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A triple-modality ultrasound computed tomography based on full-waveform data for industrial processes

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A Triple-Modality Ultrasound Computed
Tomography Based on Full-Waveform
Data for Industrial Processes
Panagiotis Koulountzios, Tomasz Rymarczyk ,
Member, IEEE
, and Manuchehr Soleimani
Ultrasound computed tomography (USCT) is
gaining interests in many application areas in industrial
processes. The recent scientific research focuses on the
possible uses of USCT for varied fields of industry such
as flow monitoring in pipes, non-destructive inspection, and
monitoring of stirred tanks chemical processes. Until now,
most transmission tomography (UTT) and reflection tomog-
raphy (URT) have been demonstrated individually for these
applications. A full waveform USCT contain large amount
of information on process under evaluation. The developed
approach in this paper is focusing on demonstration of a
triple modality USCT. First, an optimised transmission image
is formed by fusion of time-of-flight (TOF) and acoustic atten-
uation (AA) images. Secondly,a reflectionimage is being opti-
mised by using the information from the transmission image.
This triple modality method enables integration of a shape-
based approach obtained by URT mode with the quantitative
image-based approach UTT mode. A delicate combination of
the different information provided by various features of the
full-wave signal offers optimal and increased spatial resolution and provides complementary information. Verification
tests have been implemented using experimental phantoms of different combinations, sizes, and shapes, to investigate
the qualitative imaging features. Moreover, experiments with different concentrations solutions further validate the
quantitative traits to benefit from both reflection and transmission modes. This work displays the potential of the full-
waveform USCT for industrial applications.
Index Terms
Ultrasound computed tomography (USCT), ultrasound process tomography (UPT), industrial processes,
multi-modality ultrasound tomography, TOF imaging, AA imaging, reflection imaging, full-waveform rich tomography.
ULTRASOUND computed tomography (USCT) has been
studied lately on a broad spectrum of industrial appli-
cations with significant success [1]–[10]. Its usage has drawn
a special attention notably relating to the imaging of bipha-
sic medium and liquid mixtures in pipe flows and stirred
reactors environments [11]–[15]. USCT works by analysing
Manuscript received June 24, 2021; revised July 22, 2021; accepted
July 23, 2021. Date of publication July 27, 2021; date of current ver-
sion September 15, 2021. This work was supported by the European
Union’s Horizon 2020 Research and Innovation Program through Marie
Skłodowska-Curie Grant 764902. The associate editor coordinating the
review of this article and approving it for publication was Prof. Yongqiang
(Corresponding author: Manuchehr Soleimani.)
Panagiotis Koulountzios and Manuchehr Soleimani are with the
Electronic and Electrical Engineering Department, University of
Bath, Bath BA2 7AY, U.K. (e-mail:;
Tomasz Rymarczyk is with Research and Development Centre, Netrix
S.A., 20-704 Lublin, Poland (e-mail:
Digital Object Identifier 10.1109/JSEN.2021.3100391
the acoustic wave propagation, via sound velocity or pulse
amplitude decays of different materials. It aims to the mapping
of medium’s acoustical properties. It is non-invasive and non-
destructive, compatible with high dynamical processes, like
oil and gas flow. A better understanding of the measurement
process and fast reconstructions algorithms are imperative for
the use of USCT within the industry. Moreover, complex
stirred tank processes, require sophisticated algorithms, which
can provide accurate results. Due to the complex physical
behaviour of acoustics propagation, there are multiple recon-
struction modes, which use different waveform’s properties.
The transmission and reflection modes have been traditionally
used in ultrasound tomography reconstructions, accounting for
transmitted diffracted and reflected waves. Functional features
of these reconstruction modes can be complementary. For
instance, reflection tomography offers good resolution at the
boundary of different media, while the transmission method
has better resolution in distinguishing discontinuities along the
signals’ propagation path. Transmission mode properties, such
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et al.
as acoustic attenuation (AA) or the time-of-flight (TOF), can
be used to determine the amplitude and sound-speed profiles of
the region of interest (ROI), offering quantitative information.
All the AA, TOF, and reflection modes have drawbacks
with artefacts under certain biphasic medium distributions.
Thus, the performance of single-modality Ultrasonic Process
Tomography (UPT) is limited. However, these shortcomings
may be compensated with a multi-modality reconstruction.
For instance, in a liquid-liquid mixture, the reflected signals
will be significantly low, leading to a possible reflection
reconstruction failure. However, transmission image should
be more meaningful in such scenarios. On the other hand,
in a liquid-solid or liquid-gas medium, reflected waves may
be exploited. For instance, in many stirred tanks chemi-
cal processes like fermentation and crystallization, localised
super-saturated suspensions may be formed due to process
malfunction e.g., stirrer malfunction. In this case, a drastic
structural phase difference may occur. Thereafter, reflection
mode might be used as a malfunction detection by detecting
the localised high concentrated suspensions. It would be also
possible to detect complex dynamic phenomena such as a gas-
flow or vortexes coming from a high stirring effect. Although,
the use of reflection mode in that direction needs to be further
The multiple mechanisms (transmission, diffraction, reflec-
tion) during ultrasound propagation and the rich information
(attenuation, time-delay, distortion) contained in an ultrasonic
full signal, establishes the need for a multi-modality method.
Therefore, a multi-modality approach, that can facilitate mul-
tiple reconstruction methods, is expected to result in more
accurate imaging, as it can process measurements coming
from different signal’s features. Several studies show that dual-
modality UPT (transmission/reflection) is superior to single-
modality, confirming that multi-modality offers tremendous
benefits [16], [17]. As a result, a novel triple-modality image
reconstruction method combining AA and TOF transmission
as well as TOF reflection is proposed.
In a small circular setup filled with a non-homogeneous
medium, significant back-scattering and reflections are
expected to happen. Thus, the “noise” levels are higher. Most
common issues in ultrasound tomography revolve around the
estimation of TOF and AA from the full-waveforms, especially
in instruments that are not calibrated or that are characterised
by high “noise” levels [18]–[21]. A novel reflection TOF
picking method was built to tackle this problem. It exploits
a forward reflection solver based on ray acoustics, to opti-
mise the recorded reflected TOF values and subsequently the
reflected image. The proposed method fits well in the robust
triple-modality proposed approach. The amplitude of the trans-
mitted pulses and time-of-flight of both the transmitted and
reflected pulses have been used to produce three different
reconstructions (TOF, AA, reflection). Finally, a method of
image fusion, using the results of TOF-UTT, AA-UTT and
URT methods, was developed and used to generate the final
The paper is organised as follows. Section II presents
the main functionality of the tomographic system and
details its specifications. Moreover, the methods undertaken
for transmitted and reflected TOF and AA picking are
Fig. 1. Triple-modality ultrasonic tomography (transmission/reflection).
