sensors
Article
Hyperspectral Imaging Tera Hertz System for Soil
Analysis: Initial Results
Volker Dworak 1,*, Benjamin Mahns 1, Jörn Selbeck 1, Robin Gebbers 1and
Cornelia Weltzien 1,2
1Department Engineering for Crop Production, Leibniz-Institute for Agricultural Engineering and
2Faculty V of Mechanical Engineering and Transport Systems, Chair of Agromechatronics,
Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
*Correspondence: [email protected]; Tel.: +49-331-5699-420; Fax: +49-331-5699-849
Received: 7 August 2020; Accepted: 30 September 2020; Published: 3 October 2020
Abstract:
Analyzing soils using conventional methods is often time consuming and costly due to
their complexity. These methods require soil sampling (e.g., by augering), pretreatment of samples
(e.g., sieving, extraction), and wet chemical analysis in the laboratory. Researchers are seeking
alternative sensor-based methods that can provide immediate results with little or no excavation and
pretreatment of samples. Currently, visible and infrared spectroscopy, electrical resistivity, gamma ray
spectroscopy, and X-ray spectroscopy have been investigated extensively for their potential utility in
soil sensing. Little research has been conducted on the application of THz (Tera Hertz) spectroscopy
in soil science. The Tera Hertz band covers the frequency range between 100 GHz and 10 THz of
the electromagnetic spectrum. One important feature of THz radiation is its correspondence with
the particle size of the fine fraction of soil minerals (clay <2
µ
m to sand <2 mm). The particle size
distribution is a fundamental soil property that governs soil water and nutrient content, among other
characteristics. The interaction of THz radiation with soil particles creates detectable Mie scattering,
which is the elastic scattering of electromagnetic waves by particles whose diameter corresponds
approximately to the wavelength of the radiation. However, single-spot Mie scattering spectra are
difficult to analyze and the understanding of interaction between THz radiation and soil material
requires basic research. To improve the interpretation of THz spectra, a hyperspectral imaging
system was developed. The addition of the spatial dimension to THz spectra helps to detect relevant
features. Additionally, multiple samples can be scanned in parallel and measured under identical
conditions, and the high number of data points within an image can improve the statistical accuracy.
Technical details of the newly designed hyperspectral imaging THz system working from 250 to
370 GHz are provided. Results from measurements of different soil samples and buried objects
in soil demonstrated its performance. The system achieved an optical resolution of about 2 mm.
The sensitivity of signal damping to the changes in particle size of 100
µ
m is about 10 dB. Therefore,
particle size variations in the
µ
m range should be detectable. In conclusion, automated hyperspectral
imaging reduced experimental effort and time consumption, and provided reliable results because
of the measurement of hundreds of sample positions in one run. At this stage, the proposed setup
cannot replace the current standard laboratory methods, but the present study represents the initial
step to develop a new automated method for soil analysis and imaging.
Keywords: hyperspectral imaging; Mie scattering; soil imaging; soil sensing
Sensors 2020,20, 5660; doi:10.3390/s20195660 www.mdpi.com/journal/sensors
Sensors 2020,20, 5660 2 of 22
1. Introduction
Soil is a fundamental resource in the earth’s ecosystems and for human life. The understanding
of the soil’s status and function is highly relevant because soils contribute to the recycling, filtering,
transformation, and buffering of substances, in addition to the production of food, forage, and biogenic
raw materials. In particular, for sustainable agriculture soils must be analyzed regularly to assess
their fertility. However, soil analysis with conventional sampling and laboratory-based methods
is expensive and time consuming. Thus, scientists are searching for new, sensor-based methods
that can analyze soils more efficiently. The development of soil sensors is a challenging task due to
the complexity of the soil and its many interfering parameters. This is also true for proximal soil
sensing [
1
,
2
]. To date, visible and infrared spectroscopy, electrical resistivity, gamma ray spectroscopy,
and X-ray spectroscopy have been investigated extensively [
2
]. One versatile candidate sensor for
performing nondestructive soil measurements is Tera Hertz (THz) spectroscopy, which covers the
electromagnetic frequency range between 100 GHz and 10 THz [
3
]. An important feature of THz
radiation is its correspondence with the particle size of the fine fraction of soil minerals (clay <2
µ
m
to sand <2 mm). The particle size distribution is a fundamental soil property which governs soil
water and nutrient content, among other characteristics. Another important feature of THz radiation
is its ability to penetrate materials. Furthermore, it is nondestructive and not hazardous. However,
little research has been conducted on the application of THz spectroscopy in soil science. Moreover,
the development of THz systems is ongoing. Some non-continuous wave systems are used and
the applications are in their infancy [
4
,
5
]. Even fewer studies have been performed on continuous
wave (CW) THz systems [
6
] and hyperspectral imaging [
7
] in soil samples. The first results using
THz radiation for soil analysis in the range of 258–375 GHz demonstrated a specific interaction with
soil particles [
8
]. In this frequency band, the particle size in the range of a millimeter causes Mie
scattering [
9
–
11
]. Mie scattering, named after the physicist Gustav Mie, is the elastic scattering of
electromagnetic waves by particles whose diameter corresponds approximately to the wavelength
of the radiation. In the case of multiparticle scattering, Mie scattering shows a complex spectral
behavior and varies depending on the local position of the beam. Hyperspectral imaging overcomes
the problem of the local variability within the sample and the problem of the interpretation of a single
measurement because it combines imagery and spectral behavior. Therefore, most hyperspectral
applications and research result from this combination [
12
–
23
]. The human eye can easily interpret the
image and identify different areas, interface regions, and buried objects. Therefore, THz imaging is
used for defect or artifact detection [
24
]. Additionally, critical samples can be simultaneously measured
under identical conditions, with fewer time effects caused by the long measuring time. Conversely,
the time effects can be compared in a simultaneous measurement, and exchanges between different
samples can be analyzed. The measurement of multiple data points helps to overcome individual
effects, and common areas can be interpreted statistically. In this way, new images can be created.
A disadvantage of this imaging method is the additional complexity of the focus plane. Sharp results
can be produced only for features in the focus plane. The high Mie scattering of sand particles prevents
beam formation in the material, and a focus plane does not exist under such conditions. This makes
generating imagery of soil samples difficult. In order to develop a THz measurement system for a
challenging task such as soil characterization, an experimental setup must be developed that allows
differentiating and isolating the many different influencing parameters, and at the same time enables an
imaging approach by precise localization of each measurement reading within the sample’s dimension.
Such an experimental setup will enable basic research on the potential of soil sample characterization
through hyperspectral analysis of THz radiation transmission/reflection patterns. This paper describes
the development of a THz hyperspectral imaging experimental system for soil sample characterization.
With this setup, the authors note the advantages of this method for testing complex samples such as
soil samples. This paper discusses the following research questions:
•Can the effect of scattering on image quality be demonstrated by hyperspectral imaging?
Sensors 2020,20, 5660 3 of 22
•Can the imaging localize artifacts or measurement errors?
•How can the imaging identify homogenous sample regions for statistical comparisons?
2. Materials and Methods
Hyperspectral imaging of difficult samples with terahertz radiation is a complex task because of
the influence of many physical parameters. It starts with the complicated behavior of the Rayleigh
and Mie scattering of thousands of particles. In previous studies, the CELES software [
25
] enabled
the simulation of such complex Mie scattering arrangements and can be used to visualize the results.
However, the simulation is not a part of the current work; rather, the measurement possibilities of the
presented setup will be demonstrated. The experimental setup described consists of the soil samples
and holders, the THz spectrometer, the sample positioning system, the operating software, and the
data analysis.
Additionally, natural soil is a complex sample material and soil functionality depends on multiple
parameters, including particle size distribution, mineral content, carbon content or organic matter,
water, biology, and physical and chemical properties. Therefore, all first measurements were made on
simplified soil samples to reduce the number of parameters. The results in this article focus on the
imaging possibility of hyperspectral THz measurement.
2.1. Soil Samples and Holders
The measurement is influenced by the sample holder, the preparation of the sample, the filling
of the sample holder, and the compaction (process) in the sample holder. Even the measurement of
the empty sample holder is not adequate for calibration because of the different interface situation
at the sample holder walls. The best filling substance for calibration is oil [
26
], but this discussion is
not part of this work. The sample holders demonstrated may not be the best solution but rather are
a good practical approach. All samples in this study were placed in sample holders made of HDPE
(high density polyethylene) with a wall thickness of 2 mm. The holders were parallel, box-shaped,
or wedge-shaped. The wedge-shaped sample holder enables simultaneous measurements of different
thickness. The sample thickness was addressed accordingly. In some cases, the sample holder was
separated into domains with different samples (Figures 1–4) to demonstrate the resulting contrast in
the corresponding image. Figure 1shows a box-shaped sample holder with a 10 mm sample thickness.
The box was divided with a 2 mm thick piece of paper and filled with quartz particles in different
size fractions.
Sensors 2019, 19, x FOR PEER REVIEW 3 of 23
2. Materials and Methods
Hyperspectral imaging of difficult samples with terahertz radiation is a complex task because of
the influence of many physical parameters. It starts with the complicated behavior of the Rayleigh
and Mie scattering of thousands of particles. In previous studies, the CELES software [25] enabled
the simulation of such complex Mie scattering arrangements and can be used to visualize the results.
However, the simulation is not a part of the current work; rather, the measurement possibilities of
the presented setup will be demonstrated. The experimental setup described consists of the soil
samples and holders, the THz spectrometer, the sample positioning system, the operating software,
and the data analysis.
