1. Assessment of flatness of assumed planar surfaces for ultrasound investigation of elastic surfaces
Alejandro González-Gonzáleza, Esther Novo Blancoa, Martin Christian Hemmsena, Henrik Jensenb,
Jørgen Arendt Jensena, Jens E. Wilhjelma
aBiomedical
Engineering
Group,
Department
of
Electrical
Engineering,
Technical
University
of
Denmark,
Building
349,
DK-­‐2800
Kgs
Lyngby,
Denmark
bBK
Medical
Aps,
Mileparken
34,
DK-­‐2730
Herlev,
Denmark
One of the challenges in experimental
investigation of the behavior of the
electrically received signal from a
given transducer due to smooth and
rough interfaces is that the
measurement conditions must be very
precisely controlled.
This study investigate the planarity
of an assumed planar surface made
of an elasomer fixed on its perimeter
by a square acrylic frame.
• Assess planarity of rubber surface
phantoms used to mimic human
tissue.
• Material is elastic and soft, hence
planarity cannot be assumed.
Height profiles
Lateral Displacement [mm]
-50 0 50
VerticalDisplacement[mm]
-50
-40
-30
-20
-10
0
10
20
30
40
50
Elevation[µm]
-160
-140
-120
-100
-80
-60
-40
-20
Fig 7: Transducer 8811 at 12MHz (λ = 120.8μm).
Lateral Displacement [mm]
-50 0 50
VerticalDisplacement[mm]
-50
-40
-30
-20
-10
0
10
20
30
40
50
Elevation[µm]
-80
-70
-60
-50
-40
-30
-20
-10
Fig 8: Transducer 8811 at 6MHz (λ = 241μm).
Lateral Displacement [mm]
-50 0 50
VerticalDisplacement[mm]
-50
-40
-30
-20
-10
0
10
20
30
40
50
Elevation[µm]
-120
-100
-80
-60
-40
-20
Fig 10: Transducer 8670 at 6MHz (λ = 241μm).
Lateral Displacement [mm]
-50 0 50
VerticalDisplacement[mm]
-50
-40
-30
-20
-10
0
10
20
30
40
50
Elevation[µm]
-160
-140
-120
-100
-80
-60
-40
Fig 9: Transducer 8670 at 12MHz (λ = 120.8μm).
1) The surface:
The 2D profiles have roughly the same bending, but
are more similar within a transducer than from
transducer to transducer. It bends in a concave manner.
The maximal span over the entire surface is in the order
of a half to one and a half wavelength.
It is somewhat elevated in its upper right and lower left
corners.
2) The data was validated using the cross-correlation
coefficient function. This yielded values of 0.99± 0.01
(mean± std) when the algorithm was applied to scan-
lines in the same image plane and 0.93± 0.05 when it
was applied to scanlines in different image planes.
Observations
Conclusions
1) The small curvature observed here should constitute a
very small problem when investigations are
conducted with focused transducers.
2) A change of 150 μm over a distance of 5 cm yield a
change in angle of the normal to the surface of 0.17
degrees.
3) Bending should be taken into account when considering
very distant scan lines or when very accurate
measurements are needed.
Motivation
Objectives
Equipment
Array transducer
Scanning tank
with water
angle
adjustment
Azimuth
Vertical angle
Dual angle
rotation holder Rough
reflector
frame
Support
Bearing
To scannerzt
yt
xt
Azimuth
angle,
The tank was filled with demineralized degassed water.
The central part of the surface is insonified with two different linear array transducers (types 8811 and
8670, BK Medical), yielding 11 images forming two 3D data sets.
Methods
The gradient matrices elements were added starting from the center of the surface and outwards. To finish,
the resulting surface was fitted to the nearest quadratic surface to remove outliers.
Scanning tank Smooth reflector phantom Scanning seen from above
CCCfv (τ,n,m) = gr (t;n,m,θ, z0, Rq )− gr (t;n,m ±1,θ, z0, Rq )★