Japanese Journal of Applied Physics
Vol. 46, No. 7B, 2007, pp. 4873–4880#2007 The Japan Society of Applied Physics

Measurement of Angular Dependence of Ultrasonic Echofor Estimation of Surface Roughness
Kazuki K UDO, Hideyuki H ASEGAWA, and Hiroshi K ANAI
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan(Received November 24, 2006; accepted March 22, 2007; published online July 26, 2007)

Atherosclerosis is the main cause of circulatory diseases, and it is very important to diagnose atherosclerosis in its early stage.
In an early stage of atherosclerosis, the luminal surface of an arterial wall becomes rough due to injury of the endothelium.
Conventional ultrasonic diagnostic equipments cannot detect such micron-order surface roughness because their spatial
resolution is, at most, 100 mm. In this study, for the accurate detection of surface roughness, ultrasonic beams were insoniﬁed
from various angles relative to the surface of an object that has a micron-order asperity. Then, we focused on the angulardependence of echo amplitude and frequency characteristics in both temporal and spatial domains. Using this method, it isshown that the angular dependence and frequency characteristics vary when an object has a surface roughness that cannot be
detected by conventional B-mode imaging using linear scanning. [DOI: 10.1143/JJAP.46.4873]
KEYWORDS: surface roughness, ultrasonic beam steering, angular dependence, temporal and spatial frequency, atherosclerosis

1.

Introduction

Recently, the increases in the number of circulatory
diseases such as myocardial and cerebral infarctions havebecome a serious problem. Therefore, it is important todiagnose atherosclerosis in an early stage because suchcirculatory diseases are mainly caused by atherosclerosis.
For the diagnosis of atherosclerosis, intima-media thickness
is a useful marker.1) Mashiyama et al. measured the intimamedia thickness at the carotid sinus, which is a site that is
easily aﬀected by atherosclerosis, by beam steering thatmakes all ultrasonic beams perpendicular to the arterial
wall.2) Furthermore, the evaluation of the elasticity of anarterial wall is also useful for the diagnosis of atherosclerosis,3) and the measurement of the regional elasticity of anarterial wall using the phased tracking method was reported.4,5) This method was applied for classiﬁcation of tissues in
the arterial wall on the basis of the statistical properties ofelasticity distribution.6–8)
Although these methods are useful for the diagnosis ofatherosclerotic changes of the intima-media region, theinitial step of atherosclerosis development was reported to
be endothelial damage.9) Therefore, for the diagnosis ofatherosclerosis in an early stage, it is more eﬀective toevaluate endothelial damage. For the evaluation of endothelial function, several methods have been reported including
the measurement of changes in diameter10) and intima-media
elasticity11) caused by ﬂow-mediated dilation. In thesemethods, the measured changes in diameter or intima-media
elasticity are caused by the response of the media to nitricoxide generated by the endothelium. Therefore, if theendothelium is injured, the response of the media to nitricoxide generated by the endothelium does not occur.
In the early stage of atherosclerosis, it was also reported
that the luminal surface proﬁle changes. The luminal surface
of a clinically healthy artery is covered by a layer composedof endothelial cells and it is smooth. In the early stage ofatherosclerosis, endothelial cells on the luminal surface aredamaged,9) edema develops under the endothelium, endothelial cells are separated from the intima, and then thelumen of the artery has a micron-order surface roughness.12)E-mail address: hkanai@ecei.tohoku.ac.jp

