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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022 4502714
A 4-D Ultrasound Tomography for Industrial
Process Reactors Investigation
Panagiotis Koulountzios , Tomasz Rymarczyk ,Member, IEEE, and Manuchehr Soleimani
Abstract— A volumetric ultrasound tomography (UST) system
and method are established for industrial process applications.
A two-plane ring-array UST system is developed for 3-D imaging
of the process under test. Such a 3-D system allows capturing
axial variations, which is not possible in 2-D or 2.5-D imaging.
A ray-voxel intersection method is used to create the sensitivity
matrix needed for the 3-D or 4-D image reconstruction. Acquiring
and processing time series data lead to 4-D imaging, generating
dynamical volumetric image by using a time correlative total
variation (TV) algorithm. The 3-D forward model using the
ray propagation model offers a computationally efficient tool
for modeling the measurement process in UST and is used for
image reconstruction. In combination with the advanced 4-D
TV algorithm, high-quality information is gained from time and
space. At first, the 3-D imaging methodology was tested and
verified using static objects. Second, 4-D imaging was investigated
by using a moving rod in an experimental tank. The system
was then implanted to carry out dynamical process monitoring,
imaging 4-D crystallization process. Finally, the results are
evaluated using quantitative image evaluation in the 3-D mode
and process dynamics in the 4-D imaging mode.
Index Terms—4-D imaging, crystallization process tomogra-
phy, process tomography, ultrasound tomography (UST).
I. INTRODUCTION
ULTRASOUND tomography (UST) has been studied and
developed in 2-D and 3-D setups for various medical
and industrial process imaging applications. Volumetric (3-D)
industrial tomography is more informative than the 2-D setups,
as it provides full information from the 3-D region-of-interest
(ROI) using modalities such as electrical impedance tomog-
raphy (EIT), electrical capacitance tomography (ECT), X-ray
computed tomography (XCT), and others [1]–[5]. Volumetric
imaging in all the above modalities provides a more detailed
understanding of the industrial process under investigation.
The 2-D imaging is always an approximation to the actual
physical scenario. Considering full geometrical conditions
allows producing high-quality images with more information.
The benefits of 3-D imaging were displayed on industrial
process tomography against traditional 2-D and 2.5-D imaging
Manuscript received November 21, 2021; revised March 14, 2022; accepted
March 18, 2022. Date of publication April 1, 2022; date of current ver-
sion April 18, 2022. This work was supported by the European Union’s
Horizon 2020 Research and Innovation Program through the Marie
Skłodowska-Curie under Grant 764902. The Associate Editor coordinating
the review process was Dr. Ziqiang Cui. (Corresponding author:
Manuchehr Soleimani.)
Panagiotis Koulountzios and Manuchehr Soleimani are with the Engi-
neering Tomography Laboratory (ETL), Department of Electronic and Elec-
trical Engineering, University of Bath, Bath BA2 7AY, U.K. (e-mail:
m.soleimani@bath.ac.uk).
Tomasz Rymarczyk is with Research and Development Centre,
Netrix S.A., 20-704 Lublin, Poland.
Digital Object Identifier 10.1109/TIM.2022.3164166
in [6]. The 2.5-D imaging is prior to the 3-D technique and
is conducted by interpolating independent 2-D images into a
3-D volume, being considered as an approximation method.
UST has been studied in 3-D fashion in transmission
and multimodality techniques, mainly for medical applica-
tions [7]–[10]. Medical applications of the UST [11]–[13]
have been very promising in breast cancer imaging, where
the advanced 3-D full-waveform inversion (FWI) or other
computationally complex algorithms [14]–[16] can provide
images reaching the quality standards of XCT or to mag-
netic resonance imaging (MRI). Aiming at high spatial
resolution, medical systems require not only heavy com-
putational reconstruction algorithms but also many sensors
(e.g., 1000 transducers). This leads to time-consuming data
collection, and eventually, imaging is too slow and not suitable
for agile industrial applications. On the other hand, almost all
newly developed UST systems for industrial applications are
based on 2-D imaging [17]–[20]. UST industrial applications
are mainly focused on liquid transportation pipelines and
multiphase flow monitoring [21]–[23]. Ultrasound computed
tomography (USCT) also finds great need in and liquid/gas
flow imaging, which is a process widespread in the chemical,
oil and gas, pharmaceutical, and energy industries [24]–[26].
However, the significant need for volumetric monitoring in
industrial process imaging leads to new incorporated 3-D
developments. Regarding the high temporal changes of the
live industrial processes, developing a fast imaging system is
crucial. Therefore, the number of sensors and the form of
the acquired data are designed optimally for high temporal
imaging, satisfying the spatial resolution requirements.
Early tomographic developments have been focused on
enhancing the spatial resolution of single-frame data. Con-
ventional single-step reconstruction algorithms are based on
single-frame data. However, in a real-time environment, mul-
tiple data frames need to be processed. In that case, dynamic
regularization algorithms, accounting for temporal resolution,
need to be addressed. First attempts of such algorithms were
made in 2-D tomographic problems [27], [28]. Nevertheless,
the need for established 3-D systems drove to the development
of temporal 4-D regularization algorithms [1], [5], [24]–[31].
