Fruit quality control by surface analysis using a bio-inspired soft tactile sensor

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Fruit quality control by surface analysis
using a bio-inspired soft tactile sensor
Pedro Ribeiro1,2,4, Susana Cardoso1,2, Alexandre Bernardino3and Lorenzo Jamone4
Abstract— The growing consumer demand for large volumes
of high quality fruit has generated an increasing need for auto-
mated fruit quality control during production. Optical methods
have been proved successful in a few cases, but with limitations
related to the variability of fruit colors and lighting conditions
during tests. Tactile sensing provides a valuable alternative,
although it comes with the need of a physical interaction that
could damage the fruit. To overcome these limitations, we
propose the usage of a recently developed soft tactile sensor for
non-invasive fruit quality control. The ability of the sensor to
detect very small forces and to finely analyze surfaces allows the
collection of relevant information about the fruit by performing
a very delicate physical interaction, that does not cause any
damage. We report experiments in which such information is
used to determine whether apples and strawberries are ripe
or senescent. We test different configurations of the sensor and
different classification algorithms, achieving very good accuracy
for both apples (96%) and strawberries (83%).
I. INTRODUCTION
Fruit and vegetable consumption has steadily increased
during the last two decades, having more than doubled since
1990 [1]. The larger production volumes required, together
with a rising consumer demand for value and quality [2],
have generated the need for a higher number of automated
facilities [3]. In this context, the implementation of novel
sensors and signal processing techniques to monitor food
quality during the whole processing pipeline have gained
traction recently [4].
Automatic fruit quality control is usually realized using
either optical or tactile sensors. Optical technologies are
the most developed and commonly used, as they are both
non-invasive and easy to implement (often requiring only
a camera). In what concerns the classification of fruits in
regards to quality, various techniques have been presented
in the past, reporting classification accuracy better than 90%
for various parameters of interest in fruits and vegetables
[5]. Although some industrial devices have been developed
and are currently commercialized [6], automatic fruit control
has not yet met widespread acceptance, as wide variability
of defect types and fruit skin colour, in addition to changing
lighting conditions, pose classification reliability issues [7].
In an effort to overcome the difficulties of optical de-
tection, or to complement the optical detection information,
tactile testing may provide useful data regarding the quality
1INESC - Microsystems and Nanotechnologies, Lisbon, Portugal
2Department of Physics, Instituto Superior Tecnico, University of Lisbon,
Portugal
3Institute for Systems and Robotics, Lisbon, Portugal
4ARQ, School of Electronic Engineering and Computer Science, Queen
Mary University of London, London, United Kingdom
Geomagic
Touch
Arduino
MRK1000
Fruit under
test
To PC
Vice
c)
a) b)
Cilium
PCB
c)
Apple
18 mm
14 mm
1 cm
1 cm
Fig. 1. a) Full experimental setup.b) Detail of the data acquisition PCB with
mounted cilia. c) Single cilia scanning an apple surface. The red rectangle
indicates where the data acquisition PCB is located.
of the fruit, especially in what concerns its internal condition.
Two types of tactile measurements can be performed on
fruits: palpation (determining the stiffness of the fruit) and
textural analysis (determining the fruit surface topography).
The palpation technique has been the first developed and
standardized type of tactile measurement, with the invention
of the Magness-Taylor probe (a destructive measurement
instrument) [8] and has since been used as the standardized
method of measuring fruit quality through stiffness [9]. Non-
destructive stiffness measurement devices and techniques
have been developed in recent years, by lowering testing
forces [10] and compacting testing devices [11]. In both these
works a correlation between stiffness and quality is reported,
but no attempt at quality classification is made. These types
of sensors have also been integrated in robotic platforms,
having reached a classification accuracy in distinguishing
between ripe and green mangoes of 88% [12].
Although the surface characteristics of a fruit are gen-
erally accepted as a sensory factor in the perception of
fruit quality, the quantification and analysis of this type
of characteristics is still greatly underdeveloped [13]. The
oldest reported tactile device used to measure this quantity
on food products employed a tribometer to measure the
coefficient of drag between the device and the surface of the
food, thus providing an indirect measurement of the surface
roughness [14]. The correlation between the age of peaches
and their surface roughness, directly measured using atomic
force microscopy, was reported in the same year [15]. Later,
the usage of a tactile sensor to classify various fruit species
given their textural characteristics was reported, achieving a

Fig. 2. a) Cilia sensor, with a 3x3 cilia matrix configuration. Inset:
Schematic side view of the cilia sensor, with the magnetic field emitted
by the cilia ( ~
H). b) Microphotograph of the sensor die. The white arrows
indicate the sensitive direction of each sensor region. Regions of the same
colour have the same sensitive direction. The dashed circles show the cilia
position on top of the sensor.