Therefore, for the detection of atherosclerosis in an earlystage, it is necessary to detect a micron-order surface
roughness on the luminal surface. In conventional ultrasonicdiagnostic equipments, the lateral interval of ultrasonicbeams is, at most, 100 mm, and the axial resolution of a Bmode image depends on the ultrasonic wavelength of
150 mm at 10 MHz because a B-mode image is constructedusing the amplitude of the received echo. From these facts,
the spatial resolution of a B-mode image obtained using
ultrasonic diagnostic equipment is, at most, 100 mm in bothlateral and axial directions. Therefore, the surface roughnesscaused by atherosclerosis in an early stage cannot be
detected by conventional B-mode imaging using ultrasonicdiagnostic equipment. There are several studies of theultrasonic detection of micron-order surface roughness.
Sukmana et al. measured the surface roughness of sandpaperusing air-coupled ultrasound, and showed that higherfrequency components in echo are attenuated when thesurface of the object has a micron-order surface roughness.13,14) Arihara et al. measured the micron-order surface
proﬁle of an object made of silicone rubber using the phaseof RF echo.15) However, these methods are still not suﬃcient
for accurate imaging of a surface with micron-order asperity.
In this study, various objects of diﬀerent micron-ordersurface proﬁles were measured to obtain the angulardependences of ultrasonic echoes. Ultrasonic beams wereinsoniﬁed from various angles relative to the surface of an
object that has micron-order asperity. Then, for the evaluation of micron-order surface roughness, we focused on theangle-dependent characteristics of echo amplitude andfrequency characteristics in both temporal and spatial
domains.
2.

Principles

2.1 Data acquisition
Figures 1(a) and 1(b) show the schematic views of theexperimental system and beam scanning, respectively. A
linear-type ultrasonic probe (center frequency f0 ¼ 10 MHz,
interval of aperture centers for transmitted beams
L ¼ 0:4 mm) of conventional ultrasonic diagnostic equipment (Aloka SSD-6500) is used in this study. The number ofelectronically scanned beams, N, is 30 per frame. UltrasonicRF echoes are sampled at 40 MHz with a 16-bit resolution.

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(a)ultrasonicprobe

time t [µs]xzultrasonicdiagnostic
equipment

0.4
0.2

0.4

0

0.6

-0.2

0.8

-0.4
Amplitude1
1.2-25 -20 -15 -10 -5 0 5 10 15 20 25
beam angle θi [degree]lwater O0 Oj
controller

0
0.2

OM

Fig. 2. RF echo from a point scatterer at each beam angle i .

objectXYZ stage

(b)
Amp.

−θ

+θ

probe
A1

l

point of interest

a0 a1 a2

L

Im
A2

A0

aN-1

x

.........

A N-2
AN-1
θ

∆θ1 ∆θ2∆θ3

∆θN-1

2
......... W
W1
W0
Re
0
N-1
W
.........
WN-2

Θ

Oj
Fig. 1. (a) Experimental system for measurement of an object surface. (b)Schematic diagram of beam scanning.

The method using steering the ultrasonic beam proposed
by Nakagawa et al.16) and shown in Fig. 1(b) is used in thisstudy. Using this method, the direction of all ultrasonicbeams can be designed so as to pass through a point ofinterest. As shown in Fig. 1(b), all beams pass through a
point, Oj , at the surface of the object. When an ultrasonicbeam is insoniﬁed from the position ai of the aperture centeri, the beam angle i is expressed as follows:


N1
L i
2
i ¼ tan1
:
ð2:1Þ
l
The distance l from the surface of the probe to the surface ofthe object is set to be 13.7 mm, and then the maximum beam
angle max is 24.3 .
Furthermore, the ultrasonic probe is used to scan theobject by changing its position xj using a stage in order tomeasure RF echo from multiple points of interest on thesurface along the x-direction. At each position xj in j-thframe (j ¼ 1; 2; . . . ; M), all beams pass through a point Oj ,which is set at the surface of the object. The position xj ischanged by 5 mm per frame for 2 s (frame rate: FR ¼ 434 Hz,
speed of stage motion: 2.17 mm/s).
2.2 Analysis of angular dependence
Figure 2 shows RF echo from a point scatterer at eachbeam angle i . The amplitude of RF echo is normalized by
the acoustic pressure that corresponds to the maximum 16bit discrete value.
In this measurement, the distance from the point ofinterest to the receiving position varies as the beam angle ichanges. Thus, the propagation time ti at each ultrasonicbeam should be corrected by the diﬀerence in propagation
distance. The propagation time ti at a position ai , where theultrasonic beam is insoniﬁed, is given by

Fig. 3. Schematic diagram of the unequally spaced discrete Fouriertransform.