This work provides a method for 3-D and 4-D imaging for
UST that fulfills the needs of industrial process tomography.
A 3-D transmission UST was developed, using the first-
arrival pulse’s time-of-flight (TOF) and incorporating multiple
ring arrays. UST in transmission mode can be considered
as a hard-field tomography, and thereafter, an improved ray-
voxel intersection adjustment is proposed similar to those
implemented in XCT. Ultrasound transmission tomography
involves some ill condition inverse problem, requiring a
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4502714 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 1. (a) UST system and sensors attached in the 20-cm-diameter tank
and a zoomed-in view of the two layers of 16 sensors each. (b) 1024 TOF
background measurements coming from 32 sensors in the two-ring array.
regularization-based image reconstruction method. The work
contributes to the field of UST as it is the first deployment of a
3-D UST system for process reactors monitoring. Moreover,
this work’s additional contribution is the application of the
4-D regularization algorithm in a 3-D UST system, as it offers
temporally correlated dynamical imaging. The 4-D imaging is
accomplished via a 4-D total variation (TV) algorithm in a
3-D UST system.
This article is organized as follows. Section II describes
the volumetric UST system and 4-D regularization algo-
rithm. Section III is dedicated to several static and dynamical
experiments, including the crystallization process. Finally, the
conclusions are drawn in Section IV.
II. VOLUMETRIC UST SYSTEM AND METHOD
A. UST Hardware System
Fig. 1(a) shows the ultrasonic tomograph with 32 channels
where the travel-time data can be collected between two
rings of 16 sensors each. Sensors can be used as transmitters
or receivers. In total, 1024 measurements are possible, with
the exciting sensor’s received signal to be considered null.
Fig. 1(b) shows the TOF data for a homogeneous liquid
background, a 1024 TOF data value coming from 32 exci-
tations, with 32 recordings per excitation. The data were
displayed in an image form. Every image’s row accounts for a
different excitation during every column for another recording.
The zero diagonal line indicates the zero values of the self-
measurements, namely, the measurements coming from the
same sensor as the excitation sensor.
Furthermore, with a closer look at the first 32 recordings,
which account for the first excitation (first row), it can be
noticed that the first 16 values are related to the interplane
excitation and the rest 16 to the same plane excitation, as the
later 16 TOF values seem to be higher. Thus, there is a
TAB L E I
UST SYSTEM’SSETTINGS
noticeable pattern on this image that can distinguish between
quadrants. This TOF data’s pattern exists due to the topology
of sensors and the excitation sequence and can describe the
tomographic setup. The interplane data plays an important
role in volumetric image reconstruction, providing an axial
resolution that may not be possible in typical 2.5-D imaging.
The UST hardware system has a configurable range of
settings. It can provide raw full-waveform data (full-waveform
mode) or processed TOF and amplitude values of the
travel-time pulse (transmission mode). It also offers adjustable
features on the acquisition’s wavelength range. These settings
are adapted to the needs of the specific process as they
significantly affect the data acquisition process. For example,
the transmission mode is a lot less time-consuming than the
full-waveform mode due to the size of the processed data.
Therefore, the settings adjustment depends on the investigation
process and the range of measured data. Regarding real-time
monitoring, the tomograph is preferably set to transmission
mode. Table I shows the system’s parameters.
The tomograph in transmission mode measures pulse’s TOF
and amplitude. The device automatically finds the minimum
and maximum values of the signal, based on which it converts
the percentage value into the numerical value of the analog-
to-digital converter (ADC). The comparator threshold works
only in the signal area beyond the value specified by the
following parameter. The moment the signal exceeds the
comparator threshold, the measurement window opens. The
most considerable amplitude value from this area is stored
and processed to compute its TOF.
The developed UST system has been described priorly
in [32]. The hardware design provides 84 measurement chan-
nels for possible use. Each sensor has its signal conditioning
and measurement circuit, so all measurements for each exci-
tation can be done simultaneously. The designed measuring
cards have a maximum sampling rate of 4 MBPS per channel.
Each channel is equipped with a separate generator of ac
rectangular waveforms with amplitude up to 144Vp−pand
an instantaneous current capacity of 3 A. It is possible to
sample the analog signal on all channels simultaneously.
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KOULOUNTZIOS et al.: 4-D UST FOR INDUSTRIAL PROCESS REACTORS INVESTIGATION 4502714
Three eight-order filters are built into each channel for
effective harmonic filtering, triggered by analog keys. The
350-kHz bandpass filter with 200-kHz center frequency and
200-kHz bandwidth for 300- and 400-kHz transducers was
used. The unit has two-stage gain control on each channel.
The first stage is from +7.5 to +55.5 dB (AD8331), while
the second stage is from +6to+36 dB [six settings—
STM32’s built-in programmable gain amplifier (PGA)]. Each
channel is shielded, so the channels are very well isolated
from each other. The device’s implemented signal filtering
is particularly important. Built-in filters allow to get rid of
harmonics of other frequencies, but they also affect the signal
strength. Overall, the device’s temporal resolution is 4 fps. The
measurement system uses MCUSD11A400B11RS ultrasonic
sensors with frequency 400, ±16 kHz, diameter 11 mm,
a material made of aluminum, input voltage 300Vp−p, direc-
tivity (−3dB)7
◦±2◦, and operating temperature −20 ◦C
to 80 ◦C. For each transmitter, an excitation of five cycles
(tone burst) pulse takes place. However, they have a slightly
smaller wave propagation angle compared to 40-kHz sensors.