Design of transmitted and reflected signals’ paths.
further characterised. Section III describes the reconstruction
formulas for transmission and reflection tomography, while
section IV presents the proposed algorithm for reflected TOF
picking, which helps optimising the recordings. Section V
presents the developed fusion method. Finally, in section VI,
the experimental results are presented and evaluated, and in
section VII, the conclusions and discussion occur.
Figure 1 depicts the design of such a triple-modality ultra-
sound tomographic concept. For a 16-channel transducer
system each sensor acts as both transmitter and receiver
and complete tomographic data is collected by exciting each
sensor in turn. When Tx1 is an excitation transducer Rx1,
Rx2,…,Rx15 represent the receivers. The transmission mode
uses AA and TOF data for Rx3, Rx4, Rx5, ..., Rx13 and
for reflection mode Rx1, Rx2, Rx14, Rx15 data are used.
The actuated receivers in transmission mode are those that
are included in the fan beam of 120-degree angle where the
best quality of transmission data is possible. Those, located
in the neighbourhood of the transmitter are excluded from
transmission mode data but used in reflection mode.
The multi-modality USCT approach utilizes TOF and
amplitude information from transmission and reflection waves.
These waves come from the interaction of different phase
structure within the medium. Acoustical properties are depen-
dent on changes in the structural phases (i.e., acoustic
impedance, velocity). Sound transmission and reflection
would, therefore, change within these phases. Acoustic
impedance Z affects the propagation and nature of pulse
excitation and is dependent on the material’s structural phase.
It indicates the intensity of a medium’s regions to block the
vibrations of the particles in the acoustic field [22]. The
ratio of the reflected pulse’s amplitude, Pr,to the incident
wave’s amplitude, Po, is called the acoustic pressure reflection
coefficient R [23], and it is defined as:
By the same way, the acoustic pressure transmission coef-
ficient, T, is defined as:
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where Pr,Ptdefine the reflection and transmitted wave’s
acoustic pressure; θ0,θtrepresent the wave’s angle of inci-
dence and angle of transmission, respectively; P0is the
acoustic pressure of the incident wave. Z1and Z2are the
acoustic impedances of medium 1 and medium 2.
When a sound wave propagates through a medium, its
intensity decreases with the distance travelled, as expressed
in eq. (3).
where A0is the amplitude of the propagating wave at a given
location. A is the reduced amplitude at another location. In this
case, his the distance travelled between the two locations,
and μis the attenuation coefficient in Neper (Np)/length. The
two primary mechanisms that cause the attenuation of sound
energy are absorption and scattering. Industrial processes
usually consist of multiple phase media with a drastic dif-
ference in structural phase. Such conditions are favourable
for a multi-modality approach in ultrasonic reconstructions,
exploiting attenuation, sound-speed and acoustic impedance
change within the medium.
A. Tomographic Device
The ultrasonic tomograph has 32 independently working
channels that can perform measurements in transmission and
reflection modes. In this paper, we use 16 channel sensors in a
single plan 2D USCT mode. The bottom layer was used for the
data collection. At the same time, a sensor sends an ultrasonic
signal of 5 cycles (tone burst), while remaining sensors record.
Respectively, receivers measure the full-waveform signal. The
sequence repeats until every sensor produces an excitation
signal. The system inside the reinforced suitcase consists of
eight four-channel measurement cards connected via a FD
CAN bus to the measurement module. The measurement mod-
ule is a bridge between a microprocessor measuring system
and a touch panel or external control application (Figure 2).
Each device channel has its own analogue signal processing
module and its own 12-bit ADC 4MSPS converter. In TOF
and amplitude measurement mode, the signal is normalised to
voltages from 0-3.3V, according to the transducer’s reference
voltage. The sampling frequency is 0.25 samples per micro-
second, which results directly from the ADC converter speed.
A Built-in envelope converter was used for converting an
analogue acoustic signal to the envelope with the possibility
of switching its configuration to a frequency of 400 kHz.
In addition, the measurement module can monitor the mea-
suring sequence, store user-specific parameters, control the
high voltage inverter, and switch the USB HS bus between the
front panel’s socket and the touch panel. The touch panel was
made using a RaspberryPi 4B 2GB RAM board and a 7-inch
capacitive touch screen. The most crucial data buses have been
led to the front panel of the device. Each sensor has its own
signal conditioning for both transmission and receiving mode
as shown in green box in figure 2a.
B. TOF/ AA Picking Method for Transmission
Transmission signals directly travel from the transmitter to
the receivers without any reflection. These signals undergo
Fig. 2. (a) Measurement system: Ultrasonic tomograph block diagram.
(b) ultrasound tomographic system. (c) tank with sensors.
either diffraction or direct transmission, without significant
change of direction. A transmission pulse usually travels faster
and transmits at a larger amplitude. Figure 3(a) shows a full-
waveform signal and its envelope, recorded by Rx6 upon
Tx1 excitation. Moreover, it illustrates signal specific TOF
and AA picked points, calculated by the applied method.
Figure 3(b),(c) present background and full calculated TOF
and amplitude data. The picking method of transmitted TOF
values is described below.
First, the analytic envelope of the signal processed using
Hilbert transform. Using the envelope, signal oscillation can
be removed, facilitating more accurate peak detection. The
advantage of using the envelope is to migrate the effect of arbi-
trariness and to eliminate the effect of phase changes. Then,
the enveloped is processed to detect the transmitted pulse and
record its x-value, defining the pulse’s travel-time, and y-value,
determining the recorded pressure. The method is described in
eq. (4-8), where v(i)represents an enveloped signal, in our
experiments the receiving signal contains 1665 samples or
time steps. A minimum threshold of 10%, th,is used to
cut down the minor pulses caused by back-scattering or
equipment-related noise, eq. (4). TOF value is determined
by the projection of the first signal’s point after threshold, th,
to the x-axis. According to the sampling frequency, the TOF
must be multiplied by 0.25, to be converted in μsec. Eq. (5-7)
describe this in a linearised fashion. Comparatively, the biggest
y-value within a 20% signal’s window in the transmitted pulse
“region” indicates the recorded pulse’s amplitude, eq. (8).
th =0.1max(v(i)) ,where i ={1,2,...,n},q=1665
v(i)=v(i)for v(i)>th
0for v(i)<th (5)
kj=i|v(i)= 0,j={1,2,...,m}where m n(6)
TOF =0.25k1(7)
AA =max(v(l)),
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et al.
