|Título/s:||Rapid prototyping of pyramidal structured absorbers for ultrasounds|
|Autor/es:||Acquaticci, Fabián; Yommi, Maximiliano M.; Gwirc, Sergio N.; Lew, Sergio E.|
|Institución:||Instituto Nacional de Tecnología Industrial. Laboratorio de Transductores Piezoeléctricos. INTI. Buenos Aires, AR |
Universidad de Buenos Aires. Instituto de Ingeniería Biomédica. UBA. Buenos Aires, AR
|Palabras clave:||Ultrasonido; Acústica; Absorción sonora; Ensayos ultrasónicos; Ondas ultrasónicas; Viscoelastícidad; Prototipos; Frecuencia|
| Ver+/- |
Open Journal of Acoustics, 2017, 7, 83-93
ISSN Online: 2162-5794
ISSN Print: 2162-5786
DOI: 10.4236/oja.2017.73008 Sep. 20, 2017 83 Open Journal of Acoustics
Rapid Prototyping of Pyramidal Structured
Absorbers for Ultrasound
Fabián Acquaticci1,2, Maximiliano M. Yommi2, Sergio N. Gwirc2*, Sergio E. Lew1
1Instituto de Ingeniería Biomédica, Universidad de Buenos Aires, Buenos Aires, Argentina
2Laboratorio de Transductores Piezoeléctricos, Instituto Nacional de Tecnología Industrial, Buenos Aires, Argentina
Acoustic measurements or ultrasonic testing can be strongly affected by ref-
lections or echoes from test tank walls. In order to create a non-reflecting en-
vironment equivalent to infinite medium, a pyramidal structured absorber
(PSA) can be used to coat the walls of an ultrasonic tank. In this work, we
model an array of tetragonal pyramid ultrasonic wave absorbers. This model
is based on two coupled first-order equations describing the stress and particle
velocity within an isotropic medium. For absorbing media, the Kelvin-Voigt
model of viscoelasticity is used. The equations are discretized in 2D using an
efficient time-stepping pseudo-spectral scheme that takes in consideration
both, the acoustic properties and attenuation characteristics of the composite
materials. We then built a 3D printed PSA using a Stratasys Objet500 Connex
3D printer, which allows to combine photopolymers in specific concentra-
tions and microstructures. We designed PSA covering the frequency ranges
from 0.5 MHz to 5 MHz and from 1 MHz to 10 MHz, with double homoge-
neous layer: a core of rubber material with a skin of a variety of elastomers by
combining rigid and flexible materials. Each single pyramid contains two ma-
jor parts: the ground of the pyramid (9.4 mm base × 4.7 mm height, for 0.5
MHz and 4.7 mm base × 2.35 mm height, for 1 MHz) and the body of the py-
ramid (23.5 mm height, for 0.5 MHZ and 11.75 mm height, for 1 MHz). The
measured echo-reduction was greater than 35 dB at the covering frequency
range and the transmission loss was estimated by 20 dB. Echoes increase ra-
pidly for frequencies below the minimum frequency of the covering range.
The modeling and 3D printing of PSA with different sizes, in a wide range of
frequencies, is a cost-effective custom solution for a wide range of applications
including for example, radiation force balances, hydrophone mounts and
medical ultrasound equipment.
Pyramidal Absorbers, Medical Ultrasonic Measurements, Absorbing Targets,
How to cite this paper: Acquaticci, F.,
Yommi, M.M., Gwirc, S.N. and Lew, S.E.
(2017) Rapid Prototyping of Pyramidal
Structured Absorbers for Ultrasound. Open
Journal of Acoustics, 7, 83-93.
Received: August 26, 2017
Accepted: September 17, 2017
Published: September 20, 2017
Copyright ? 201 7 by authors and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY 4.0).