As a result, the wave period is much smaller so that the
TOF measurement error is almost ten times smaller. Therefore,
400-kHz transmitters are the most accurate and are suitable for
transmission measurements.
In addition, single excitation reference measurements were
carried out to measure the width of wave propagation for
a 400-kHz transducer. For this purpose, 32 measuring points
were placed at appropriate intervals around the circumference
of the tank. The results of the measurements are shown
in Table I and the characteristics are shown in Fig. 2.
A high keying voltage is required to achieve good quality
measurements. The amplitude measurements address that the
transducer works optimally in the range of ±90◦.Abovethat,
its signal is much weaker. The TOF data seem to be reliable,
and measurement errors are minimal.
The proposed reconstruction method uses the subtraction
of experimental data and reference data. Such methods are
categorized as “difference imaging” and constitute relative
reconstructions of the ROI due to the subtraction of the actual
experimental measurement from the background measurement.
Incorporating such logic focuses on the changes described
between the prior (background) and the later phase (exper-
iments). TOF measurement data result from subtracting the
background from the full data, defining the travel-time delays
in microseconds (μs), as shown in the following equation:
δT=Tfull −Tback.(1)
B. 3-D Forward Model
A 3-D ultrasound transmission tomography method was
developed and applied to this work based on the TOF of
the first arrival pulse, whose trajectory is assumed as a
straight line. The travel-time reconstruction method was used
accounting for time delays resulting from the subtraction of
TOF reference data and TOF experimental data. Considering
high emission frequency, the ray trajectory can be solved by
d
dl 1
c
dx
dl =1
c2∇c(2)
Fig. 2. 400-kHz transducers: (a) TOF characteristics and (b) amplitude
characteristics.
where lis the arc length along the ray trajectory, xis the
position vector, and cis the speed of sound [33]. With the
position of the source and take-off angle of the source, one
can specify the ray path. Assuming a uniform travel-time
delays model that only depends on the depth, one can use
a simplified method for the wave propagation based on the
ray-approximation approach
δT=ray
δs(x)dl (3)
where the above integral is based on a single ray path,
δsdenotes the “travel-time delays” distributions in the
microsecond scale, and, finally, δT gives the “travel-time
delay” of the pulse. The term “travel-time delays” defines the
time difference between a propagating in the reference medium
signal and a propagating experimental signal. Assuming that
the ray path is sensitive to a small travel-time perturbation, the
perturbation in travel time is given by the path integral of the
average travel-time perturbation along the ray. It will allow a
linear inversion algorithm based on a linear forward model.
A linear method requires data from a background state (prior
state) and a state where the domain has changed (experimental
state). For a linearized forward problem, (3) can be expressed
as
δT=Aδs(4)
where δsis differences in arrival time, Ais the modeling
operator, which describes the sensitivity distribution, and
δTis the travel-time distribution.
For solving the 3-D forward problem of (4), a domain needs
to be addressed. Then, the software for 3-D UST sensitivity
matrix computation is based on the ray-voxel intersection algo-
rithms of tray-tracing methods [34]–[36]. Thus, by calculating
the intersection region, the weighted values can be assigned.
In the specific experimental cases, the sensor rings have
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4502714 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
a perimeter of 200 mm, and they are positioned in layers of
a 70-mm distance. A (32 ×32) spatial resolution was applied
for the cross-sectional planes of a 200-mm edge. For the
z-axis, a study was followed to compare and provide a well-
arranged discretization, following the cross-sectional planes’
sensitivity distribution. Finally, a (32 ×32 ×4) cuboid voxels
grid was used. Comparing the sensitivity distributions between
different cases of different discretization along the z-axis,
the proposed seems to overcome sparsity and be superior.
A ray-based algorithm is computationally efficient in lin-
ear image reconstruction, especially FWI, making it a good
candidate for industrial application. The matrix A can be
precalculated and evaluated before it can be used for the image
reconstruction process.
C. Optimized Ray-Voxel Intersection
An optimized ray-voxel intersection method was developed
for assigning values to the sensitivity matrix. In the predevel-
oped 2-D UST algorithm, the pixel was considered circular
instead of square. The inscribed circle of a pixel defines
the circular pixel. Thus, the imaging software becomes much
faster, particularly important in cases where “online” imaging
is needed [37]. Regarding this modification, an approximation
of this method for 3-D models was developed. Prior studies
have shown the efficiency of this concept in 3-D problems
[38]. Furthermore, the voxel has been treated as an inscribed
sphere of a voxel rather than as a cube. Thus, the method’s
main objective is to compare the distance from the ray to the
voxel’s center, with the voxel’s radius. Subsequently, only one
task needs to be executed instead of four complicated ones,
leading to less complexity. Therefore, the distance of the ray
to the voxel’s center is computed, as shown in the following
equation:
d=(v1−v2)×(pt −v2)
v1−v2(5)
where pt,v1,andv2are the 3-D coordinates of the point, one
vertex of the line, and a second vertex of the line, respectively.
