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Japanese Journal of Applied Physics 52 (2013) 127301
http://dx.doi.org/10.7567/JJAP.52.127301

Object Characterization Based on Multispectral Acoustic Imaging
Xinhua Guo, Yosuke Mizuno, and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
E-mail: guoxinhua@sonic.pi.titech.ac.jp
Received February 26, 2013; accepted September 25, 2013; published online November 19, 2013
In previous studies, acoustic imaging was conducted using a single frequency or a limited number of frequencies that were not sufficient to clearly
describe and explain the object characteristics. In this study, multispectral acoustic imaging (MSAI) is proposed to reveal rich information of object
characteristics. An experimental study on object surfaces is conducted to verify the validity of the technique. Acoustic imaging of object surfaces isperformed on the basis of a significant number of spectra over a wide frequency range. Using the frequency-swept irradiation from 1 to 20 kHz at
30 Hz intervals, we demonstrate the visualization of the following three different object surfaces: a rigid surface with small holes with and without apiece of thin paper covering the surface, and a boundary between wood and rubber plates. The distributions of sound pressure reconstructed ateach frequency by a near-field acoustic holography (NAH) technique are shown. In multispectral acoustic imaging, frequency dependence
provides us rich information about the surface shape and material properties of the objects; thus, the characteristics of the surfaces are
successfully visualized. # 2013 The Japan Society of Applied Physics

1. Introduction

Since acoustic waves travel into materials in whichelectromagnetic waves do not propagate, visualizations
in water, the human body, and solid objects have been
carried out using acoustic waves. Typical successful
examples include underwater sound navigation and ranging(SONAR),1–3) medical ultrasonic echography,4,5) and nondestructive evaluation.6,7) In these visualization techniques,
the target object is irradiated with acoustic waves, and thereﬂected or transmitted waves are observed. Acousticallyobtained images provide diﬀerent information from opticalimages, and are greatly aﬀected by the elastic properties
and surface structures of the object. These are reﬂected in
the frequency responses since frequency-dependent phenomena, such as resonance, diﬀraction, and attenuation are
essentially related to the properties of the object. Consequently, frequency band width is important in acoustic
imaging for obtaining more highly functional information.
In optical observations, recently the use of a multispectral
camera8,9) has been spreading in studies on remote sensing
and medical tissue diagnostics. As an analogy to themultispectral imaging in optics, a few studies on acoustics
have been reported, but only a single frequency or a limited
number of frequencies were used in such conventional
acoustic imaging.10)
We demonstrate, in this study, acoustic imaging utilizing
a wide frequency band with a ﬁne frequency step, whichis called multispectral acoustic imaging (MSAI). Images
are obtained for one object at a large number of frequencies,
and analysis of the relationship between the multispectral
acoustic images and the physical properties of the object
is carried out. In this paper, ﬁrst, the experimental setup is
explained. Next, the image reconstruction technique basedon near-ﬁeld acoustic holography (NAH) is brieﬂy reviewed,
which is used to reconstruct the images on the object surface
from the sound pressure distribution measured on a planelocated near the object surface. Finally, demonstrations
on the following three surfaces are carried out to verify thefeasibility and usefulness of MSAI in practice: (i) a rigid
surface with drilled holes with diﬀerent diameters anddepths, (ii) a drilled surface covered by a piece of thin paper,and (iii) a boundary between two diﬀerent materials.

Fig. 1. (Color online) Experimental setup.

2. Experimental Methods

The complex sound pressure as a combination of amplitude
and phase information was measured at the hologram plane(measurement plane) using the experimental setup shownin Fig. 1. The object was irradiated with frequency-swept
sound from 1 to 20 kHz emitted from a small loudspeaker(Fostex T90A). The loudspeaker had a frequency response
from 5 to 35 kHz that did not aﬀect the experimental results,
since the normalization was carried out at each frequency togenerate an image. The sound pressure at the measurement
plane was in the range from 90 to 115 dB. The distance
between the sound source and the object was 500 mm, andthe incident angle was 20 . A needle microphone (B&K
4182) was scanned two-dimensionally over a plane near theobject using a motorized stage. The microphone had analmost constant sensitivity of 3.16 mV/Pa in the frequency
range from 1 Hz to 20 kHz. The X–Y scanning area wasdetermined depending on the dimensions of the object
surface. The received signal was processed using a frequency response analyzer (FRA; NF5097), and the amplitude and phase at each frequency were sent to a personal
computer (PC) for further processing. The reconstructed
images (zr ¼ 0 mm) were obtained on the object surface by
NAH. The distance between the measurement plane (zh ) andthe object surface was 10 mm throughout the experiments.

