(τ)= Rss(τ−d)+Rn1n2(τ)
=δ(τ−d)∗∞
−∞
Gss(f)e−j2πf τ df
+∞
−∞
Gn1n2(f)e−j2πfτ df (8)
where Gss(f)is the auto power spectral density of s(t),
Gn1n2(f)is the cross power spectral density of n1(t)and n2(t).
Rn1n2(τ)is not equal to 0. It will cause the peak position of
RIII2(τ)deviate from the time delay d. To solve this problem,
we should use a general cross correlation, which is robust to the
correlated noise to suppress the noise power.
Therefore, in order to achieve high positioning accuracy, we
should first set an extraction time according to the environment
noise, and extract the largest bandwidth signal segment, then
estimate the time delay of the extracted signal segments by
using a general cross correlation.
III. POSITIONING ALGORITHM
The proposed positioning algorithm consists of the following
steps:
Step 1: Set extraction time.
Through the long-term analysis, we find the environment
phase noise is almost constant during the observation time of
10 millisecond order of magnitude. In order to meet the re-
striction in Section II and obtain sufficient data for time delay
estimation, we set the extraction time as 0.02 s by compromise.
Step 2: Exact the largest bandwidth signal segment based on
zero-crossing rate.
Fig. 2. Flow chart of the improved positioning algorithm.
Step 3: Use general cross correlation based on Wiener filtering
and Gnn subtraction weighting function (WG-GCC) to estimate
the time delay of the extracted signal, which is robust to the
correlated noise.
The flow chart and diagram of the positioning algorithm is
shown as in Fig. 2.
A. Signal Extraction Based on ZCR
In acoustic signal processing applications such as speech
recognition, zero-crossing analysis is commonly used to dis-
tinguish the sounds of different frequencies [14]. In the context
of discrete-time signals, zero crossing will occur if successive
samples have different algebraic signs. Being a simple method
for signal frequency analysis, zero-crossing rate is a measure-
ment of number of times in a given frame that the amplitude of
the signals passes through zero.
A definition of zero-crossings rate is
ZCRn=∞
−∞ |sgn[x(m)] −sgn[x(m−1)]|ω(n−m)
sgn[x(n)] = 1x(n)≥0
−1x(n)<0and ω(n)
=1/2N0≤n≤N−1
0 otherwise (9)
where Nis the length of a selected frame. The distribution
of the zero-crossing rates can be obtained by applying (9) to
the signal. Zero-crossing rate is measurement of “frequency
composition” of a signal. This is more valid for narrowband
signals such as sinusoids. The interference signal is a broadband
signal and the interpretation of zero-crossing rate is, therefore,
much less precise, but we can roughly estimate the spectral
properties according to the short time average zero-crossing rate
value [13], [14]. Since larger bandwidth indicates more high-
CHEN et al.: AN IMPROVED POSITIONING ALGORITHM WITH HIGH PRECISION FOR DUAL MACH–ZEHNDER INTERFEROMETRY 1957
frequency components, there is a strong correlation between
zero-crossing rate and bandwidth.
We can easily find the peak position of the zero-crossing rate
curve, which corresponds to largest bandwidth. Then, we can
extract the signal segment around the peak position.
B. Time Delay Estimation Based On WG-GCC
After extracting the largest bandwidth signal segments, we
can estimate the time delay between the selected signals. If we
assumed that the correlated noises are stationary or short-time
stationary, we can estimate Gn1n2(ω)and |Ni(ω)|2through
undisturbed signal [12]. According to (8), estimation error,
Fourier transformed of Rn1n2(τ), is mainly determined by
Gn1n2(ω). So we can subtract the noise spectrum to reduce
the estimation error.
Based on the aforementioned analysis, we use WG-GCC,
which is robust in the correlated and reverberate noise environ-
ment to estimate the time delay [16]–[18]. The general cross
correlation method based on Wiener filtering and Gnn subtrac-
tion can be expressed as follows:
τ= arg max Rs1s2(τ)
Rs1s2(τ)= 1
2ππ
−π
Gs1s2(ω)ejωτ dω
≈1
2ππ
−π
W1(ω)W2(ω)(GI1I2(ω)
−Gn1n2(ω))ejωτ dω
Wi(ω)= (|Ii(ω)|2−|Ni(ω)|2)/|Ii(ω)|2,i =1,2
(10)
where Rs1s2(τ)is the cross correlation between s1(t)and s2(t)
in (6), which is equivalent to the inverse Fourier transform of
Gs1s2(ω).Wi(ω)is the Wiener filtering weighting function.