The symbol xdefines the cross-product equation. Then, the
distance, d, is compared to a fixed value, which usually
is the radius, r, of the spherical voxel [39]. By increasing
the intersection criterion value, the calculated rays turn to
“thick lines” tackling sparsity that might be introduced [40].
To enhance the sensitivity distribution and subsequently the
inversion’s outcomes, we chose to apply a “thick lines” model.
Such a model is more realistic to the real setup because it
accounts for the piezoelectric transducers’ characteristics.
Rymarzyck et al. [41] presented a method of incorporating
smoother sensitivity distribution by using the circumscribed
sphere’s radius instead of using the inscribed spheres’ radius of
the voxel. The circumscribed sphere’s radius represents half of
the diagonal value of the voxel. The diagonal, dg, is calculated
by the following equation:
dg =(r)2+(r)2.(6)
This approach works better than the previous approach, which
used the inscribed circle to the voxel. Moreover, it proved to
offer less sparsity in the outcomes. The method was tested
in a cubic voxels grid. However, in the specific case of
(32 ×32 ×4) resolution, the grid consists of spheroid voxels.
A spheroid has not had a unique radius value. Instead, it can be
defined by two radii. The longer radius is called the semimajor
axis, and the shorter radius is called the semiminor axis. There-
fore, we proposed two radii to be used in the mathematical
function of the algorithm to calculate the diagonal, dg
r1=vl1
2,where vl1=200
32 mm (7)
r2=vl2
2,where vl2=70
4mm.(8)
Thus, (6), in respect of (7) and (8), becomes
dg =(r1)2+(r2)2(9)
where dg is the distance that defines the radius of the circum-
scribed spheroid on cuboid voxel. Elements of matrix A can
be produced by the ratio of the radius length to the distance
from the ray to the center of the voxel as per the following
equation:
Ai,j=⎧
⎪
⎨
⎪
⎩
0,for d>dg
1−d
R2
,for d≤dg.(10)
Equation (10) includes the distance criterion, which defines the
ray-voxel intersection. Thus, for voxels that are not intersected
with the ray, zero values are assigned.
For every other voxel, the assigned value is described as
a weighted value proportional to the amount of the ray that
intersects the voxel’s area. For the computation regarding rays
on a single plane and for interplanar rays, the corresponding
radius’ combination between (r1,r1)and (r1,r2)was used.
Thus, the sensitivity matrix contains weighted values that
define the regional sensitivity according to the effect of rays
on every voxel of the ROI.
To evaluate the proposed methodology, the values of the
experimental reference measurement data are compared with
the synthetic background data produced by three generated
sensitivity matrices based on different methodologies. At first,
a method that uses as an intersection convergence criterion, the
inscribed sphere’s radius, is noted as “SM1.” Then, a sensitiv-
ity matrix that uses the circumscribed sphere’s radius is noted
as “SM2.” Finally, the sensitivity matrix that incorporates both
radii to calculate dg for the interplanar computations is noted
as “SM3.” All three matrices are multiplied by a unity vector
to produce the so-called “synthetic” data. The first 32 values
of these data and the experimental reference data are plotted
together in Fig. 3. It represents how well each matrix can
produce data from a measurement of uniform background
(e.g., water background). As it can be seen, “SM3” provides
a better approximation against the real measured data.
D. Inverse Problem With 4-D Regularization
In dynamical 3-D imaging, the image reconstruction process
deals with many frames of data and images. Certain infor-
mation in x, y, and z space can be temporally regularized,
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KOULOUNTZIOS et al.: 4-D UST FOR INDUSTRIAL PROCESS REACTORS INVESTIGATION 4502714
Fig. 3. Observed and synthetic TOF data plotted together with simulated
linear forward model.
providing 4-D imaging. We use a 4-D TV algorithm proven
very successful in various other imaging modalities [24]–[26]
arg min
δS
∇x,y,zδs
1+∇tδs1
s.t.
˜
Aδs−δT
2
2≤e(11)
where spatial and temporal TV-based regularization terms [first
two terms in (10)] and srepresent a 4-D travel-time delays
distribution, ˜
Arepresents the linear sensitivity matrix, and
e represents the expected noise level in the measuring system
and model uncertainty.
The split Bregman (SB) method [42], [43] will be used to
solve the constrained optimization problem of (10). Using the
Bregman iteration can lead to an iterative scheme
δsk+1=arg min
s
∇x,y,zδs
1+∇tδs1
+
I
i=1
μ
2
˜
Aδs−δTk
2
2
(12)
δTk+1=δTk−˜
Aδsk+1+δ. (13)
Including auxiliary variables in the SB algorithm allows split-
ting L1- and L2-functional to easily solve them in separate
steps. Images δsare given analytically by solving a linear
system, and L1-functional is solved using shrinkage formulas.