94% accuracy [16].
In this paper we demonstrate the use of a recently devel-
oped tactile sensor [17] for a fruit quality control task (Fig.
1). The sensor is inspired on the ciliary structure often found
in living organisms: this structure consists of an elongated
hair-like element known as cilium that is attached and
protrudes out of a dendrite at its root, and is commonly found
in insects and mammals allowing them to sense smalls forces
and fluid flows [18]. Because of its geometry, our tactile
sensor excels at measuring tangential forces and textures, and
therefore it is a very good candidate for any application that
can benefit from textural and surface topography information
[17]. Moreover, because of the small size and extreme
softness of the cilia, our sensor can detect very small forces,
and therefore the exploration of the surface of the fruits
can be done in a completely non-invasive way, i.e. without
bringing any damage to the fruits. Therefore, the proposed
method overcomes the limitations of optical systems (e.g.
variability of fruit skin colour and effect of variable lighting
conditions) without the need for an invasive exploration that
could damage the fruit. Furthermore, due to its softness, this
device is able to extract the fruit fine textural and hardness
parameters simultaneously. The proposed detection method
uses features extracted from the surface topography of a fruit
and it applies machine learning techniques to classify fruits
into ripe or senescent.
II. SENSOR DESCRIPTION
To measure the surface topography of the fruit, a bio-
inspired cilia sensing element was used [19], and is shown in
Fig. 2a). An array of magnetized elastic hairs is placed on top
of a magnetic sensor. When these hairs bend, the magnetic
signal over the sensor changes, and a monotonic relation
between the cilia angle and the device signal is observed.
A. Magnetic cilia
The cilia in the sensor are composed of a mixture of 35%
(in mass) polydimethylsiloxane (PDMS)1with 65% NdFeB
1PDMS was prepared from Sylgard 184 at a mass proportion of 15 parts
of elastomer to 1 part of curing agent
particles with an average diameter of 5 µm. The composite
was shaped using a laser cut Poly(methylmethacrylate) mold
(PMMA), into which the magnetic elastic composite was
poured and left to cure for 90 minutes in an oven set at 70◦
C. After curing, to maximize the magnetic signal emitted by
the composite, the moulded composite was further heated
up to 100◦C for 1 hour and 30 minutes under a magnetic
field 1 T in the cilia axial direction. Finally, the composite
(which is now moulded in cilia shape) is removed from
mold and is then bonded to the magnetic sensor using a
oxygen plasma bonding process. The produced cilia present
a Young’s modulus of approximately 1 MPa [20], resulting
in an applied pressure of 3.5 kPa, much lower than cutting
stresses for apples, which range from 200 kPa to 1 MPa [21].
B. Magnetic sensor
The underlying magnetic sensor (microfabricated at
INESC-MN), is a 2D magnetic sensor based on the tun-
neling magnetoresistance (TMR) effect. A stack of metal-
lic layers (with the structure, from top to bottom: [Ta
5/Ru 15]x3/Ni80Fe20 4/Al2O31.4/(Co80 Fe20)90B10 3/Ru
0.6/Ni80Fe20 3/Mn75 Ir25 18/Ru 5/Ta 5, thicknesses in nm)
was deposited and patterned into 640 sensing elements of
2x20 µm2area connected in series within a 3x3 mm2die
(Fig. 2b).
To provide added robustness and easier signal conditioning
[22] [23], the sensor was designed using a Wheatstone
bridge architecture [24], which allows the measurements to
be taken as a voltage differential centered around 0 V (in
the ideal case) by combining TMR sensitive elements with
anti-parallel sensitivities.
C. Electronic interface
An analog front-end was designed with the capability
of eliminating the offset of the sensor and amplifying the
corrected signal with a gain of up to 128 (V/V). This signal
is then converted to a digital word by a 24-bit precision ADC
unit at a 1 kSPS sampling rate, and the digital information
is then transmitted to an Arduino MKR1000 through an
I2C connection (and then relayed by the Arduino to the
computer).
