Reprinted from

REGULAR PAPER

Multi Element Diverging Beam from a Linear Array Transducer
for Transverse Cross Sectional Imaging of Carotid Artery:
Simulations and Phantom Vessel Validation
Akinlolu Ponnle, Hideyuki Hasegawa, and Hiroshi Kanai

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REGULAR PAPER

Japanese Journal of Applied Physics 50 (2011) 07HF05
DOI: 10.1143/JJAP.50.07HF05

Multi Element Diverging Beam from a Linear Array Transducer
for Transverse Cross Sectional Imaging of Carotid Artery:
Simulations and Phantom Vessel Validation
Akinlolu Ponnle1 , Hideyuki Hasegawa2;1 , and Hiroshi Kanai1;2 
12Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan

Received December 13, 2010; accepted March 9, 2011; published online July 20, 2011
Transverse cross sectional imaging of the intima–media complex of the carotid arterial wall is difficult to obtain by conventional linear scanning.
The angular widths of imaged regions of the anterior and posterior walls are limited. In this study, multi element diverging beam from a linear arraytransducer was investigated by simulations and experiments. B-mode image was reconstructed, using combinations of multi angle receiving
beams from multiple transmissions per frame. The images obtained by the proposed method from simulations and silicone-rubber tube phantom
showed an increase in the angular width over that in the case of conventional linear scanning. Also, images were investigated for sub aperturesizes of 36, 56, and 96 elements with different beam-spread angles. On the basis of the results of the present study, the sub aperture size of 36
elements and beam-spread angle of 90 are recommended for achieving the optimum results for this application in in-vivo imaging.
# 2011 The Japan Society of Applied Physics

1. Introduction

One of the main causes of cardiovascular disease isatherosclerosis and hence its diagnosis at an early stage has
become very important.1,2) A typical arterial wall consists ofthree layers: an innermost layer, ‘‘the intima’’; a middle layer,‘‘the media’’; and an outer layer, ‘‘the adventitia’’.3,4) The
intima–media region of the artery is a useful place to probe in
the diagnosis of atherosclerosis.5–7) In a longitudinal crosssectional image obtained by conventional linear scanning, theanterior and posterior walls are displayed (double line patternwhich represents echoes from the lumen–intima and media–
adventitia boundaries),6) but in transverse cross sectional
imaging, the intima–media complex of the carotid arterial
wall is diﬃcult to image because reﬂection of ultrasoundis highly angle-dependent,8) and the ultrasound beams areperpendicular to the wall in a limited region. The angularwidth of this limited imaged region of the arterial wall is ameasure of the extent of the anterior and posterior walls of thearterial cross section that are clearly imaged, if the transverse
cross section of the arterial lumen is assumed to be circular.
Intravascular imaging9) has some practical drawbacks: it isinvasive, expensive and can only be applied to patients thathave already undergone surgical operation.10,11) It is therefore
clinically imperative for absolute diagnosis of the arterial wall
to be able to visualize, noninvasively, the entire wall since any
part of the wall (including side walls) could become defective
but may not be imaged by conventional linear scanning.
Previous eﬀorts to increase the angular width generally
involves steering of focused transmit beams, as used inspatial multi angle compound imaging (MACI),12) or
speciﬁcally designing each scan beam to pass through thecenter of the artery over a limited region13,14) or perpendicular to vascular walls at predetermined positions along thewall.1) However, transmit steering angle is limited because ofincrease in the amplitude of grating lobes with steering. Also,
in some cases, combination of multiple frames reduces theoverall compound frame rate as well as producing temporalcompounding in real-time applications, where the frame rateis the number of image frames displayed per second.


E-mail address: kanai@ecei.tohoku.ac.jp

Although reduction in the overall frame rate or longer
acquisition time for image reconstruction may pose no
problem for static objects, it is a disadvantage for dynamic
structures, for example, arterial vessels within the body.
The arterial vessel changes within one heart cycle. If
MACI is employed, the overall frame rate decreases by afactor equivalent to the number of angular image frames thatare compounded. For example, a typical scheme involves
each spatial compound frame being produced from moving
average of sequential frames. Averaging up to nine sequential
frames typically improves the quality of the image in several
ways, such as reduced speckle; reduced clutter caused byartifacts; and visualization of structures previously hidden
beneath highly attenuating objects.15) If each angular frameis acquired for a period of 10 ms, then the overall frame
rate becomes 11.1 Hz (90 ms). The arterial vessel changes
signiﬁcantly within this period. The minimum arterial
diameter, which corresponds to maximum intima–media
thickness, is consistently located around the R wave of theelectrocardiogram (ECG).16) Apart from reduction of theoverall compound frame rate, temporal compounding is also
simultaneously performed, and this may result in the blurringof fast-moving objects in the ﬁeld of view.17) Therefore, there
is a need to develop methods by which angular combination
can be performed to reveal more features without extending
the acquisition time or reducing the overall frame rate and/or
if possible, increasing the overall frame rate.
The use of unfocused wide beams in transmit can increase
the frame rate, for example, in parallel beamforming for fast
imaging of the heart and artery.18,19) In applications whereframe rate is critical, ultrasound imaging techniques such asparallel receive beamforming,20) explososcan21) or ultrafast
ultrasound imaging22,23) are used. In these imaging techniques, the transmitted ultrasound beam is broader (slightly
focused or plane waves) and it interrogates the entire volumeof tissue. The backscattered ultrasound signal, received on
the desired elements of the array transducer at once, is used
to form several receiving beams or the entire ultrasoundimage. Ultrafast imaging is an extreme form of high-framerate imaging because, here, a plane wave is transmitted using
the entire array transducer aperture and the echo signals
are received using every element of the array transducer