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(a)Fig. 2. (Color online) Example of frequency response.

3. Data Acquisition and Signal Processing
3.1 Data acquisition for the complex sound pressure

The signal driving the loudspeaker was generated by the
FRA, and was used as the reference signal for determining
the phase of the sound pressure measured using the microphone. The frequency responses from 1 to 20 kHz at 30 Hzintervals were recorded for all the scanning positions.
Figure 2 shows one of the typical recorded data (for theobject of the ﬁrst demonstration) of amplitude and phasejust on a point located at the center of the hole of 4 mm indiameter and 20 mm in depth. The amplitude was displayed
as a relative value, where 0 dB is equal to the sound pressureof 144 dB. This frequency-swept measurement was repeatedat every scanning point. After the measurement was ﬁnished,
the acquired data were arranged into two-dimensional
distributions of the amplitude and phase at each frequency,
as shown in Fig. 3, which means that we have acoustic
holograms from 1 to 20 kHz at 30 Hz intervals. The total
number of holograms obtained was 635.
3.2 Reconstruction of sound pressure distribution basedon NAHTo visualize the characteristics of object surfaces, theplanar NAH11,12) was applied to the measured soundpressure. Here, let us brieﬂy review the procedure that we
employed. The fundamental equation for the pressure
distribution on the surface is derived from the Rayleighintegral equation13)
pr ðx; y; zÞZ1 Z1¼
ph ðxh ; yh ; zh ÞgD ðx  xh ; y  yh ; z  zh Þ dxh dyh ;
1

1

ð1Þ
where pr ðx; y; zÞ is the complex acoustic pressure at a point
ðx; y; zÞ on the reconstruction plane, ph ðxh ; yh ; zh Þ is thecomplex acoustic pressure at a point ðxh ; yh ; zh Þ on thehologram plane, and gD is the Dirichlet Green’s function thatacts as the transfer function of the sound pressure ﬁeld fromone point to another. The expression of two-dimensional
Fourier transforms13) is employed to express the sound ﬁeld
in the k-space:
Z1 Z1~ x ; ky Þ ¼Fðkf ðx; yÞ eiðkx xþky yÞ dx dy  F½ f ðx; yÞ;
1

1

ð2Þ

(b)
Fig. 3. (Color online) Distributions of the amplitude and phase in thewhole frequency range: (a) amplitude and (b) phase distributions.

where ðkx ; ky Þ refers to the k-space, and ðx; yÞ refers to
the real space. Since Eq. (1) is expressed as a twodimensional convolution integral of ph ðxh ; yh ; zh Þ andgD ðx  xh ; y  yh ; z  zh Þ, being based on the convolution
theorem,14,15) Eq. (1) yields
pr ðx; y; zÞ ¼ F  ½P~r ðkx ; ky ; zÞ¼ F  ½P~h ðkx ; ky ; zh ÞG~ D ðkx ; ky ; zÞ;ð3Þ

where F indicates the inverse Fourier transform. This gives
the holographic reconstruction of the sound pressure in thethree-dimensional space pr ðx; y; zÞ in terms of the Fouriertransformed form P~h ðkx ; ky ; zh Þ derived from the hologram
data ph ðxh ; yh ; zh Þ. The operator G~ D ðkx ; ky ; zÞ, that is, the twodimensional spatial Fourier transform of the Dirichlet
Green’s function, is given as
8
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ< exp ðiz k2  k2  k2 Þ k2 þ k2  k2xyxy
G~ D ðkx ; ky ; zÞ ¼
: ð4Þ
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ: exp ðz k2 þ k2  k2 Þ k2 þ k2 > k2xyxyThe pressure ﬁeld in k-space is divided into two types
of wave by the radiation circle represented by kx2 þ ky2 ¼ k2 .
An evanescent wave exists inside the circle, while thepropagating wave exists in the rest of the area.
4. Experimental Results