Fig. 3. (a) Recorded full-waveform signals from Tx1-Rx6 pair, with its envelope. Each timestep is 1/4 µsec. (b) TOF data computed from the
enveloped signals. (c) AA data calculated from the enveloped signals.
All reconstructions are generated by using difference imag-
ing, collecting background data (reference data), TOFback ,and
full data (data collected by scanning a non-uniform medium),
TOFfull. TOF measurement data, TOFtr, originates from the
subtraction of full data from the background data and define
the travel-time delays (μs), eq. (9).
TOF tr =TOF back TOFfull where
TOF tr 0forTOF
tr <0
TOF tr for TOFtr >0(9)
AA measurement data are computed by eq. (10) [24].
AAtr =1
ln AAback
AAfull (10)
where AAback is the signal’s amplitude at each receiver when
there is only water (reference data) in the field of view (FOV)
and AAfull is the amplitude of the full data. fcis the centre
frequency of the excitation pulse.
In both TOF and amplitude data, the “Deleting Outliers”
statistical filtering method was used to handle this noise for all
the datasets [25]. Specifically, “outlier” TOF values usually are
generated from back-scattering or reflected signals. Iterative
implementation of the Grubbs Test was used to identify the
outlier signals. In any given iteration, the tested value is either
the highest or lowest value, represented by the furthest value
from the sample mean.
C. TOF Picking Method for Reflection Tomography
The “traditional” picking method of reflected pulses is
described in this section. This method makes full use of all
the four transducers positioned in pairs, on each side of the
emitter. Contrasting full and background measurements, can-
cels tank-related back-scattering and reflection, as expressed
in eq. (11). As both background and full data are assumed
to present similar tank specific back-scattering and reflection.
The recorded maximum pulse peak is assumed as the observed
reflected TOF, TOF
rfl, as shown in eq. (12).
v(i)back v(i)full|,
where i ={1,2,...,1665}(11)
rf =max (pi),where i ={1,2,...,900}(12)
Figure 4(a) illustrates the experimental setting. Figure 4(b)
represents the plots of full (background and inclusions) and
background waveforms and their respective envelopes. The
first peak comes from the transmission pulse and exists in
both signals. The two second peaks come from the reflected
pulse within the inclusion surface and exist only in Full
data. Lastly, the third peak represents tank-related back-
scattered signal, existing in both signals as well. Absolute
subtraction optimises reflected pulses measurements, reducing
overall noise and back-scattered effects. As the reflected pulse
remain unchanged, it is easily trackable. Figure 4(c) depicts
the absolute subtracted signal.
A. Transmission Mode Reconstruction
Transmission can be measured either via a travel-time or
an acoustic attenuation technique. Transmission reconstruction
would take place via either travel-time or the amplitude decay
of the first-arrival pulse [26]. The most used approximation for
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Fig. 4. (a) Schematic of the setup. (b) Background and Full measurements in full waveforms. (c) Difference data in full waveforms. Each timestep
is 1/4 µsec.
transmission USCT is the ray-based method. It is fundamental
in most tomographic schemes, as the line integral defines
the path of a high frequency propagating pulse between an
emitter and a receiver. It is a simplified approach, which
does not account for the diffraction effect caused by non-
homogeneous medium. Therefore, a computational model
based on diffraction on the 1st Fresnel zone [27], was used.
Fresnel volume or ‘fat ray’ tomography is an appealing
compromise between the efficient ray theory tomography and
the computationally intensive full waveform tomography [28].
Using a finite frequency approximation to the wave equation
leads to a sensitivity kernel where the sensitivity of the travel-
time delay also appears in a zone around the fastest ray path.
The delay time is given as:
Here t(s, x) and t(x, r) are the travel-time from
the source (s) to x and from x to the receiver (r) and t0(s,r)
is the travel-time along the ray path from the source to
receiver. The times of travelling can be evaluated using the ray-
tracing method. A point x is always within the first Fresnel
zone if the corresponding travel-time satisfies the eq. (14),
in which T defines the emitted wave’s period:
The following function defines the sensitivity of a Frechet
kernel based on the first Fresnel zone:
S(x)=KV(s,x)V(x,r)cos 2πt(χ)
where S(x)is the sensitivity at x,V
(s,x)and V (x,r)are
the amplitude values of the wavefield at xpropagating from
sto xand from xto r, respectively, andk is a constant
value for normalisation purpose. The cosine factor models
the alternating sensitivity being positive in the odd Fresnel
zones and negative in the even Fresnel zones. The a,inthe
Gaussian factor controls the degree of cancellation in Fresnel
zones. The geometrical spreading approximates the amplitude
factors in a homogeneous medium. The normalisation of the
kernels is achieved by ensuring that the integrated sensitivity
over the whole medium is equal to the length of the reference
ray path [29]. SIPPI MATLAB software has been used to
generate these sensitivity kernels [30]. These kernels represent
the acoustic distribution of the medium of each sensor’s
excitation, forming the sensitivity matrix. A Normalisation
method based on the geometric wave path was applied to
the generated kernels to ensure an accurate time-of-flight
(TOF) and acoustic-attenuation (AA) mapping, as described
in eq. (16).
where Hi,jis the sensitivity matrix based on the Frechet
method and Ai,jis the normalized matrix, used for recon-
structions, and for m measured data and n number pixels,
i=[1,...m]and j =[1,...,n].
In a tomographic approach, the transmission sensitivity
matrix simulate the propagation of the measured energy from
a excitation sensor. The measurement data for UTT includes
TOF and AA data. The so-called forward problem is formed
by the multiplication of the sensitivity matrix with the mea-
surement data. Below the notation defines Mstands for
both TOF and AA data for TOF and AA reconstructions,
respectively. A generalised tomographic forward problem can
be expressed as:
where Sis the reconstructed distribution based on acoustic
features, A is the modelling operator which expresses the sen-
sitivity distribution in the FOV, Mis the sensor’s recorded
data, and eis the noise in the measurements. A simplified
inversion can be done using back projection.