To perform the split, we include dx=∇
x,dy=∇
y,dz=
∇z,and dt=∇
t, so (12) becomes
δsk+1,dx,dy,dz,dt
=arg min
δs,dx,dy,dz,dt
dx,dy,dz
1+dt1+μ
2
˜
Aδs−δTk
2
2
st.di=∇
iδs.(14)
Constraints in (14) can be handled using the Bregman iteration
as above, which leads to an iterative scheme.
III. EXPERIMENTAL RESULTS
A. Static Experiments
The imaging performance was tested through various
experimental configurations in terms of 3-D static and
dynamical imaging. This section presents, at first, results
and experimental analysis on static experimental configura-
tions. Then, quantitative indications on suspension character-
ization are presented by conducting static experiments with
water/sucrose suspensions.
Eight cases were conducted using cylindrical plastic objects
in different combinations and positions with static objects.
Objects of 10, 20, and 30 mm diameter have been tested.
Any object less than 20 mm was difficult to reconstruct as the
sensors could not be sensitive to those. In this work, cases with
20- and 30-mm objects are presented. Various combinations
of these objects were tested. Fig. 4(a) shows the experimental
photographs of all the conducted experiments, Fig. 4(b) shows
the reconstructed volumetric data by using cross-sectional
slices, and Fig. 4(c) shows the reconstructed volumetric data
by isosurfaces, imposing 3-D travel-time tomography. At first,
simple tests with the single object at the center of ROI were
executed, distinguishing well between a 20- and 30-mm object.
Items were being positioned at different distances from each
other. The variety and amount of different topologies in total
applied offer a great indication of the system’s overall spatial
resolution and potential in industrial processes.
A version of the structural similarity (SSIM) index based
on volumetric data has been used [44] to acquire a quanti-
tative index for the reconstructions. The SSIM is an image
quality assessment metric that overall outperforms the error
sensitivity-based image quality assessment techniques, such
as mean squared error (MSE) and peak signal-to-noise ratio
(PSNR) [45]. A more advanced form of SSIM, called mul-
tiscale SSIM (MS-SSIM), is conducted over multiple scales
through a process of multiple stages of subsampling [46].
This image quality metric has been shown equal or better
performance than SSIM on different subjective image and
video databases. Thus, it is considered a more robust method
for image quality assessment. In this work, MS-SSIM was
used. MS-SSIM is presented
MS −SSIM =[lM(δstrue,δsrec)]aM
M
j=1cj(δstrue,δsrec)βj
×sj(δstrue,δsrec)γj(15)
where δstrue and δsrec are the 3-D signals to compare, namely,
the true and the reconstructed volume; aM,βj,and γjare
the weighted parameters to define the importance of the three
components laccounting for luminance, caccounting for
contrast, and saccounting for SSIM. A higher MS-SSIM
shows better image quality, with the region of the possible
values to be in [0, 1]. Fig. 5 presents the MS-SSIM values of
the eight experimental cases’ reconstructed data. The quality
metrics provide consistency to the nature of the experiment.
At first, relatively high values result from the first four cases
containing single objects as inclusions. Then, in the multiple
inclusions case, the MS-SSIM values show a noticeable decay
that is expected.
In addition, specific experiments based on different con-
centrations of fine sucrose particles in water were conducted.
These experiments aimed to test the quantitative response of
the system. Travel-time delays are assumed to remain at a
minimum level when the medium is almost homogeneous.
On the other hand, delays of sound travel time are increased if
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4502714 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 4. Eight positions of single and multiple circular static objects of 30 and 20 mm diameter. (a) True positions, (b) volumetric reconstructions with
cross-sectional slices, and (c) volumetric reconstructions of isosurfaces.
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KOULOUNTZIOS et al.: 4-D UST FOR INDUSTRIAL PROCESS REACTORS INVESTIGATION 4502714
Fig. 4. (Continued.) Eight positions of single and multiple circular static objects of 30 and 20 mm diameter. (a) True positions, (b) volumetric reconstructions
with cross-sectional slices, and (c) volumetric reconstructions of isosurfaces.
Fig. 5. MS-SSIM values for all the eight experimental configurations with
static cylindrical objects.
the differences in density and structure of materials within the
medium remain significant. TOF delays result from different
imaging and are defined in (1).
In this case, reference data (background) were collected by
scanning the tank filled with water. Single inclusions of 20%,
42%, and 70% kg/m3mixtures were tested. Fig. 6(a) shows
the photographs of the experimental setup with water/sucrose
inclusions, and Fig. 6(b) shows each case’s reconstructed
volumetric data. The solutions filled plastic cups of 1-mm
wall thickness. The thin wall of the plastic cup ensures
ultrasonic wave transmissivity. In cases of 20% and 42%,
the delays are negative as the difference data addresses. The
scale of these two reconstructions introduces a quantification
indication as the reconstruction scale’s absolute values are
increased. The increasing number of negative values defines
the ultrasound acceleration within the tested liquid compared
to the background. In the case of 70%, the difference data are
positive, and subsequently, the reconstruction includes positive
TOF delays. Therefore, an opposite-color bar reconstructed
image than the previous cases was noticed.