III. FRUIT QUALITY MEASUREMENT AND
CL ASS IFICATION
A. Setup
The number and geometry of the cilia placed on top of the
sensor can be reconfigured, as different cilia geometries and
configurations may perform better on specific types of fruits.
Arrays of multiple cilia were found to present better detec-
tivity when resolving unpatterned textured surfaces (since
a larger number of cilia correspond to a higher magnetic
material content and thus a stronger magnetic field), while
single cilia devices can better resolve patterned features on a
textured surface (due to a lower contact area with the sample)
[19]. The following cilia configurations were tested:
•Configuration A: Single cilia with 400 µm diameter
and 3 mm height.

Sensor
Cilium
1
23
Scanned zone
4
Fruit under test
Sensor Sensor Sensor
Fig. 3. Scanning sequence of the sensor. This sequence is repeated 10
times for each zone.
•Configuration B: Nine cilia in a 3x3 array over the
sensor, each with 360 µm diameter and 1.6 mm height.
•Configuration C: Nine cilia in a 3x3 array over the
sensor, each with 400 µm diameter and 3 mm height.
The sensing device is attached to a Geomagic Touch desktop
haptic feedback interface, used as a desktop robotic arm in
this work. Data acquisition and robot control was performed
using a custom C# GUI based on the OpenHaptics libraries,
running on a Windows 10 operating system.
B. Data acquisition and measurement procedure
The surface characteristics of a fruit are measured by
scanning the sensor at a constant speed over its surface.
However, as the sensor is facing the fruit under study upside
down (as shown in Fig. 1c), care has to be taken when
controlling the robotic arm, in order to avoid crushing the
cilia against the sensor, which would produce an inaccurate
surface topography measurement. The following measure-
ment procedure was implemented (illustrated in Fig. 3):
1) Cilia is lowered against the surface of the fruit. When
the derivative of the signal achieves a pre-determined
threshold (meaning the cilia is bending upon contact
with an obstacle), the arm stops its lowering move-
ment.
2) The arm makes a fast short movement in one direction
to tilt the cilia to a known direction (only to set the
cilia tilting direction, but not its tilting angle).
3) The arm moves at a set speed of 1 mm/s, for a set
distance (1 cm both types of fruit). The sensor signal
and the arm position is recorded for the duration of
this movement.
4) When the distance has been covered, the arm returns
to its initial position and repeats the sequence from the
beginning, for an arbitrary number of scans.
The robotic arm is controlled in open-loop for the whole
duration of the measurement, expect for step 1, where sensor
data is used to detect when the cilia is touching the fruit
surface.
Five adjustment scans (for which the data is not recorded)
were done to ensure the cilia were in contact with the fruit
for the whole scan duration, followed by 10 measurement
scans over the same zone of the fruit.
Strawberries (Sabrina variety) and Apples (Braeburn va-
riety) are among the most produced fruits in the United
Fig. 4. Tested fruit pieces. a) Braeburn apples. b) Sabrina strawberries.
Kingdom [25] and were chosen to be tested (Fig. 4). For each
type, a set of 12 ripe and 12 senescent fruits (performing a
total of 24 fruits) were tested, with the scanning sequence
being performed over two different sections of the same fruit
(randomly chosen over the fruit equator). To ensure the fruit
does not move during testing, a vice was used to gently
clamp the piece of fruit (1a). Senescence in strawberries was
achieved by natural processes, by keeping them for one week
since the day of purchase at room temperature. As for apples,
senescence was triggered by cold, placing fresh apples (at the
day of purchase) in a freezer at -18◦C for 24 hours, followed
by a 24 hour thawing period at room temperature [26].
C. Features
As time passes, fruit starts becoming softer and more
textured, as cells breakdown [27] and water is lost through
evaporation [28].
For each scan of the analyzed fruit, a raw signal as shown
in Fig. 5 is obtained, from which three features can be
extracted:
•Smoothness (S): A moving average filter with a 1000
point moving window was applied to signal, and its
derivative was then computed. The standard deviation of
this derivative was taken as an estimation of smoothness
(Fig. 5b).
•Stiffness (E): The average of the first 100 points of
the measured signal were used as a metric of the fruit
stiffness (Fig. 5a).