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 84 Open Journal of Acoustics
Anechoic Linings, Acoustic Materials
Energy may be lost from a propagating ultrasonic beam either by conversion to
other forms of energy in the material (absorption) or by re-direction of small
fractions of the beam (scattering) . Many geometrical structures are com-
monly employed as ultrasound (US) wave absorbers, such as wedge, pyramid,
honeycomb, layered block and flat sheet. In anechoic test tanks, they are used to
both, prevent unwanted reflections during medical ultrasound measurements
and absorb targets or apertures for radiation force balances. Ultrasonic power is
a key quantity required for acoustic output measurements in medical ultrasonic
equipment. They are conventionally made using the radiation force principle
and many commercially available balances use reflecting targets, even though
application of such targets can lead to errors of up to 20% for highly diverging
transducers fields. Reflecting targets may also be impractical for measurements
on linear array transducers, where their physical dimensions may be smaller
than the ultrasonic beam.
It might at first appear that an absorbing target makes the measuring system
simpler because it does not have some of the disadvantages listed above for re-
flecting targets. However, absorbing targets introduce different problems of
measurement, since it is difficult to produce a material that will completely ab-
sorb incident ultrasound with no reflections. In addition, the absorbed ultra-
sound will cause the target material to heat up resulting in thermal expansion
and a change in buoyancy. This in turn may cause the weight of the target to
drift and give rise to significant errors in the measurement of the radiation force.
Work is currently in progress to produce alternative absorbers and to minimise
buoyancy changes whilst maintaining a simple system .
To create non-reflecting environment equivalent to infinite test tank, the ma-
terials that are commonly used in the absorber design are polystyrene, polyure-
thane rubber, syntactic foam among others with US-absorption capabilities.
Good ultrasound absorbers include specially-made rubbers which have the cha-
racteristic of acoustic impedance close to that of water and a high attenuation,
often produced by including scattering particles in the rubber . For high
power applications, significant temperature rises can be generated within the
absorber material. A pyramidal geometry makes it easier for the water to cool
the absorber. The same type of pyramidal absorbers was reported in previous
microwave investigations, for example in   .
In this work, we create a 3D printed Pyramidal Structured Absorber (PSA) for
ultrasonic frequency higher than 0.5 MHz. The array of tetragonal pyramids re-
duces specular reflections and provides the highest echo reduction and good in-
sertion loss performance. We modeled the absorber as a two-layer pyramidal
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 85 Open Journal of Acoustics
structure. However, this does not ensure the absorption of the wave within the
absorber unless it is lossy enough to restrict the transmission of the wave. The
benefit of this approach is that most of the energy of the incident wave is atte-
nuated gradually and a wave with weak amplitude will arrive at the coating-core
interface . A parametric analysis of different materials and absorber shapes
was done by means of the open-source k-Wave Matlab Toolbox which allows
simulations of wave propagation in one, two or three dimensions in homogene-
ous or heterogeneous media, and power law acoustic absorption using a k-space
pseudo-spectral method . Compared to models based on finite-difference
time domain (FDTD) schemes as in , the main advantage of k-Wave numeri-
cal model is that fewer spatial and temporal grid points are needed in order to
obtain accurate simulations. This means the models run faster and use less
There are three main stages in this work: the pyramidal absorber model defi-
nition, the pyramidal absorber fabrication, and the measurements performed to
determine reflection loss performance.
2. Experimental Development
2.1. Absorber theory
Absorbers are employed to eliminate unwanted ultrasonic energy, because they
present an impedance to the incoming wave equal to the acoustic impedance of
the medium (water). At a material interface, the incident, reflected and refracted
waves should obey the following boundary condition: the angle of incidence (θi)
measured from a perpendicular axis to the plane of the material, must be less
than the critical angle (θc), so that there is no total reflection. This condition de-
termines the maximum angle the pyramid can have in accordance with .