This effect may come from the floating particles, as the
mixture is a saturated solution, with its concentration being
close to the saturation point of the mixture (66.7%). Therefore,
the sound may be blocked by a significant number of undis-
solved particles, which will need more time to be dissolved
or sediment. Difference data plots provide a good indication
of quantification, as differences can be noticed in all three
cases. Between the first two cases, the difference in negative
data values indicates the inclusion density change, while few
positive values come from noise in the measurements. On the
other hand, in the third case of 70%, the higher positive
values are established, showing the difference in medium’s
distributions
Continuing with the tests, multi-inclusion scenarios with
concentrated solutions have been conducted. Four different
combinations have been chosen to challenge the system’s
quantitative response in more depth. Similar to before, the
60.78% case produced positive TOF delays, resulting in higher
reconstructed values than the medium (water). However, this
was the only case that decreased the sound propagation.
The difference between inclusions positioned simultane-
ously in the tank is evident in all the cases. Thus, the system
provides relatively good substance characterization incorpo-
rating a robust approach of travel-time imaging. Particular
interest can be drawn in Fig. 7(c), where the two inclusions
of 42% and 50% concentration have been put very close
to each other. In addition to the objects’ location, their
concentration is very close, too. Therefore, the case itself
makes a special and challenging experiment. Nevertheless, the
reconstruction is clear, indicating the concentrated regions of
the medium. Moreover, one can notice a clear relation of the
total cumulative sucrose concentration to the resulting scale
bar of reconstructions among all the tests. They result in
a clear indication of the quantitative travel-time imaging in
concentrated solutions tests.
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4502714 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 6. (a) Photograph of the experimental tank and of the inclusions filled with sucrose/water solutions, (b) 20%, (c) 42%, and (d) 70% kg/m3solutions’
reconstructed volumes presented.
Fig. 7. Multi-inclusions of sucrose/water solutions of (a) 20%–42%, (b) 42%–50% far-positioned, (c) 42%–50% near-positioned, and (d) 70%–20% kg/m3.
Figure includes experimental photographs and reconstructed volumes.
B. Dynamical Experiments (4-D)
This section presents the results using the predescribed 4-D
regularization algorithm. Multiple frames have been used for
reconstructions. The system was able to provide a high frame
resolution of up to 4 fps. The system provides high temporal
resolution as its electronic design can filter the waveform data
and capture the TOF values of the first-arrival pulse, which
saves much time from the data transferring process. Achieving
such high temporal resolution regarding the UST system’s
limitations, we were able to test cases of real-time movement
of objects. These tests can offer a first impression of real-time
changes leading to a robust system for industrial tanks and
pipes. The need of such a system is crucial as ultrasound
process tomography gains more attention [45], [47]–[49].
A dynamical test was conducted incorporating a writing
technique in 3-D. This test aimed to efficiently produce a
3-D letter of the English alphabet, tracking the individual
generated frame’s movement and superimposing them to a
unified volume.
A plastic rod of 20 mm in diameter, acting as a writing
object, was used. The pen is manually shifted inside the tank
to produce the shape of a 3-D letter. Fig. 8(a) shows a planar
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KOULOUNTZIOS et al.: 4-D UST FOR INDUSTRIAL PROCESS REACTORS INVESTIGATION 4502714
Fig. 8. Multiframe 4-D reconstruction of a moving plastic rod of 20 mm diameter, drawing the letter “Y.” (a) Scheme describes the overall experiment and,
more specifically, the motion of the plastic rod. The rod is inserted at the start of the process, at “00:00:03” reaches position “2,” at “00:00:045” reaches
position 3, at “00:00:06” is at position “4,” and, finally, at “00:00:07” reaches the last position “5.” (b) Volumetric 4-D reconstruction of the super-imposed
volume depicting the engraved letter. (c) Individual volumetric frames presented with the respected times.
Fig. 9. Mean values of difference TOF data displayed together with
reconstructed isosurfaces.
and a panoramic scheme describing the experiment. At first,
the object is inserted into the tank. Then, a motion begins
driving the object linearly into five different spots of the
Fig. 10. Planar and panoramic photographs of the crystallization experimental
apparatus.
tank, shaping letter “Y.” Fig. 8(c) shows the 4-D volumetric
reconstructions of different frames with the respected times,
and finally, Fig. 8(b) shows the reconstructed letter “Y.” The
reconstructed letter results from the individual superimposed
frames into a unified volume. The resulting volume constitutes
all the motion of the rod in the tank and defines the engraved
letter.
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4502714 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 11. (a) Experimental photographs and (b) reconstructed frames presented regarding the case of 27-mL/min injection rate with no stirring over thefirst
minute of the injection.
In Fig. 9, the mean values of TOF delays have been
presented. In contrast to the previous experiment, the TOF data
start from zero values as the tank’s medium is homogeneous
at the beginning, and after the insertion of the object, the
values start increasing. During the small object’ movement,
a decrease in TOF delays has been recognized. Thus, it seems
that the object’s movement is not preventing the pulse’s trans-
mission as a static object would. Reconstructed isosurfaces
have been displayed in this graph to highlight the rod’s inser-
tion frames and the five different spots of its movement inside
the tank. A 4-D approach to image reconstruction captures
the 3-D frame in their natural dynamical situation, providing
a seamless method for motion tracking in tank reactors.