ti ¼

2l
;
c  cos ið2:2Þ

where c is the sound speed in water. As shown in Fig. 2, thewaveform of RF echo is not distorted and the wavefront of
the echo at each ultrasonic beam aligns in the case that theobject is a point scatterer. Thus, received RF echoes atvarious beam angles are plotted as a function of the beam
angle i and the time t, which is corrected by the diﬀerencein propagation time.
In this study, for the more detailed analysis of received RFecho, the Fourier transform in the angle () and time (t)domains was applied. However, as shown in eq. (2.1), thebeam angle i is assigned unequally spaced discrete values,
while the sampling period in the time domain is assigned
equally spaced values. Therefore, the spatial frequency
spectrum should be obtained by the unequally spaced
discrete Fourier transform (DFT) in the -direction. Figure 3
shows a schematic diagram of unequally spaced DFT andthe twiddle factor WðiÞ. When a sampling interval between
the (i  1)-th and i-th beams in the -direction is deﬁned as
i (0 is deﬁned as 0), the twiddle factor WðiÞ is obtained
as follows:!
i2 XWðiÞ ¼ exp jnði ¼ 1; 2; . . . ; N  1Þ; ð2:3Þ
 n¼0
where  is the signal length in the -direction. Then, whenan echo amplitude of at the i-th beam is deﬁned as Ai shownin Fig. 3, the power spectrum YðuÞ is obtained as follows:
  X
N 1
i
¼
An ðWðnÞÞi ;ð2:4Þ
YðuÞ ¼ Y
n¼0
where u is the spatial frequency whose unit is deﬁned asdeg1 . To prevent aliasing, the spatial frequency u must be
less than 1=max (max is the largest i ).

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1(a)
Object No. d [µm]
1
35
2
57
90
3

(b)

Object No. d [µm]
4
30
5
58
33
6
7
60

d
w

rT =0.95
0.9
correlation coefficient rdw [µm]
62
64
120
122

0.8
0.7
0.6

0.4

0

1
2
lateral position
x [mm]

3

4

0

Fig. 7. Change in correlation coeﬃcient of the angular dependence.

1function of the beam angle i and the lateral position xj .
Figure 6(a) shows the measured angular dependence of the
maximum amplitude of object No. 1 (step: d ¼ 35 mm), andFig. 6(b) shows the angular dependence at the position of thesurface that is smooth (xj ¼ 0 mm). As shown in Fig. 6(a),the angular dependence at the region where the surface has a
step diﬀers from that at the region where the surface does
not have a step. Therefore, we focused our attention on thechange in angular dependences to determine the position xaof a step or a gap.
The change in the angular dependence at each point ofinterest is quantitatively evaluated by the correlation
function between the angular dependence obtained at thesmooth surface shown in Fig. 6(b) and that at each point ofinterest. In Fig. 7, the correlation coeﬃcient of the angulardependence is plotted as a function of the lateral position xj .
As shown in Fig. 7, the correlation coeﬃcient decreases at
the region where the surface has a step, while the correlationcoeﬃcient is consistently more than rj ¼ 0:99 at the region
where the surface is smooth. The position xa of a step or a
gap is supposed to be the median point of the positions
where the correlation coeﬃcient drops from rj ’ 1 andwhere the the correlation coeﬃcient returns to rj ’ 1.
Therefore, in this study, the median points of the position
where the correlation coeﬃcient falls below the thresholdrT ¼ 0:95 were determined as the analyzed point xa .

2
3
0

1
2
3
4
distance x [mm]5Fig. 5. B-mode image of object No. 1 (step: d ¼ 35 mm).