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aperture at once.24) However, in this application, theaforementioned techniques produce no signiﬁcant improvement over unsteered focused beam of conventional linear
scanning because the wavefronts of the transmit beams are
all oriented in one direction spatially throughout the beam.
By using a diverging beam over a wide angle from a linear
array transducer, a greater angular width of the imaged
region can be obtained (and can increase with increasing
number of transmissions) without steering of transmit beams
and at the same frame rate as in conventional linear
scanning. Also, the problem of receive grating lobes canbe reduced (with improved resolution) by combining steered
receiving beams from multiple transmissions.
A single element can produce a spherical wave if it isassumed to be a point radiator. Also, a sub aperture
consisting of multiple elements can be used to emulate theradiation pattern of a virtual acoustic (point) source behind
the transducer array.25) This type of beam has previously
been investigated by some researchers for diverse purposes.
It was investigated by Karaman et al. using phased arraytransducers in synthetic transmit aperture (STA) imaging
for small-scale systems,26) by Lockwood et al. for sparse
synthetic aperture systems with primary focus on threedimensional (3D) ultrasound imaging,27) and by Nikolov
et al. for recursive STA imaging.28) By properly delaying
individual elements in the transmit sub aperture, goodemulation of spherical waves diverging from the sub
aperture surface can be obtained. An illustration of such abeam is shown in Fig. 1(a).
In this study, a wide-angled multi element diverging beamfrom a linear array transducer for transverse cross-sectional
imaging of cylindrical vessels was investigated and images
were reconstructed by combination of multi angle receiving
beams from multiple sequential transmissions. Although
receive beamforming from multiple transmissions increases
the signal-to-noise ratio (SNR), its acceptance in many
applications, particularly medical imaging is still limited.26)
By forming several steered receiving beams, one of thereceive beams will pass through the center of the arteryand thus be perpendicular to the arterial wall. By coherent
combination of the multiple steered receiving beams(formed from several sequential transmissions stepped
across the entire arterial cross section) at all image points
of interest, a large angular width of the imaged region of thearterial wall could be obtained, thus eliminating the need forsteering of transmit beams.
In the present study, acoustic ﬁeld simulation and virtualscanning of a simulated ‘‘reﬂector tube’’ were performed
using the Field II program.29) Acoustic ﬁeld measurement
and scanning of a silicone-rubber tube phantom in water
were also performed and the optimization of parameters wasconsidered using results from simulations and phantom
experiments.

V

Φ

fd

Linear transducer
array probe
L(a)
Virtualpoint
source

τ d1

τdN-1

V(0,zf)

τd2

τdi

τdN

i

N

Ri

fd
Transducer
element12......

-x0
Sub aperture, L(xi,zi) p+x

Spherical wavefronts

(b)

+z

Fig. 1. (Color online) Multi element diverging beam from a linear arraytransducer. (a) Illustration of the beam. (b) Time-delay determination foreach element of the transmit sub aperture. V is the virtual point source
behind the array surface; fd is the axial distance from the array surface to thevirtual point source; L is the sub aperture length of N elements and  is thebeam-spread angle (aperture angle or divergence angle).

wavefronts are produced in front of the transducer arrayover a limited angle. The time delays are governed by thelocation of the virtual point source with respect to thepositions of the individual physical elements on the sub
aperture. The time-delay calculation for each element is
illustrated in Fig. 1(b) for an image plane on the x–z
plane at y ¼ 0 and a transmit sub aperture surface that lies
along the x-axis with the sub aperture center at the origin
ð0; 0Þ.
The time delay  di for a speciﬁc element, i (i ¼ 1; 2;
3; . . . ; N), is calculated by
 di ¼

Ri  fd;cð1Þ

where Ri is the distance from the virtual point source V ð0; zf Þto the center of element i, fd is the axial distance from thearray surface at z ¼ 0 to point V and c is the speed of soundin the medium.
Virtual focal distance fd is related to the beam-spreadangle  and the transmit sub aperture length L by

2. Materials and Methods

fd ¼

2.1 Principle
2.1.1 Transmit beamforming and element time-delay
calculation

Diverging
wavefrontsL:
2 tanð=2Þð2Þ

Sub aperture length L is related to the number of elements N
in the transmit sub aperture by

In multi element diverging beam production, the excitation of each of the elements that make up the transmit
sub aperture is time-delayed so that spherical resultant

L ¼ pðN  1Þ;

ð3Þ

where p is the inter element pitch.

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Φcovered by the transmit wavefront to the image point p is
given byVirtual source
V(0,zf)point, Vrp ¼ Ra  r:
Ra

fd

La

Receive sub aperture, L

1 2 3Distance r is related to the receive sub aperture bypﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
r ¼ La 2 þ fd 2 ;

r

...