C. Crystallization Imaging
A reactive calcium carbonate crystallization is applied in a
batch concept. Fig. 10 shows the entire experimental setup in
which the UST system is utilized to conduct process monitor-
ing. The crystallization reactor is made of plexiglass with an
inner diameter of 190 mm. In the micrometer-sized, liquid–
liquid crystallization system, aqueous CO2−
3as the reagent
solution flows through an inlet pipe (diameter: 2 mm) into the
crystallizer containing calcium chloride. A detailed description
of the membrane contactor-based CO2capture unit and its
integration with a calcium carbonate crystallization process is
given in [50] and [51], respectively.
The chemical reaction governing the crystallization of cal-
cium carbonate is presented in the following equation:
CO2−(aq)
3+2NA+
(aq)→CaCO3(aq)↓+2NaCl(aq).(16)
Ultrasound transmission-based tomographic measurements
are used to detect localized crystalline suspensions and mon-
itor the reactive crystallization of the calcium carbonate
process. Other works proposed the use of the reflection
measurements to detect the localized forming suspensions
by incorporating machine learning techniques [52]. In the
investigated crystallization experiments, the initial concentra-
tion of calcium chloride is 1.6 g/L; the feed flow rate is
27 mL/min. Feed solution composition is NaOH at pH 12.1 ±
0.05 and CO2−
3concentration of 0.14 mol/L ±0.02 mol/L.
Due to the fast kinetic nature of the particulate system, the
nucleation phenomena are instantaneous, resulting in the for-
mation of micrometer-sized particles. The ultrasonic excitation
of 400 kHz is not sensitive enough to react significantly to
the onset of inherently stochastic nucleation, which begins
at approximately 30 s after the first recorded frame of the
process. After initiating the feed solution, the formation of
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Fig. 12. (a) Experimental photographs and (b) reconstructed frames presented regarding the case of 27-mL/min injection rate with no stirring.
amorphous calcium carbonate (ACC) could be an alternative
cause of the TOF delay. Due to these delays, the system
can display the injection point and the gradual increase of
concentration/suspension density at this specific point.
Fig. 11 shows the photographs of the first minute of the
process. The photo sequence describes the start of ACC for-
mation and its gradual growth in the time window of approx-
imately 1 min. Fig. 11 presents six reconstructed volumes of
the tank during this time window. The UST images depict the
ACC’s formation and propagation in the tank, as after a few
seconds, its sediments slowly to the bottom of the tank. The
white circle points to the injection point. The 4-D imaging
responded well in the z-dimension, too, as the layers depicted
the axial difference over time. Nucleation is an important first
step in the crystallization process. Due to the zero mixing
conditions, the compounds’ transformation happens slower,
and instead of producing clear calcite, a mesostructured calcite
product occurs. It is worth noting that the early part of the feed
may not be clear in UST images due to the limited resolution
expected by two rings of 16 channel sensors.
Fig. 12 shows the experimental photographs of the whole
experiment with a few corresponding frames. The sequence
of the photographs shows the progress of the medium’s phase
changes. Reconstructions are also presented in the specific
times of the captured experimental photographs. Reconstruc-
tions show the injection point and the propagation of denser
suspension through the medium. Also, the homogeneity of
the medium can be noticed from the 37th min and onward
appointed by the reconstructions. However, the injection point
could still be visible as injection continuously runs and provide
higher concentrations.
The following experiment was conducted with the same
27-mL/min feeding rate and stirring using a flat-blade pro-
peller with 100 rpm that was used. Crystalline forms of vaterite
and calcite were produced, depending on the pH of the solution
and the mixing conditions [53]. In the current precipitation
system, there is a possibility for the following succession
of the mechanism to occur [54], [55]: 1) the development
and expansion of ACC; 2) the ACC advancement and the
surface complexation can lead to precipitation of the calcite;
3) further calcite expansion from ACC; 4) more calcite surface
complexation is created allowing for the further precipitation
of calcite. Moreover, due to the nature of the experiment,
lower concentration distributions are expected in the feeding
region as stirring quickly dissolves and propagates the forming
suspensions. Experimental photographs of Fig. 13(a) confirm
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4502714 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 71, 2022
Fig. 13. (a) Experimental photographs and (b) reconstructed frames presented regarding the case of 27-mL/min injection rate and 100-rpm stirring rate.
the theoretical background of the process. Compared to the
no-stirring case, more clear polymorphs are formed, and the
medium’s phase is more dispersed with small micrometer-
sized particles. According to the reconstructions in Fig. 13(b),
no localized suspensions in the feeding region were noticed.
On the other hand, the reconstructed volumes showed higher
disturbances gradually increasing, reaching a peak and then
decreasing again. These disturbances located at the center of
the tank, around the stirring region. The disturbances define
higher concentrations that occurred through the process as
after a while start disappearing. Stirring finally dissolves them
as depicted in reconstructions. Stirring might also be the
reason for the high disturbances noticed at the center of the
tank. The crystalline formations move to the center and bottom
of the ROI, and finally, after frame “00:18:39,” the TOF delays
values start decreasing. The images are produced for every
stage of the experiments. The UST images show the material
phase changes during the crystallization process.
