<s>
Electrical	B-Algorithm
capacitance	I-Algorithm
volume	I-Algorithm
tomography	I-Algorithm
(	O
ECVT	O
)	O
is	O
a	O
non-invasive	O
3D	B-Algorithm
imaging	I-Algorithm
technology	O
originally	O
developed	O
in	O
UK	O
and	O
Poland	O
and	O
applied	O
primarily	O
to	O
multiphase	O
flows	O
.	O
</s>
<s>
Fan	O
inspired	O
by	O
the	O
early	O
publications	O
of	O
the	O
UK	O
and	O
Polish	O
teams	O
an	O
extension	O
of	O
the	O
conventional	O
electrical	O
capacitance	O
tomography	B-Algorithm
(	O
ECT	O
)	O
.	O
</s>
<s>
Measured	O
capacitance	O
between	O
plate	O
combinations	O
is	O
used	O
to	O
reconstruct	O
2D	O
images	O
(	O
tomograms	B-Algorithm
)	O
of	O
material	O
distribution	O
.	O
</s>
<s>
The	O
sensitivity	O
matrix	O
of	O
an	O
ECVT	O
sensor	O
is	O
more	O
ill-conditioned	O
and	O
the	O
overall	O
reconstruction	O
problem	O
is	O
more	O
ill-posed	B-Algorithm
compared	O
to	O
ECT	O
.	O
</s>
<s>
The	O
ECVT	O
approach	O
to	O
sensor	O
design	O
allows	O
direct	O
3D	B-Algorithm
imaging	I-Algorithm
of	O
the	O
outrounded	O
geometry	O
.	O
</s>
<s>
Electrical	B-Algorithm
Capacitance	I-Algorithm
Volume	I-Algorithm
Tomography	I-Algorithm
was	O
first	O
introduced	O
by	O
W	O
.	O
Warsito	O
and	O
L.-S	O
.	O
</s>
<s>
Fan	O
in	O
a	O
presentation	O
at	O
the	O
3rd	O
World	O
Congress	O
in	O
Process	O
Tomography	B-Algorithm
in	O
Banff	O
Canada	O
in	O
2003	O
.	O
</s>
<s>
Fan	O
with	O
the	O
emphasis	O
on	O
volume	O
to	O
distinguish	O
the	O
technology	O
from	O
earlier	O
and	O
ongoing	O
development	O
of	O
a	O
form	O
called	O
3D-ECT	O
where	O
2D	O
tomograms	B-Algorithm
are	O
stacked	O
on	O
top	O
of	O
each	O
other	O
to	O
create	O
a	O
pseudo	O
3D	O
image	O
.	O
</s>
<s>
This	O
traditional	O
3D-ECT	O
approach	O
limited	O
the	O
use	O
of	O
3D	B-Algorithm
imaging	I-Algorithm
as	O
the	O
significant	O
length	O
of	O
ECT	O
electrodes	O
introduced	O
a	O
major	O
penalty	O
on	O
axial	O
resolution	O
of	O
such	O
3D	O
images	O
.	O
</s>
<s>
ECVT	O
provides	O
direct	O
3D	B-Algorithm
imaging	I-Algorithm
by	O
exploiting	O
the	O
X	O
,	O
Y	O
,	O
and	O
Z	O
components	O
of	O
the	O
electric	O
field	O
,	O
which	O
are	O
a	O
function	O
of	O
sensor	O
design	O
.	O
</s>
<s>
Assuming	O
a	O
static	O
or	O
quasi-static	O
regime	O
and	O
the	O
presence	O
of	O
a	O
lossless	B-Algorithm
dielectric	O
medium	O
,	O
such	O
as	O
a	O
perfect	O
insulator	O
,	O
in	O
the	O
region	O
between	O
the	O
plates	O
,	O
the	O
field	O
obeys	O
the	O
following	O
equation	O
:	O
</s>
<s>
In	O
a	O
homogeneous	B-General_Concept
medium	O
with	O
uniform	O
,	O
this	O
equation	O
reduces	O
to	O
the	O
Laplace	O
equation	O
.	O
</s>
<s>
In	O
a	O
lossy	B-Algorithm
medium	O
with	O
finite	O
conductivity	O
,	O
such	O
as	O
water	O
,	O
the	O
field	O
obeys	O
the	O
generalized	O
Ampere	O
equation	O
,	O
</s>
<s>
By	O
taking	O
divergence	B-Application
of	O
this	O
equation	O
and	O
using	O
the	O
fact	O
that	O
,	O
it	O
follows	O
:	O
</s>
<s>
Soft-field	O
tomography	B-Algorithm
refers	O
to	O
a	O
set	O
of	O
imaging	O
modalities	O
such	O
as	O
electrical	O
capacitance	O
tomography	B-Algorithm
(	O
ECT	O
)	O
,	O
electrical	O
impedance	O
tomography	B-Algorithm
(	O
EIT	O
)	O
,	O
electrical	O
