Hydroacoustic Pressure Gradient Recording by a System of Two Fiber-Optic Accelerometers

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135
ISSN 1068-3356, Bulletin of the Lebedev Physics Institute, 2021, Vol. 48, No. 5, pp. 135–138. © Allerton Press, Inc., 2021.
Russian Text © The Author(s), 2021, published in Kratkie Soobshcheniya po Fizike, 2021, Vol. 48, No. 5, pp. 18–24.
Hydroacoustic Pressure Gradient Recording
by a System of Two Fiber-Optic Accelerometers
O. T. Kameneva,b, Yu. S. Petrova, A. A. Podlesnykhb, V. A. Kolchinskiya,
I. N. Zavestovskayac,d, Yu. N. Kulchina,d, and R. V. Romashkoa,b,*
a Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences,
Vladivostok, 690041 Russia
b Far-Eastern Federal University, Vladivostok, 690950 Russia
c Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia
d National Research Nuclear University MEPhI, Moscow, 115409 Russia
* e-mail: romashko@iacp.dvo.ru
Received September 5, 2020; revised September 15, 2020; accepted September 16, 2020
Abstract—The paper presents the results of experimental studies of a portable measuring system based
on two inertial fiber-optic accelerometers with a multiturn optomechanical transducer placed in a
Mach—Zehnder fiber-optic interferometer arm used as a sensitive element. Passive phase demodula-
tion using a fiber-optic splitter 3 × 3 makes it possible to record interferometer output signals in the
presence of a thermal drift of the operating point. The possibility of recording using such an acoustic
and hydroacoustic pressure gradient system is shown.
Keywords: fiber-optical sensor, interferometer, accelerometer, hydroacoustic signal
DOI: 10.3103/S1068335621050043
In [1], the possibility of recording the hydroacoustic pressure by an inertial accelerometer based on the
Mach—Zehnder fiber-optic interferometer was demonstrated. It was shown that an accelerometer fixed
on the surfaces of an elastic membrane interacting with an acoustic or hydroacoustic wave can record
vibrations caused by acoustic pressure. Such a method for receiving hydroacoustic signals should be used,
e.g., when deploying systems of acoustic monitoring and seismic exploration on the ice surface [2, 3] or
when an accelerometer is placed within an underwater vehicle whose hull is a natural receiver of hydro-
acoustic signals.
In this paper, we present the portable measuring system based on two inertial fiber-optic accelerome-
ters with a multiturn optomechanical transducer placed in the Mach—Zehnder fiber-optic interferometer
arm as a sensitive element. The possibility of recording the gradient of acoustic and hydroacoustic pressure
using such a system was experimentally shown.
The block diagram of the structure of the multiturn optomechanical transducer based on the a Mach—
Zehnder fiber-optic interferometer is presented in [4]. Phase demodulation of the accelerometer output
signal was performed by a method based on a fiber-optic splitter 3 × 3 [5] whose signals of the output of
three ports are shifted in phase by 120°. Such an approach negates the need for control of the interferom-
eter operating point position and enables recording of weak signals even under conditions of significant
external influences on the accelerometer (wind load, acoustic perturbations, temperature drift, and
others).
Figure 1a shows the block diagram of the measuring system.
The system includes two vertical inertial fiber-optic accelerometers, a recorder, and a computer.
The use of the passive form of phase demodulation based on a fiber-optic splitter 3 × 3 requires record-
ing of three interferometric signals shifted in phase by 2π/3 with respect to each other.
Therefore, six signals are recorded, by three from each accelerometer, by which the change in the phase
difference Δϕ between signal and reference waves of the Mach—Zehnder interferometer is then recon-
structed [5]. For the developed accelerometers, this change in the phase difference appears proportional
to the acceleration a of the membrane surface on which the accelerometer is fixed [1].