Basic Experiments

3.1 Determination of position of step or gap
Three diﬀerent objects whose surfaces have single steps,
as shown in Fig. 4(a), and four diﬀerent objects whose
surfaces have single gaps, as shown in Fig. 4(b), were usedin basic experiments. These objects were made of aluminum,and their surfaces were ﬂat except for the steps or gaps. As
shown in Fig. 4, objects Nos. 1– 3 have steps with diﬀerent
step heights, d, and objects Nos. 4 – 7 have gaps with
diﬀerent depths, d, and widths, w. Figure 5 shows a B-mode
image of object No. 1 (step: d ¼ 35 mm) obtained using
ultrasonic diagnostic equipment. As shown in Fig. 5, a stepcannot be recognized by conventional B-mode imaging
using linear scanning. Therefore, the position of a step or agap, xa , must be determined by a method other thanconventional B-mode imaging.
For the determination of the position of a step or a gap, theangular dependence of the maximum amplitude of ultrasonicRF echo at each point of interest Oj was measured using
the stage. As shown in Fig. 1(a), angular dependence wasmeasured at each point of interest Oj by moving theultrasonic probe, and the angular dependence is shown as a

3.2 Angular dependence of echo from a step on a surface
Figures 8(a)–8(d) show RF echoes at the corresponding
beam angles fi g of an object with a smooth surface and theobjects Nos. 1– 3, respectively. As shown in Fig. 8, thewaveform of the RF echo is not distorted and the wavefrontof echo at each ultrasonic beam aligns when the point

lateral position x j [mm]

(a)

(b)
4
3
2
1

0.4
0.3
0.2
0.1
0
Amplitude

0-25 -20 -15 -10 -5 0 5 10 15 20 25
beam angle θi [degree]

0.5
amplitude

distance x [mm]Fig. 4. Surface proﬁles of the objects. (a) With steps. (b) With gaps.

3.

analyzed position x a

0.5

0.4
0.3
0.2
0.1
0

-20-15 -10 -5 0 5 10 15 20
beam angle θi [degree]

Fig. 6. (a) Angular dependence of maximum amplitude (object No. 1). (b) Angular dependence at a smooth surface.

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(b) object No. 1 (d=35 µm)(a) smooth surface(b) object No. 1 ( d=35 µm )(c) object No. 2 (d=57 µm)(d) object No. 3 ( d= 90 µm )(c) object No. 2 (d=57 µm)(d) object No. 3 (d=90 µm)−θbeam angle

temporal frequency

time t [ µ s]

f [MHz](a) smooth surface+θ−θ

spatial frequency

θ i [degree]

Fig. 8. RF echoes at corresponding beam angles i . (a) Smooth surface.
(b) d ¼ 35 mm. (c) d ¼ 57 mm. (d) d ¼ 90 mm.

+θ

u [degree -1 ]Fig. 10. 2-D power spectrum of RF echo. (a) Smooth surface. (b) d ¼
35 mm. (c) d ¼ 57 mm. (d) d ¼ 90 mm.

(a) smooth surface(b) object No. 1 (d=35 µm)(c) object No. 2 (d=57 µm)(d) object No. 3 (d=90 µm)

−θ

+θ

−θ

beam angle+θ(b) object No. 4( d=30 µ m, w= 62 µm )(c) object No. 5( d=58 µ m, w=64 µm )(d) object No. 6( d=33 µ m, w=120 µ m )(e) object No. 7( d=60 µ m, w=122 µm )time t [ µ s]

temporal frequency

f [MHz](a) smooth surface

θ i [degree]

Fig. 9. Temporal frequency characteristic at each beam angle i . (a)Smooth surface. (b) d ¼ 35 mm. (c) d ¼ 57 mm. (d) d ¼ 90 mm.