•Texture (R): A equiripple finite impulse response (FIR)
high-pass filter with a cut-off frequency of 120 Hz was
applied to the signal, with the standard deviation of the
filtered signal being taken as a metric of the fruit texture

a)
b) c)
Stiffness
(Average of first
100 points)
Waviness profile (W) Roughness profile (U)
Raw signal
Derivative of low pass filtered voltage (nV s )
Senescent apple
Ripe apple
Fig. 5. Measured signal for an apple scan and derived values. a) Raw signal
of the scan for a ripe and a senescent apple. b) Waviness profile, computed
by low pass filtering and deriving the raw signal, used to determine the
smoothness metric (inset). c) Roughness profile, computed by high pass
filtering the raw signal, used to determine the texture metric (inset).
(Fig. 5c).
D. Classification algorithm
As the goal of this work is to classify fruit quality, and
each fruit surface is scanned multiple times, a classifier
capable of returning its decision margin of confidence is of
interest, as it can be later plugged into a Bayesian update
algorithm to achieve more accurate classification results. A
data-driven approach was chosen, as the fruit surface analysis
correlation with quality is scarce in literature, and such an
approach allows for the usage of the optimal thresholds for
determining quality using the aforementioned parameters.
Each classifier was trained independently for each type of
fruit2. For each type of fruit, two supervised classification
algorithms were tested:
1) Gaussian Naive Bayes classifier: It was assumed that
the measurements could be described by a trivariate Gaussian
distribution,
P(Si, Ei, Ri|Fk)∼N(Si, Ei, Ri|µk,Σk),(1)
where µkis the mean vector and Σkis the covariance matrix
for the observations made of a certain type of fruit Fk, where
kis the class of the fruit (ripe or senescent).
2I.e., the classifier trained for classifying the quality of apples was not
used to classify strawberries and vice-versa
Therefore, as each passage of the sensor is made on the
fruit, a new set of Si,Ei,Rifeatures is obtained, and can be
used to determine the probabilty of a fruit being of a certain
class. As each passage is made on a fruit and a new set of
metrics is obtained, the probability can be updated using
P(Fk|Si, Ei, Ri) = P(Fk)
n
Y
i
P(Si, Ei, Ri|Fk)
P(Si, Ei, Ri)(2)
and a decision is made based on which class of fruit presents
the highest probability.
2) Random forest classifier: The random forest classifier
uses an ensemble of classification trees trained with the
given data and expected responses for each data point. Each
tree computes a prediction given a data point, and the
class chosen by the greatest number of trees becomes the
predicted class by the forest. Furthermore, the number of
trees providing each verdict is known with the probability
that the forest verdict is true being estimated by
P(Fk|Si, Ei, Ri) = Tk
TT
,(3)
where Tkis the number of trees in the forest supporting that
a fruit belongs to a class kand TTis the total number of
trees. Given this probability, the joint probability of all the
measurements belonging to a certain fruit kare then given
by
P(Fk) =
n
Y
i
P(Fk|Si, Ei, Ri)(4)
and the classification can be done by choosing the class
presenting the highest probability. In this work, a Matlab
R2018a implementation of this algorithm (TreeBagger class)
was employed. A Forest of 100 trees was trained.
IV. RES U LTS
All fruits were measured with the three different sensor
configurations and classified with the methods presented in
the previous section. Verification of the prediction was made
using a leave-one-out cross-validation for each fruit. One
of the two left out scans (chosen at random) was used
for validation. This process was repeated for each of the
fruits in the dataset. Outliers (usually caused by loss or poor
contact between the cilia and the fruit during measurement)
were removed by fitting all the measured data to a trivariate
Gaussian distribution (using the 3 computed features) and
eliminating all points that lied beyond a 95% interval of
confidence (with one distribuion fitted for each type and
quality of fruit).
The methods were compared in what concerns effective-
ness in classifying ripe and senescent fruits, and a study of
the number of passages required to maximize the classifica-
tion accuracy was also made.
A. Algorithm setup and performance assessment
Each testing set contains 10 scans (taking approximately
10 seconds per scan, for a total of 1 minute and 40 seconds
of scan time per fruit) relative to the same zone of the

TABLE I
CLASSIFICATION PERFORMANCE USING THE THREE EXTRACTED FEATURES
Method Fruit Configuration A sensor Configuration B sensor Configuration C sensor
TP TN Accuracy TP TN Accuracy TP TN Accuracy
Gaussian
Naive Bayes
Braeburn apple 11/12 12/12 0.96 10/12 11/12 0.88 9/12 8/12 0.71
Sabrina strawberry 7/12 10/12 0.71 10/12 7/12 0.71 10/12 10/12 0.83
Random Forest Braeburn apple 10/12 12/12 0.92 10/12 11/12 0.88 9/12 11/12 0.83
Sabrina strawberry 8/12 11/12 0.79 10/12 10/12 0.83 10/12 10/12 0.83
Fig. 6. Number of misclassified fruits for the three used sensor configurations as a function of the number of sensor scans over the fruit surface.