1 2sin c c cθ = (1)
maxi cθ θ= (2)
where c1 and c2 are the propagation velocities in the media considered. The ref-
lection coefficient (R) for the acoustic pressure (signal amplitude) at each of the
points at which radiation is reflected is given by:
( ) ( ) ( ) ( )2 1 2 1cos cos cos cost i t iR z z z zθ θ θ θ = − + (3)
( )22 22 1cos 1 sin 1 sint t ic cθ θ θ= − = − (4)
( ) ( )2 22 22 1 2 12 2
1 sin 1 sin
c c c cz z
− − = − +
where θt, θi are respectively the transmission angle and the incidence angle, and
z1, z2 are the specific acoustic impedances of the materials. Equation (5) gives the
reflection coefficient as a function of θi. Reflection coefficients at the interface
are only half the story. Eventually, the wave will reach the other side of the ab-
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 86 Open Journal of Acoustics
sorber and reflect. At the interface between the coating material and water, the
incident field is partially reflected and partially transmitted into the pyramid.
The transmitted field is attenuated inside the core material. For angles within a
particular range of incidence, the propagation direction of the reflected field is
not back towards the source, but instead towards another surface of the coating
material. The process of partial reflection and partial transmission with subse-
quent attenuation is repeated until de field reaches the base of the pyramid. The
amplitude of the field at the base of the pyramid is drastically reduced and so the
reflection from the absorber at this point is marginal. The process is illustrated
in Figure 1.
An alternative method of prediction is to treat the problem as a transmission
line containing an absorber with input impedance (zin) at the front of the absor-
ber. The reflection coefficient is then
( ) ( )in water in waterR z z z z= − + (6)
Reflection coefficients are usually expressed in dB as:
( ) ( )2REFLECTION dB 10log R= (7)
The impedance model is computationally easier than the reflection-transmission
model but it is not able to predict performance at off normal angles. The input
impedance method can model multiple layer absorbers by replacing the load
impedance by the input impedance of the preceding layer in Equation (6).
2.2. Model Definition
Figure 2 shows the unit structure of PSA used in this work. Each single pyramid
contains two major parts: the ground of the pyramid (GL, GW and GH) and its
Figure 1. The incident wave is partially transmitted into the pyramid where it is subse-
quently attenuated. For angles within a particular range of normal incidence, the reflected
component of the field propagates towards another surface where the process is repeated.
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 87 Open Journal of Acoustics
Figure 2. Unit structure of the pyramidal absorber considered in this study.
body (PH). Two different materials are used: the one for the core of the pyramid
(CM) provides high attenuation while the other, for its coating (SM), reduces
specular reflection whilst providing a smooth transition in acoustic impedance
between the two layers.
2.3. Design Absorber and Direct Digital Manufacturing
A parametric 3D CAD model has been created using OpenScad 2015.03-3 soft-
ware. The design concept for this pyramidal absorber is based on the commer-
cially available microwave absorber of TDKTM, type number is IS-030A. The
sample of 3D model of PSA is shown in Figure 3.
The materials used for the PSA was produced by combining individual pho-
topolymers offers by StratasysTM in specific concentrations and microstructures
to create a composite material with absorbing properties. The acoustic properties
of these materials are shown in Table 1. The velocity of sound was determined
by time of flight technique using an ultrasonic echoscope Digital-Echograph
1090 of Karl Deutsch. This measurement was performed in reflection mode with
2 MHz probe Karl Deutsch S6WB2.25. The Attenuation of ultrasound was de-
termined in reflection at the applied frequency of 2 MHz. The dimensions and
weight of the test-samples were measured by a caliper and a digital scale, respec-
The transmission coefficient between the two layers of the pyramid structure
is equal to 0.987, which means that almost all the energy goes from the outer to
the inner layer of the pyramid without reflection. So, the portion of the trans-
mitted energy from the initial incident wave in the first layer (approx. 90%) can
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 88 Open Journal of Acoustics
Figure 3. Left: Pyramidal absorber 3D model. Right: 3D printed PSA using a Stratasys
Objet500 Connex 3D printer. The internal structure of the pyramidal absorber is shown.
Table 1. Acoustic properties of digital composite materials produced and distilled water.