of interest is a smooth surface. On the other hand, thewavefronts of RF echoes are distorted and the echo
amplitude decreases, particularly when the beam angle iis about 0 , in the case that a point of interest is a position
with a step.
Figure 9 shows the power spectrum of RF echo at eachbeam angle i . As shown in Fig. 9, in the case of a smoothsurface, the frequency component at f ¼ 7:5 MHz, whichcorresponds to the center frequency of RF echo from thepoint scatterer shown in Fig. 2, are maximum at most of thebeam angles, and the power spectrum decreases as the beam
angle i increases. On the other hand, in the case that the
point of interest is at the position with a step, the power
spectra at i ’ 10 are higher than that of a smooth surface(d ¼ 0 mm). However, the power spectra are lower than thatof d ¼ 0 mm when the beam angle i is about 0 . Moreover,the power spectra where the beam angle i is about 10
decrease as the step height d increases.
Figure 10 shows the two-dimensional spectrum of RF
echo obtained by the two-dimensional Fourier transform of
the RF echo obtained at each beam angle shown in Fig. 8. In
Fig. 10, the power spectra are also represented in contours.
As shown in Figs. 10(b)–10(d), the frequency components at
f ¼ 7:5 MHz (center frequency) increase as the step height dincreases, whereas the other frequency components does notincrease so much. From these results, the bandwidth of thepower spectrum of RF echo was found to be narrow in thetemporal frequency domain as the step height d increases. It
corresponds to the increment in the number of cycles of echo

beam angle

θi [degree]

Fig. 11. RF echoes at corresponding beam angles i . (a) Smooth surface.
(b) d ¼ 30 mm, w ¼ 62 mm. (c) d ¼ 58 mm, w ¼ 64 mm. (d) d ¼ 33 mm,
w ¼ 120 mm. (e) d ¼ 60 mm, w ¼ 122 mm.

in the temporal axis on the right-hand side of Figs. 8(a)–8(d). From these results, it is supposed that the bandwidth ofthe power spectrum of RF echoes is narrow in the temporalfrequency domain as the step height d increases.
3.3 Angular dependence of echo from a gap on a surface
Figures 11(a)–11(e) show RF echoes at the corresponding
beam angles fi g of the object with a smooth surface andobjects Nos. 4 – 7, respectively. In the case that the surface
has a gap, the distortion of the wavefront of RF echo shownin Figs. 8(b)–8(c) does not occur. However, as shown in
Fig. 11, the echo amplitudes in the range ji j  15 arehigher than that of the smooth surface, whereas in the case of
the smooth surface, the echo amplitude is almost 0 whenji j  15 .
Figure 12 shows the power spectrum of RF echo at eachbeam angle i . As shown in Fig. 12, when the surface has agap, the power spectra where ji j is greater than 15 increaseas the gap width w increases. The supposed reason for the4876

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K. KUDO et al.

(a) smooth surface(a) smooth surface(b) object No. 4( d=30 µ m, w= 62 µm )(c) object No. 5( d=58 µ m, w=64 µm )(d) object No. 6( d=33 µ m, w=120 µ m )(e) object No. 7( d=60 µ m, w=122 µm )(c) object No. 5( d=58 µ m, w=64 µm )(d) object No. 6( d=33 µ m, w=120 µ m )(e) object No. 7( d=60 µ m, w=122 µm )spatial frequency u [degree-1 ]θi [degree]

Fig. 12. Temporal frequency characteristic at each beam angle i . (a)Smooth surface. (b) d ¼ 30 mm, w ¼ 62 mm. (c) d ¼ 58 mm, w ¼ 64 mm.
(d) d ¼ 33 mm, w ¼ 120 mm. (e) d ¼ 60 mm, w ¼ 122 mm.

increase in power spectra when ji j is greater than 15 is thatthe eﬀects of the gap on the power spectrum increase as thegap width w increases.
Figure 13 shows the two-dimensional spectrum of RF
echo obtained by the two-dimensional Fourier transform of
the spatial distribution of the echo amplitude shown in
Fig. 11. As shown in Fig. 13, the power spectra are also
represented in contours as in Fig. 10. As shown in Fig. 13,
the components in the range of 0:05  u  0:10 increases in
the case of objects Nos. 5 and 7 whose gap depth d are larger
than those of objects Nos. 4 and 6. This corresponds to theobservation that the region along the -axis where theamplitude is high narrows. Therefore, it is supposed that thecomponents at high frequencies in the spatial frequency
domain increase as the gap depth d increases.
4.