Additionally, natural soil is a complex sample material and soil functionality depends on
multiple parameters, including particle size distribution, mineral content, carbon content or organic
matter, water, biology, and physical and chemical properties. Therefore, all first measurements were
made on simplified soil samples to reduce the number of parameters. The results in this article focus
on the imaging possibility of hyperspectral THz measurement.
2.1. Soil Samples and Holders
The measurement is influenced by the sample holder, the preparation of the sample, the filling
of the sample holder, and the compaction (process) in the sample holder. Even the measurement of
the empty sample holder is not adequate for calibration because of the different interface situation at
the sample holder walls. The best filling substance for calibration is oil [26], but this discussion is not
part of this work. The sample holders demonstrated may not be the best solution but rather are a
good practical approach. All samples in this study were placed in sample holders made of HDPE (high
density polyethylene) with a wall thickness of 2 mm. The holders were parallel, box-shaped, or wedge-
shaped. The wedge-shaped sample holder enables simultaneous measurements of different thickness.
The sample thickness was addressed accordingly. In some cases, the sample holder was separated into
domains with different samples (Figures 1–4) to demonstrate the resulting contrast in the
corresponding image. Figure 1 shows a box-shaped sample holder with a 10 mm sample thickness. The
box was divided with a 2 mm thick piece of paper and filled with quartz particles in different size
fractions.
Figure 1. HDPE (high density polyethylene) sample holder for 10 mm sample thickness. A two
millimeter thick piece of paper separates the holder in the middle. The left chamber is filled with the
63–100 µm quartz fraction, and the right chamber is filled with 400–500 µm quartz particles.
The free configuration of the scan positions helps to reduce measurement times. For a sample
preparation as shown in Figure 1, only the interface regions are sampled with smaller step widths for
higher resolution. Areas in a homogenous sample region can be represented with a few measurements
and can be scanned with a larger step width.
Figure 1.
HDPE (high density polyethylene) sample holder for 10 mm sample thickness.
A two millimeter thick piece of paper separates the holder in the middle. The left chamber is filled with
the 63–100 µm quartz fraction, and the right chamber is filled with 400–500 µm quartz particles.
Sensors 2020,20, 5660 4 of 22
The free configuration of the scan positions helps to reduce measurement times. For a sample
preparation as shown in Figure 1, only the interface regions are sampled with smaller step widths for
higher resolution. Areas in a homogenous sample region can be represented with a few measurements
and can be scanned with a larger step width.
Sensors 2019, 19, x FOR PEER REVIEW 4 of 23
Additionally, the dependency of the sample thickness can be analyzed simultaneously if a wedge-
shaped sample holder is used (Figure 2). The sample holder was filled with quartz sand of three
different particle sizes. The overlay in Figure 2 with the blue lines indicates the boundary between the
three samples. These sample holders have a length-to-thickness ratio of 5:1. The smallest sample holder
started at zero thickness, the middle sample holder started at 5 mm, and the largest sample holder
started at 10 mm.
Figure 2. Wedge-shaped sample holder filled with three different soil samples. The blue horizontal
lines show the lines between the samples. Samples are quartz sand with different particle sizes. At
the bottom is the 100–200 µm fraction, in the middle is the 400–500 µm fraction, and on top is the 500–
600 µm fraction. The red rectangle shows the measurement area for this example.
Additionally, the sample holder can be filled with different materials, as shown in Figures 3 and
4. Therefore, identical measurement conditions are established, and quantitative differentiation is
enabled. For samples that change over time, the fastest scan line across the different materials is selected
to minimize the time difference. Every scan pattern for the image can be implemented by the user (see
Section 2.4).
Figure 3. HDPE sample holder for 10 mm sample thickness filled with four different soil samples. The
topsoil is pure Luvos
®
Healing Earth. The next sample is Luvos with 20% sulfur added. The third
Luvos
S
P2O5
K2CO3
Figure 2.
Wedge-shaped sample holder filled with three different soil samples. The blue horizontal
lines show the lines between the samples. Samples are quartz sand with different particle sizes. At the
bottom is the 100–200
µ
m fraction, in the middle is the 400–500
µ
m fraction, and on top is the 500–600
µ
m
fraction. The red rectangle shows the measurement area for this example.
Sensors 2019, 19, x FOR PEER REVIEW 4 of 23
Additionally, the dependency of the sample thickness can be analyzed simultaneously if a wedge-
shaped sample holder is used (Figure 2). The sample holder was filled with quartz sand of three
different particle sizes. The overlay in Figure 2 with the blue lines indicates the boundary between the
three samples. These sample holders have a length-to-thickness ratio of 5:1. The smallest sample holder
started at zero thickness, the middle sample holder started at 5 mm, and the largest sample holder
started at 10 mm.
Figure 2. Wedge-shaped sample holder filled with three different soil samples. The blue horizontal
lines show the lines between the samples. Samples are quartz sand with different particle sizes. At
the bottom is the 100–200 µm fraction, in the middle is the 400–500 µm fraction, and on top is the 500–
600 µm fraction. The red rectangle shows the measurement area for this example.
Additionally, the sample holder can be filled with different materials, as shown in Figures 3 and
4. Therefore, identical measurement conditions are established, and quantitative differentiation is
enabled. For samples that change over time, the fastest scan line across the different materials is selected
to minimize the time difference. Every scan pattern for the image can be implemented by the user (see
Section 2.4).
Figure 3. HDPE sample holder for 10 mm sample thickness filled with four different soil samples. The
topsoil is pure Luvos
®
Healing Earth. The next sample is Luvos with 20% sulfur added. The third
Luvos
S
P2O5
K2CO3
Figure 3.
HDPE sample holder for 10 mm sample thickness filled with four different soil samples.
The topsoil is pure Luvos
®
Healing Earth. The next sample is Luvos with 20% sulfur added. The third
sample is Luvos with 20% P
2
O
5
, and the bottom sample is Luvos with 20% K
2
CO
3
. All layers are
separated with 50 µm thick aluminum foil.
Additionally, the dependency of the sample thickness can be analyzed simultaneously if a
wedge-shaped sample holder is used (Figure 2). The sample holder was filled with quartz sand of three
different particle sizes. The overlay in Figure 2with the blue lines indicates the boundary between
Sensors 2020,20, 5660 5 of 22
the three samples. These sample holders have a length-to-thickness ratio of 5:1. The smallest sample
holder started at zero thickness, the middle sample holder started at 5 mm, and the largest sample
holder started at 10 mm.
Sensors 2019, 19, x FOR PEER REVIEW 5 of 23
sample is Luvos with 20% P2O5, and the bottom sample is Luvos with 20% K2CO3. All layers are
separated with 50 µm thick aluminum foil.
Luvos
®
Healing Earth is a commercial product (Heilerde-Gesellschaft Luvos Just GmbH & Co. KG,
Otto-Hahn-Strasse 23, 61,381 Friedrichsdorf, Germany) available in most drugstores. A 100 g quantity
of Luvos was prepared twice in four different mixtures containing K
2
CO
3
, P
2
O
5
, S, and MgCO
3
. The
LUVOS healing clay with precisely weighed additives was homogenized with a MUK mixer from
Fluxana (FLUXANA GmbH & Co. KG, Borschelstr. 3, 47,551 Bedburg-Hau, Germany) for 10 min at
3000 rpm in a mixing cup. Figure 3 shows the maximum concentration of 20% of each additive to
generate a contrast in the THz image.
Figure 4. HDPE sample holder for 10 mm sample thickness with three different soil samples. The
samples are natural soil samples from the Potsdam region and have different compositions.
Figure 4 shows the rectangle sample holder filled with three sieved natural soil samples. All
aggregates were broken by hand pestling. The color of the soil sample indicates the amount of organic
content. Table 1 shows the associated results.
Table 1. Analysis of the air-dried soil samples. The difference to 100% is the remainder, which is so-
called “mineral ashes”.
Sample name DM105 OM C N S
% % % % %
T1 99.97 0.238 0.010 0.001 0.006
T2 99.75 1.554 0.451 0.017 0.030
T3 93.50 30.50 15.50 0.142 3.61
DM 105 is the dry matter of the sample after oven-drying for 24 h at 105 °C; OM is the amount of organic
matter; C, N, and S are the concentrations of carbon, nitrogen, and sulfur, respectively.
Buried objects are often used to demonstrate the penetration capability of THz radiation.
Organic material such as carrot pieces (Figure 5), for example, in silt or clay, is detectable, but
detection is not possible in sand because of the strong Mie scattering. With hyperspectral imaging,
all images at the different frequencies can be averaged, and the mean damping can be estimated.
Additionally, the focus is adjusted to the middle position of the sample holder and thereby to the
surface of the carrot. Therefore, the interface region between the carrot and the scattering sand is
T1
T2
T3
Figure 4.
HDPE sample holder for 10 mm sample thickness with three different soil samples.
The samples are natural soil samples from the Potsdam region and have different compositions.
Additionally, the sample holder can be filled with different materials, as shown in Figures 3
and 4. Therefore, identical measurement conditions are established, and quantitative differentiation
is enabled. For samples that change over time, the fastest scan line across the different materials is
selected to minimize the time difference. Every scan pattern for the image can be implemented by the
user (see Section 2.4).
Luvos
®
Healing Earth is a commercial product (Heilerde-Gesellschaft Luvos Just GmbH & Co.