Then, we can estimate the time delay dby locating the peak
position of Rs1s2(τ).
IV. EXPERIMENTS
In this section, we first analyze the signals in different intru-
sion events to demonstrate the rationality of the assumptions in
the positioning theory. Then, we conduct a positioning experi-
ment based on zero-crossing technique and WG-GCC to verify
the validation of the proposed algorithm. Finally, 500 sets of po-
sitioning tests by using three different algorithms are conducted
to illustrate the performance of the algorithm.
The experiment setup is shown in Fig. 1. Laser source was
a 1550 nm distributed feedback laser. The output light with
3.5 mW is split equally at C1, and then, the two light are
launched into the dual Mach–Zehnder interferometer formed
by C4 and C5. The two light beams propagate oppositely in
clockwise and counter-clockwise directions along a 2.25 km
(L=2.25 km) single mode sensing cable, which is attached
to perimeter fence, and interfere at the peer coupler. The in-
terference outputs are detected by PD1 and PD2, respectively,
collected by DAQ and processed by IPC. The data sampling
rate of DAQ is set to 10 MHz and the theoretical resolution is
Fig. 3. A typical sensing cable configuration on chain link fence.
Fig. 4. Two second output signals in different events. (a) No intrusion.
(b) Fence climb. (c) Fence cut.
10 m. In the experiments, the intrusion is generated by people
of 60 kg weight climbing and cutting the fence near the post and
the distance between the vibration point P and point A is 620 m.
The implementation of the sensor as a fence perimeter sys-
tem is achieved by attaching the sensing cable directly to the
fence. The recommended fence fabrics include chain link, weld
mesh, and palisade styles, which vibrate strongly when intru-
sion occurs. In order to maintain the long-term stability of the
state of polarization and avoid excessive nuisance signals, the
fence construction needs to follow an acceptable standard and
the sensing cable should be directly attached to the fence fabric
through hose clamps. Fig. 3 shows a sensing cable configuration
on chain link fence. We loop the cable up and down along the
posts to improve the detection sensitivity of fence when peo-
ple climb at or near the rigid posts. It should be noted that the
cable configuration depends on the required level of security,
the type of intrusion, and the skill level of intruder. Whatever
the configuration is, it will induce a significant environment
noise ξ(t), which cannot be neglected since it blows and rains in
the outdoor environments.
A. Demonstration of the Theory
Fig. 4 shows the signals in three different events including no
intrusion, fence climb and fence cut. As can be seen from the
figure, the environment noise changes much more slowly than
the phase change induced by the intrusion event. It means that the
restriction of the theory is reasonable. The output signal induced
by intrusion action shows great irregularity during the intrusion,
1958 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, MAY 15, 2015
Fig. 5. Short-time Fourier transform of the fence climb signal in Fig. 4 (b).
Fig. 6. A Two second period of fence climb signal. (a) Time domain repre-
sentation. (b) Zero crossing rate representation.
intuitively showing that there are different signal densities at
different time periods. It is difficult to determine the start point
of the event, so the positioning algorithm based on endpoint
detection is unpractical in this situation.
Fig. 5 shows the short-time Fourier transform of the fence
climb signal in Fig. 4(b). We can see that the disturbance signal
is a non-stationary signal and there are irregular changes in
spectrum with time. The dense regions of the signal have more
high frequency components, which is corresponding to larger
bandwidth, while the sparse regions have less high frequency
components, which is corresponding to smaller bandwidth. It
agrees with the corollary under Assumption band supports the
theory in Section II.
B. Validation of the Algorithm
We conduct a positioning experiment to a fence climb signal
shown in Fig. 6 to verify the validation of the proposed algo-
rithm. Fig. 6(b) shows the distribution of the zero crossing rate
of the signal. According to the positioning theory, the signal
segment with higher zero crossing rate, which is correspond-
ing to larger bandwidth has higher positioning accuracy. So we
extract the signal region 1 as shown in Fig. 6, which is around
the peak position of the distribution of the zero crossing rates
for time delay estimation. 200 k samples are selected accord-
ing to the extraction time (0.02 s). We also extract the other
TAB LE I
POSITIONING ERRORS OF DIFFERENT SIGNAL REGIONS
Region 12345
Maximum ZCR of region 0.117 0.105 0.078 0.050 0.039
Positioning error/m (CC) 20 30 80 90 120
Positioning error/m (WG-GCC) 10 20 80 70 120
TAB LE II
POSITIONING ERROR STATISTICS OF DIFFERENT ALGORITHMS
TDE algorithm Mean absolute error Standard deviation
WG-GCC with extraction 4.4000 7.0345
CC with extraction 11.2000 13.8137
CC without extraction 50.8000 59.3993
four regions with low zero-crossing rate as shown in Fig. 6
and apply crossing correlation and WG-GCC to the five signal
regions, where the zero-crossing rate is sorted in descending
order. Table I shows the positioning errors of the five regions.
