Demodulation method combining virtual reference
interferometry and minimum mean square error for
fiber-optic Fabry–Perot sensors
Xinwang Gui (桂新旺)
1,2
, Michael Anthony Galle
3
, Li Qian (钱 黎)
1,3
,
Weilong Liang (梁伟龙)
1,2
, Ciming Zhou (周次明)
1,2,
*, Yiwen Ou (欧艺文)
1,2
,
and Dian Fan (范 典)
1,2
1
National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology,
Wuhan 430070, China
2
Key Laboratory of Fiber Optic Sensing Technology and Information Processing, Ministry of Education,
Wuhan University of Technology, Wuhan 430070, China
3
Department of Electrical and Computer Engineering, University of Toronto, Toronto M5S-3G4, Canada
*Corresponding author: zcm@whut.edu.cn
Received July 29, 2017; accepted November 23, 2017; posted online December 6, 2017
We propose a cavity length demodulation method that combines virtual reference interferometry (VRI) and
minimum mean square error (MMSE) algorithm for fiber-optic Fabry–Perot (F-P) sensors. In contrast to
the conventional demodulating method that uses fast Fourier transform (FFT) for cavity length estimation,
our method employs the VRI technique to obtain a raw cavity length, which is further refined by the MMSE
algorithm. As an experimental demonstration, a fiber-optic F-P sensor based on a sapphire wafer is fabricated for
temperature sensing. The VRI-MMSE method is employed to interrogate cavity lengths of the sensor under
different temperatures ranging from 28°C to 1000°C. It eliminates the “mode jumping” problem in the
FFT-MMSE method and obtains a precision of 4.8 nm, corresponding to a temperature resolution of 2.0°C over
a range of 1000°C. The experimental results reveal that the proposed method provides a promising, high pre-
cision alternative for demodulating fiber-optic F-P sensors.
OCIS codes: 060.2370, 060.2300, 050.2230.
doi: 10.3788/COL201816.010606.
Fiber-optic sensors have been widely employed for the
advantages of simple structure, high sensitivity, freedom
from electromagnetic interference, and suitability for harsh
environments
[1,2]
. In recent years, fiber-optic high tempera-
ture sensors have received widespread attention. Various
high temperature sensors based on long period fiber
gratings (LPFG)
[3]
,Fabry–Perot interferometers (FPI)
[4,5]
,
and fiber Bragg gratings (FBG)
[2]
are demonstrated.
Because sapphire fibers have a very high melting point,
which is the most important performance for the sensing
applications at a very high temperature, a lot of Letters
presented the sensors combined with Fabry–Perot (F-P)
and sapphire fibers. But, the fringe contrast of the sensor
output depended on many factors, such as the quality of the
silica-to-sapphire fiber splice, the surface roughness of the
fiber end, and the F-P surface, which are hard to control.
For obtaining the high precision and resolution of the
measurement, a variety of demodulation methods have
been developed to extract the cavity length of the F-P sen-
sors accurately through different algorithms. The wave-
length tracking method offers high sensitivity. However,
it is limited to measuring only relative changes in the
F-P cavity length, and the dynamic range is limited
as well
[6]
. The fast Fourier transform (FFT) method is a
classic method for cavity length demodulation and is
widely used as the first step to obtain raw cavity length
estimation. It transforms the signal from an optical
wavelength domain to a cavity length domain and gives
the raw absolute cavity length. The FFT method is fast,
has a wide dynamic range, and is less affected by noise.
However, the resolution is much lower than that of the
wavelength tracking met hod
[7]
, and the demodulating
precision is limited by the optical frequency range. To
circumvent these disadvantages, researchers have to
find other algorithms for different experimental
environments. Wang et al. used the FFT method to
obtain an estimated optical path difference (OPD)
and, subsequently, obtained a more accurate value
using the frequency estimation algorithm, achieving a
resolution of 3.0 nm
[8]
. A wavelet phase extracting
demodulation algorithm was proposed for optical fiber
F-P sensing. The FFT method was also used to obtain
the estimated cavity length first. This algorithm have
the advantage of speed and simplicity
[9]
. A demodula-
tion system based on the frequency modulated continu-
ous wave (FMCW) technique in an air-gap FPI has a
temperature resolution of ∼0.02°C, whi ch is m uch
higher than the measurement resolution using the tradi-
tional wavelength shift detection method
[10]
.Yinget al.
provided a novel algorithm combining the minimum
mean square error (MMSE) estimation and the
Fibonacci method based on FFT
[11]
. The resolution
COL 16(1), 010606(2018) CHINESE OPTICS LETTERS January 10, 2018
1671-7694/2018/010606(4) 010606-1 © 2018 Chinese Optics Letters