KG, Otto-Hahn-Strasse 23, 61,381 Friedrichsdorf, Germany) available in most drugstores. A 100 g
quantity of Luvos was prepared twice in four different mixtures containing K
2
CO
3
, P
2
O
5
, S, and MgCO
3
.
The LUVOS healing clay with precisely weighed additives was homogenized with a MUK mixer from
Fluxana (FLUXANA GmbH & Co. KG, Borschelstr. 3, 47,551 Bedburg-Hau, Germany) for 10 min at
3000 rpm in a mixing cup. Figure 3shows the maximum concentration of 20% of each additive to
generate a contrast in the THz image.
Figure 4shows the rectangle sample holder filled with three sieved natural soil samples.
All aggregates were broken by hand pestling. The color of the soil sample indicates the amount of
organic content. Table 1shows the associated results.
Table 1.
Analysis of the air-dried soil samples. The difference to 100% is the remainder, which is
so-called “mineral ashes”.
Sample Name DM105 OM C N S
% % % % %
T1 99.97 0.238 0.010 0.001 0.006
T2 99.75 1.554 0.451 0.017 0.030
T3 93.50 30.50 15.50 0.142 3.61
DM 105 is the dry matter of the sample after oven-drying for 24 h at 105
◦
C; OM is the amount of organic matter;
C, N, and S are the concentrations of carbon, nitrogen, and sulfur, respectively.
Sensors 2020,20, 5660 6 of 22
Buried objects are often used to demonstrate the penetration capability of THz radiation.
Organic material such as carrot pieces (Figure 5), for example, in silt or clay, is detectable, but detection
is not possible in sand because of the strong Mie scattering. With hyperspectral imaging, all images
at the different frequencies can be averaged, and the mean damping can be estimated. Additionally,
the focus is adjusted to the middle position of the sample holder and thereby to the surface of the
carrot. Therefore, the interface region between the carrot and the scattering sand is addressed, but more
scattering will avoid a sharp focus. The interface region tends to result in more scattering if addressed
with a sharp focus.
Sensors 2019, 19, x FOR PEER REVIEW 6 of 23
addressed, but more scattering will avoid a sharp focus. The interface region tends to result in more
scattering if addressed with a sharp focus.
(a)
(b)
Figure 5. Cut carrot pieces for demonstration: (a) carrot pieces forming the letters “ATII”; (b) a carrot
piece in the shape of the letter “A”.
The carrot samples in Figure 5 were placed in the sample holder, and the sample was filled with
quartz material in different particle fractions. The next example in Figure 6 shows a setup with metal
pieces buried in the 10 mm sample holder. The imaging is demonstrated in this paper, but the
complicated task of detecting conducting materials and their surface waves is not described in detail.
Figure 6. Additional filling of the sample holder in Figure 1. Three steel tubes were fixed with tape
and buried in quartz sand. The left side was filled with the 0.063–0.1 mm fraction, and the right side
was filled with the 0.4–0.5 mm fraction. The divider is 2 mm thick paper.
2.2. THz Spectrometer
The THz spectrometer in Figure 7 is the same as that described by Dworak et al. [8], and the full
electronic setup is described in detail. The system has an emitter and a receiver, and sweeps from 258
to 375 GHz. The applied distance between each spectral measurement point is adjustable, and the
practical range is from 0.3 to 0.01 GHz. The system consists of two backward wave oscillator tubes,
which generate the main RF power. The frequencies are up converted with a frequency doubler and
tripler. The receiver side follows the frequency sweep of the emitter side with an offset of 300.5 MHz.
Figure 5.
Cut carrot pieces for demonstration: (
a
) carrot pieces forming the letters “ATII”; (
b
) a carrot
piece in the shape of the letter “A”.
The carrot samples in Figure 5were placed in the sample holder, and the sample was filled
with quartz material in different particle fractions. The next example in Figure 6shows a setup with
metal pieces buried in the 10 mm sample holder. The imaging is demonstrated in this paper, but the
complicated task of detecting conducting materials and their surface waves is not described in detail.
Sensors 2019, 19, x FOR PEER REVIEW 6 of 23
addressed, but more scattering will avoid a sharp focus. The interface region tends to result in more
scattering if addressed with a sharp focus.
(a)
(b)
Figure 5. Cut carrot pieces for demonstration: (a) carrot pieces forming the letters “ATII”; (b) a carrot
piece in the shape of the letter “A”.
The carrot samples in Figure 5 were placed in the sample holder, and the sample was filled with
quartz material in different particle fractions. The next example in Figure 6 shows a setup with metal
pieces buried in the 10 mm sample holder. The imaging is demonstrated in this paper, but the
complicated task of detecting conducting materials and their surface waves is not described in detail.
Figure 6. Additional filling of the sample holder in Figure 1. Three steel tubes were fixed with tape
and buried in quartz sand. The left side was filled with the 0.063–0.1 mm fraction, and the right side
was filled with the 0.4–0.5 mm fraction. The divider is 2 mm thick paper.
2.2. THz Spectrometer
The THz spectrometer in Figure 7 is the same as that described by Dworak et al. [8], and the full
electronic setup is described in detail. The system has an emitter and a receiver, and sweeps from 258
to 375 GHz. The applied distance between each spectral measurement point is adjustable, and the
practical range is from 0.3 to 0.01 GHz. The system consists of two backward wave oscillator tubes,
which generate the main RF power. The frequencies are up converted with a frequency doubler and
tripler. The receiver side follows the frequency sweep of the emitter side with an offset of 300.5 MHz.
Figure 6.
Additional filling of the sample holder in Figure 1. Three steel tubes were fixed with tape and
buried in quartz sand. The left side was filled with the 0.063–0.1 mm fraction, and the right side was
filled with the 0.4–0.5 mm fraction. The divider is 2 mm thick paper.
Sensors 2020,20, 5660 7 of 22
2.2. THz Spectrometer
The THz spectrometer in Figure 7is the same as that described by Dworak et al. [
8
], and the
full electronic setup is described in detail. The system has an emitter and a receiver, and sweeps
from 258 to 375 GHz. The applied distance between each spectral measurement point is adjustable,
and the practical range is from 0.3 to 0.01 GHz. The system consists of two backward wave oscillator
tubes, which generate the main RF power. The frequencies are up converted with a frequency doubler
and tripler. The receiver side follows the frequency sweep of the emitter side with an offset of
300.5 MHz. Both signals are multiplied in a second harmonic mixer and down converted to 905 MHz.
An additional down conversion results in a 1.5 MHz measurement signal. The consequent AC
measurement establishes a 1/f noise free sample signal and the high dynamic range of the system.
The dynamic range of the system is about 100 dB.
Sensors 2019, 19, x FOR PEER REVIEW 7 of 23
Both signals are multiplied in a second harmonic mixer and down converted to 905 MHz. An
additional down conversion results in a 1.5 MHz measurement signal. The consequent AC
measurement establishes a 1/f noise free sample signal and the high dynamic range of the system.
The dynamic range of the system is about 100 dB.
Figure 7. THz spectrometer setup on an optical damping table. TX is the transmitter setup, and RX is
the receiver setup.
The spectrometer includes an optical system that focuses on the image plane and collects the
THz radiation. The TPX lenses are from TYDEX® (Kavalergardskaya str. 16, 191,015 St. Petersburg,
Russia).
2.3. Sample Positioning
The sample positioning setup in Figure 8 is custom made and consists of four motorized axes. The
axes can move ±8 cm in the XYZ directions, and the rotation axis can move ±360° in the Z direction. The
minimal step width in micro step mode 32 is 0.4 nm, and the minimal step width allowed by the self-
developed control software is 10 µm. The minimal rotational step width in micro step mode 32 is
0.005625°. Each axis motor has its own microcontroller, which are connected to a master controller. The
master is connected to a PC. The PC runs the self-developed operating software, sends the position
commands to the master, and waits for the “done” response.
TX
RX
Sample
holder
Figure 7.
THz spectrometer setup on an optical damping table. TX is the transmitter setup, and RX is
the receiver setup.
The spectrometer includes an optical system that focuses on the image plane and collects the THz
radiation. The TPX lenses are from TYDEX
®
(Kavalergardskaya str. 16, 191,015 St. Petersburg, Russia).
2.3. Sample Positioning
The sample positioning setup in Figure 8is custom made and consists of four motorized axes.
The axes can move
±
8 cm in the XYZ directions, and the rotation axis can move
±
360
◦
in the Z direction.
The minimal step width in micro step mode 32 is 0.4 nm, and the minimal step width allowed by the
self-developed control software is 10
µ
m. The minimal rotational step width in micro step mode 32 is
0.005625
◦
. Each axis motor has its own microcontroller, which are connected to a master controller.
The master is connected to a PC. The PC runs the self-developed operating software, sends the position
commands to the master, and waits for the “done” response.
Sensors 2020,20, 5660 8 of 22
Sensors 2019, 19, x FOR PEER REVIEW 8 of 23
Figure 8. Image of the hardware setup. The optical setup of the THz beam is on the left side. The
positioning table is in the center.
2.4. Operating Software
The operating software consists of two parts. The first part is the THz scanner control software
from ELVA-1, St. Petersburg, Russia. The second part is the self-developed user GUI (Figure 9) that
combines the scanner software with the positioning control. The user can navigate to a dedicated
measuring position or can load an Excel spreadsheet with a list of positions. The software will move
the sample to the positions in the order of the list and perform the preset number of measurements
at each position. The list of positions is externally set and loaded through the software; in this way,
any scan pattern can be generated.
