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Japanese Journal of Applied Physics 56, 127301 (2017)https://doi.org/10.7567/JJAP.56.127301

Sound intensity probe for ultrasonic ﬁeld in water using light-emitting diodes
and piezoelectric elements
Xi Zeng*, Yosuke Mizuno, and Kentaro Nakamura
Laboratory for Future Interdisciplinary Research of Science and Technology, Tokyo Institute of Technology, Yokohama 226-8503, Japan*E-mail: zeng.x.ab@m.titech.ac.jp
Received May 10, 2017; accepted September 6, 2017; published online November 9, 2017
The sound intensity vector provides useful information on the state of an ultrasonic ﬁeld in water, since sound intensity is a vector quantity
expressing the direction and magnitude of the sound ﬁeld. In the previous studies on sound intensity measurement in water, conventionalpiezoelectric sensors and metal cables were used, and the transmission distance was limited. A new conﬁguration of a sound intensity probe
suitable for ultrasonic measurement in water is proposed and constructed for trial in this study. The probe consists of light-emitting diodes andpiezoelectric elements, and the output signals are transmitted through ﬁber optic cables as intensity-modulated light. Sound intensity measurements of a 26 kHz ultrasonic ﬁeld in water are demonstrated. The difference in the intensity vector state between the water tank with and withoutsound-absorbing material on its walls was successfully observed. © 2017 The Japan Society of Applied Physics

1.

Introduction

It is essential to determine the sound pressure distribution in theultrasonic ﬁeld1) both in industrial applications and fundamental researches2,3) on high-intensity ultrasonic waves inliquid. Piezoelectric (PZT) hydrophones have long been used
as a common tool to measure ultrasonic ﬁelds.4,5) Opticaltechniques such as the Schlieren method6–9) and the use of ﬁber
optic hydrophones10–15) are also used as alternatives. On theother hand, sound intensity measurement is a well-establishedmethod of determining the state of sound ﬁelds in the audible
range in air, since sound intensity is a vector quantity expressing both the direction and the magnitude of the energy
ﬂow transmitted by sound waves.16) A sound intensity probe
consisting of multiple condenser microphones is commercially
produced by several companies and widely used for noise
source measurements. Moreover, sound intensity measurements have been applied to underwater sound ﬁelds.17–19)
Piezoelectric hydrophones were used instead of condenser
microphones for underwater applications. However, the lengthof the metal cable is limited owing to the high output impedance of piezoelectric hydrophones. This sometimes causes
practical diﬃculties in measuring ultrasonic ﬁelds in water
since the electronics for instrumentation should be placed in a
dry area and a long transmission distance is required. For
industrial applications of high-power ultrasound, this usually
becomes a problem since large water tanks are used in commercial factories and the transmission distance is rather long.
Multiple sensors are required for sound intensity measurement because the intensity is deﬁned as the product of soundpressure and particle velocity. Particle velocity is usuallycalculated from the gradient of sound pressure, and a pair ofpressure sensors are used to determine particle velocity. To
ﬁnd the two- or three-dimensional intensity vector, twoor three pairs of pressure sensors are needed. As a result, thenumber of coaxial cables increases for practical soundintensity measurement. The problems of both the number
and the length of metal cables are practical limitations in
intensity measurement in water. These limitations makeintensity measurement impossible in the case of huge tanks
used in industrial applications.
The authors proposed a novel hydrophone conﬁguration inwhich a light-emitting diode (LED) and a ﬁber optic cable are

Fig. 1. Conﬁguration of single LED-PZT sensor.

integrated with a piezoelectric element.20–22) Sound pressureis transformed to electrical voltage through the piezoelectriceﬀect, and transformed again to optical signal using the LED.
The optical signal is transmitted through the ﬁber optic cable.
Using this technology, intensity measurement in water will
become more streamlined because there is little limitation inextending cable length and the weight of the cable can be
reduced markedly.
In this study, we integrate four of the ultrasonic sensors
using LEDs and piezoelectric elements to a novel soundintensity probe for an ultrasonic ﬁeld in liquid. To verify theoperation of the proposed intensity probe, the measurement of
the sound intensity distribution in a water bath is demonstrated for ultrasonic excitation at approximately 26 kHz.
The diﬀerence between the measurements with and withoutsound-absorbing material on the walls of the bath was
successfully observed from the intensity vector patterns measured using the proposed probe.
2.