N

i

-x

where

+x
xi

0
rp

θm

rps,i

p(x p,zp) Transmit

l1

wf0 at t = 0

wavefronts

lM

lm

ð8Þ

ð9Þ

ð10Þ

and time p isp ¼+zFig. 2. (Color online) Receive steering and focusing on an image point
within a transmit beam.

In terms of the coordinates,i
1 hpﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
xi 2 þ ðzf  zi Þ2  zf ;
di ¼
c

ð4Þ

where xi , zi are the coordinates of the position of the centerof element i.
Since the array surface lies along the x-axis [as shown in
Fig. 1(b)], for each element i in the transmit sub aperture,zi ¼ 0. Therefore, xi is expressed as



Nþ1
xi ¼ p i ;ð5Þ2and  di simpliﬁes to di ¼N1:2

Also, Ra is related to point p by
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
R a ¼ xp 2 þ ð f d þ zp Þ 2 ;

wfτ p

l2


La ¼ pð7Þ

ﬃ
1 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
xi 2 þ zf 2  zf :c

ð6ÞIn transmission, active sub apertures are stepped across thearray at a pitch of one element with coincident transmit andreceive sub apertures.
2.1.2 Receive beamforming

Since the beams are wide and can be assumed to be uniform,
many steered receiving beams (or image lines) can beformed per transmission.21) In any direction, the receive sub
aperture must focus dynamically within the transmit beam.
Focusing on an image point along a steered receiving beam
within a transmit beam is illustrated in Fig. 2.
For a receive-focusing point (or image point) p at
position (xp ; zp ) lying on receiving beam (or image line) lm
formed on the x–z image plane at y ¼ 0 (m ¼ 1; 2; 3; . . . ; M
where M is the total number of receiving beams formed for
one transmit beam), the receiving beam is steered by the
sub aperture through angle m to receive-focus at p. The
wf0 is the wavefront at the beginning of reception (t ¼ 0),
and wf p represents the wavefront that traverses point p attime t ¼  p . If Ra is the radius of wavefront wf  p and r is
the radius of wavefront wf0 , then the distance rp (along theradial line joining point p to the virtual point source V )

rp
:
c

ð11Þ

Distance rps;i covered by the scattered signal from point p
to receive element i at point ½ðxi ; zi Þ; zi ¼ 0, is given by
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ð12Þ
rps;i ¼ ðxi  xp Þ2 þ zp 2 ;and time taken ps;i isps;i ¼

rps;i
:
c

ð13Þ

Total time of ﬂight tp;i taken by ultrasound from the
beginning of reception to reach receive element i via point
p is given bytp;i ¼ p þ ps;i ¼

rp þ rps;i
;
c

ð14Þ

Upon substituting eqs. (8), (10), and (12) into eq. (14),pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1 hpﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
tp;i ¼
xp 2 þ ð fd þ zp Þ2  La 2 þ fd 2cpﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃi
þ ðxi  xp Þ2 þ zp 2 ;ð15Þ
where element position xi is determined using eq. (5).
Equation (15) describes the time at which the scatteredsignal from the image point, p, is received at thereceive element i after reception commences at t ¼ 0.
Keeping the transmission ﬁxed, eq. (15) determines whichsample should be selected from among the sampled
received signals to obtain a receive focus at the image
point p.
If ynt;i ðtÞ represents the received echo signal on element ifor the nt-th transmission (nt ¼ 1; 2; 3; . . . ; NT , where NT is
the total number of transmissions per frame), the beamformed image at point p, snt;lm ðpÞ along the receive beam lm
is then given by
snt;lm ðpÞ ¼

NX

wi ynt;i ðtp;i Þ;

ð16Þ

i¼1

where wi is the apodization weight for element i.
2.1.3 Angular receiving beams combination from multiple
transmissions

For one transmit beam from a transmit sub aperture,
it is possible to form several steered receiving beams in

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Table I. Parameters for the acoustic ﬁeld simulation.

Transmit beamFirst-order receive
grating lobe
Probe

.

.

A receiving beamFirst-order receive
grating lobe(a)Receive sub apertures for eachconsecutive transmission

Lnt-1

Lnt+k
Vnt-1 Vnt Vnt+1

Vnt+k. . . . . . . . . . . . . . . . .
BeamntBeamnt-1 Beamnt+1

Array surface

Element
pitch, pθrs,nt+1

....

(b)

p

.