X
Y
Z
Figure 8.
Image of the hardware setup. The optical setup of the THz beam is on the left side.
The positioning table is in the center.
2.4. Operating Software
The operating software consists of two parts. The first part is the THz scanner control software
from ELVA-1, St. Petersburg, Russia. The second part is the self-developed user GUI (Figure 9) that
combines the scanner software with the positioning control. The user can navigate to a dedicated
measuring position or can load an Excel spreadsheet with a list of positions. The software will move
the sample to the positions in the order of the list and perform the preset number of measurements
at each position. The list of positions is externally set and loaded through the software; in this way,
any scan pattern can be generated.
Sensors 2020,20, 5660 9 of 22
Sensors 2019, 19, x FOR PEER REVIEW 9 of 23
Figure 9. Control software for the motorized sample positioning table. Measurement points are
established by an external table. The software automatically starts with the selected number of
spectral scans at each local measurement point.
2.5. Data Analysis
The third part of the software is a self-developed MATLAB
®
GUI for visualizing the spectral
cube and performing the data analysis. The image in Figure 10 displays the amplitude of a selected
frequency. Clicking on an image pixel with the mouse opens the spectral plot at this measurement
point. Additional data analyses, such as the mean values, dynamic factors, and spike counts, can be
displayed. The MATLAB environment allows the possibility of implementing any conceivable
analysis.
Figure 9.
Control software for the motorized sample positioning table. Measurement points are
established by an external table. The software automatically starts with the selected number of spectral
scans at each local measurement point.
2.5. Data Analysis
The third part of the software is a self-developed MATLAB
®
GUI for visualizing the spectral
cube and performing the data analysis. The image in Figure 10 displays the amplitude of a selected
frequency. Clicking on an image pixel with the mouse opens the spectral plot at this measurement
point. Additional data analyses, such as the mean values, dynamic factors, and spike counts, can be
displayed. The MATLAB environment allows the possibility of implementing any conceivable analysis.
Sensors 2020,20, 5660 10 of 22
Sensors 2019, 19, x FOR PEER REVIEW 10 of 23
Figure 10. MATLAB GUI for the hyperspectral image display. Example of the control menu, which
can be adapted for adequate evaluation.
The MATLAB GUI in Figure 10 shows 22 rows and 21 columns for this example, but there are
no restrictions in any direction. Additionally, new functionalities can be developed and run by
adding new buttons.
2.6. Dynamic Factor
The MATLAB GUI can perform all kinds of analysis that can be designed in MATLAB. One
example of this capability is the “dynamic factor” (DF). Soil samples with high Mie scattering show
highly dynamic behavior in the spectrum [8]. The “dynamic factor” describes this behavior, where
DF is the dynamic factor, i is the index, and A(fi) is the amplitude of the transmitted signal at the
specific frequency i in the spectrum:
𝐷𝐹 =
∑|
𝐴
(
𝑓
)−
𝐴
(
𝑓
)|
(4)
DF only represents the sum of the difference between neighbors; therefore, it is less sensitive to
the general shape or tendency of the spectrum.
2.7. Spatial Resolution
The optical setup shown in Figures 8 and 9 focuses the beam on the sample layer. The spatial
resolution can be analyzed by moving dedicated samples through the beam. The resulting damping
of the signal amplitude represents the convolution of the beam shape and the sample geometry. The
knowledge of the sample shape enables the deconvolution of the measured signal and the beam
shape can be generated. A common approach is to use a small aperture “pinhole” as the sample.
Measurements with a hole diameter of one millimeter are performed in two planes. The first plane is
the image plane, and the second plane is along the beam axis. To reduce the search and scan time
required to find the pinhole with the beam, the setup was preadjusted with green LED light (Figure
11).
Figure 10.
MATLAB GUI for the hyperspectral image display. Example of the control menu, which can
be adapted for adequate evaluation.
The MATLAB GUI in Figure 10 shows 22 rows and 21 columns for this example, but there are no
restrictions in any direction. Additionally, new functionalities can be developed and run by adding
new buttons.
2.6. Dynamic Factor
The MATLAB GUI can perform all kinds of analysis that can be designed in MATLAB. One example
of this capability is the “dynamic factor” (DF). Soil samples with high Mie scattering show highly
dynamic behavior in the spectrum [
8
]. The “dynamic factor” describes this behavior, where DF is
the dynamic factor, i is the index, and A(f
i
) is the amplitude of the transmitted signal at the specific
frequency i in the spectrum:
DF =1
iEndFreq −iStartFreq XiStartFreq
iStartFreq+1
A(fi)−A(fi−1)
(1)
DF only represents the sum of the difference between neighbors; therefore, it is less sensitive to
the general shape or tendency of the spectrum.
2.7. Spatial Resolution
The optical setup shown in Figures 8and 9focuses the beam on the sample layer. The spatial
resolution can be analyzed by moving dedicated samples through the beam. The resulting damping
of the signal amplitude represents the convolution of the beam shape and the sample geometry.
The knowledge of the sample shape enables the deconvolution of the measured signal and the beam
shape can be generated. A common approach is to use a small aperture “pinhole” as the sample.
Measurements with a hole diameter of one millimeter are performed in two planes. The first plane
is the image plane, and the second plane is along the beam axis. To reduce the search and scan time
required to find the pinhole with the beam, the setup was preadjusted with green LED light (Figure 11).
Sensors 2020,20, 5660 11 of 22
Sensors 2019, 19, x FOR PEER REVIEW 11 of 23
(a)
(b)
Figure 11. Green LED light enables axis adjustment: (a) view from the incoming side; (b) view from
the outgoing side with a pinhole sample.
3. Results
The results demonstrate the imaging possibilities of the described setup. The hyperspectral
results always consist of a full spectrum for each image pixel. Therefore, each frequency step has its
own image. Not all images are shown, and just one image of one frequency step is provided. More
often, processed image data such as the mean values or DF are shown.
3.1. Characterization of the Setup
The characterization of the optical performance of the THz setup demonstrates that the behavior
is similar to that in optical systems with visible light but with lower resolution. The in-axis
measurement with the 1 mm aperture (pinhole) in Figure 12a shows the typical waist of a lens-
focused beam. The waist arises due to the imperfections of the source geometry and the imperfections
in the lenses.
(a)
(b)
Figure 12. Measurement of the transmitted signal intensity through a 1 mm pinhole aperture on a dB
scale: (a) Mean intensity along the beam axis. The black line represents the expected focus plane, and
the blue line represents the real focus plane. (b) Mean intensity orthogonal to the beam axis in the
focus plane.
The image of the focus plane in Figure 12b shows the typical Gaussian shape of the intensity.
The pixel size is 1 mm
2
, and the focus is acceptably good, especially with respect to the waveguide
and the horn antenna as the source emitter.
Figure 11.
Green LED light enables axis adjustment: (
a
) view from the incoming side; (
b
) view from
the outgoing side with a pinhole sample.
3. Results
The results demonstrate the imaging possibilities of the described setup. The hyperspectral results
always consist of a full spectrum for each image pixel. Therefore, each frequency step has its own
image. Not all images are shown, and just one image of one frequency step is provided. More often,
processed image data such as the mean values or DF are shown.
3.1. Characterization of the Setup
The characterization of the optical performance of the THz setup demonstrates that the behavior is
similar to that in optical systems with visible light but with lower resolution. The in-axis measurement
with the 1 mm aperture (pinhole) in Figure 12a shows the typical waist of a lens-focused beam.
The waist arises due to the imperfections of the source geometry and the imperfections in the lenses.
Sensors 2019, 19, x FOR PEER REVIEW 11 of 23
(a)
(b)
Figure 11. Green LED light enables axis adjustment: (a) view from the incoming side; (b) view from
the outgoing side with a pinhole sample.
3. Results
The results demonstrate the imaging possibilities of the described setup. The hyperspectral
results always consist of a full spectrum for each image pixel. Therefore, each frequency step has its
own image. Not all images are shown, and just one image of one frequency step is provided. More
often, processed image data such as the mean values or DF are shown.
3.1. Characterization of the Setup
The characterization of the optical performance of the THz setup demonstrates that the behavior
is similar to that in optical systems with visible light but with lower resolution. The in-axis
measurement with the 1 mm aperture (pinhole) in Figure 12a shows the typical waist of a lens-
focused beam. The waist arises due to the imperfections of the source geometry and the imperfections
in the lenses.
(a)
(b)
Figure 12. Measurement of the transmitted signal intensity through a 1 mm pinhole aperture on a dB
scale: (a) Mean intensity along the beam axis. The black line represents the expected focus plane, and
the blue line represents the real focus plane. (b) Mean intensity orthogonal to the beam axis in the
focus plane.
The image of the focus plane in Figure 12b shows the typical Gaussian shape of the intensity.
The pixel size is 1 mm
2
, and the focus is acceptably good, especially with respect to the waveguide
and the horn antenna as the source emitter.
Figure 12.
Measurement of the transmitted signal intensity through a 1 mm pinhole aperture on a
dB scale: (
a
) Mean intensity along the beam axis. The black line represents the expected focus plane,
and the blue line represents the real focus plane. (
b
) Mean intensity orthogonal to the beam axis in the
focus plane.
The image of the focus plane in Figure 12b shows the typical Gaussian shape of the intensity.