LED-PZT sound intensity probe

2.1

Basic structure of LED-PZT sensor
Figure 1 shows the conﬁguration of the sound pressure
sensor with LED and a piezoelectric element. An LED is
directly connected to a cylindrical PZT element (5 mm in diameter and 10 mm in height). Here, the piezoelectric element

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X. Zeng et al.

Fig. 2. (Color online) Conﬁguration of four-channel LED-PZT intensity probe.

is made of lead zirconate titanate ceramics and polarized in
its axial direction. Its top and bottom surfaces are electroplated with thin silver layers. The leads of the LED are
soldered to the electrodes. A DC bias is provided via a 330 Ω
resistor and a 10 nF capacitor. The operation voltage of the
LED is set in the linear region beyond the threshold voltage
by adjusting the DC power supply. When sound pressure at
an ultrasonic frequency is applied to the PZT element, an AC
voltage is induced across the PZT element, leading to themodulation of the LED current and thus the optical output.
The dynamic change in the LED output is proportional to thatin sound pressure. An optical signal is led to a detector
located at a remote place using a plastic optical ﬁber (POF)
with a diameter of 1 mm. A metal cap is attached to the
LED to ﬁrmly connect the POF cable.
2.2 Sound intensity probe with LED-PZT sensors
Four LED-PZT sensors are integrated into a two-dimensionalsound intensity probe, as illustrated in Fig. 2. The outputs ofthe sensors are received by four independent photodiodes
with ampliﬁers through four POF cables. There is no need
to use diﬀerent colors for the light sources in this setup,
however, four colors at wavelengths of 660 (red), 606(amber), 520 (green), and 465 nm (blue) are selected for theLEDs. This is because, in future studies, wavelength divisionmultiplexing (WDM) should be attempted over a single ﬁber
cable to handle a larger number of sensors. In this paper,
diﬀerent wavelengths (colors) of light sources are employed
for the preliminary investigation. The use of diﬀerent colors
provides a practical advantage in identifying the channel
at the other end of ﬁber cables even in the case of using afour-channel sensor head.
Figure 3 shows the photodetector outputs versus the DC
bias voltage of the four LED-PZT sensors. The bias DC
voltages for the red, amber, green, and blue sensors are set
at 2.8, 3.0, 3.5, and 3.8 V, respectively, so that all the DC
optical outputs at the photoreceivers would fall at aroundthe center of the dynamic range of the photodetector circuit.
The sensors do not respond to low sound pressure without
the bias voltage. The slopes of the linear part for the four
LED-PZT sensors are nearly the same. However, the acoustic
sensitivities are distributed by a factor of two, as measured
and plotted in Fig. 4. Here, sound pressure was measured
with a widely used hydrophone, Brüel&Kjær, 8103, withcalibrated absolute sensitivity. The developed LED-PZT
sensors showed good linearity up to 10 kPa. The diﬀerencesamong the outputs might be due to the diﬀerence in thewaterproof coating of the PZT elements and the variation in
the optical coupling between the LED and the ﬁber. The
weight of one LED-PZT sensor, including a 6 m ﬁber cable,

Fig. 3. (Color online) Output voltages of the photodetectors as functionsof the DC voltage applied to the four LEDs. The operation points areindicated with black circles.

Fig. 4. (Color online) Output voltages of sensors as functions of appliedsound pressure.

was 52 g, while that of the commercialized hydrophone(Brüel&Kjær 8103) with the same length of cable is 156 g.
The weight of a conventional hydrophone is three time
greater than a LED-PZT sensor.
3.

Signal processing for sound intensity

3.1

Deﬁnition of sound intensity
Sound intensity, also known as acoustic intensity, is deﬁned
as the power ﬂow across a unit area and measured in W=m2.

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The sound intensity I is a vector quantity and given by the
product of the sound pressure p and the particle velocity
vector v as
I ¼ pv:

ð1Þ

This expression gives instantaneous intensity, and the timeaveraged value is usually used in practical sound intensity
measurement since the time-averaged intensity gives the net
energy ﬂow, which is called “active intensity”.
3.2 Complex expression of sound intensity
Assuming a sinusoidal continuous sound ﬁeld, a complex
expression is applied for sound pressure and particle velocity.
The complex sound pressure P~ and particle velocity vector V~
are written using their amplitudes and phases P, V, φ, and θasP~ ¼ Pe j’ ;V~ ¼ Ve j ;

ð2ÞFig. 5. (Color online) Measurement setup and coordinate system.