7.5

Sampling frequency (MHz)
Assumed speed of soundin water (m/s)
Assumed attenuationin water (dB/cm)

30
1500
0.2170Transmit apodization

Hanning-modulated
sinusoid of two cycles
BoxcarBeam-spread angle (deg)86

Virtual source point

10 mm behind array surface

Beamnt+k

θrs,ntθrs,nt1-

0.2

Ultrasound transmit frequency (MHz)96

Element excitation

Lnt+1

Lnt

Transmit sub aperture size
(elements)
Inter element pitch (mm)Wavefronts of each transmission
arrive at p at different orientationand curvaturepoints outside the beam. The maximum steering angle ofreceiving beams in each transmit beam is limited to 65
because of the limitation posed by the transducer array/element directivity.
Therefore, in Fig. 3(b), the ﬁnal beamformed image SðpÞat p is expressed as
NTPX
snt;lm ðpÞ;ð17ÞSðpÞ ¼nt¼1

Fig. 3. (Color online) Receive-grating lobes and multiple steered

receiving beams combination. (a) Illustration of ﬁrst-order receive-grating
lobes associated with a receiving beam. (b) Multiple steered receiving
beams combination at point p, from transmissions in which transmit beam
engulfs p and excludes others.

parallel.21) In this work, several steered receiving beams
within one transmit beam are formed in parallel. Corresponding steered receiving beams formed from eachsequential transmit beam could be stacked to form anangular B-mode image. Many image frames (from diﬀerent
steered receive beams) could be combined to form acompounded image, as in MACI. However, because thetransmit beam is wide and diverging, each receiving beamsuﬀers from receive lateral sidelobes and receive grating
lobes. Sidelobes and grating lobes are both unwanted partsof the ultrasound beam (oﬀ-axis) and may produce image
artifacts as a result of error in positioning the returning
echo.30) Receive grating lobes associated with a receiving
beam is illustrated in Fig. 3(a). If the separate angular Bmode images are averaged, the ﬁnal compounded image
would contain artifacts due to these lobes.
In order to reduce these eﬀects, therefore, instead of
combining the angular B-mode image frames formed fromeach steered receiving beam of each transmission, thefocused RF signals snt;lm ðpÞ [eq. (16)] of steered receiving
beams from multiple transmissions at each image point ofinterest are summed. This is illustrated in Fig. 3(b). If theimage point p is associated with a reﬂector, coherent
summation will occur, resulting in a large beamformed
signal, but for grating lobes and depth sidelobes, coherent
summation will not occur. The intervals of the centers oftransmit sub apertures is of one-element pitch. The transmit
beam proﬁle (for some beam-spread angle ) could bealmost uniform within the beam but signiﬁcantly low forwhere NTP is the number of transmissions for which point p
lies within their transmit beams and having associatedreceiving beam with point p whose steered angle rs;nt does
not exceed the maximum receive steering angle. The NTP isgoverned by the beam-spread angle , the position of point
p and the intervals of receive steering angles.
This method is utilized in order to be able to obtain the
maximum possible angular width of the imaged region.
Coherence summing of the RF signal at each image pointfrom multiple transmissions is employed in synthetic
aperture focusing technique (SAFT) and its variants, which
provides very high resolution.31,32) However, if SAFT is usedin its classic form, the maximum angular width of theimaged region obtained would be less because, in thisapplication, large beam-spread angle  and large transmit
sub aperture size are used, so the region of interest (carotid
arterial region which is at depths of 10 to 20 mm) therefore
lies within the near ﬁeld of the beam. Also, the use ofsynthetic transmit aperture (STA)33) (which involves using
all the elements in the entire transducer array to receive echo
signals, thereby giving the highest image quality), would
require a larger data memory and is more prone to motion
artifacts, phase cancellation and speed errors at large
receive-steering angles if the entire transducer array apertureis used for receive beamforming.
2.2 Simulations and experiments
2.2.1 Simulations
I Transmitted acoustic field

The acoustic ﬁeld of the beam was simulated using the
Field II program29) with the simulation parameters listed inTable I. The program returns the values of the emitted
pulsed pressure waves with time at all positions of interest
within the beam. Speciﬁc depths of interest are 10, 15, and
20 mm.

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Table II. Parameters for the virtual scanning.

Coincident transmit/receive sub
aperture size (elements)
Inter element pitch (mm)0.2Transmit frequency (MHz)

7.5

96

Sampling frequency (MHz)30

Assumed speed of sound in water (m/s)

1500

Assumed attenuation in water (dB/cm)

0

Transmit apodization

BoxcarReceive apodization
Assumed frequency-dependent
attenuation [dB/(m Hz)]

BoxcarElement excitation
Interval of centers of transmit
sub apertures (mm)Number of transmissions for both scans
Mode of scanning for both scans
Transmit focus for thefocused beam (mm)Virtual source point forthe diverging beam

UltrasoundEquipment
ManualXYZ
stage

Linear multielementtransducer arrayprobe

Amplifier

x
Water
tank

PC (for data
analysis)yzOscilloscope

Clamp
Water

0
Hanning-modulated
sinusoid of two cycles

Hydrophone

Fig. 4. (Color online) Schematic of the setup of the experimental system
for the acoustic ﬁeld measurement.

0.2 (1-element pitch)95
Linear sequential scanning
14.1

direction and at depths of 10, 15, and 20 mm below thetransducer surface using a manual XYZ stage.