fruit, and all fruits were manually classified and labelled
regarding their ripeness or senescence before starting the
experiment. An equiprobability prior (50% probability for
a ripe or senescent fruits being detected) was used for the
Bayesian update. A fruit classified as ripe or senescent is
considered a positive or negative occurrence respectively,
and the classifier performance was rated in terms of its true
positive and negative rates.
B. Classification performance
The classification performance was assessed in terms of
the classification accuracy, which is presented alongside the
true positive (TP) and true negative (TN) classifications
in table I. The random forest algorithm was observed to
have equivalent or marginally better performance than the
Gaussian Naive Bayes algorithm.
The best overall performance was obtained for the apple
tested using the sensor with configuration A cilia, with both
algorithms providing accuracies above 90% (96% for the
Gaussian Naive Bayes and 92% for the Random Forest algo-
rithm). This is in contrast with the strawberry classification
performance for this configuration, with an accuracy below
80%.
On the other hand, configuration B and C sensors per-
formed better than configuration A in the classification for
both employed algorithms, with a maximum accuracy of 83%
being obtained when the random forest algorithm was used
to classify strawberries with configuration B and C sensor
data.
C. Bayesian update performance
The evolution of the classification error rate with the
number of performed scans on the fruit was computed and
is presented in figure 6.
For the most accurate classification cases (apples measured
with configuration A cilia and strawberries measured with
configuration C cilia), the number of misclassified fruits
tends monotonically to lower values with an increasing
number of scans when using the Random Forest algorithm. It
is interesting to note that the progression of the error with the
number of scans tends to oscillate instead of lowering mono-
tonically when using the Naive Bayes algorithm, despite
being of equivalent performance to the random forest in some
cases (particularly for apples measured with configuration
B sensor and strawberries measured with configuration C
sensor), even when the end result of the classification is the
same. This is indicative that the Random Forest algorithm
should require less scans to achieve the best possible classi-
fication accuracy than the Naive Bayes algorithm.
The best performing combination (apples measured with
configuration A sensor using Gaussian Naive Bayes algo-
rithm) reached the minimum error in 7 scans, while the best
performing Random Forest combination (apples measured
with configuration A sensor) reached its minimum error in 3
scans. Thus, the number of required scans in a final device
should be much lower than the 10 performed in our test,
given that the right combination of cilia configuration is used
for each fruit.

TABLE II
ACC UR ACY V S NU MB ER O F FE ATU RE S US ED F OR C LA SS IFI CATI O N WI TH
GAUS SI AN NA IV E BAYES ALGORITHM
Sensor Fruit 1 feature
(E)
2 features
(E+R)
3 features
(S+E+R)
AApple 0.83 0.92 0.96
Strawberry 0.63 0.79 0.71
BApple 0.71 0.88 0.88
Strawberry 0.67 0.67 0.71
CApple 0.58 0.71 0.71
Strawberry 0.63 0.83 0.83
D. Parameter influence on performance
The influence of the number of features used to train the
classification algorithms on their performance was studied.
The performance was evaluated using the data from the 10
measurements, with the same leave-one-out cross-validation
method as described in subsection IV-A.
The accuracies obtained for the various sets of features is
presented in tables II and III for the Gaussian Naive Bayes
and Random Forest classification algorithms respectively.
The stiffness parameter is used for the single parameter per-
formance and the stiffness and texture parameter combination
for the double parameter performance, as these provided the
best classification performance in their respective categories.
For both algorithms, an improvement in classification
performance is observed when two features are used in
combination instead of a single parameter. However, when
using the 3 features in combination, the performance im-
provement is either non-existent or marginal when compared
with classification using two features. It is worth noticing that
in some cases there is a loss in performance when using the
3 features.
V. DISCUSSION
The main defining difference between these configurations
is the number of cilia on top of the sensor, with configuration
A using a single cilia while B and C use a square matrix of 9
cilia. This is directly correlated with the area of contact of the
sensor with the fruit under test and has a direct impact on the
spatial resolution of the device, with devices using a lower
number of cilia having been reported to have higher spatial
resolution at the cost of providing a lower signal amplitude
[19].