+θ(b) object No. 4( d=30 µ m, w= 62 µm )Discussion

4.1 Angular dependence of echo from a step on a surface
As shown in Fig. 8, RF echoes from a step at thecorresponding beam angles of fi g are asymmetrical owing
to an asymmetric shape of a surface proﬁle, while RF echoesfrom a gap are symmetrical. In addition, the angulardependence of a step has a characteristic that the numberof cycles of echo in the temporal axis on the right-hand sidesof Figs. 8(b)–8(d) increases as step height increases. To
examine such a characteristic, another object was measured.
This object has a step whose height d is 300 mm (d issuﬃciently higher than ultrasonic wave length,  ¼ 200mm). Figure 14 shows RF echoes at the corresponding beam
angles fi g of this object (d ¼ 300 mm). As shown in
Fig. 14, at most of the beam angles fi g, the received signals
contain echoes from the upper and lower surfaces around thestep owing to a large beam diameter. Echo amplitudes fromthe lower surface of the step are high in the range þ5 

Fig. 13. 2-D power spectrum of RF echo. (a) Smooth surface. (b) d ¼
30 mm, w ¼ 62 mm. (c) d ¼ 58 mm, w ¼ 64 mm. (d) d ¼ 33 mm, w ¼ 120
mm. (e) d ¼ 60 mm, w ¼ 122 mm.

time t [ µ s]

beam angle−θ+θ

temporal frequency f [MHz]temporal frequency f [MHz]

−θ

0

0.8

0.5

0.4

1
1.5
2

0
-0.4
-0.8
amplitude

2.5-25 -20 -15 -10 -5 0 5 10 15 20 25
beam angle θ i [degree]
Fig. 14. RF echoes from a step (d ¼ 300 mm) at the corresponding beam
angles.

  þ15 and those are almost 0 in the range 15   
5 . On the other hand, echo amplitudes from the uppersurface of the step are high in the range 15    5 andthose are low in the range þ5    þ15 . However, as
shown in Fig. 14, echoes from the upper surface in the range
þ5    þ15 do not decrease so much in comparison
with those from the lower surface in the range 15   5 . This is considered to be a reason that echo durationin the range þ5    þ15 increased as observed in
Figs. 8(b)–8(d), whereas that in the range 15    5
did not increase.
4.2 Angular dependence of echo from a gap on a surface
In this study, the angular dependence of echo from a gap
on a surface was measured in addition to that from a step.
Let us consider the angular dependences of echoes from a
gap on a surface by summing up those from steps. Figure 15
shows a schematic diagram for simulating a shape of a gap
using a shape of a step on the basis of the superposition
principle. In this study, the employed objects have a step dof about 30 or 60 mm and a gap width w of 60 or 120 mm.
Therefore, the angular dependences of echoes from a gap

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5

d

d
w
xa

=

0.5w

xa

+ 0.5w

-

xa

0
-5
5

xa

Fig. 15. Schematic diagram for simulation of a shape of a gap bysumming up shapes of steps.

-510(b) d =57 µm, w =60 µm

height(c) d =35 µm, w =120 µm

Object No. B ( Rq=0.982 µm )0h(x) [ µm](a) d =35 µm, w =60 µm

time t [ µ s]

Object No. A ( Rq=0.206 µm )d(d) d =57 µm, w =120 µm

Object No. C ( Rq=2.454 µm )

5
0
-5
-10
15

Object No. D ( Rq=4.131 µm )105

beam angle

θ i [degree]

0-5Fig. 16. Angular dependences from gaps calculated on the basis ofsuperposition principle.

5.

-15

0

0.5

1
1.5
lateral position x [mm]

2.0

2.5

Fig. 17. Surface proﬁles of objects Nos. A–D measured by the stylus
method.

(a)01depth z [mm]whose depth d is about 30 mm were simulated by superposition of those from a step whose height d is 35 mm.
Similarly, the angular dependences of echoes from a gap
whose depth d is about 60 mm were simulated by superposition of those from a step whose height d is 57 mm.
Figure 16 shows the simulated angular dependences of
echoes from gaps calculated on the basis of the superposition
principle. The simulated angular dependences of echoes
shown in Figs. 16(a)–16(d) correspond to those measured
for objects Nos. 4 – 7 shown in Figs. 11(b)–11(e), respectively. As shown in Fig. 16, the echo amplitudes in theregion where the beam angle i is about 0 of the object witha height d of 57 mm are larger than those of the object with aheight d of 35 mm. Furthermore, echo amplitudes in therange ji j  15 increase as the width w of a gap increases.
These results well correspond to those shown in Fig. 11.
Therefore, the angular dependences of echoes from a gap on
a surface can be considered from those of echoes from a
step.