10 mm behind
the array surface

II Transverse cross sectional scanning of silicone-rubber
tube phantom in waterII

Virtual scanning of simulated ‘‘tube-shaped’’ reflector

Virtual (simulated) sequential linear scanning of a simulated‘‘tube-shaped’’ reﬂector was also performed using the
Field II program.29) The transverse cross section of the‘‘tube-shaped’’ reﬂector was simulated by dividing the walls
into small point scatterers of equal strength with an interscatterer spacing of 20 m. The reﬂector has an inner radiusof 4 mm and an outer radius of 5 mm with its center locatedat a depth of 14.1 mm below the transducer surface. The‘‘simulated scanning’’ was performed by assuming thereﬂector to be in water with no attenuation with depth.
Two separate ‘‘virtual’’ scans were performed using thetransmit parameters in Table II. The ﬁrst scan involves using
unsteered focused beams, and in the second scan, diverging
beams were used. The Field II program calculates andreturns the values of the received RF signals (received
voltage trace) for each of the elements in the receive sub
aperture and for each transmission. These generated data
were used for image reconstruction.

Transverse cross sectional scanning of a silicone-rubber tube
phantom in water using the same ultrasound machine andtransducer probe as described above was performed. The
silicone-rubber tube phantom had an outer diameter of
10 mm and wall thickness of 1.0 mm. Its center was locatedat a depth of 14 mm below the transducer surface. Two
separate scans were performed. In the ﬁrst scan, unsteered
focused beams with a focus at 14.1 mm were used and in thesecond scan, diverging beams with a virtual point source at
10 mm behind the array surface were used. The transmit/
receive sub aperture for each transmission is composed of 96
elements. The two scans were performed with 95 transmissions per frame at a frame rate of 109 Hz with an interval ofcenters of coincident transmit/receive sub apertures of oneelement pitch. Received ultrasonic echoes were sampled at afrequency of 40 MHz. No transmit apodization was used.
Received RF signals for each of the elements in the receive
sub aperture and for each transmission were acquired for
oﬄine image reconstruction.
3. Results

2.2.2 Experiments
I Measurement of transmitted acoustic field

3.1 Acoustic field
3.1.1 Simulations

The acoustic ﬁeld in water was measured using a hydrophone (Toray H025-002) in order to observe the pressure
waveforms transmitted by the actual imaging system that weused. Figure 4 shows the schematic of the setup for themeasurement of acoustic ﬁeld using -10 ALOKA ultrasound equipment with a 192-element linear array transducerof 10 MHz nominal frequency. The emission was set with anactive transmit sub aperture of 96 elements and virtual
acoustic source of 10 mm behind the array surface. Notransmit apodization was used. The output from thehydrophone was ampliﬁed by the NF 5305 diﬀerential
ampliﬁer (DC-10 MHz) with a factor of 10, and the output
from the ampliﬁer was acquired with the TDS224 digital
oscilloscope (Tektronix). Measurements were taken over a
distance of 33 mm at intervals of 1 mm in the lateral

Figure 5(a) shows the simulated ultrasonic time-pressure
waves at depths of 10, 15, and 20 mm below the transducer
surface. From the ﬁgures, it can be seen that emulation ofdiverging waves is possible in the depth range from 10 to
20 mm, which corresponds to the typical depth of the carotid
artery below the skin surface.
Figure 5(b) shows the time plot along the white lines inFig. 5(a), for the waveform of the pressure waves that
correspond to points at axial depths of 10, 15, and 20 mm
below the center of the transmit sub aperture. The time axis
in Figs. 5(a) and 5(b) is referenced to the time of the lastelement(s) to be ﬁred, which in this case are the two extreme
elements in the transmit sub aperture.
The middle plot of Fig. 5(b) shows the simulated emittedpressure waveform as it passes a point below the center of

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(a)

(a)

Main pulses

Main pulses

Trailing pulses

Trailing pulses

(b)

(b)
Fig. 5. (Color online) Simulated emitted waves. (a) At axial depths of 10,15, and 20 mm. (b) Plots of the emitted waves along the white lines in (a).

Fig. 6. (Color online) Acoustic pressure as measured with thehydrophone. (a) At depths of 10, 15, and 20 mm. (b) Waveform of the RF
signals along the white lines in (a).

the aperture at an axial depth of 15 mm. The emittedpressure waveform is a composite of two components: themain pulses and the trailing component. The main pulses are
the resultant edge wavefront from the wavefronts of theindividual elements and they are eﬀective for imaging. The
trailing component is the wavefronts (at a given position
within the beam) resulting from the interference of delayed
wavefronts which arrives at the point after the resultant edge
wavefront has passed the point. Its length (spatial andtemporal) and amplitude, which vary for diﬀerent points
within the beam, also depend on the number of elements, N,
in the transmit sub aperture and the beam-spread angle, .
The trailing components cause temporal sidelobes (or depth
sidelobes) in the image obtained using conventional receive
beamforming, which may manifest as noise. It can also
produce ‘‘ghost’’ structures in the image. With multiple
transmissions and multi angle receive beamforming, such aneﬀect is reduced.

In the ﬁgures, it can be seen that emulation of sphericallydiverging waves was achieved in the depth range from 10 to
20 mm, which corresponds to the typical depth of the carotid
artery below the skin surface. Figure 6(b) shows the time
plot of the waveform of the acquired RF signal along thewhite lines in Fig. 6(a), which correspond to points at axial
depths of 10, 15, and 20 mm below the center of the transmit
sub aperture.
Similarities can be seen between Figs. 5(a) and 6(a) as
well as between Figs. 5(b) and 6(b). As the simulation
result shows, the RF signals in Fig. 6(b) also contain two
components: the main pulses and the trailing pulses. The
time axis in Figs. 6(a) and 6(b) is referenced to the time of
the last element(s) to be ﬁred, which in this case are the two
extreme elements in the transmit sub aperture.