The pixel size is 1 mm
2
, and the focus is acceptably good, especially with respect to the waveguide and
the horn antenna as the source emitter.
Sensors 2020,20, 5660 12 of 22
Figure 13 shows the Gaussian profile in one dimension, and subtraction of the aperture diameter
of one millimeter from the FWHM results in a resolution of approximately 9 mm on the dB scale. On the
linear scale, the half-height is
−
55.5 dB, and the resulting resolution is approximately 2 mm. Therefore,
all images are blurred in that range. Considering the setup, this is a good resolution, but it is four times
worse than the theoretical Abbe resolution of 0.5 mm at 1 mm wavelength with maximum aperture
angle. Additionally, all of the following images are displayed on the logarithmic scale to enhance
visibility. Otherwise, the high dynamic range would result in only black and white images. Often,
automatic scaling of the image colors is activated. This must be taken into account when comparing
the colors. If the comparison is important, absolute scaling is applied.
Sensors 2019, 19, x FOR PEER REVIEW 12 of 23
Figure 13 shows the Gaussian profile in one dimension, and subtraction of the aperture diameter
of one millimeter from the FWHM results in a resolution of approximately 9 mm on the dB scale. On
the linear scale, the half-height is −55.5 dB, and the resulting resolution is approximately 2 mm.
Therefore, all images are blurred in that range. Considering the setup, this is a good resolution, but
it is four times worse than the theoretical Abbe resolution of 0.5 mm at 1 mm wavelength with
maximum aperture angle. Additionally, all of the following images are displayed on the logarithmic
scale to enhance visibility. Otherwise, the high dynamic range would result in only black and white
images. Often, automatic scaling of the image colors is activated. This must be taken into account
when comparing the colors. If the comparison is important, absolute scaling is applied.
(a)
(b)
Figure 13. Intensity plot of the central line: (a) the full width at half maximum (FWHM, −67.5 dB) is
10 mm on the dB scale; (b) the FWHM is approximately 3 mm on the linear scale.
3.2. Simultaneous Measurement of Multiple Samples
The simultaneous measurement of multiple samples has several benefits. First, the direct
contrast between the samples in the image gives a good overview of the image and locates the regions
of the different materials in the image. Areas of artifacts can also be identified. Second, changes to the
measurement setup are typically avoided in simultaneous measurement. Even small changes in the
frequency response could induce incorrect results if the spectral differences between somewhat
similar samples were analyzed. In particular, the DF of a low-scattering material is highly affected by
these small changes. Additionally, the scattering of interface regions is higher than that of bulk
material.
The mean (damping) values of the 100–200 µm and 400–500 µm particle size fractions in Figure 14
are −11 and –43 dB, respectively. It is clear that the interface regions vary due to the beam divergence
and the frequency-dependent scattering behavior indicated by the DF. The comparison of the mean
values and the DF indicates that the 400–500 µm fraction shows much higher scattering than the 100–
200 µm fraction. This could be explained by Mie scattering [10].
(a)
(b)
(c)
Figure 14. Images resulting from the setup in Figure 1 are shown. Different step widths between the
measurement pixels were applied. The transmitted signals were recorded: (a) amplitude in dB of the
Figure 13.
Intensity plot of the central line: (
a
) the full width at half maximum (FWHM,
−
67.5 dB) is
10 mm on the dB scale; (b) the FWHM is approximately 3 mm on the linear scale.
3.2. Simultaneous Measurement of Multiple Samples
The simultaneous measurement of multiple samples has several benefits. First, the direct contrast
between the samples in the image gives a good overview of the image and locates the regions of
the different materials in the image. Areas of artifacts can also be identified. Second, changes to the
measurement setup are typically avoided in simultaneous measurement. Even small changes in the
frequency response could induce incorrect results if the spectral differences between somewhat similar
samples were analyzed. In particular, the DF of a low-scattering material is highly affected by these
small changes. Additionally, the scattering of interface regions is higher than that of bulk material.
The mean (damping) values of the 100–200
µ
m and 400–500
µ
m particle size fractions in Figure 14
are
−
11 and –43 dB, respectively. It is clear that the interface regions vary due to the beam divergence
and the frequency-dependent scattering behavior indicated by the DF. The comparison of the mean
values and the DF indicates that the 400–500
µ
m fraction shows much higher scattering than the
100–200 µm fraction. This could be explained by Mie scattering [10].
Mie scattering depends on the frequency and local composition of the particles in the sample.
Figure 15a demonstrates that at a fixed frequency the geometrical position changes the amplitude
depending on the random arrangement of the particles, which is homogeneous in the far field.
The minima and maxima change positions at other frequencies. Hyperspectral imaging helps to explain
this situation. Additionally, the mean value and the DF in Figure 15b,c show the principal differences
among the three particle fractions. Going from low to high particle size, mean damping values around
12, 40, and 50 dB are observed; the DF also increases, with values around 0.7, 1.3, and 1.5. The higher
scattering causes more damping and more dynamic behavior, and even the small difference between
400–500
µ
m and 500–600
µ
m is precisely indicated. Before analyzing the spectral information in depth,
it is important to know the sample position at which the spectrum will be collected.
Sensors 2020,20, 5660 13 of 22
Sensors 2019, 19, x FOR PEER REVIEW 12 of 23
Figure 13 shows the Gaussian profile in one dimension, and subtraction of the aperture diameter
of one millimeter from the FWHM results in a resolution of approximately 9 mm on the dB scale. On
the linear scale, the half-height is −55.5 dB, and the resulting resolution is approximately 2 mm.
Therefore, all images are blurred in that range. Considering the setup, this is a good resolution, but
it is four times worse than the theoretical Abbe resolution of 0.5 mm at 1 mm wavelength with
maximum aperture angle. Additionally, all of the following images are displayed on the logarithmic
scale to enhance visibility. Otherwise, the high dynamic range would result in only black and white
images. Often, automatic scaling of the image colors is activated. This must be taken into account
when comparing the colors. If the comparison is important, absolute scaling is applied.
(a)
(b)
Figure 13. Intensity plot of the central line: (a) the full width at half maximum (FWHM, −67.5 dB) is
10 mm on the dB scale; (b) the FWHM is approximately 3 mm on the linear scale.
3.2. Simultaneous Measurement of Multiple Samples
The simultaneous measurement of multiple samples has several benefits. First, the direct
contrast between the samples in the image gives a good overview of the image and locates the regions
of the different materials in the image. Areas of artifacts can also be identified. Second, changes to the
measurement setup are typically avoided in simultaneous measurement. Even small changes in the
frequency response could induce incorrect results if the spectral differences between somewhat
similar samples were analyzed. In particular, the DF of a low-scattering material is highly affected by
these small changes. Additionally, the scattering of interface regions is higher than that of bulk
material.
The mean (damping) values of the 100–200 µm and 400–500 µm particle size fractions in Figure 14
are −11 and –43 dB, respectively. It is clear that the interface regions vary due to the beam divergence
and the frequency-dependent scattering behavior indicated by the DF. The comparison of the mean
values and the DF indicates that the 400–500 µm fraction shows much higher scattering than the 100–
200 µm fraction. This could be explained by Mie scattering [10].
(a)
(b)
(c)
Figure 14. Images resulting from the setup in Figure 1 are shown. Different step widths between the
measurement pixels were applied. The transmitted signals were recorded: (a) amplitude in dB of the
Figure 14.
Images resulting from the setup in Figure 1are shown. Different step widths between the
measurement pixels were applied. The transmitted signals were recorded: (
a
) amplitude in dB of
the center frequency of 316.5 GHz; (
b
) mean value in dB of the spectral range from 258 to 343 GHz;
(c) dynamic factor (DF) for the same spectral range.
Sensors 2019, 19, x FOR PEER REVIEW 13 of 23
center frequency of 316.5 GHz; (b) mean value in dB of the spectral range from 258 to 343 GHz; (c)
dynamic factor (DF) for the same spectral range.
Mie scattering depends on the frequency and local composition of the particles in the sample.
Figure 15a demonstrates that at a fixed frequency the geometrical position changes the amplitude
depending on the random arrangement of the particles, which is homogeneous in the far field. The
minima and maxima change positions at other frequencies. Hyperspectral imaging helps to explain
this situation. Additionally, the mean value and the DF in Figure 15b,c show the principal differences
among the three particle fractions. Going from low to high particle size, mean damping values
around 12, 40, and 50 dB are observed; the DF also increases, with values around 0.7, 1.3, and 1.5. The
higher scattering causes more damping and more dynamic behavior, and even the small difference
between 400–500 µm and 500–600 µm is precisely indicated. Before analyzing the spectral
information in depth, it is important to know the sample position at which the spectrum will be
collected.
(a)
(b)
(c)
Figure 15. This figure shows the results for the setup in Figure 2. Samples are quartz sand with
different particle sizes. At the bottom is the 100–200 µm fraction, in the middle is the 400–500 µm
fraction, and on top is the 500–600 µm fraction: (a) amplitude in dB of the center frequency of 316.5
GHz; (b) mean value in dB of the spectral range from 258 to 343 GHz; (c) DF for the same spectral
range.
The images in Figure 16 show that some artifacts can exist, and it is important not to use these
areas in the spectral analysis.
Figure 16. This figure shows the results for the setup in Figure 3. The first two samples are Luvos and
Luvos with 20% sulfur added. The third sample is Luvos with 20% P
2
O
5
, and the bottom sample is
Luvos with 20% K
2
CO
3
: (a) amplitude of the center frequency of 316.5 GHz; (b) mean value of the
spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
(a)
(b)
(c)
Figure 15.