Total Variation regularisation (TV) [31], [32] was used,
which has more significant potential in solving the regularised
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et al.
Fig. 5. (a) Functionality of the reflection tomography and geometrical
computation of reflection points
2.(b) Reflection image by
superimposing all the ellipses.
inverse problem in a stabilised fashion. The TV problem is
defined as an optimisation problem, minimizing
where a, the regularisation parameter, is the gradient and
||.||1is the l1norm. Then the problem to be solved is the
constrained optimisation problem, as shown in eq. (20).
xa=argminS(α||S||1)such that
where p is determined based on our knowledge of measure-
ment noise. The problem is solved by the Split Bregman
based TV algorithm [33], [34]. Then, carefully choosing the
regularisation parameters, we optimise the image by deleting
undesired artefacts.
B. Reflection Reconstruction
A time-of-flight reflection method has been applied to
reconstruct the captured reflected pulse travel-times. The
objective of this method is to locate the reflected pulses, which
lie between the interaction of the object’s boundaries with
the medium. Figure 5 (a) presents a geometric representation
of the sensors and directly transmitted and reflected waves.
Tx1 emits a tone burst pulse while Rx1, Rx2, Rx14, and
Rx15 record the reflection signals. In this case, a relevant
algorithm is developed to connect every Tx with its four Rx
points. For instance, in Tx1-Rx1, the algorithm connects the
two points, finds the mid-point P of the line, then connects P
to the centre of the circle (centre of the circular object); the
intersection point C is the estimated reflection point. Using
the coordinates of C, one can compute the travelling distance
of the pulse and subsequently the reflected TOF data. This
method comprises the reflection forward problem and can be
used to calculate simulated reflection TOF data.
To reconstruct the acoustic profile of the medium using
captured reflected TOF data, a reflection reconstruction
model based on an ellipse intersecting algorithm was used
[35], [36], [37], [38]. If transmitter and receiver are different,
the back-projection is an ellipsoidal locus with the ellipse’s
foci at transducer positions. The image is reconstructed by
drawing arcs of an ellipse along the reflection path. Input TOF
values are translated to the pulse’s travelled distance by using
the prior information of the sensors’ coordinates, as shown in
eq. (21).
ref l
where d =dT×1C+dR×1C(21)
where dR×1Cand dT×1Cdenote the axial distance between
the reflection point and the receiver and between the reflection
point and the transmitter, respectively. TOF
ref l represents
the time of flight and s0is the sound speed in the water.
Superimposing the arcs of ellipses generate an image where
the intersection of these ellipses highlights the boundary of
the circular object. The eq. (16) is used to produce all these
ellipses that can define the edges of the medium that allow
AC +CB =2a=d(22)
A and B are two foci of the ellipse, and C is a point located
in the ellipse curve, astands for the long axis length of
the ellipse. A and B represent the transmitter and receiver;
respectively, C stands for a particular point of the target
surface, reflecting the ultrasound wave. The value of acan be
easily calculated, using also the ellipse equation of eq. (23).
The value of b and c can also be easily obtained where b is
the short axis length of the ellipse and c is the distance between
focus and the ellipse centre. The distance can be calculated by
the equation:
where xr,xR,yr,yRare the transducer coordinates, their
subscripts indicate the transducer mode. When all ellipse
parameters are obtained, a particular ellipse can be drawn in a
determined position and dimension. At last, the target image
can be found by many ellipses that are mutually intersected.
Figure 5 (b) presents ellipses generated by the developed
reflection reconstruction program.
Dual modality ultrasound imaging, fusing transmission and
reflection reconstructions, have been recently researched as
an optimised ultrasound tomography method [9], [16], [39].
Indeed, combining the two different modalities, which use
different full-waveform’s features, can aid reconstructions by
combining complementary information. Despite the good per-
formance of transmission imaging, reflection imaging can aid
more towards the improvement of outcomes, especially in
well-characterizing the domain boundaries. Therefore, a robust
algorithm for reflection reconstruction needs to exploit the
medium’s boundaries. In practice however, picking algorithms
struggle to locate the correct reflection pulse many times,
and noise is added to the measurements. This is a common
issue of all ultrasonic tomographic instruments, caused by
the back-scattering effect [16]. Therefore, a reflection TOF
picking method guided by transmission image was developed.
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Fig. 6. (a),(d) True images. (b),(e) Fused transmission images. (c),(f) Segmented Images used as domain in forward reflection solver.
(g),(h) Reflection simulated data.
The developed method is based on the reflection for-
ward solver to produce better-reflected TOF values than
those coming from picking the reflected pulses, described
in section IV.
A. Image Segmentation & Reflection Forward Solver
An acoustic profile domain of the ROI is created by trans-
mission image and used from the reflection forward solver
to produce the simulated reflected data, TOF
rf .Inthat
case, the fused transmission image is used as described below
in Section V. A segmentation approach has been developed
to define the acoustic distribution on the fused transmission
image. First, the global Otsu’s thresholding method was
used [40]. Then, a labelling method calculates the number
of noncontinuous detected regions [42]. For every region,
the centre of mass and its boundaries’ shape are calculated.
The solver uses the regions’ information to find the closest
region to the corresponding pair of transmitter-receiver, to
avoid multiple reflection signals.
This aims to improve accuracy, notably considering the
impact of more complex distributions on the reflective forward
solver. Then, as shown in Figure 5(a), a line is computed from
the middle point of sensors to the region’s centre of mass. The
intersection of this line with the region’s boundaries forms
the intersection point C. Using eq. (22), given that A and
B represent the two sensors, calculates the wave’s travelled
distance d. Finally, the simulated reflected data, TOF
rf ,are
generated by eq. (25).
rf =s0
Figure 6(a-f) present the true, transmission reconstructed
and segmentation images of two single and double inclusions
cases. Figure 6(g-h) present the recorded, TOF
rf ,andthe
simulated, TOF
rf , reflection data, using the reflection for-
ward solver. In the reflected data, there are lower-values region
for every positioned object, coming from the time-delays that
they introduce. In Figure 6(g), a single low-values region
can be noticed, while Figure 6(h) two of them. Furthermore,
a clear resemblance between simulated and observed data
can be noticed, showing the good performance of the reflec-
tion forward solver. The number of reflection points reduces
significantly in multiple inclusions cases, which is clearly a
disadvantage of the method. However, a ring setup with more
sensors would increase the spatial resolution and the accuracy
of the method.