3.1.2 Acoustic field measured with hydrophone

Figure 6(a) shows the ampliﬁed ultrasonic RF signals,
acquired by the oscilloscope, from the hydrophone placed
at depths of 10, 15, and 20 mm below the transducer surface.

3.2 Reconstructed images

Figure 7 shows the reconstructed B-mode images of thesimulated tube-reﬂector obtained by simulated (virtual)scanning performed with the Field II program.29) Boxcar
apodization was used in receive. The angular width of theimaged region of the tube’s anterior and posterior walls[illustrated in Fig. 7(b)] is wider in the image from the07HF05-6# 2011 The Japan Society of Applied Physics

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A. Ponnle et al.

Angular width ofimaged region(a)Lateral distance [mm]

(b)

(a)

Fig. 7. Reconstructed B-mode images of the simulated tube-reﬂector.
(a) Conventional linear scanning. (b) Proposed method.

(a)

(b-2)

(b-1)

(b-3)

Fig. 9. B-mode images of the simulated tube reﬂector for diﬀerent
numbers of transmissions. (a) Conventional, focal distance of 14.1 mm.
(b) Diverging beam scanning, virtual source distance fd of 10 mm: (b-1) 29
transmissions, (b-2) 95 transmissions, (b-3) 157 transmissions with sub
aperture of 36 elements and fd of 4.1 mm.

(b)
(a)

Fig. 8. Reconstructed B-mode images of the silicone-rubber tube

(b)

(c)

phantom. (a) Conventional linear scanning. (b) Proposed method.

diverging beam than that in the image from the conventional focused beam. Figure 8 shows the reconstructed
B-mode images of the silicone-rubber tube phantom.
There is improvement in the lateral resolution in thereconstructed images using the diverging beam comparedwith that in reconstructed images using the conventional
focused beam. For improved resolution and suppression ofgrating lobes and sidelobes, the minimum angular separation
between the combined angular receive beams should be
about 0.5 . A discrete angular interval of 0.5 was used inthis study.
Figure 9 shows the reconstructed B-mode images
obtained using focused beam and diverging beam forvarious numbers of consecutive sequential transmissions
for the simulated tube reﬂector. It can be seen that a wider
angle is obtained for 95 transmissions than that of 29
transmissions and a much wider angle is obtained for 157
transmissions using sub aperture size of 36 elements andfd ¼ 4:1 mm.
Increase in the angular width of the imaged region ispossible with the diverging beam because by receive
beamforming several angular beams within the transmit
beams, at least one of the receive beams would pass throughthe center of the tube and thus be perpendicular to the tube
wall. This part of the tube’s surface will be diﬀerent for
diﬀerent transmissions as they are stepped sequentiallyacross the entire cross section. This is demonstrated in
Figs. 10(a)–10(c), which are separate B-mode images (fromsimulation) formed with diﬀerent angular receive beams.
Each image is a partial view that does not portray the tube as
a complete circular structure.

Fig. 10. B-mode images of the simulated tube reﬂector at various receive
steering angles. (a) 15 receive-steering angle. (b) 0 receive-steering
angle. (c) +20 receive-steering angle. Artifacts due to receive lateralsidelobes, depth sidelobes and receive grating lobes can be seen in theimages.

3.3 Optimization
3.3.1 Simulations

Figures 11(a)–11(d) show the B-mode images (from simulation) of the simulated tube reﬂector for beam-spread angles
 of 86, 120, 150, and 180 , respectively for a sub aperturesize of 96 elements and 97 transmissions. The plot in
Fig. 12(a) shows the variation of the angular width of theimaged region (from simulated images) with diﬀerent beamspread angles  for three diﬀerent sub aperture sizes of 36,
56, and 96 elements in comparison with the angular width
obtained by focused beam scanning. The angular width
increases with increasing  until about 120 , after which it
decreases, and with increasing degradation in image quality.
The worst image for all sub aperture sizes was obtained for ¼ 180 . It should be noted that a 192-element linear arraytransducer was simulated, so diﬀerent sub aperture sizes
make it possible to achieve diﬀerent maximum number oftransmissions, NTmax , given by
NTmax ¼ NeðtotalÞ  Neðsub-apertureÞ þ 1;

ð18Þ

assuming the interval of centers of transmit sub apertures isof one-element pitch. The NeðtotalÞ is the total number of
elements in the transducer array and Neðsub-apertureÞ is thenumber of elements in the transmit sub aperture. Applyingeq. (18), for a sub aperture size of 96 elements, NTmax ¼ 97;
for a sub aperture size of 56 elements, NTmax ¼ 137, and fora sub aperture size of 36 elements, NTmax ¼ 157. Therefore,

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A. Ponnle et al.