Composite material Velocity mm/µs Density g/cm3 Impedance MRayl Loss dB/cm@2 MHz
CMa 1.63 1.34 2.18 62.4
SMb 2.32 1.19 2.75 18.4
Water (20˚C) 1.48 1.00 1.483 0.08
aStratasys rubber-like material: TangoBlackPlus FLX 980; bStratasys simulated polypropylene material: Ve-
roClear-RGD810/TangoBlackPlus FLX 980.
be completely attenuated through the lossy material located inside the pyramid
and the background plate.
A 10 × 10 array of PSA, with dimensions 94 mm × 94 mm × 28.2 mm and two
homogeneous layers of different composite materials, has been printed using the
Stratasys Objet500 Connex 3D printer. The coating thickness (SE) does not affect
the external dimensions of the object, which remain unchanged. The coating
layer replaces part of the main model material. Because the coating material
thickness remains constant, if a part’s thickness is below ~0.8 mm, the core ma-
terial will not be printed at all. The entire part will be printed using the coating
material. The pyramidal shaped absorber must be larger compared to the longest
wavelength so that the side to reflect the incident wave and the height of the
pyramid must be greater than the half wavelength . The dimensions of single
pyramid of the designed absorber are shown in Table 2.
2.4. Reflection Loss Measurement
The frequency range investigated in this work is 0.5 MHz to 10 MHz. PSA per-
formance is specified by echo reduction (ER) at normal incidence and is stated
in dB. ER is defined as
( ) ( ) ( )10 10 in water in water20 log 20logr iER P P z z z z = − = − − + (8)
where Pr is the acoustic pressure reflected from the sample, Pi is the acoustic
pressure incident upon the sample, and zin and zwater are the input impedance at
the front of the absorber and the acoustic impedance of water, respectively. This
has been experimentally determined for a PSA sample in distilled water at 20˚C
using the ultrasonic echoscope for frequencies of 0.5 MHz, 2 MHz and 8 MHz,
as shown in Figure 4.
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 89 Open Journal of Acoustics
Figure 4. Reflection loss measurement setup. The acoustic pressure reflected as compared
to that reflected from a 304-stainless-steel reference block. Left (a): The reference block
has reflectivity of 0 dB down. The reference is the signal reflected from the surface of the
reference block with the same area as the sample (not shown in the photo). The bottom
plate has a reflectivity of −7 dB; Right (b): The sample of PSA reflects one fortieth of the
energy which reflects the bottom plate.
Table 2. Dimension of pyramidal absorber.
Parameter Symbol Dimension (mm)
Pyramid height PH 23.5
Ground height GH 4.7
Ground length GL 9.4
Ground width GW 9.4
Coating thickness ST 1.5
2.5. Numerical Simulations
The simulation functions used in k-Wave require four input structures. These
structures define the properties of the computational grid, the material proper-
ties of the medium, the properties and locations of any acoustic sources, and the
properties and locations of the sensor points used to record the evolution of the
pressure field over time . Ultrasonic absorption in water, at a given tempera-
ture and frequency, was calculated using a 7th order polynomial fitted to the da-
ta given by Pinkerton .
Simulations were performed in two-dimensions. To simulate free-field condi-
tions, a perfectly matched layer (PML) is also applied as to absorb the waves at
the edge of the computational domain . By default, this layer occupies a strip
of 20 grid points around the edge of the domain. Without this boundary layer,
the computation of the spatial derivates via the FFT causes waves leaving one
side of the domain to reappear at the opposite side. The use of PML thus facili-
tates infinite domain simulations without the need of an increase in the size of
the computational grid.
The positioning of the transducer with normal incident field, each sensor
point for the detection of the pressure field generated by incident pressure (Pi),
reflected pressure (Pr) and transmitted pressure (Pt), and the visualisation of the
computational model outputs are shown in Figure 5.
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 90 Open Journal of Acoustics
Figure 5. Up-Left: Normalized incident field of acoustic pressure at a frequency of 2 MHz
for PSA with single homogeneous layer, and position of the individual sensor elements to
record the acoustic pressures. Up-Right: Periodic structure of pyramidal shape cause dif-
fracted waves and scattered waves. Down-Left: Ultrasound field is dissipated by the ab-
sorber for frequency 2 MHz. Down-right: Comparison of the incident, reflected and
transmitted pressure fields.