B. Optimised Reflection TOF Picking Method
This method incorporates an optimised travel-time picking
method. It picks a signal’s value, using as an a priori infor-
mation the simulated reflection data, TOF
rf , to optimise the
observed data, TOF
rf . At first, an appropriate threshold was
set, and all the potential reflected peaks above that threshold
were stored, (Pm,n).
In this way, no peak is being excluded. Then, the algorithm
calculates the “closest” peak to the corresponding simulated
TOF value, TOF
rf . The calculated point represents the
predicted travel-time value, TOFpred
rf , eq. (26).
rf =P|min
rf )(26)
where Pis a m=[1,...,M]by n=[1,...,N]matrix,
containing the peaks of the full-waveforms; Mis the number
of the measurements and Nthe number of peaks for each
measurement. Usually, the generated TOFpred
rf data were opti-
mised compared to the observed ones, TOF
rf . Nevertheless,
the data were occasionally highly affected by the simulated
data, leading to overfitting cases. Therefore, a polynomial least
square fitting model was used between the observed reflection
data and the “optimal” data, to smooth the data. A conver-
gence criterion of the average percentage of similarity of the
observed data, TOF
rf ,and the predicted data, TOFpred
rf ,was
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et al.
Fig. 7. (a) Subtracted full-waveform signal with Peaks, observed, simulated, optimised data depicted. The corresponding pulse is represented
zoomed. (b) The plot of experimental, simulated, and “optimal” data of all waveforms.
also used. Eq. (27) describes this criterion
rf TOFpr ed
with C <0.1 (27)
If the convergence criterion is true, then the optimisation is
applied to the data. Such a technique is widespread in concepts
of full-waveform inversion [43], [44], [45] The simulated data
are used to optimise the already captured data, solving the cost
function in eq. (27).
rf (m)TOFpred
rf (m)2
ξopt =arg min||ε(ξ)|| (29)
where ξrepresents the acoustical property distribution to be
recovered, and ε(ξ) is the error functional. This final step
produces the last reflection data TOF
rf , which is optimal.
Figure 7(a) shows the difference data signal, computed by
eq. (12), and a zoomed window of the reflection pulse. The
black dot represents the travel-time of the reflected pulse com-
ing from the straightforward method of section II.B (TOF
rf ).
The green dot is the simulated travel-time, TOF
rf .
The red dots represent all the captured peaks of the
waveform above the threshold value. Finally, the blue circle
represents the “optimal” reflected travel-time value that results
from the “minimal distances method”, TOFopt
rf . The effect of
the method is noticeable in Figure 7(b). The blue function
represents the optimised data, there red function the simulated
data and the black function the recorded data. The black
function missed calculating a correct TOF value in few cases,
where zeros are observed. However, the zeros have been
replaced with estimated values, in the optimised data, with
the aid of simulated data, concluding in the well-behaviour
of the optimization. These travel-time values are assumed to
be refined when compared to the observed data. This method
ensures a significantly richer dataset than the straightforward
way of picking the reflected pulses. This method is named as
“minimum distances method”.
Figure 8 presents the reflection data optimisation process
for two single and double inclusions cases. Specifically,
Figure 8 (a),(d), show the true images, while Figures 8 (b)-(e)
present reflection reconstructions using the straightforward
“traditional” way for reflection TOF picking data from
and “proposed” reflection TOF picking methods. Finally,
figure 8 (f) presents the reflection TOF of observed, simulated
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Fig. 8. (a) True images of two tested configurations. (b),(d) Reflection images generated by the “traditional” method. (c),(e) Reflection images
generated by the “proposed” method. (f) Plots of observed, simulated and optimal reflection data.
and optimal data. The observed data come from the “tradi-
tional” method, the simulated data come from the reflection
forward solver, and the optimal one come from the “proposed”
method. Both two stages of “minimal distances” and “least-
square fitting” were plotted for optimal data. In the first case,
the two functions coming from optimal data are the same,
which means that the convergence criterion is not valid. On the
contrary, in the second case, these functions differ. In both
cases, the effect of the simulated data for the computation
of optimal data is pronounced. Optimal data seem to be a
processed function dragged by the optimised ones.
The novel reflection data picking algorithm consists of all
the previously described methods and aims to provide optimal
reflection TOF data. The proposed algorithm fits the optimal
data to the captured ones with respect to a priori information
of the simulated data, as shown in Figure 7. It can be sum-
marised into the following steps: (i) execution of transmission
reconstruction; (ii) segmentation using Otsu’s threshold; (iii)
execution of reflection forward solver to produce simulated
data; (iv) calculation of optimised reflection TOF by “mini-
mum distances”; (v) checking the convergence criterion and
if true, finding the misfit data TOF
rf by solving the cost
function for TOF
rf and TOFpr ed
rf . The whole method is
displayed in Algorithm 1.
The developed triple modality approach consists of three
sets of information, and the fusing method is described by a
specific pipeline which is depicted in Figure 9.First,theTOF
and AA transmission images are fused using a “wavelet trans-
form method” [46]. This intensity-based method was chosen
due to the similarities of the TOF and AA images as they both
come from transmission reconstruction. The two images were
normalised, before being merged, to have the same scale. The
result contains both the information coming from TOF and
Algorithm 1 Novel Reflection Signal Picking
1:Compute TOF
rfl by using the “traditional” TOF
picking method.
2:Produce fused AA-TOF transmission image.
3:Create the acoustic domain by segmentation of fused
transmission image.
4:Compute TOFsim
rfl by solving the reflection forward
5:Detect all waveform’s peaks, P,above a
minimum threshold.
6:Calculate TOFpr ed
relf by locating the shortest
distance peaks from TOF
rfl by using the minimum
distance method.
7:Calculate the average percentage of similarity, C.
8:If (C<0.1)
9:Solve the cost function of TOFpr ed
relf and
10 : end
AA data subsequently proved as an optimised reconstructed
image. Then, the transmission image is combined with the
reflection image.
Because of the different nature of the transmission and
reflection images, a different fusion method was used. The
transmission images usually contain high “regions” in the
position where the objects are located, due to significantly
high TOF-delays and amplitude attenuation due to object
introduction. On the other hand, the reflection image has
almost zero values to the locations of the objects, as all the
reflections are encountered in their boundaries and, according
to the ellipse algorithm, no ellipse interaction is happening
within the object. Therefore, a method that accounts for these
characteristics, by superimposing regions of the images, was
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et al.
