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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,

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

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.

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.

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

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.

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

KOULOUNTZIOS et al.: 4-D UST FOR INDUSTRIAL PROCESS REACTORS INVESTIGATION 4502714

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

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

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.