The reactive components Jx and Jy are written as
1
P2  P21

Im½P~ V~ x  ¼ 2
;
2
4!
1
P2  P23
:
Jy ¼ Im½P~ V~ y  ¼ 4
2
4!

ð3Þ
respectively, where j denotes the imaginary unit. Thus, theactive intensity I is expressed as the real part:23)
1

I ¼ Re½P~ V~ :
2

ð4Þ



Here, V is the complex conjugate of V. The imaginary part J,
which is referred to as “reactive intensity”, implies the stored
energy in a standing wave ﬁeld:
J¼

1Im½P~ V~ :2

ð5Þ

3.3 Sound intensity measurement with discrete
points of sound pressures

Particle velocity is calculated from the ﬁnite diﬀerence insound pressures at adjacent points, since only sound pressureis actually measurable with the sensor. From the equation of
motion~j!V~ ¼ gradP;

ð6Þ

the particle velocity vector V~ ¼ ðV~ x ; V~ y Þ is written in ﬁnite
diﬀerence forms as
P~ 2  P~ 1;
ð7Þ
V~ x ¼j!
P~ 4  P~ 3
V~ y ¼:
ð8Þ
j!
Here, ω, ρ, and Δ are the angular frequency, the densityof media, and the small distance between the two pressure
measurement points. P~ 1 , P~ 2 , P~ 3 , and P~ 4 are the complex
sound pressures measured at the positions shown in Fig. 2.
The amplitudes and phases for these sound pressures
are P1, P2, P3, P4, φ1, φ2, φ3, and φ4, and their values
will be actually measured in the experiments, as stated in
Sect. 4.
P~ i ¼ Pi e j’iði ¼ 1; 2; 3; 4Þð9ÞUsing these measured values, the active components of thesound intensities Ix and Iy are written as
1
P1 P2

Re½P~ V~ x  ¼
sinð’2  ’1 Þ;
2
2!
1
P3 P4

sinð’4  ’3 Þ:
Iy ¼ Re½P~ V~ y  ¼
2
2!
Ix ¼

ð10Þ
ð11Þ

Jx ¼

4.

ð12Þ
ð13Þ

Measurement

4.1

Measurement setup
Figure 5 shows the setup and coordinate system for thedemonstration of measurement. An ultrasonic transducer
operating at 26.35 kHz is mounted on one of the walls of awater bath of 420 × 320 mm2. The transducer is composed ofa half-wavelength straight horn and a bolt-clamped Langevintransducer.24) The horn is clamped at its node to the wall andhas a circular radiation surface of 50 mm diameter. The centerof the transducer is 65 mm below the water surface and
110 mm above the bottom.
The LED-PZT sensor array scanned 117 positions in 7.5mm steps in the two-dimensional region indicated in Fig. 5.
This means 13 points along the X-axis and 9 points along
the Y-axis. The x-component of sound intensity was always
measured with the amber LED sensor (P1) and the blue
LED sensor (P2), while the y-component was measured withthe red LED sensor (P3) and the green LED sensor (P4).
The spacing between sensors Δ was chosen to be 10.6 mm(Fig. 2), which corresponds to 0.186 times the wavelength of
26.35 kHz ultrasonic waves in water. The spacing Δ should
be suﬃciently smaller than the wavelength. However, it is
known that a too small spacing ampliﬁes noise in the ﬁnite
diﬀerence calculation.25)
4.2 Reference result with piezoelectric hydrophone
Before sound intensity measurement with the proposed
probe, the sound pressure distribution was measured using
a conventional piezoelectric hydrophone (Brüel&Kjær 8103).
The single hydrophone was mechanically scanned, and theamplitude is mapped in Fig. 6(a). A standing wave distribution is clearly observed along the x-direction. The measurement was conducted under almost the same conditions
using the proposed four-channel LED-PZT sensor array. The
average of four sensors is plotted in Fig. 6(b) on a linear
scale. We carefully measured such that the center of thehydrophone and the LED-PZT sensor array were at the same
depth in water. As can be seen from Figs. 6(a) and 6(b),standing wave patterns are observed. The error between these
two results are possibly attributed to the instability of the127301-3© 2017 The Japan Society of Applied Physics

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(a)
(a)

(b)
Fig. 7. Sound intensity distributions without sound-absorbing material in
the water tank: (a) active intensity and (b) reactive intensity. The lengths ofarrows are indicated on a logarithmic scale.