This figure shows the results for the setup in Figure 2. Samples are quartz sand with different
particle sizes. At the bottom is the 100–200
µ
m fraction, in the middle is the 400–500
µ
m fraction, and on
top is the 500–600
µ
m fraction: (
a
) amplitude in dB of the center frequency of 316.5 GHz; (
b
) mean
value in dB of the spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
The images in Figure 16 show that some artifacts can exist, and it is important not to use these
areas in the spectral analysis.
Sensors 2019, 19, x FOR PEER REVIEW 13 of 23
center frequency of 316.5 GHz; (b) mean value in dB of the spectral range from 258 to 343 GHz; (c)
dynamic factor (DF) for the same spectral range.
Mie scattering depends on the frequency and local composition of the particles in the sample.
Figure 15a demonstrates that at a fixed frequency the geometrical position changes the amplitude
depending on the random arrangement of the particles, which is homogeneous in the far field. The
minima and maxima change positions at other frequencies. Hyperspectral imaging helps to explain
this situation. Additionally, the mean value and the DF in Figure 15b,c show the principal differences
among the three particle fractions. Going from low to high particle size, mean damping values
around 12, 40, and 50 dB are observed; the DF also increases, with values around 0.7, 1.3, and 1.5. The
higher scattering causes more damping and more dynamic behavior, and even the small difference
between 400–500 µm and 500–600 µm is precisely indicated. Before analyzing the spectral
information in depth, it is important to know the sample position at which the spectrum will be
collected.
(a)
(b)
(c)
Figure 15. This figure shows the results for the setup in Figure 2. Samples are quartz sand with
different particle sizes. At the bottom is the 100–200 µm fraction, in the middle is the 400–500 µm
fraction, and on top is the 500–600 µm fraction: (a) amplitude in dB of the center frequency of 316.5
GHz; (b) mean value in dB of the spectral range from 258 to 343 GHz; (c) DF for the same spectral
range.
The images in Figure 16 show that some artifacts can exist, and it is important not to use these
areas in the spectral analysis.
Figure 16. This figure shows the results for the setup in Figure 3. The first two samples are Luvos and
Luvos with 20% sulfur added. The third sample is Luvos with 20% P
2
O
5
, and the bottom sample is
Luvos with 20% K
2
CO
3
: (a) amplitude of the center frequency of 316.5 GHz; (b) mean value of the
spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
(a)
(b)
(c)
Figure 16.
This figure shows the results for the setup in Figure 3. The first two samples are Luvos and
Luvos with 20% sulfur added. The third sample is Luvos with 20% P
2
O
5
, and the bottom sample is
Luvos with 20% K
2
CO
3
: (
a
) amplitude of the center frequency of 316.5 GHz; (
b
) mean value of the
spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
Sensors 2020,20, 5660 14 of 22
An investigation of this artifact is not part of this work, but appears to be an artifact of preparation.
The high concentration of phosphorus in sample 3 induces a tendency to agglutinate. Therefore,
it could be possible that the higher DF value indicates the shape of an agglomerate. Furthermore,
the interface heights are addressed by the DF. However, it is still precisely indicated in the image,
which demonstrates the advantages of hyperspectral imaging. Additionally, the difference in the
spectral amplitudes in Figure 16 is not analyzed here. To speculate, doping the same matrix with
different chemicals could cause changes in the hygroscopic/hydrophobic behavior of the material;
higher or lower amounts of water could be causing the effect. Figure 17 shows the spectral behavior of
the three doped samples.
Sensors 2019, 19, x FOR PEER REVIEW 14 of 23
An investigation of this artifact is not part of this work, but appears to be an artifact of
preparation. The high concentration of phosphorus in sample 3 induces a tendency to agglutinate.
Therefore, it could be possible that the higher DF value indicates the shape of an agglomerate.
Furthermore, the interface heights are addressed by the DF. However, it is still precisely indicated in
the image, which demonstrates the advantages of hyperspectral imaging. Additionally, the difference
in the spectral amplitudes in Figure 16 is not analyzed here. To speculate, doping the same matrix
with different chemicals could cause changes in the hygroscopic/hydrophobic behavior of the
material; higher or lower amounts of water could be causing the effect. Figure 17 shows the spectral
behavior of the three doped samples.
Figure 17. Spectral plot of the Luvos sample with three different dopings. Each spectrum represents
one pixel from the respective doped LUVOS fraction.
The sulfur and the potassium samples (yellow and red lines) are offset by approximately 7 dB,
which could have been induced by their different water levels. The phosphorus sample (blue line)
shows nonlinear behavior, and the highest damping occurs in the range between 343 and 347 GHz.
This cannot be explained only by the presence of more water and must be analyzed in future studies.
Nevertheless, hyperspectral imaging enables the detection of complex behaviors.
The three different soil samples in Figure 18 show different damping and scattering patterns,
and their typical spectral responses are displayed in Figure 19. The scattering amplitudes vary by the
local position, and the interface region cannot be precisely localized by the DF.
Figure 18. This figure shows the results for the setup in Figure 4. Samples are natural soils: (a)
amplitude in dB of the center frequency of 316.5 GHz; (b) mean value in dB of the spectral range from
258 to 343 GHz; (c) DF for the same spectral range.
260 270 280 290 300 310 320 330 340 350 360
Frequency in GHz
-80
-60
-40
-20
0
Transmission in dBc
LUVOS and 20 Percent P2O5
LUVOS and 20 Percent K2CO3
LUVOS and 20 Percent Sulfur
(a)
(b)
(c)
Figure 17.
Spectral plot of the Luvos sample with three different dopings. Each spectrum represents
one pixel from the respective doped LUVOS fraction.
The sulfur and the potassium samples (yellow and red lines) are offset by approximately 7 dB,
which could have been induced by their different water levels. The phosphorus sample (blue line)
shows nonlinear behavior, and the highest damping occurs in the range between 343 and 347 GHz.
This cannot be explained only by the presence of more water and must be analyzed in future studies.
Nevertheless, hyperspectral imaging enables the detection of complex behaviors.
The three different soil samples in Figure 18 show different damping and scattering patterns,
and their typical spectral responses are displayed in Figure 19. The scattering amplitudes vary by the
local position, and the interface region cannot be precisely localized by the DF.
Sensors 2019, 19, x FOR PEER REVIEW 14 of 23
An investigation of this artifact is not part of this work, but appears to be an artifact of
preparation. The high concentration of phosphorus in sample 3 induces a tendency to agglutinate.
Therefore, it could be possible that the higher DF value indicates the shape of an agglomerate.
Furthermore, the interface heights are addressed by the DF. However, it is still precisely indicated in
the image, which demonstrates the advantages of hyperspectral imaging. Additionally, the difference
in the spectral amplitudes in Figure 16 is not analyzed here. To speculate, doping the same matrix
with different chemicals could cause changes in the hygroscopic/hydrophobic behavior of the
material; higher or lower amounts of water could be causing the effect. Figure 17 shows the spectral
behavior of the three doped samples.
Figure 17. Spectral plot of the Luvos sample with three different dopings. Each spectrum represents
one pixel from the respective doped LUVOS fraction.
The sulfur and the potassium samples (yellow and red lines) are offset by approximately 7 dB,
which could have been induced by their different water levels. The phosphorus sample (blue line)
shows nonlinear behavior, and the highest damping occurs in the range between 343 and 347 GHz.
This cannot be explained only by the presence of more water and must be analyzed in future studies.
Nevertheless, hyperspectral imaging enables the detection of complex behaviors.
The three different soil samples in Figure 18 show different damping and scattering patterns,
and their typical spectral responses are displayed in Figure 19. The scattering amplitudes vary by the
local position, and the interface region cannot be precisely localized by the DF.
Figure 18. This figure shows the results for the setup in Figure 4. Samples are natural soils: (a)
amplitude in dB of the center frequency of 316.5 GHz; (b) mean value in dB of the spectral range from
258 to 343 GHz; (c) DF for the same spectral range.
260 270 280 290 300 310 320 330 340 350 360
Frequency in GHz
-80
-60
-40
-20
0
Transmission in dBc
LUVOS and 20 Percent P2O5
LUVOS and 20 Percent K2CO3
LUVOS and 20 Percent Sulfur
(a)
(b)
(c)
Figure 18.
This figure shows the results for the setup in Figure 4. Samples are natural soils: (
a
) amplitude
in dB of the center frequency of 316.5 GHz; (
b
) mean value in dB of the spectral range from 258 to 343
GHz; (c) DF for the same spectral range.
Sensors 2020,20, 5660 15 of 22
Sensors 2019, 19, x FOR PEER REVIEW 15 of 23
Figure 19. Spectral plot of the three soil samples. T3 is the bottom sample with the most organic
content. T2 is the sample in the middle. Each spectrum represents one pixel from the respective soil
fraction.
The main difference among these soil samples is the damping-related offset in the spectrum.
Sample T2 also has a higher slope than the other samples and some variation at approximately 300
GHz. A similar slope for sample T3 stops at approximately 290 GHz and is then horizontal. Damping
values of soil T3 with the most organic content are 50 dB higher than those for soil T1 that is
dominated by quartz sand. The results are not remarkable, but hyperspectral imaging enables the
comparison of spectral features in addition to the visual differentiation of multiple samples in one
run.