As mentioned in Sect. 1, acoustic images were easily inﬂuenced by the shape, size, structure, and material property ofthe objects. Three examples will be demonstrated in thispaper. The ﬁrst two examples exhibit clear resonances related
to the structure. The resonant frequencies of a cylindricalcavity were studied by Harris et al.,16) and are given assﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ﬃ
 2 
c
A
mn 2
fmn ¼
þ
;
ð5Þ
2
d
r0

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when the depth was the same (¼ 20 mm), the holes with
diﬀerent diameters (5 and 6 mm) showed diﬀerent frequency
responses, which demonstrates that the diameter has some
eﬀects on the frequency responses.
4.1.2 Images at every frequency

Fig. 4. (Color online) Frequency responses under four diﬀerent
conditions: diameter and depth.

where c is the sound speed in air, and d and r0 represent
the depth and radius of the cylindrical cavity, respectively.
A denotes the integer number (0; 1; 2; 3; . . .), and the coeﬃcient mn is the n-th solution of the equation Jm0 ðrÞ ¼ 0;
here, Jm is the m-th order cylindrical Bessel function. The
resonance frequency is related to the depth d and radius rof the cylindrical cavity.
In this experiment, the holes that were closed at one end
and open at the other end were excited by acoustic incident
waves. Here, a simple case was considered, where only thedepth modes were excited. Then, the resonance frequencies
are expressed as17)
f0 ¼

Bc
;
4d

B ¼ 1; 3; 5; 7; . . . :ð6Þ

4.1 Demonstration 1: Surface profile

The sample for the ﬁrst demonstration was a resin block with
9 holes of diﬀerent diameters (4, 5, and 6 mm) and depths(8, 15, and 20 mm) on one surface, as shown in Fig. 5(a).
The scanning area for the microphone was 33  33 mm2
near the object surface, and the grid spacing of the scannedarea was 1  1 mm2 .

All of the 635 holograms from 1 to 20 kHz at a 30 Hz step
were reconstructed using the discrete form of the Rayleighintegral in Eq. (3). Five reconstructed images in threedimensional form of the object picked up from the whole
range of frequencies are shown in Figs. 5(b)–5(f ). With
increasing frequency, the holes at each line and column
showed diﬀerent responses since the holes had acoustic
resonances characterized by the depth: the deepest holes had
the responses at lower frequencies, as shown in Fig. 5(b).
The holes at the second and third lines are observed in
Figs. 5(c) and 5(e). The diameter had some eﬀects on thefrequency responses. The holes of the second line with different diameters were not observed simultaneously although
the holes had the same depth, as shown in Fig. 5(d).
Although it was diﬃcult to identify the holes with the same
diameters from optical images, depth information was easily
obtained by the multispectral acoustic imaging technique.
The holes at each column were not observed at the sametime except for the higher harmonics, as shown in Fig. 5(f ).
In addition to the holes at the third line, the response of thesecond harmonic was observed in the ﬁrst line.
The holes of the ﬁrst line were observed in the band from
3.5 to 5.5 kHz, since they had the same depth and diﬀerent
diameters, but the diﬀerent diameters had some eﬀects on
the frequency responses so that there was a slight ﬂuctuation
in a certain frequency range. For example, the two holes
ð5; 20Þ and ð6; 20Þ had closed resonance frequencies, as
shown in Fig. 4. From 5.5 to 7.5 kHz, responses were foundin the second line, and the band from 10.5 to 14.0 kHz forthe last line. From these results, the detailed structures of theobject seem to correspond to their characteristic acoustic
spectral bands.