-10

2
(b)
0
1
2
0
1
2
3
4
lateral position x [mm]Applying Angular Dependences to Estimation ofSurface Roughness

5.1 Objects
Four metal plates that have diﬀerent surface roughnesses
obtained by polishing with sandpaper were measured.
Figure 17 shows the surface proﬁles hðxi Þ at lateral position
xi of objects Nos. A–D measured by the stylus method.
Figure 18 shows the conventional linear scanning B-mode
images of objects Nos. A and D. As shown in Fig. 18, thesurface proﬁle hðxi Þ in the micron-order shown in Fig. 17
cannot be detected by the conventional B-mode imaging
using linear scanning.
In this study, the rms roughness Rq, which is the standard
deviation of the surface height hðxi Þ, is used for the statisticalevaluation of surface roughness. The rms roughness Rq is
obtained as follows:

Fig. 18. Conventional B-mode images of objects No. A (a) and No. D (b).

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u N1
u 1 X
2
Rq ¼ thðxi Þ  hðxÞ ;
N i¼0

ð5:1Þ

where N is the total number of lateral positions fxi g and hðxÞis the average height of the surface proﬁle. Figure 17 also
shows Rq of each object used in these measurements.
5.2 Estimation of surface roughness
Figures 19(a) and 19(b) show RF echoes from object
No. A (Rq ¼ 0:206 mm), which has the most smooth surface

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θ=0
θ =10
θ =20
θ =30

(a)

0.4

temporal freqency f [MHz]amplitude

0.2

0

-0.2

-0.4
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.8

2

(c)

(d)

contour
0dB
-10dB
-20dB

beam angle θ [degree]

0.2
amplitude

(b)

θ=0
θ =10
θ =20
θ =30

(b)

0.4

1.6

(a)

Fig. 20. Average power spectrum of RF echo at each beam angle i foreach object shown in Fig. 17.

0

-0.2

(a) f=5 MHz(b) f= 6 MHz
5

5

0

0.2

0.4

0.6

0.8
1
1.2
time t [ µ s]

1.4

1.6

1.8

Power spectrum [dB]-0.4
2Fig. 19. RF echoes from objects No. A (a) and No. D (b).

0

0

-5

-5

-10

-10

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

-20
-25
-30

0

5

10

-25
15

20

25

30

35

Power spectrum [dB]