3.3. Measurement of Buried Objects
THz imaging is well known for its use in detecting buried objects. Detecting buried objects in
soil samples is much more difficult than detecting buried objects in other substrates because of the
scattering of sand particles. This scattering disorders the focus of the beam, and a sharp image of the
objects cannot be obtained.
Figure 20 shows the high absorption of water by the carrot letters. The image is blurred, and
some artifacts are visible around the middle letter “T” but, to the human eye, the letters are still
readable. The distortion in the image depends directly on the scattering behavior of the matrix. The
demonstration of this effect is shown in Figure 21 with the test letter “A” from Figure 5b. The sample
holder is consequently filled with larger sand particles, and therefore, the scattering also increases.
Here, the defocusing also increases and, unlike in the case with clay, the interface between carrot and
sand cannot be addressed.
(a)
(b)
(c)
Figure 20. This figure shows the results for the setup in Figure 5a. Three carrot letters are buried under
quartz clay: (a) amplitude in dB of the center frequency of 316.5 GHz; (b) mean value in dB of the
spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
260 270 280 290 300 310 320 330 340
Frequency in GHz
-100
-80
-60
-40
-20
0
T3
T1
T2
Figure 19.
Spectral plot of the three soil samples. T3 is the bottom sample with the most organic content.
T2 is the sample in the middle. Each spectrum represents one pixel from the respective soil fraction.
The main difference among these soil samples is the damping-related offset in the spectrum.
Sample T2 also has a higher slope than the other samples and some variation at approximately 300 GHz.
A similar slope for sample T3 stops at approximately 290 GHz and is then horizontal. Damping values
of soil T3 with the most organic content are 50 dB higher than those for soil T1 that is dominated by
quartz sand. The results are not remarkable, but hyperspectral imaging enables the comparison of
spectral features in addition to the visual differentiation of multiple samples in one run.
3.3. Measurement of Buried Objects
THz imaging is well known for its use in detecting buried objects. Detecting buried objects in
soil samples is much more difficult than detecting buried objects in other substrates because of the
scattering of sand particles. This scattering disorders the focus of the beam, and a sharp image of the
objects cannot be obtained.
Figure 20 shows the high absorption of water by the carrot letters. The image is blurred, and some
artifacts are visible around the middle letter “T” but, to the human eye, the letters are still readable.
The distortion in the image depends directly on the scattering behavior of the matrix. The demonstration
of this effect is shown in Figure 21 with the test letter “A” from Figure 5b. The sample holder is
consequently filled with larger sand particles, and therefore, the scattering also increases. Here,
the defocusing also increases and, unlike in the case with clay, the interface between carrot and sand
cannot be addressed.
Sensors 2019, 19, x FOR PEER REVIEW 15 of 23
Figure 19. Spectral plot of the three soil samples. T3 is the bottom sample with the most organic
content. T2 is the sample in the middle. Each spectrum represents one pixel from the respective soil
fraction.
The main difference among these soil samples is the damping-related offset in the spectrum.
Sample T2 also has a higher slope than the other samples and some variation at approximately 300
GHz. A similar slope for sample T3 stops at approximately 290 GHz and is then horizontal. Damping
values of soil T3 with the most organic content are 50 dB higher than those for soil T1 that is
dominated by quartz sand. The results are not remarkable, but hyperspectral imaging enables the
comparison of spectral features in addition to the visual differentiation of multiple samples in one
run.
3.3. Measurement of Buried Objects
THz imaging is well known for its use in detecting buried objects. Detecting buried objects in
soil samples is much more difficult than detecting buried objects in other substrates because of the
scattering of sand particles. This scattering disorders the focus of the beam, and a sharp image of the
objects cannot be obtained.
Figure 20 shows the high absorption of water by the carrot letters. The image is blurred, and
some artifacts are visible around the middle letter “T” but, to the human eye, the letters are still
readable. The distortion in the image depends directly on the scattering behavior of the matrix. The
demonstration of this effect is shown in Figure 21 with the test letter “A” from Figure 5b. The sample
holder is consequently filled with larger sand particles, and therefore, the scattering also increases.
Here, the defocusing also increases and, unlike in the case with clay, the interface between carrot and
sand cannot be addressed.
(a)
(b)
(c)
Figure 20. This figure shows the results for the setup in Figure 5a. Three carrot letters are buried under
quartz clay: (a) amplitude in dB of the center frequency of 316.5 GHz; (b) mean value in dB of the
spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
260 270 280 290 300 310 320 330 340
Frequency in GHz
-100
-80
-60
-40
-20
0
T3
T1
T2
Figure 20.
This figure shows the results for the setup in Figure 5a. Three carrot letters are buried under
quartz clay: (
a
) amplitude in dB of the center frequency of 316.5 GHz; (
b
) mean value in dB of the
spectral range from 258 to 343 GHz; (c) DF for the same spectral range.
Sensors 2020,20, 5660 16 of 22
Sensors 2019, 19, x FOR PEER REVIEW 16 of 23
Quartz
filling
Center frequency 316
GHz
Mean value DF
Clay
(a)
(b)
(c)
100–200 µm
(d)
(e)
(f)
300–400 µm
(g)
(h)
(i)
400–500 µm
(j)
(k)
(l)
500–630 µm
(m)
(n)
(o)
Figure 21. Cont.
Sensors 2020,20, 5660 17 of 22
Sensors 2019, 19, x FOR PEER REVIEW 17 of 23
1000–1250 µm
(p)
(q)
(r)
Figure 21. The letter in Figure 5b was buried under different quartz sand fractions. The size of the
fractions increases in every row: (a, d, g, j, m, p) amplitude of the center frequency of 312.5 GHz; (b,
e, h, k, n, q) mean value of the spectral range from 258 to 343 GHz; (c, f, i, l, o, r) DF for the same
spectral range.
Figure 21 demonstrates the effect of image distortion caused by the scattering matrixes. An
artifact is detected in d, f, and g. Regarding the previous artifacts, sample preparation caused this
effect, which is not visible in the other images. It is notable that the letter is not visible in Figure 21m,p,
but the corresponding mean values clearly show the “A”. The average of the high number of images
filters out the general higher damping of the carrot. However, averaging is not always a sufficient
filter. Without autoscaling and a common color bar for all images, the general tendency toward
higher damping in the larger sand fractions can be noted. Figure 22 is identical to Figure 21, except
for the common scale and the size of the images.
Clay
(a)
(b)
(c)
100–200 µm
(d)
(e)
(f)
300–400 µm
(g)
(h)
(i)
400–500 µm
(j)
(k)
(l)
500–630 µm
(m)
(n)
(o)
Figure 21.
The letter in Figure 5b was buried under different quartz sand fractions. The size of
the fractions increases in every row: (
a
,
d
,
g
,
j
,
m
,
p
) amplitude of the center frequency of 312.5 GHz;
(
b
,
e
,
h
,
k
,
n
,
q
) mean value of the spectral range from 258 to 343 GHz; (
c
,
f
,
i
,
l
,
o
,
r
) DF for the same
spectral range.
Figure 21 demonstrates the effect of image distortion caused by the scattering matrixes. An artifact
is detected in d, f, and g. Regarding the previous artifacts, sample preparation caused this effect,
which is not visible in the other images. It is notable that the letter is not visible in Figure 21m,p,
but the corresponding mean values clearly show the “A”. The average of the high number of images
filters out the general higher damping of the carrot. However, averaging is not always a sufficient
filter. Without autoscaling and a common color bar for all images, the general tendency toward higher
damping in the larger sand fractions can be noted. Figure 22 is identical to Figure 21, except for the
common scale and the size of the images.
Sensors 2019, 19, x FOR PEER REVIEW 17 of 23
1000–1250 µm
(p)
(q)
(r)
Figure 21. The letter in Figure 5b was buried under different quartz sand fractions. The size of the
fractions increases in every row: (a, d, g, j, m, p) amplitude of the center frequency of 312.5 GHz; (b,
e, h, k, n, q) mean value of the spectral range from 258 to 343 GHz; (c, f, i, l, o, r) DF for the same
spectral range.
Figure 21 demonstrates the effect of image distortion caused by the scattering matrixes. An
artifact is detected in d, f, and g. Regarding the previous artifacts, sample preparation caused this
effect, which is not visible in the other images. It is notable that the letter is not visible in Figure 21m,p,
but the corresponding mean values clearly show the “A”. The average of the high number of images
filters out the general higher damping of the carrot. However, averaging is not always a sufficient
filter. Without autoscaling and a common color bar for all images, the general tendency toward
higher damping in the larger sand fractions can be noted. Figure 22 is identical to Figure 21, except
for the common scale and the size of the images.
Clay
(a)
(b)
(c)
100–200 µm
(d)
(e)
(f)
300–400 µm
(g)
(h)
(i)
400–500 µm
(j)
(k)
(l)
500–630 µm
(m)
(n)
(o)
Figure 22. Cont.
Sensors 2020,20, 5660 18 of 22
Sensors 2019, 19, x FOR PEER REVIEW 18 of 23
1000–1250
µm
(p)
(q)
(r)
Figure 22. The same images from Figure 21, but with a common scale for the frequency of 316.5 GHz
and the mean value.
The logarithmic scale still enables the “A” to be visible in the mean images. The values of all
pixels in the vertical right corner line of fraction dependent images in Figure 22 were averaged to
obtain the common values of the quartz particle size dependent DF and mean values (damping)
(Figure 23a). The green pixels in Figure 23b indicate the used pixels for the analysis of the carrot area.