Fig. 9. Image fusion algorithm for triple modality USCT.
applied to fuse the transmission and reflection images. This is
described in eq. (30) method.
i,j=Ti,jwhere Ri,j>0
0where Ri,j=0where,
where Ti,jis the transmitted image, Ri,jis the reflection image
and TM
i,jis the triple-modality image; i,jrepresents the
rows and columns of the image that is 32 by 32.
The system was experimentally validated by applying sev-
eral single and multiple static inclusions tests with different
shapes and sizes. All the inclusions are made from plas-
tic (PVC) and are not compact; thus, the sound can only
be diffracted and reflected. Circular inclusions of 1cm, 2cm
and 3cm of diameter, square inclusion of 4cm side-length and
an equilateral triangle inclusion of 3cm were used to provide
various testing cases. These tests aimed to simulate dispersed
phases of a liquid mixture existing in industrial processes. The
change in the structural phase aims to simulate the change
happening during a crystallization or fermentation process.
Figure 10 presents results using different reconstruction meth-
ods of 10 different experimental configurations. Among the
reconstructed methods are TOF, AA, fused transmission, “tra-
ditional” reflection, “proposed” reflection and triple-modality
reconstructions. It is evident that transmission mode can be
used in object localisation, notably upon multiple inclusions.
On the other hand, reflection is significantly better in detecting
the boundaries of the domain accurately. However, reflection
has a clear disadvantage in reconstructing regions that lie
between two objects. Therefore, in those cases, the trans-
mission mode aid more the triple-modality results than the
To quantify the imaging quality of the proposed reconstruc-
tion approach, Correlation Coefficient (CC) and Root Mean
Square Error (RMSE) were calculated, eq. (31) and eq. (32)
respectively. The segmentation method described in section IV.
Normalisation was applied to all the images to turn them into
a uniform form, aiming at quantitative similarities.
CC =
where σis the calculated acoustic distribution by the recon-
struction algorithms and σis the real one (true image), σn
and σ
nare nth elements of σand σrespectively, δand
δare the mean values of σand σ
n, respectively. Figure 11
shows the CC and the RMSE of TOF, AA, fused trans-
mission, “traditional” reflection, “proposed” reflection and
triple-modality reconstructions. In almost all the cases, the
proposed algorithm proved to be more efficient by acquiring
the overall highest CC and lowest RMSE value. CC was
higher and RMSE was lower in single inclusion cases com-
paring with the multiple inclusions cases due to the medium’s
Concluding in the supremacy of the proposed reflection
algorithm, a triple modality approach was applied using TOF,
AA and reflection images. The MRSE of triple-mode images
is generally smaller, while CC is more prominent than all
the other methods. TOF and AA images converted to binary
form using a high threshold to segment the inclusions. Then
transmission and reflection images were fused in binary for-
mat. Regarding CC, in almost all cases, the final image is
closer to the real geometry. The significant aid of the triple
modality method can clearly be noticed as, in all cases, the
TOF, AA and reflection reconstructions’ accuracy differs, but
the triple-modality reconstruction is always higher.
The qualitative difference can be noticed in multiple inclu-
sions cases, as they consist of more complex nature. The
quantitative analysis indicates that the multi-modality method
provides more accurate reconstruction on both the area and
the location of the objects than a single modality of either
transmission or reflection mode.
To further test the performance of the proposed system and
the multi-modality approach, different setups of water/sucrose
solutions were used. These experimental scenarios simulate
miscible liquids and multi-phase flow in industrial tanks and
pipes scenarios. A plastic cup of 1mm length, filled with the
solutions, was used as a static inclusion. The cup’s sound
transmissivity has been tested and approved. The system
acquired transmitted signals passed through the water/sucrose
solutions and reflected signals came from the cup’s surface.
Figure 12 displays experimental photos and reconstructions
of three different water/sucrose cases. Figure 12(a) shows
a 60.7% solution positioned in the centre, Figure 12(b) a
combination of 50% and 42.8%, and Figure 12(c) acom-
bination of 20% and 42.8%. The TOF mapping distin-
guished well between different concentrations in multiple
inclusions experiments. Furthermore, the tests TOF-delays
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Fig. 10. Image reconstructions of the Triple-Modality USCT.
scale follows the overall concentration increase, as shown
in Figure 12(b),(c). Additionally, six different single inclu-
sions cases with water/sucrose concentrations of 20%, 33%,
42.8%, 50%, 56.7% and 60.7% were reconstructed. Tab le I
shows the TOF delays caused due to the existence of the
solution. The presented TOF-delays, calculated as the object
was segmented and its mean value was calculated. Difference
imaging was used by subtracting the background from the
full TOF measurements. Since the sound velocity of the
concentrations is higher than the medium (water in 20C),
the produced difference data were negative. Small positive
values were caused by noise and therefore were neglected.
TOF delays showed good response, as they form an ascending
function over the increasing concentration of the solutions.
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et al.
Fig. 11. (a) CC and (b) RMSE of several different reconstruction methods.
Fig. 12. Experimental photos and reconstructions of water/sucrose solutions of (a) 60.7% in the centre (b) 50% down-left and 42.8% up-right
(c) 20% down-left and 42.8% up-right.
The solutions experiment proved efficient in distinguishing
between low changes of concentration, showing the high
quantitative resolution that the system can provide.
This work presents the advantages of triple-modality ultra-
sound tomographic imaging for real industrial processes.
Accurate results of multiple solid objects and various concen-
trated solutions could significantly benefit complex industrial
processes of two-phase media and multi-material interactions.
Reflection and transmission reconstruction methods can work
in a complementary way and provide optimal results. More-
over, acoustic attenuation measurements were proven effective,
facilitating the transmission of TOF reconstructions, especially
in more inhomogeneous media. So, there is great potential in
the combination of two types of transmission mode tomogra-
phy. This kind of rich full-waveform tomography proved to
work well in exploiting full-waveform information. Without
introducing heavy computational algorithms, it can benefit
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from combining different reconstructions and at the same time
perform at a high temporal frequency. Therefore, it comprises
a potential solution to many industrial processes that need
inspection over time and a good temporal resolution.
The developed methods provided good qualitative and quan-
titative performance regarding the quality image measurements
and the correlation of TOF-delays with various solutions.