-30

5

10

15

20

25

30

35

15

20

25

30

35

15

20

25

30

35

5

0

0

-5

-5

-10

-10
-15

-15

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

-20
-25
0

5

10

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

-20
-25
15

20

25

30

35

(e) f=9 MHz

-30

0

5

10

(f) f= 10 MHz
5

5
0

0

-5

-5

-10

-10
-15

-15

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

-20
-25
-30

0

(d) f= 8 MHz

5-30

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

-20(c) f=7 MHz

Power spectrum [dB]among the measured objects in these experiments, and fromobject No. D (Rq ¼ 4:131 mm), which has the roughest
surface, respectively. In these experiments, the distance lfrom the surface of the probe to the surface of the object was
set to be 9.4 mm, and the maximum beam angle max was
32.6 . As shown in Fig. 19(a), in the case of the smoothsurface, the amplitude of RF echo at the beam angle  ¼ 20
is low and that at the beam angle  ¼ 30 cannot be detected.
On the other hand, in the case of the rough surface, theamplitude of RF echo at the beam angle  ¼ 30 can bedetected as shown in Fig. 19(b). These results correspond tothe case in which the amplitudes of echoes from surfaces
with gaps are larger in the range   20 than those from thesmooth surface as shown in Fig. 11. From these results in
Fig. 19, the echo amplitudes in the range   20 increase as
the surface of the objects becomes rough.
The angular dependences of ultrasonic echoes from four
diﬀerent objects that have diﬀerent surface roughnesses, as
shown in Fig. 17, were measured and the power spectra of
RF echoes at the corresponding beam angles fi g wereacquired. In these experiments, the experimental system issimilar to the system shown in Fig. 1. The angular dependences of RF echo were measured by moving the ultrasonicprobe automatically using a stage. RF echoes were acquired
during 4 mm movement at 10 mm intervals (the number ofmeasurement points fxi g ¼ 400).
Figure 20 shows the averaged power spectra of RF echo ateach beam angle  for each object shown in Fig. 17. As
shown in Fig. 20, for the beam angle  of about 0 , thepower spectra shown in Figs. 20(a)–20(d) are similar
whereas the surface roughness Rq diﬀers. However, in thecase of   20 , the center frequency component increases
as surface roughness Rq increases.
Figure 21 shows the power spectra shown in Fig. 20 for
the temporal frequencies from 5 to 10 MHz. As shown in
Figs. 21(c)–21(e), the power spectra at about the center
frequency ( f ¼ 7:5 MHz) increase as surface roughness Rq

-15

-15

0

5

10

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

-20
-25
15

20

25

beam angle θ [degree]

30

35

-30

0

5

10

beam angle θ [degree]

Fig. 21. Power spectra at f ¼ 5 MHz (a), f ¼ 6 MHz (b), f ¼ 7 MHz (c),f ¼ 8 MHz (d), f ¼ 9 MHz (e), and f ¼ 10 MHz (f).

increases when the beam angle  is greater than 20 . The
power of RF echo, PðÞ, is obtained as follows:
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
N 1 q2
1X
V ðtÞ  V ðtÞ ;ð5:2Þ
PðÞ ¼N i¼0
where V ðtÞ is the RF echo signal at time t and V ðtÞ is its
average. Figure 22 shows the changes in the power PðÞ of
RF echo at the corresponding beam angles  for all objects.
In Fig. 22, the power PðÞ of RF echo is normalized by thepower Pð0 Þ at  ¼ 0 . As shown in Fig. 22, the normalized
power PðÞ=Pð0 Þ of RF echo in the region of   20
increases as the surface roughness Rq increases. The
relationship between the surface roughness Rq and thenormalized power PðÞ=Pð0 Þ of RF echo is shown in
Fig. 23. From Fig. 23, it is found that the increase in thesurface roughness Rq causes the increase in the power of RF
echo in the region of   20 .

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Jpn. J. Appl. Phys., Vol. 46, No. 7B (2007)

Rq= 0.206 µm
0.982 µm2.454 µm
4.131 µm

0

normalized power P(θ)/P(0 ) [dB]normarized power P(θ)/P(0 ) [dB]5

K. KUDO et al.

-5

-10

-15

-20

-10
-12
-14
-16

5

10

15
20
25
beam angle θ [degree]

30

35

θ =20
θ =25
θ =30

-18
-20

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

surface roughness Rq [ µ m]

Fig. 22. Changes in the normalized power PðÞ=Pð0 Þ of RF echoes atcorresponding beam angles  for all objects.

6.

-8Conclusions

In this study, the angular dependence of ultrasonic echoes
was measured by steering the ultrasonic beam. Objects thathave a micron-order step and gap that cannot be detected byconventional B-mode imaging using linear scanning wereused in these measurements. Using the proposed method, it
was found that the spatial distribution of echo amplitude andthe frequency characteristics of echo in both temporal andspatial domains diﬀer as the surface proﬁle diﬀers. Furthermore, using the proposed method, it was shown that theincrease in the surface roughness Rq causes the increase in
the power of RF echo in the region of   20 . These results
provide a possibility that a micron-order surface roughness
can be quantitatively evaluated using the angular dependence of ultrasonic echo.
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Fig. 23. Relationship between the surface roughness Rq and the normalized power PðÞ=Pð0 Þ of RF echo in the range   20 .

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