The mean value data of UST are plotted, in Fig. 14,
to show a global picture of the process dynamics. The rate
of changes on these mean values will also give further insight
into process dynamics. Two additional nonstirring experiments
were undertaken using an 18- and 27-mL/min injection rate.
Fig. 14. Mean value plots of 36-, 27-, and 18-mL/min injection rate,
all nonstirring. The mean value graph for the 27 mL/min–100 rpm case is
presented. A total 150 frames cover 60 min of the experiments.
Fig. 14 presents the mean value plots for the experimental
cases using 18-, 27-, and 36-mL/min injection rates. In all
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KOULOUNTZIOS et al.: 4-D UST FOR INDUSTRIAL PROCESS REACTORS INVESTIGATION 4502714
the three graphs, the same pattern of first increasing and at
some point, and after decreasing existence of TOF delays, can
be recognized. The εlines were used to depict the point at
which the change of the function’s direction happened. It is
the point for every experiment when all the dense suspensions
sediment to the bottom or dissolve to the tank’s medium and
TOF delays decrease. Comparing the ε2,ε3,andε3points, one
can conclude the difference in the reaction between different
injection rates. As higher is the injection rate, the quicker this
point appears in the graphs. Because of the faster injection,
the chemical reaction forms faster and the maximum peak
point always comes faster in time. Regarding the stirring
and no-stirring crystallization cases, the ε1and ε3lines are
compared. ε1maximum point comes faster than ε3, due to
high dynamics in stirring case. In stirring experiment, the ACC
distributes and dissolves faster than in no-stirring cases. This
aids to the uniformity of the medium and subsequently to
lower TOF delays. Among all no-stirring crystallization cases,
it was noticeable the decreasing effect of the mean values of
TOF difference data after a specific point related to the rate
of injection. The effects of stirring were also presented in the
data.
IV. CONCLUSION
The 3-D and 4-D UST imaging for static and dynamical
imaging are presented. In the 3-D imaging mode, the axial
varying information can be extracted to provide unique infor-
mation, which is not possible in traditional 2-D imaging. For
example, different behaviors in different z-axis positions in the
crystallization process are important in describing the process
dynamics allowing for deriving additional information from
axial variation in volumetric image. Separate two rings of 2-D
can give useful information on each level in the z-axis, but
the 3-D imaging by collecting interplan data can also retrieve
information for the volume between two rings of sensor giving
a fully volumetric picture of the process under investigation.
In addition, the 4-D implementation will further enhance
the 3-D imaging results by providing additional stabilities due
to time-correlated data and time-correlated image regulariza-
tion. The proposed method is applicable to the crystallization
process, where 4-D crystallization monitoring provides real-
time information on feed points, mixing, process, and crystal
formation. This holistic time- and space-based information
can then be used to optimize the yield and avoid process
malfunction.
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Panagiotis Koulountzios received the M.Eng.
degree in electrical and computer engineering from
the Technical University of Crete, Chania, Greece,
in 2017. He is currently pursuing the Ph.D. degree in
ultrasound tomography for industrial process appli-
cations with the Engineering Tomography Labora-
tory (ETL), University of Bath, Bath, U.K.
Since April 2018, he has been with ETL, Univer-
sity of Bath, as an Early Career Researcher (ESR)
for Tomocon Project, an EU Training Network
Project.
Tomasz Rymarczyk (Member, IEEE) received the
Ph.D. degree in electrical engineering (application
of level set method in electrical impedance tomog-
raphy) from the Institute of Electrical Engineering,
Warsaw, Poland, in 2010, and the D.Sc. degree
in computer science and telecommunication (non-
invasive tomographic imaging methods in complex
systems) from the Lodz University of Technology,
Lodz, Poland, in 2020.
He is currently the Director of the Research and
Development Centre, Netrix S.A., Lublin, Poland,
and the Director of the Institute of Computer Science and Innovative Tech-
nologies, University of Economics and Innovation, Lublin. He worked in many
companies and institutes developing innovative projects and managing teams
of employees. His research area focuses on the application of noninvasive
imaging techniques, electrical tomography, ultrasound tomography, radio
tomography, image reconstruction, numerical modeling, image processing and
analysis, process tomography, software engineering, knowledge engineering,
artificial intelligence, and computer measurement systems.
Manuchehr Soleimani received the B.Sc. degree in
electrical engineering, the M.Sc. degree in biomed-
ical engineering, and the Ph.D. degree in inverse
problems and electromagnetic tomography from
The University of Manchester, Manchester, U.K.,
in 2005.
From 2005 to 2007, he was a Research Associate
with the School of Materials, The University of
Manchester. In 2007, he joined the Department of
Electronic and Electrical Engineering, University of
Bath, Bath, U.K., where he was a Research Asso-
ciate and became a Lecturer in 2008, a Senior Lecturer in 2013, a Reader
in 2015, and a Full Professor in 2016. In 2011, he founded the Engineering
Tomography Laboratory (ETL), University of Bath, working on various areas
of tomographic imaging, in particular multimodality tomographic imaging.
He has authored or coauthored well more than 300 publications in the field.
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