Static experiments showed good system performance in dis-
tinguishing objects of different sizes and shapes in single and
multiple objects. The solutions used in the experiments showed
that the triple-modality imaging could also use the TOF scale
to characterise small changes in the density of biphasic media,
which is a significant addition to the system. The results of
this research show that this rich full-waveform USCT can
aid industrial processes and may be used for stirred tanks
chemical processes. Given the existence of biphasic media,
which include integration of liquid solutions and suspensions,
the added value of the multi-modality full-waveform system
will become apparent in our future studies. In case of cup
with multiple percentage solution both a reflection image due
to the cup and a quantitative transmission image due to particle
concentration can be produced.
The authors would like to thank Dr. Dana Beiki (University
of Bath) for proofreading the manuscript.
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Panagiotis Koulountzios received the M.Eng.
degree in electrical and computer engineering
(ECE) from the Technical University of Crete
(TUC). He is currently pursuing the Ph.D. degree
with the Engineering Tomography Laboratory
(ETL), Electronic and Electrical Engineering
Department, University of Bath (UoB). Since
April 2018, he has been with ETL as a Research
Associate for Tomocon, an EU Training Network
Project. His Ph.D. is in ultrasound tomography for
industrial process applications.
Tomasz Rymarczyk (Member, IEEE) is the
Director of the Research and Development Cen-
tre, Netrix S.A., and also the Director of the
Institute of Computer Science and Innovative
Technologies, University of Economics and Inno-
vation, Lublin, Poland. He worked in many
companies and institutes developing innovative
projects and managing teams of employees. His
research interests include application of non-
invasive imaging techniques, electrical tomogra-
phy, ultrasound tomography, radio tomography,
image reconstruction, numerical modeling, image processing and analy-
sis, process tomography, software engineering, knowledge engineering,
artificial intelligence, and computer measurement systems.
Manuchehr Soleimani received the B.Sc.
degree in electrical engineering and the M.Sc.
degree in biomedical 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.
He joined the Department of Electronic and Elec-
trical Engineering, University of Bath, Bath, U.K.,
in 2007, where he was a Research Associate and
became a Lecturer in 2008, a Senior Lecturer in 2013, a Reader in 2015,
and a Full Professor in 2016. He founded the Engineering Tomography
Laboratory (ETL), University of Bath, in 2011, working on various areas
of tomographic imaging, in particular multimodality tomographic imaging.
He has authored or coauthored well over 300 publications in the field.
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ResearchGate has not been able to resolve any citations for this publication.
Full-text available
Crystallisation is a crucial step in many industrial processes. Many sensors are being investigated for monitoring such processes to enhance the efficiency of them. Ultrasound techniques have been used for particle sizing characterization of liquid suspensions, in crystallisation process. An ultrasound tomography system with an array of ultrasound sensors can provide spatial information inside the process when compared to single-measurement systems. In this study, the batch crystallisation experiments have been conducted in a lab-scale reactor in calcium carbonate crystal-lisation. Real-time ultrasound tomographic imaging is done via a contactless ultrasound tomogra-phy sensor array. The effect of the injection rate and the stirring speed was considered as two control parameters in these crystallisation functions. Transmission mode ultrasound tomography comprises 32 piezoelectric transducers with central frequency of 40 kHz has been used. The process-based experimental investigation shows the capability of the proposed ultrasound tomography system for crystallisation process monitoring. Information on process dynamics, as well as process malfunction , can be obtained via the ultrasound tomography system.
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Three-phase material imaging such as oil, gas and water is a critical problem in many processes. Monitoring and separation of each phase before corresponding process can be a key to realise cost efficiency production. In the oil and gas industry such a tool can generate great environmental benefits. In recent years, several multi-modality imaging systems are being adapted for such an application. It is not possible to gain information on three phase flow using a single imaging modality that can be deployed in production field. For a three-phase flow dominated by water phase, this is more challenging. The capability of the majority of current dual-modality systems was only demonstrated under limited flow regime conditions. This paper presents a novel combined imaging system including electrical impedance tomography (EIT), and ultrasound transmission tomography (UTT) for mapping three-phase flow. In water dominate mode, the EIT is able to image the nonconductive phases of oil and gas in a water dominate background phase, but not able to separate oil and gas. The EIT two-phase imaging then complimented with the speed of sound imaging of the UTT, which can separate liquid (oil and water) and gas. A dual modality EIT-UTT system combining a 32-electrode EIT array and a 32-transducer UTT sensor array is developed to demonstrate this novel three-phase material imaging. The concept was demonstrated using simulation study and then shown with experimental lab tests. Measurement principles and method are described, experiment based on several three-phase flow scenarios are established, and the results show successful distinguishably for all three phases.
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This work presents an ultrasound tomography imaging system and method for quantitative mapping of the sound speed in liquid masses. It is highly desirable to be able to inspect vessel fluid mass distribution, notably in the chemical and food industrial operations. Optimization of industrial reactors has been crucial to the improvement of industrial processes. There is a great need to investigate how and if tomographic imaging sensors could aid the automatic control of these process tanks. Single-measurement ultrasound techniques and especially spectrometric methods have been a subject of study of industrial applications. Tomographic systems provide key multi-dimensional and spatial information when compared to the well-established single-channel measurement system. Recently, ultrasound tomography has attracted a great deal of interest in a wide spectrum of industrial applications. The system has been designed as 32 piezoelectric ring-array positioned in a 30 cm tank, with an excitation frequency of 40 kHz. Two-dimensional transmission travel-time tomography was developed to reconstruct the fluid mass distributions. Prior experiments are mainly based on inclusions of a few centimetres and on a liquid solution of different concentrations. They have been conducted to test the spatial and quantitative resolution of the ultrasound imaging device. Analysing the reconstructed images, it is possible to provide accurate spatial resolution with low position errors. The system also demonstrated inclusion movement with a temporal resolution of 4 frames per second (fps) in dynamical imaging sense. Sound velocity quantitative imaging was developed for the investigation of ultrasonic propagation in different liquids. This work, for the first time, shows how quantitative sound velocity imaging using transmission mode time of flight data could be used to characterize liquid density distribution of industrial reactors. The results suggest that ultrasound tomography can be used to quantitatively monitor important process parameters.