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BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE Vol. 48 No. 5 2021
KAMENEV et al.
According to the results of experimental studies of accelerometers, their frequency responses were con-
structed at a vibroacceleration amplitude of 0.02 m/s2 (Fig. 1b). We can see that the sensitivity of the first
transducer is two times the sensitivity of the second one. Since the sensitivity of two transducers in the gra-
dient receiver should be identical, all obtained values for transducer D2 were multiplied by a correcting
coefficient k equal to the ratio of sensitivities of the second and first transducers (k = 2). With
allowance for correction, the sensitivity of accelerometers in the frequency range of 100–1000 Hz was
200–1.2 rad · m–1 s2. At the frequency used in the experiment (630 Hz), the accelerometer sensitivity was
8 rad · m–1 s2. To convert the acceleration to the acoustic/hydroacoustic pressure, a conversion coefficient
was determined, which for the presented measuring system was 8.5 × 10–7 m s–2/Pa. Thus, the sensitivity
of the measuring system to pressure at a frequency of 630 Hz was 6.8 × 10–6 rad/Pa.
At the first stage, the measuring system was tested in an air medium. The experimental scheme is
shown in Fig. 2.
The acoustic emitter, i.e., a broadband head of a 3GDSh-8 electrodynamic loudspeaker, was initially
placed at the point O equidistant from transducer centers (points C and D), then, at the point A under the
transducer D1, after that, the point B under the transducer D2. The distances are as follows: AC = BD =
0.38 m, AD = BC = 0.57 m, and AB = CD = 0.42 m.
Figures 3a and 3c show the output signals of transducers for different emitter positions (at points O and A).
Fig. 1. (a) Block diagram of the measuring system based on fiber-optic accelerometers: PC is a computer, ADC is an ana-
log-to-digital converter, PS is the self contained power supply, PC is the personal computer, and D1 and D2 are fiber-
optic accelerometers and (b) their frequency responses.
(a) (b)
D1
D2
ADC
PS
channel 1
channel 6
PC
Recorder Frequency, Hz
Responsivity, rad · m
‒1
s
2
D2
D1
5
0
10
15
20
25
30
35
200 400 600 800 1000 12000
Fig. 2. Schematic of the experimental setup for recording the acoustic field gradient: (1) transducer D1, (2) transducer
D2, (3) metal membranes, (4) frame stands, (5) acoustic/hydroacoustic emitter, (6) pool (was filled with water in the sec-
ond testing stage).
1
3
4
2
ABO
CD
5
6
x

BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE Vol. 48 No. 5 2021
HYDROACOUSTIC PRESSURE GRADIENT RECORDING 137
The time shift between signals of transducers D1 and D2 equal to 536 ± 11 μs, observed when the emit-
ter is at points A and B (Fig. 3c for point A) corresponds to the speed of sound in air at a temperature of
22°C, 344.2 m/s, which is completely consistent with experimental conditions.
At the second stage, the measuring system was tested in a pool 1.4 × 2.8 m2 in size with rigid walls and
filled with water up to a level of 1 m.
The acoustic emitter had a directional pattern with a width of 120° and provided an acoustic pressure
of 1000 Pa at its center.
Similarly to the procedure performed at the first stage, the emitter was initially placed at the point O
equidistant from transducers, then, at the point A under transducer D1, and, after that, at the point B under
transducer D2. The distances are as follows: AC = BD = 0.38 m, AD = BC = 0.68 m, and CD = 0.56 m.
Figures 3b and 3d show the output signals of transducers for different emitter positions (at points O
and A) when the pool was partially filled with water. The time shift between signals of transducer D1 and
D2 equal to (210 ± 5) μs observed when the emitter is placed at points A and B (Fig. 3d for point A) cor-
responds to the speed of sound in water at a temperature of 10°C, 14 47 m/s, w hich i s com pletely consistent
with experimental conditions.
Fig. 3. Output signals recorded by two transducers of the measuring system, and their difference for different acoustic
emitter positions: (a, b) at the point O and (c, d) at the point A when the acoustic wave propagates in air (a, c) and
in water (b, d).
0
2000
2000
P, Pa
20 40 60 80
D1
D2
0100
0
2000
2000
'P, Pa
20
(a)
40 60
Time, u67 Ps
800100
0
1000
1000
1000
1000
P, Pa
100 200 300 400
D1
D2
0
0
'P, Pa
100
(b)
200 300
Time, u15 Ps
4000
0
2000
2000
P, Pa
20 40 60 80
D1
D2
0100
0
2000
2000
'P, Pa
20
(c)
40 60
Time, u67 Ps
800100
0
1000
1000
1000
1000
P, Pa
100 200 300 400
D1
D2
0
0
'P, Pa
100
(d)
200 300
Time, u15 Ps
4000

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BULLETIN OF THE LEBEDEV PHYSICS INSTITUTE Vol. 48 No. 5 2021
KAMENEV et al.
These pressure differences ΔPt shown in Fig. 3 are used to obtain the projection of the acoustic pressure
gradient onto the X axis, calculated as
(1)
where is the Fourier transform, is the cyclic frequency of the acoustic field, and Δx is the
distance between centers of accelerometers (CD distance).
Figure 4 shows the pressure gradient amplitudes and phases φω measured at various positions of
the acoustic emitter on the X axis. As can be seen, they are identical with high accuracy (within experi-
mental error) to the corresponding data calculated based on the experimental geometry.
Thus, the two-channel measuring system based on two inertial fiber-optic accelerometers was pro-
posed. A multiturn optico-mechanical converter placed in the arm of the Mach–Zehnder fiber-optic
interferometer was used as a sensitive element of accelerometers. The possibility of recording the acoustic
and hydroacoustic pressure gradient using such a system was experimentally shown.
FUNDING
This study was supported by the Russian Science Foundation, project no. 19-12-00323.
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Translated by A. Kazantsev
ωωω
Δ
∇=∇ φ=
Δ
()
||exp ,
t
FP
PPi
x
(..)
F
ω= π
2
f
ω
∇
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P
Fig. 4. (a) Amplitudes of the acoustic pressure gradient and (b) its phases as functions of the acoustic emitter position,
determined using the measuring system and calculated from the experimental geometry.
(b)
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