(b)Fig. 6. Sound pressure distributions measured using (a) commercial
piezoelectric hydrophone and (b) LED-PZT sensor array.

ultrasonic standing wave ﬁeld, which was sensitive to theinsertion of the sensors and water surface disturbance.
4.3 Sound intensity measurement
The active and reactive components of sound intensity
vectors measured with the proposed LED-PZT array probe
are shown in Figs. 7(a) and 7(b), respectively. Note that alogarithmic scale is adopted for determining the lengths ofarrows. As no sound-absorbing material is set on the walls
and a high reﬂection is expected at the walls, as well as at
the water surface and the bottom, it is thought that a highstanding wave ﬁeld is excited.
As for the reactive intensity component, the direction of
the x-components of arrows changed its periodicity frompositive to negative along the x-axis. This is a typical natureof a standing wave ﬁeld. The x-components of active
intensity around the transducer axis are almost positive.
However, little clear tendency is found in other places.
Next, sound-absorbing materials were ﬁxed on all thewalls and the bottom surfaces of the tank, except the water
surface. We arranged the orientations of the sound-absorbing
materials such that there exists no parallel pair of surfaces tosuppress the generation of standing waves. Sponge with acorrugated surfaces was used as the sound-absorbing material. The depth of the corrugated surface was about 35 mm,
which was 63% of the ultrasonic wavelength. We can expect
a reduction in the standing waves generated to some extent
by using this sound-absorbing material, but it should be notedthat it is diﬃcult in practice to fully suppress the reﬂections.

The results of measurement with sound-absorbing materials
are shown in Fig. 8. The x-components in the active intensity
vector are all positive over the measured region. As a whole, apositive overall ﬂow is apparently observed in this result. As
for the reactive intensity components, the x-components
still alternated regularly from positive to negative along thex-axis. From these results, we can understand that the reﬂection was reduced when using the sound-absorbing material
and the intensity of the traveling wave component increased.
To compare the results in Fig. 7 and Fig. 8 more quantitatively, the average active intensity was calculated and its
ratio to the reactive intensity is summarized in Table I.
The intensity of the travelling wave component increased
obviously in the case of the measurement with soundabsorbing material. Data shown in Figs. 7 and 8 are raw data
without correction for the sensitivity of each LED-PZT
sensor. In future research, we should develop a calibration
procedure for the intensity probe.
In this experimental setup at this frequency, it was, inpractice, very diﬃcult to suppress the reﬂections from thewalls, bottom, and water surface. As a result, we were unable
to conduct the calibration under a pure traveling wave ﬁeld.
In addition, the three-dimensional structure of the acoustic
ﬁeld in the water bath might aﬀect the results obtained using
the two-dimensional probe developed here.
5.

Conclusions

A two-dimensional sound intensity probe consisting of fourchannels of LED-PZT sensors was fabricated, and soundintensity measurement under water was conducted in theultrasonic frequency range. The outputs of the sensors were127301-4© 2017 The Japan Society of Applied Physics

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electronics for signal processing. In this paper, we adopted
four diﬀerent colors of the LEDs and four separate ﬁber
cables. We are expecting the possibility of transmitting
optical signals over one ﬁber cable using the wavelength
division multiplexing method.
In the future, ﬁrst, we must establish a precise calibration
method for the measurement system to obtain more precise
results. Second, for three-dimensional measurements, thenumber of channels of the probe will be increased with theminimum number of optical ﬁbers by adopting the wavelength division multiplexing method. The sensor elements
shall be miniaturized using tip LEDs and smaller piezoelectric elements for higher frequency operation since highpower ultrasonic applications in the MHz range are extending
in both industrial and medical ﬁelds.

(a)

(b)
Fig. 8. Intensity distributions with sound absorbing material: (a) active
intensity and (b) reactive intensity. The lengths of arrows are indicated in thelogarithmic scale.

Table I.
ﬁeld.

Ratio of active intensity to reactive intensity in the measured
Average of
Average of
top three positions all positions

Without sound-absorbing material in tank

0.9

1.0

With sound-absorbing material in tank

2.1

1.8

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for both the high standing wave ﬁeld and weakened reﬂection
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