Modified frequency-shifted interferometer:
encoding wavelength into phase
Xi Chen (陈 希)
1,2,3
, Ciming Zhou (周次明)
1
, Dian Fan (范 典)
1,
*, Li Qian (钱 黎)
1,4
,
Yandong Pang (庞彦东)
1,2
, Cong Wei (魏 聪)
1,2
, Chenguang Zhao (赵晨光)
1
,
Sijing Liang (梁斯靖)
1
, and Yuxiao Li (李宇潇)
1,2
1
National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology,
Wuhan 430070, China
2
School of Information Engineering, Wuhan University of Technology, Wuhan 430065, China
3
Department of Mechanical and Electrical Engineering, College of Post and Telecommunication,
Wuhan Institute of Technology, Wuhan 430073, China
4
Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4, Canada
*Corresponding author: fandian@whut.edu.cn
Received May 13, 2020; accepted June 23, 2020; posted online August 24, 2020
We propose a novel modified frequency-shifted interferometer, where a Mach–Zehnder interferometer is added in
order to obtain wavelength information. We use the Hilbert transform to extract the wavelength information
from the phase of the interference pattern and construct the relationship between phase and wavelength. The
laser wavelength measurement experiment is used to verify the compound interferometer. Experimental results
demonstrated that our method could obtain the wavelength from the phase, which is of great significance for
demodulation of the fiber Bragg grating based on a frequency-shifted interferometer.
Keywords: modified frequency-shifted interferometry; phase difference; Hilbert transform.
doi: 10.3788/COL202018.101203.
Recently, the frequency-shifted interferometer (FSI) has
been studied and applied to fiber-optic sensor sensing,
which attracts the interest of many researchers
[1–11]
.FSI
utilizes a frequency shifter [usually, an acoustic optic
modulator (AOM)] asymmetrically inserted in a Sagnac
loop, producing location-resolved information for multiple
sensors without resorting to wavelength-division or time-
division multiplexing. Since the Sagnac interferometer is
self-referenced, no coherence requirement is needed for
the light source. FSI also results in a high signal-to-noise
ratio (SNR) and does not require a fast detector
[9]
. How-
ever, the interference signal of FSI does not contain wave-
length information of the light reflected from the sensor. If
we need to obtain wavelength information, it is necessary
to use either a tunable laser source or a tunable filter to
scan the optical wavelength, which causes more complex-
ity and adds to the cost.
In this Letter, we propose a novel modified FSI (MFSI)
based on a compound interferometer structure to address
the above problems. We modified the optical path struc-
ture, adding a Mach–Zehnder interferometer (MZI) in the
conventional FSI, forming a compound interferometer.
Two counter-propagating light waves go through different
paths and encode wavelength information into the phase
of the interference signal. We adopt the Hilbert transform
(HT) to convert the phase into a wavelength
[12–14]
. We cal-
ibrate the system with a laser source of known wavelength
to establish the relationship between the initial phase of
the interference s ignal and this known wavelength. There-
after, the unknown wavelength can be calculated from the
initial phas e. Here, we demonstrate only the capability of
extracting wavelength information, without sensors in the
MFSI. Our method is tested with interference signals ob-
tained from the MFSI system, the results show it is fea-
sible, simple, and with low cost, and it is vital to
extend the applications of FSI.
The schematic diagram of the MFSI based on the com-
pound interferometer is depicted in Fig.
1.
A 50/50 fiber coupler C
1
, path A, and path B constitute
a Sagnac loop, and an AOM in path B acts as a frequency
shifter. An MZI is formed by a circulator (CIR-2) and a
50/50 fiber coupler C
2
(included in path A), with slightly
different path lengths L
b
and L
c
. The phase difference
(PD) between path L
b
and L
c
is a function of wavelength,
and therefore the wavelength information can be ex-
tracted from this PD. A polarization controller (PC) is
employed to improve the interference visibility.
After passing through CIR-1, the light signal is split
equally at C
1
and input in the clockwise (CW) and counter-
clockwise (CCW) directions. Then, upon returning to C
1
,
each time light passes through the AOM, and its frequency
is up-shifted by an amount equal to the frequency of the
acoustic driving signal f . The intensity signal ΔI at the bal-
anced detector (BD) is
[8,15]
ΔI ¼ A sin
2πnðλÞL
c
f −
2πnðλÞ
λ
ΔL
; (1)
A ¼ −4κ
A
κ
B
ð1 − γ
1
Þð1 − γ
2
Þγ
2
γ
1
E
2
0
; (2)
where A is the transmission coefficient, κ
A
and κ
B
are the
transmission coefficients of path A and path B, γ
1
and γ
2
COL 18(10), 101203(2020) CHINESE OPTICS LETTERS October 2020
1671-7694/2020/101203(4) 101203-1 © 2020 Chinese Optics Letters