It is obvious that positioning error based on cross correlation
is smaller in high zero-crossing rate signal region than rela-
tively low zero-crossing rate region and WG-GCC is effective
in improve positioning accuracy.
C. Performance of the Algorithm
In the real application, the signal is divided in to continuous
signal frames. Considering the real-time performance, we set
the frame length to be 0.3 s. Three different algorithms are ap-
plied to 500 sets of positioning tests. The first two algorithms
are estimating the time delay of the extracted signals by WG-
GCC and traditional cross correlation, respectively, while the
third algorithm is estimating the whole frame by traditional
cross correlation. We mark the three different algorithms as
WG-GCC with extraction, CC with exaction and CC without
extraction respectively for short. Table II shows the statistics of
the positioning error of different algorithms. We can see from
Table II that WG-GCC with extraction can effectively reduce
the mean absolute error and standard deviation of the position-
ing error compared with CC with and without extraction. In
particular, the positioning error of the proposed algorithm has
been reduced by an order of magnitude compared to CC without
extraction.
Further analysis of the positioning result reveals that the posi-
tioning error can be basically reduced to the range of 0 ∼±20 m
by applying WG-GCC with signal extraction based on zero-
crossing rate, of which the mean absolute error and standard
deviation are 4.4000 m and 7.0345 m, respectively. In particu-
lar, there is 60.16% of the positioning error distributed in the
range of 0 ∼±10 m, which is close to the theoretical precision,
and up to 83.66% distributed in the range of 0 ∼±20 m, only
a minor part of the results represent that the positioning errors
are greater than ±20 m.
Fig. 7 shows the running time of 500 sets of positioning
tests conducted by three different algorithms, we can see that
CHEN et al.: AN IMPROVED POSITIONING ALGORITHM WITH HIGH PRECISION FOR DUAL MACH–ZEHNDER INTERFEROMETRY 1959
Fig. 7. Running time of three different algorithms.
the running times of CC with extraction and WG-GCC with
extraction are much less than 0.3 s, which fully satisfy the
real-time performance, while the running times of CC without
extraction are all distributed near 1s which is far beyond the
frame length, it severely affect the efficiency and result in data
loss.
V. CONCLUSION
We theoretically analyze the positioning error of the DMZI
sensing system by taking into account the environment noise.
Following this theoretical basis, an improved positioning algo-
rithm with high precision and easy implementation is employed.
We first extract the signal segment with highest zero-crossing
rate, then use general cross correlation based on Wiener filtering
and Gnn subtraction (WG-GCC) weighting function, to estimate
the time delay of the extracted signals. Although the proposed
algorithm has advantages of high precision, easy implementa-
tion, and high efficiency, its performance is limited fundamen-
tally by the sampling interval, next step we will move on to the
study of estimating continuous time delay from sampled data
and we have already got some preliminary results. Finally, we
have experimentally demonstrated that the proposed position-
ing algorithm can greatly improve the positioning accuracy, with
the positioning error of ±20 m. The proposed algorithm has a
promising potential in real-time fence perimeter applications.
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Qinnan Chen was born in Fujian, China, in 1987. He received the B.Sc. degrees
in opto-electronic technology science (Cooperate with Nankai University) from
Tianjin University, Tianjin, China, in 2010, where he is currently working toward
the Ph.D. degree of optical engineering.
His research interests mainly focus on distributed fiber sensing.
Tiegen Liu, biography not available at the time of publication.
Kun Liu, biography not available at the time of publication.
Junfeng Jiang, biography not available at the time of publication.
Zhe Shen, biography not available at the time of publication.
1960 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 33, NO. 10, MAY 15, 2015
Zhenyang Ding, biography not available at the time of publication.
Haofeng Hu, biography not available at the time of publication.
Xiangdong Huang, biography not available at the time of publication.
Liang Pan, biography not available at the time of publication.
Chunyu Ma, biography not available at the time of publication.