8

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16

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18

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(b)

(c)

5

14
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18

18

20

20
0

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Lateral distance [mm](b)Depth [mm]Depth [mm]Lateral distance [mm]
(a)

−5

(a)
−5

5

(d)

−5

5

Lateral distance [mm]
(c)

0

5

Lateral distance [mm](d)Fig. 11. B-mode images (simulation) of the simulated tube reﬂector for a
sub aperture size of 96 elements and 97 transmissions with beam-spreadangles of (a) 86, (b) 120, (c) 150, and (d) 180 .

(e)Fig. 13. B-mode images of silicone-rubber tube phantom for diﬀerent sub
aperture sizes and diﬀerent beam-spread angles . (a)  of 87 and sub
aperture size of 96 elements (97 transmissions). (b)  of 90 and sub
aperture size of 56 elements (137 transmissions). (c)  of 90 and sub
aperture size of 36 elements (157 transmissions). The sub apertures arecoincident transmit/receive sub apertures. (d) and (e) correspond to (b) and(c), respectively, but with receive sub aperture size of 96 elements.

3.3.2 Phantom experiments
I Angular width for different beam-spread angles and sub
aperture sizes

Silicone-rubber tube phantom scanning was performed for
diﬀerent coincident transmit/receive sub apertures at
diﬀerent beam-spread angles. Figures 13(a)–13(c) show
the B-mode images of the phantom for sub aperture sizesof 96 elements ( ¼ 87 ), 56 elements ( ¼ 90 ), and 36
elements ( ¼ 90 ), respectively. Figure 14(a) shows theplot of the variation of the mean angular width of the imaged
region with sub aperture sizes of 36, 56, and 96 elements at
diﬀerent beam-spread angles in comparison with the angularwidth obtained with conventional scanning. Since theimaged region that is observable is partly dependent on theimage dynamic range, the mean value of observable angularwidth in images with dynamic ranges of 60, 50, and 40 dB
was taken. From the plot in Fig. 14(a), the highest mean
angular width is found to occur around  of 90 to 120 forall the three sub-apertures, and decreases with increasing .

(a)

II
(b)
Fig. 12. (Color online) Variation of angular width of the imaged region(from simulated images) with diﬀerent beam-spread angles, and coincident
transmit/receive sub aperture sizes of 36, 56, and 96 elements: (a) maximum
number of transmissions, (b) same number of transmissions (97).

the smaller the sub aperture size, the greater the number ofpossible transmissions and the wider the angular width
becomes, provided the limit of the transducer’s receive
directivity is not yet reached.

Contrast
The B-mode image contrast of the clearly imaged regions of
the tube phantom was evaluated by considering thediﬀerence in signal level between the two regions indicatedin Fig. 14(b). In the ﬁgure, region A is a clearly imaged
region within the posterior wall of the tube phantom andregion B is a region outside the posterior walls and tends tohave signiﬁcant noise levels.
The contrast ratio, CR, between the two regions is takenas  B
CR ¼ A;
ð19Þ
A þ B

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A. Ponnle et al.

Angular Width [deg]Angular width vs beam−spread angle (phantom)
Sub aperture size: 36 elements
Sub aperture size: 56 elements
Sub aperture size: 96 elements
Conventional (96 elements)

7060

4. Discussion

50
40
30
20
80

90

100

110

120

130

140

150

160

Beam−spread angle [deg]

(a)
14

0.9

CR

16
Depth [mm]CR vs beam−spread angle (phantom)

1

15

17
18

0.8
0.7
Sub aperture size: 36 elements
Sub aperture size: 56 elements
Sub aperture size: 96 elements

0.6

19

0.5
80

20

90

100

110

120

130

140

150

160

Beam−spread angle [deg]

21

(c)

22
23
0 1 2
Lateral distance [mm]1

CR vs beam−spread angle [same receive sub aperture (96)]: Region A: Region B

(b)

CR

0.9
0.8
0.7
0.6
0.5
80

Sub aperture size: 36 elements
Sub aperture size: 56 elements
Sub aperture size: 96 elements
90

100

110

120

130

140

150

160

Beam−spread angle [deg](d)Fig. 14. (Color online) Optimization on the basis of phantom
experiments for sub aperture sizes of 36, 56, and 96 elements. (a) Variationof mean angular width with beam-spread angle . (b) Regions considered
for CR evaluation. (c) Variation of CR for diﬀerent . (d) Variation of CR
for receive sub aperture sizes of 96 elements for the three diﬀerent transmit
sub aperture sizes.

where A is the mean signal level in region A, and B is themean signal level in region B. In eq. (19), CR of one (themaximum value) indicates the best contrast while CR of zero
indicates the worst. Negative values of CR are mostundesirable. The plot in Fig. 14(c) shows the CR obtainedwith diﬀerent  and sub apertures sizes of 36, 56, and 96
elements. Sub aperture size of 96 elements has the highest
CR at each  considered. Also, for each sub aperture, thehighest CR occurs at  close to 90 and decreases withincreasing . At  ¼ 90 , the CR of the three sub apertures
are relatively close.
The CR decreases with decreasing sub aperture size,
because coincident transmit/receive sub aperture wasused even though there is an increase in the number oftransmissions with reduced sub aperture size. If the receive
sub aperture size for each transmission of the three diﬀerent
transmit sub aperture sizes is retained at 96 elements, the CR
would improve. Figures 13(d) and 13(e) are B-mode imagesof the phantom for transmit sub aperture sizes of 56 and36 elements, respectively, but with a receive sub aperturesize of 96 elements. Also, Fig. 14(d) shows the plot of
the CR for a receive sub aperture size of 96 elements for
all the three diﬀerent transmit sub aperture sizes of 36,
56, and 96 elements. There is a relative increase in CR
for the transmit sub aperture size of 36 elements at each that was considered. For the transmit sub aperture sizeof 56 elements, there is also a relative increase in CR at
 ¼ 90 and 150 , but there is a slight decrease in CR at
 ¼ 120 .