4.1.1 Basic frequency responses

To explain the typical results, frequency responses at fourmeasurement points for the diﬀerent holes were extracted
from all the measured points on the surface, and are shownin Fig. 4. The fundamental and second-order resonancesfor each hole were observed except for the hole of 8 mm indepth. The responses to the diﬀerent depths of 8, 15, and
20 mm exhibited diﬀerent frequency dependences since theholes had acoustic resonances characterized by the depth.
The lower cutoﬀ frequency of the loudspeaker is 3.6 kHz,and may result in the slope observed from 1 to 3 kHz in
Fig. 4.
According to Eq. (6), which represents the resonant caseof a one-dimensional closed-end pipe resonating at the odd
harmonics, i.e., =4, 3=4, 5=4, and 7=4, . . . ( is thesound wavelength), the resonance frequency of each holecan be calculated to be 4250, 5667, and 10625 Hz, corresponding to the depths of 20, 15, and 8 mm, respectively.
From Fig. 4, the measured resonant frequencies were 4390,
6100, and 11680 Hz. Compared with the calculated andmeasured values, although open-end correction should
be required for precise discussion, the depths of the holes
were identiﬁed by the frequency. On the other hand, even

4.2 Demonstration 2: Surface covered by paper

In the second experiment, the surface of the sample used inFig. 5(a) was covered with a piece of paper, as shown in
Fig. 6(a). The thickness of the paper was approximately
0.1 mm. Acoustic responses were, however, still observed,
although the holes can hardly be seen optically, whichindicates that the buried structures can be identiﬁed under acertain condition. The acoustic images at the speciﬁc frequencies where the holes at the ﬁrst, second, and third lines
were recognized are shown in Figs. 6(b)–6(d), respectively.
Compared with the results in Figs. 5(b), 5(c), and 5(e),corresponding to the three frequencies of 4780, 6280, and12220 Hz, respectively, the paper had almost no eﬀect on
the reconstructed images, i.e., the holes were visualized atnearly the same frequencies as in the experiments without
the paper. The magnitude of the responses was almost
unchanged in the case of employing the paper.
4.3 Demonstration 3: Material properties of the surfaces

The last experiment was carried out to investigate the eﬀects
of the material properties on the result of MSAI. The sample
with a boundary between two regions with diﬀerent reﬂec-

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5. (Color online) (a) Optical image and (b)–(f) reconstructed images at diﬀerent frequencies of the object surface.

(b)
(a)

(c)

(d)

Fig. 6. (Color online) (a) Optical image and (b)–(d) reconstructed images at diﬀerent frequencies with the holes covered by a piece of paper.

tivities is shown in Fig. 7(a). The upper part of the sample
was a rubber plate, and the lower part was a wood plate. The
acoustic impedances of the rubber and wood plates wereapproximately 12000 and 1148000 Pas/m, respectively. The
original size of the object surface was 100  100 mm2 , andthe measurement area was 50  50 mm2 located at the centerof the sample. The spatial interval between two scanningpoints was 2 mm. The same measurement as the previous

two experiments was carried out on this sample. Five imagesof the 635 reconstructed sound pressures were pickedup, as shown in Figs. 7(b)–7(f ). The red color represents
the maximum magnitude, while the blue color denotes theminimum magnitude.
Figures 7(b) and 7(e) show the images of the reconstructedsound pressure on the surfaces at 3550 and 12790 Hz, respectively. The reconstructed sound pressure on the two plates

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7. (Color online) (a) Optical image and (b)–(f ) distributions of sound pressure on two surfaces composed of diﬀerent materials.

was diﬀerent. The reconstructed sound pressure on the rubber
plate was larger than that on the wood plate at a frequencyof 3550 Hz, while that on the wood plate was larger than thaton the rubber plate at a frequency of 12790 Hz.
In Figs. 7(c), 7(d), and 7(f ), no obvious boundary wasobserved between the two surfaces, and thus at some frequencies, it was diﬃcult to identify the two surfaces composed of diﬀerent materials. At a frequency of 5110 Hz,
the reconstructed sound pressure of the two surfaces was
distributed almost uniformly, as shown in Fig. 7(c). Fringe
patterns were observed at frequencies of 10720 and 19990
Hz, which might be aﬀected by the interference between theirradiated sound and the reﬂected one. Thus, the material
properties of the object surfaces can be identiﬁed byobservation at many frequencies, although they cannot befound by using only one or few frequencies.
5. Conclusions

measurement, a large-scale microphone array and a smart
data acquisition system are required. For more precise
characterization, the evaluation of the illuminating soundsource such as the uniformity of the strength in space andfrequency needs to be studied. MSAI provides a large
volume of data, and it is diﬃcult to display them in one
image. We also investigated how to display the MSAI datausing an RGB representation method.18)

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# 2013 The Japan Society of Applied Physics