resistivity	O
tomography	B-Algorithm
(	O
ERT	O
)	O
,	O
etc.	O
,	O
wherein	O
electric	O
(	O
or	O
magnetic	O
)	O
field	O
lines	O
undergo	O
changes	O
in	O
the	O
presence	O
of	O
a	O
perturbation	O
in	O
the	O
medium	O
.	O
</s>
<s>
This	O
is	O
in	O
contrast	O
to	O
hard-field	O
tomography	B-Algorithm
,	O
such	O
as	O
X-ray	O
CT	O
,	O
where	O
the	O
electric	O
field	O
lines	O
do	O
not	O
change	O
in	O
the	O
presence	O
of	O
a	O
test	O
subject	O
.	O
</s>
<s>
A	O
fundamental	O
characteristic	O
of	O
soft-field	O
tomography	B-Algorithm
is	O
its	O
ill-posedness	B-Algorithm
.	O
</s>
<s>
This	O
contributes	O
for	O
making	O
the	O
reconstruction	O
more	O
challenging	O
to	O
achieve	O
good	O
spatial	O
resolution	O
in	O
soft-field	O
tomography	B-Algorithm
as	O
compared	O
to	O
hard-field	O
tomography	B-Algorithm
.	O
</s>
<s>
A	O
number	O
of	O
techniques	O
,	O
such	O
Tikhonov	O
regularization	O
,	O
can	O
be	O
used	O
to	O
alleviate	O
the	O
ill-posed	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
Prior	O
to	O
the	O
actual	O
measurements	O
,	O
a	O
calibration	B-General_Concept
and	O
normalization	O
procedure	O
is	O
necessary	O
to	O
cancel	O
out	O
the	O
effects	O
of	O
stray	O
capacitance	O
and	O
any	O
insulating	O
wall	O
between	O
the	O
electrodes	O
and	O
the	O
region	O
of	O
interest	O
to	O
be	O
imaged	O
.	O
</s>
<s>
After	O
calibration	B-General_Concept
and	O
normalization	O
,	O
the	O
measurements	O
can	O
be	O
divided	O
into	O
a	O
sequence	O
of	O
acquisitions	O
where	O
two	O
separate	O
electrodes	O
are	O
involved	O
:	O
one	O
electrode	O
(	O
TX	O
)	O
is	O
excited	O
with	O
AC	O
voltage	O
source	O
in	O
the	O
quasi-electrostatic	O
regime	O
,	O
typically	O
below	O
10MHz	O
,	O
while	O
a	O
second	O
electrode	O
(	O
RX	O
)	O
is	O
placed	O
at	O
the	O
ground	O
potential	O
used	O
for	O
measuring	O
the	O
resultant	O
current	O
.	O
</s>
<s>
Increasing	O
the	O
electrode	O
size	O
,	O
on	O
the	O
other	O
hand	O
,	O
does	O
not	O
result	O
in	O
non-uniform	O
charge	O
distribution	O
over	O
the	O
plates	O
,	O
which	O
may	O
exacerbate	O
the	O
ill-posedness	B-Algorithm
of	O
the	O
problem	O
.	O
</s>
<s>
The	O
volume	O
tomography	B-Algorithm
with	O
ECVT	O
is	O
not	O
obtained	O
from	O
merging	O
of	O
2D	O
scans	O
but	O
rather	O
from	O
3D	O
discretized	O
voxels	O
sensitivities	O
.	O
</s>
<s>
Displacement-Current	O
Phase	O
Tomography	B-Algorithm
is	O
an	O
imaging	O
modality	O
that	O
relies	O
on	O
the	O
same	O
hardware	O
as	O
ECVT	O
.	O
</s>
<s>
This	O
can	O
be	O
done	O
by	O
(	O
a	O
)	O
adaptive	O
acquisitions	O
with	O
synthetic	O
electrodes	O
,	O
(	O
b	O
)	O
spatio-temporal	O
sampling	O
using	O
additional	O
measurements	O
obtained	O
when	O
objects	O
are	O
in	O
different	O
positions	O
inside	O
the	O
sensor	O
,	O
(	O
c	O
)	O
multi-frequency	O
operation	O
to	O
exploit	O
permittivity	O
variations	O
with	O
frequency	O
due	O
to	O
the	O
MWS	O
effect	O
,	O
and	O
(	O
d	O
)	O
combining	O
ECT/ECVT	O
with	O
other	O
sensing	O
modalities	O
,	O
either	O
based	O
on	O
the	O
same	O
hardware	O
(	O
such	O
as	O
DCPT	O
)	O
or	O
on	O
additional	O
hardware	O
(	O
such	O
as	O
microwave	O
tomography	B-Algorithm
)	O
.	O
</s>