As shown by the results, the angular width of the imaged
region of the tube’s wall increases with increasing numberof transmissions when the proposed receive method is usedwith diverging beam. If the radius of curvature of the tube’s
wall is large relative to the wavelength, some parts of thetube’s surface will be tangential to the diverging wavefrontsof each linear sequential transmission (assuming consistencyof wavefronts) depending on the relative position of thetube’s wall within the beam of each transmission. These
parts of the tube’s surface are eﬀective at specularlybackscattering ultrasound to the receive sub aperture andare mainly the anterior and posterior walls of the tube. These
regions act like an interface irrespective of the inter scatterer
separation on the tube’s wall, because of their almost
perpendicular orientation to the ultrasonic transmit beams
for most of the transmissions. It is the extent of these regionsthat can increase when imaged with diverging transmit beam
and with greater number of linear sequential transmissions,though it would be limited by the attenuation of the echo
signals with increasing distance, array receive-steering/element directivity, time gain compensation (TGC), andmaximum number of available transducer elements in thelinear transducer array probe.
If the linear sequential transmissions are symmetrically
stepped (about the tube’s center) across the tube crosssection, the angular width of the imaged region of theanterior and posterior parts of the tube’s wall would haveequal half-angles.
The region of the two side walls of the simulated tube
reﬂector is negligibly visible in Fig. 7, but it can still be seenin the phantom image in Fig. 8 because of scattering within
the phantom wall. For the simulated tube reﬂector, only two
widely separated reﬂecting walls are assumed. Therefore,
the two side walls cannot be imaged by specular reflection
alone as the angle of the reﬂected echoes are so large thatthey slide oﬀ the receive sub aperture for most of thetransmissions. This region of the two side walls is also
diﬃcult to image with focused beam.
Imaging of the region of the two side walls strongly
depends on the scatterers backscattering ultrasound to thereceive sub aperture. This is demonstrated in the phantom
experiment. Since the scattering of ultrasound by point
scatterers is isotropic, this region is expected to be easily
imaged. However, scatterers on the sidewalls (and within the
thickness of the sidewalls) both in phantoms and in tissues
are randomly placed with random scattering amplitudes
and random phases. Therefore, the summed scattered waves(interference of echoes) from the scatterers may experience
either constructive interference or destructive interference
depending on the relative phases of the scattered waves
which, among other factors, is inﬂuenced by the relative
positions of the scatterers and the transmit beam wavelength.
If there is constructive interference, the side walls can be
seen.
From the simulation result of the optimization ofparameters; it can be seen that for all the three sub-apertures
simulated, the optimum result lies within beam-spread angle
 of 86 to 150 . Smaller sub aperture size tends to produce
greater angular width, but correspondingly, the contrast

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A. Ponnle et al.

suﬀers. Also, if  increases beyond 150 , the beam is nolonger uniform and the ratio of the maximum amplitude of
the trailing pulses to the maximum amplitude of the main
pulses signiﬁcantly exceeds one (1) within the beam. The
phantom results show that contrast ratio CR decreases withincreasing  and the angular width remains fairly constantwithin 90 and 120 but decreases rapidly thereafter. Withan equal receive sub aperture size of 96 elements, the CR
improved.
Frame rate also decreases with decreasing sub aperturesize owing to an increase in the number of possible
maximum transmissions. Therefore, recommended parameter values are a sub aperture size of 36 elements and of 90 . This combination is expected to yield optimum
results in in vivo experiments.

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07HF05-10# 2011 The Japan Society of Applied Physics

5. Conclusions

In this study, it has been demonstrated, through simulations
and silicone-rubber tube phantom experiments, that transverse cross sectional image of cylindrical vessels could beobtained over wider regions than is possible with conventional linear scanning as a result of employing multi element
diverging beams from a linear array transducer. This strategy
eliminates steering of transmit beams and the same frame
rate as in conventional linear scanning is still retained by
combining multiple angular receiving beams from multiple
sequential transmissions of the same frame. However, since
the beams are spherically wide, there is a more stringent
requirement on the receive beamformer to be less sensitive
to receive sidelobes and grating lobes, as well as to avoid
lateral spatial under-sampling because of grating lobe
artifacts.
Also, this study revealed that optimized beam parameters
are a sub aperture size of 36 elements and beam-spread angle
 of 90 . The proposed method is intended to be applied
to in vivo transverse cross sectional scanning of carotid
arteries.

7)
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31)32)