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The main goal of the research presented in this paper was to develop a refined machine learning algorithm for industrial tomography applications. The article presents algorithms based on logistic regression in relation to image reconstruction using electrical impedance tomography (EIT) and ultrasound transmission tomography (UST). The test object was a tank filled with water in which reconstructed objects were placed. For both EIT and UST, a novel approach was used in which each pixel of the output image was reconstructed by a separately trained prediction system. Therefore, it was necessary to use many predictive systems whose number corresponds to the number of pixels of the output image. Thanks to this approach the under-completed problem was changed to an over-completed one. To reduce the number of predictors in logistic regression by removing irrelevant and mutually correlated entries, the elastic net method was used. The developed algorithm that reconstructs images pixel-by-pixel is insensitive to the shape, number and position of the reconstructed objects. In order to assess the quality of mappings obtained thanks to the new algorithm, appropriate metrics were used: compatibility ratio (CR) and relative error (RE). The obtained results enabled the assessment of the usefulness of logistic regression in the reconstruction of EIT and UST images.
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Tomographic imaging based on acoustic wave time-of-flight (TOF) measurement is considered to be a promising technique for monitoring temperature fields due to it being non-invasive, relatively low cost, having a high temporal resolution and being easy to use. Accurate estimation of the TOF is key in improving the quality of the reconstructed images. In this paper, an improved TOF estimation method based on the Akaike Information Criterion (AIC) is developed. Two improvements are studied in comparison to conventional weighted AIC TOF estimation methods against cross-talk interference and sound reflections: an adaptive window is applied for accurate AIC TOF estimation; a phase correction method is used to further improve the temporal resolution and noise robustness of the TOF estimation. The feasibility and effectiveness of the developed methods are validated in two experiments.
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The flow control and optimization system based on industrial tomography is presented in this publication. Multiphase flow measurement technologies are still being built and improved. There is a clear tendency in the industry to implement more optimally related functions with an emphasis on active inspection and monitoring. Control methods include issues related to the processing of data obtained from various sensors located in nodes. Monitoring takes place within the scope of acquired and processed data and parameter automation. The main purpose of this work is to design a system for data acquisition and analysis by image reconstruction for various tomographic methods (resistive, capacitive, ultrasonic). The practical application of ultrasonic flow measurement to study gas emissions in the heat and power station chimney is presented
Industrial Process Tomography (IPT) possesses unique advantages in biphasic medium measurement and has received broad attention in the past decades. Aiming at the widely existed low contrast biphasic medium, this paper proposed a nonlinear Ultrasonic Transmissive Tomography (UTT) approach using continuous-wave excitation. Considering the refraction effect at the biphasic interface, the reconstruction method with nonlinear forward problem and the prototype-based resolution enhancement algorithm is proposed with higher accuracy, resolution and speed. The UTT system is improved with a high-voltage excitation module and fan-beam transducer array to evaluate the proposed method, where the performance is qualitatively and quantitatively compared with the state-of-art reconstruction algorithms and measurement techniques from different perspectives. The results show that the reconstruction performance is significantly improved where the size, shape and position of the dispersed medium can be accurately discriminated. Accordingly, the ultrasonic tomography with continuous-wave excitation is proved to be feasible and efficient in the visualized measurement of low contrast biphasic medium.
Monitoring multiphase flow process and measuring its parameters have been a research topic that received broad attentions for the past decades. Ultrasonic process tomography (UPT) obtains the distribution of the two-phase flow based on ultrasound propagation in different fluids, thus is valuable to the industrial monitoring and measurement. UPT can non-intrusively explore transient hydrodynamics of the multiphase flow, but th reconstruction quality of single modality is always dependent on phase distribution. In this paper, a dual-mode UPT that fuses the attenuation and time-of-flight (TOF) of ultrasound is presented. To implement this scheme, a digital dual-mode UPT system that works under both the transmission-mode and reflection-mode is designed. A 16-channel ultrasound data acquisition system is proposed, which is flexibly programmable and reconfigurable through an FPGA. The system includes a series of functional modules, and is based on the compact peripheral component interconnect (CPCI) bus for real-time data transmission in industrial standard. Static experiments show that the system can distinguish the interface of the different inclusions and preferably reconstruct the position and size of the inclusions through fusing the transmission and reflection reconstruction, the average Relative Error and Correlation Coefficient of the reconstructed images are 0.617 and 0.626 respectively, which show preferable and stable distinguishability of different inclusions.
Time-of-flight measurement is a critical step to perform ultrasonic non-destructive testing of standing trees, with direct influence on the precision of defect detection. Aiming to increase the accuracy on the estimation, the characteristics of the ultrasonic measurement chain should be adapted to the constraints of wood testing in living condition. This study focused on the excitation signal parameters, such as shape, temporal duration, and frequency response, and then the selection of a suitable time-of-flight determination technique. A standing plane tree was tested, placing ultrasonic receivers at four different positions, with five different excitation signals and three time-of-flight detection methods. The proposed ultrasonic chain of measurement resulted in high signal-to-noise ratios in received signals for all configurations. A time-frequency analysis was used to determine the power distribution in the frequency domain, showing that only chirp signal could concentrate the power around the resonant frequency of the sensor. Threshold and Akaike information criterion method performed similar for impulsive signals with decreasing uncertainty as sensor position approached to the radial direction. Those two methods failed to accurate determine time-of-flight for Gaussian pulse and chirp signals. Cross-correlation was only suitable for the chirp signal, presenting the lower uncertainty values among all configurations.
A transmission and reflection coupled ultrasonic process tomography has been developed, which is characterized by a proposed dual-mode (DM) reconstruction algorithm, as well as an adaptive search approach to determine an optimal image threshold during the image binarization. In respect of hardware, to improve the accuracy of time-of-flight (TOF) and extend the lowest detection limit of particle size, a cylindrical miniaturized transducer using polyvinylidene fluoride (PVDF) films is designed. Besides, the development of range-gating technique for the identification of transmission and reflection waves in scanning is discussed. A particle system with four iron particles is then investigated numerically and experimentally to evaluate these proposed methods. The sound pressure distribution in imaging area is predicted numerically, followed by the analysis of the relationship between the emitting surface width of transducer and particle size. After the processing of experimental data for effective waveform extraction and fusion, the comparison between reconstructed results from transmission-mode (TM), reflection-mode (RM), and dual-mode reconstructions is carried out and the latter manifests obvious improvements from the blurring reduction to the enhancement of particle boundary.