Using both the simulated acoustic reflection and transmission pressure mea-
surements shown in Figure 6, the insertion loss (IL) was calculated as
( )1020 log t iIL P P= − (9)
where Pt is the acoustic pressure transmitted through the sample and Pi is the
acoustic pressure incident upon the sample.
The fractional power dissipation (FPD) is a parameter of an absorber material
that quantifies its inherent dissipation of acoustic energy and is usually specified
in commercial absorbers to compare the performance of different acoustic mate-
rials. The FPD has been derived from the ER and IL measurements and is de-
fined by Precision Acoustics Ltd and Acoustic Polymers Ltd as
( ) ( )2 21 r i t iFPD P P P P= − − (10)
where Pr is the acoustic pressure reflected from the sample, Pt is the acoustic
pressure transmitted through the sample and Pi is the acoustic pressure inci-
dent upon the sample. The FPD has been derived from the ER and IL mea-
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 91 Open Journal of Acoustics
Figure 6. Simulated temporal signal of reflection and transmission for PSA with single
homogeneous layer. Pi: Acoustic pressure incident upon the sample; Pt: Acoustic pressure
transmitted through the sample; Pr: Acoustic pressure reflected from the sample.
3. Results and Discussion
Impedance gradient measurement were performed using the pulse echo method
to determine the reflection loss performance of 7 test pieces of pyramidal absor-
bers printed with homogeneous material, over different portions of the material
at the front face between top and ground of the pyramid. Figure 7 shows the
experimental impedance gradient that the wave “sees” at different portions of
the material, from the front face of the pyramid. The graph shows that imped-
ance at the front face is very close to that of water but gradually increases at the
Figure 8 shows the fabricated test tank using the printed PSA’s. In the fre-
quency range of 0.5 MHz to 8 MHz, the reflectivity of the whole sample achieved
at least −29.4 dB. At the frequency range of 0.5 MHz to 2 MHz it could achieve
reflectivity beyond 38.9 dB down. The insertion loss is approximately 20 dB and
the FPD is 99% between 0.5 MHZ to 2 MHz.
Our PSAs have been designed specifically for coating the walls of an ultrasonic
test tank for a frequency range of 500 kHz to 5 MHz. Its simple design, which
allows to create a 3D printed pyramidal array with specific microstructures built
of composites materials, provides a cost-effective method of achieving high levels
of echo reduction for custom solutions. A pyramidal wedge structure provides a
smooth transition in acoustic impedance. Since there is no abrupt transition
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 92 Open Journal of Acoustics
Figure 7. Impedance gradient of the PSA. Since there is no abrupt transition layer, there
is no point which will cause a large reflection.
Figure 8. Water tank coated to prevent unwanted reflections during medical ultrasonic
layer, no point causes a large reflection. This impedance gradient is a physical
gradient: the wave “sees” a small portion of material at the front face and gradu-
ally an increasing portion as it travels into the material. This properties combi-
nation results in an absorber with impedance gradient that exhibits broadband
reflectivity performance and high echo-reduction, >38 dB over frequency range
0.5 - 2 MHz, degrading to 29 dB at 8 MHz. Without the coating layer, the ER of
the absorber was halved at 2 MHz.
In this study, the performance was predicted only at normal angle. The effects
of incident directions to PSA are not considered. Also, for high power applica-
tions, significant temperature rises can be generated within the absorber material.
F. Acquaticci et al.
DOI: 10.4236/oja.2017.73008 93 Open Journal of Acoustics
The thermal tolerance for the measurement of High Intensity Therapeutic Ul-
trasound field is limited by the thermal performance of the materials used, as
well as the exposure time. We will continue working to increase absorption and
scattering effects by adding the top acoustic impedance matched layer and small
inhomogeneities into the pyramidal layers, respectively.
This work was supported by the National Institute of Industrial Technology. The
authors would like to acknowledge the 3D printing services provided by the Ma-
terialization Laboratory of the Industrial Design Center.
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