We hypothesize that this result comes from the difference
between the surfaces of apples (which are smooth) and
strawberries (which have bumps due to the seeds being
present on the surface). When using a sensor with higher
spatial resolution (as is the case with configuration A), any
bumps on top of the surface under test will be accounted
by the classification algorithm. While this is beneficial for
a smooth fruit that starts acquiring bumps as it gets older,
this is not the case fruits that are naturally bumpy. By using
a higher contact surface, the result of the measurement will
be averaged over the whole contact area, limiting the effect
of existing bumps.
Therefore, the usage of a single cilia sensor should be
used if the fruit is smooth, as it is capable of transducing
TABLE III
ACC UR ACY V S NU MB ER O F FE ATU RE S US ED F OR C LA SS IFI CATI O N WI TH
RANDOM FOREST ALGORITHM
Sensor Fruit 1 feature
(E)
2 features
(E+R)
3 features
(S+E+R)
AApple 0.79 0.96 0.92
Strawberry 0.63 0.79 0.79
BApple 0.75 0.88 0.88
Strawberry 0.79 0.88 0.88
CApple 0.71 0.83 0.83
Strawberry 0.63 0.83 0.83
the greatest amount of information possible about the fruit
under test leading to the best possible performance. However,
should the fruit have naturally occurring surface features,
the usage of a cilia matrix is preferable even if at the cost
of some performance, as the larger contact area will create
an averaging effect of the surface texture, and with naturally
occurring features averaged out there is no risk of these being
learned by the classification algorithm.
It is also interesting to note that, in general, true negative
detection is more accurate than true positive detection in this
study, which could be advantageous in an industrial setting,
as the lower chance of a senescent fruit being misclassified
as ripe would maximize value to the final costumer, while
misclassified ripe fruits could be provided to a human
operator for a more accurate quality assessment.
VI. CONCLUSION AND FUTURE WORK
This paper reports on the performance of a cilia tactile
sensor in the quality control of apples and strawberries. Three
sensors with different cilia configurations were used to test
the fruits.
In general, across all the combinations of sensor/fruit
tested, the random forest algorithm performed better that
the Gaussian Naive Bayes, while reaching the maximum
performance by requiring less fruit scans. Note that more
sophisticated algorithms might lead to even better results:
however, the goal of this work was not to compare algo-
rithms, but to show that, regardless the specific algorithm,
good results could be achieved by the sensor on this task,
mainly because of the ability of the sensor to collect relevant
data. Overall, assuming all three parameters are used in
the classification algorithms, the best performing sensor
for apple classification was configuration A device (96%
accuracy), while for strawberries it was the configuration
B device (83% accuracy). This is indicative that these
type of sensors (configuration A) are better at classifying
smooth surfaces; on the contrary, when classifying fruits with
naturally occurring bumps on the surface (e.g. strawberries),
it is preferable to use a sensor with a larger area of contact
(configuration B), although with lower spatial resolution.
It was observed that the usage of more than one pa-
rameter brings a significant improvement in classification
performance, but the usage of three parameters provides
the best classification performance, despite being a marginal
improvement over the 2 parameter case.

For future work, the magnetic sensor under the cilia
will be improved to provide a 2D response, which would
allow the computation of the cilia angle over the sensor,
providing additional information on the fruit characteristics.
Furthermore, given the high classification performance ob-
tained, classification into more classes than binary will be
tested, which could provide interesting information on how
to maximize the value of a whole batch, e.g. a top-tier fruit
would be sold fresh, but a low-tier (but not rotten) fruit could
be processed into another food product.
ACK NO WL EDG EME NTS
We thank FabLab Lisboa for providing access
and assistance with the laser cutting equipment.
P. Ribeiro acknowledges FCT for his PhD grant
SFRH/BD/130384/2017. S. Cardoso acknowledges FCT
for grants NORTE-01-0145-FEDER-22090, MAGLINE-
LISBOA-01-0247-FEDER-17865 and MagScopy4IHC-
LISBOA-01-0145-FEDER-031200. A. Bernardino
acknowledges FCT project UID/EEA/50009/2019
and European Commission project ORIENT
(ERC/2016/693400). This work was partially supported by
the EPSRC UK (with projects MAN3, EP/S00453X/1, and
NCNR, EP/R02572X/1).
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