(a)
(b)
(c)
(d)
(e) (f)
Figure 23. Average of the right side vertical pixel lines plotted over the particle size: (a) pixel area for
bulk analysis; (b) green pixels indicate used pixels for carrot area; (c) mean values (in the middle
range the slope is about 10 dB/100 µm); (d) DF of the bulk material; (e) mean values of carrot pixels;
(f) DF of the carrot pixels.
<63
100-200
300-400
400-500
500-600
1000-1250
Fraction in µm
-60
-50
-40
-30
-20
-10
0
<63
100-200
300-400
400-500
500-600
1000-1250
Fraction in µm
0.6
0.8
1
1.2
1.4
1.6
1.8
Dynamic factor
<63
100-200
300-400
400-500
500-600
1000-1250
Fraction in µm
1.85
1.9
1.95
2
2.05
2.1
2.15
2.2
Figure 22.
The same images from Figure 21, but with a common scale for the frequency of 316.5 GHz
and the mean value.
The logarithmic scale still enables the “A” to be visible in the mean images. The values of all pixels
in the vertical right corner line of fraction dependent images in Figure 22 were averaged to obtain the
common values of the quartz particle size dependent DF and mean values (damping) (Figure 23a).
The green pixels in Figure 23b indicate the used pixels for the analysis of the carrot area.
Sensors 2019, 19, x FOR PEER REVIEW 18 of 23
1000–1250
µm
(p) (q) (r)
Figure 22. The same images from Figure 21, but with a common scale for the frequency of 316.5 GHz
and the mean value.
(a) (b)
(c) (d)
(e) (f)
Figure 23. Average of the right side vertical pixel lines plotted over the particle size: (a) pixel area for
bulk analysis; (b) green pixels indicate used pixels for carrot area; (c) mean values (in the middle
range the slope is about 10 dB/100 µm); (d) DF of the bulk material; (e) mean values of carrot pixels;
(f) DF of the carrot pixels.
<63
100-200
300-400
400-500
500-600
1000-1250
Fraction in µm
-60
-50
-40
-30
-20
-10
0
<63
100-200
300-400
400-500
500-600
1000-1250
Fraction in µm
0.6
0.8
1
1.2
1.4
1.6
1.8
Dynamic factor
<63
100-200
300-400
400-500
500-600
1000-1250
Fraction in µm
1.85
1.9
1.95
2
2.05
2.1
2.15
2.2
Figure 23. Average of the right side vertical pixel lines plotted over the particle size: (a) pixel area for
bulk analysis; (
b
) green pixels indicate used pixels for carrot area; (
c
) mean values (in the middle range
the slope is about 10 dB/100
µ
m); (
d
) DF of the bulk material; (
e
) mean values of carrot pixels; (
f
) DF of
the carrot pixels.
Sensors 2020,20, 5660 19 of 22
Figure 23 shows the particle size dependent mean (damping) values and the DF. The slope of
the bulk material in the middle fraction is about 10 dB/100
µ
m for the mean values in Figure 23c.
This demonstrates a high sensitivity for the particle size with this method. The scattering of the
1–1.25 mm particles is influenced by the saturation of the Mie scattering at about
π
D/
λ
, where D
represents the particle diameter and
λ
the respective wavelength used for measuring. Therefore,
the mean value is less reduced. The DF follows a different trend, and both values are good candidates
for machine learning inputs. The reduced scattering of the 1–1.25 mm fraction also causes a reduced
DF for that fraction. The situation is even more complicated for the carrot area. The beam focus at the
interface region induces higher scattering. Additionally, the water damping of the carrot reduces the
signals of about 30 dB. Therefore, the signal damping influences more fractions and the slope of the
mean values is reduced to 7.5 dB/100
µ
m. This damping reduces the scatter amplitudes and the higher
defocusing of lager particles causes the resulting DF to be more or less constant. The interface region
induces higher scattering, but the water damping and the defocusing reduces this effect.
Conductive materials such as metal cylinders are more difficult to detect, as expected.
The electromagnetic wave can travel around the surface of the cylinder, and the cylinder appears to be
transparent. Figure 24 shows the results of the experiment in Figure 6. Two steel tubes were buried
under quartz sand fractions from 63 to 100 µm.
Sensors 2019, 19, x FOR PEER REVIEW 19 of 23
Figure 23 shows the particle size dependent mean (damping) values and the DF. The slope of
the bulk material in the middle fraction is about 10 dB/100 µm for the mean values in Figure 23c. This
demonstrates a high sensitivity for the particle size with this method. The scattering of the 1–1.25 mm
particles is influenced by the saturation of the Mie scattering at about πD/λ, where D represents the
particle diameter and λ the respective wavelength used for measuring. Therefore, the mean value is
less reduced. The DF follows a different trend, and both values are good candidates for machine
learning inputs. The reduced scattering of the 1–1.25 mm fraction also causes a reduced DF for that
fraction. The situation is even more complicated for the carrot area. The beam focus at the interface
region induces higher scattering. Additionally, the water damping of the carrot reduces the signals
of about 30 dB. Therefore, the signal damping influences more fractions and the slope of the mean
values is reduced to 7.5 dB/100 µm. This damping reduces the scatter amplitudes and the higher
defocusing of lager particles causes the resulting DF to be more or less constant. The interface region
induces higher scattering, but the water damping and the defocusing reduces this effect.
Conductive materials such as metal cylinders are more difficult to detect, as expected. The
electromagnetic wave can travel around the surface of the cylinder, and the cylinder appears to be
transparent. Figure 24 shows the results of the experiment in Figure 6. Two steel tubes were buried
under quartz sand fractions from 63 to 100 µm.
(a) (b) (c)
Figure 24. The result of the setup in Figure 6. The left side was filled with the 0.063–0.1 mm fraction,
and the right side was filled with the 0.4–0.5 mm fraction. The two buried steel tubes are on the left
side of the images: (a) amplitude in dB of the center frequency of 316.5 GHz; (b) mean value in dB of
the spectral range from 258 to 343 GHz; the blue squares indicate the pixel position for the example
spectrum; (c) DF for the same spectral range.
Both tubes are visible, but their influence is even smaller than the scattering of the 400–500 µm
fraction of quartz sand on the right side of the image. Additionally, the interface region between the
paper and the larger fraction shows notably more scattering. This is also indicated by the average DF
of 1.5 in this area, which is significantly higher than the average DF values of 0.7 and 1.0 for the small
and big particle fractions, respectively, in the sample holder. Figure 25 shows the resulting spectral
response at the dedicated positions. Both tubes (at y = 2 and 7 mm) show somewhat similar spectral
behavior to the small sand fraction (at y = 9 mm) but with an offset of 10 dB in additional damping.
Additionally, the increased scattering behavior in the interface region (at y = 14 mm) is also visible in
the spectral response indicated by the highest average damping value of about 30 dB.
Figure 24.
The result of the setup in Figure 6. The left side was filled with the 0.063–0.1 mm fraction,
and the right side was filled with the 0.4–0.5 mm fraction. The two buried steel tubes are on the left
side of the images: (
a
) amplitude in dB of the center frequency of 316.5 GHz; (
b
) mean value in dB of
the spectral range from 258 to 343 GHz; the blue squares indicate the pixel position for the example
spectrum; (c) DF for the same spectral range.
Both tubes are visible, but their influence is even smaller than the scattering of the 400–500
µ
m
fraction of quartz sand on the right side of the image. Additionally, the interface region between the
paper and the larger fraction shows notably more scattering. This is also indicated by the average DF
of 1.5 in this area, which is significantly higher than the average DF values of 0.7 and 1.0 for the small
and big particle fractions, respectively, in the sample holder. Figure 25 shows the resulting spectral
response at the dedicated positions. Both tubes (at y =2 and 7 mm) show somewhat similar spectral
behavior to the small sand fraction (at y =9 mm) but with an offset of 10 dB in additional damping.
Additionally, the increased scattering behavior in the interface region (at y =14 mm) is also visible in
the spectral response indicated by the highest average damping value of about 30 dB.
Sensors 2020,20, 5660 20 of 22
Sensors 2019, 19, x FOR PEER REVIEW 20 of 23
Figure 25. This figure shows the five spectra indicated in Figure 24.
4. Discussion
THz hyperspectral imaging enables transmission mode analyses of difficult samples, but is
strongly influenced by Mie scattering. Thus, all of the scattering along the beam pathway disorders
the beam and causes image distortion. Therefore, the imaging of soil samples is extremely difficult
and not possible if the sample is dominated by large sand particles of approximately 1 mm.
Conversely, the amount of scattering indicates the particle size fraction and could be an important
measurement tool for soil samples. The analysis of the setup demonstrates a local resolution of
approximately 2 mm, which is reasonably good for an emitter with a wave guide and horn antenna.
Therefore, even images with smaller pixel sizes are blurred in that range. However, with respect to
the soil samples, scattering is the dominant factor that causes image distortion. Looking at image “p”
in Figure 21, the scattering blurs the image of the carrot letter “A”. The image looks like noise, but is
not noise; it is reproducible scattering. The multiple images for each frequency step enable statistical
analysis in the MATLAB environment. For example, the image of the mean value clearly reproduces
the letter “A”.
The imaging helps the user to identify local artifacts and therefore avoid taking these pixels into
account in further statistical analyses of this sample region. For example, the mechanical stress on the
carrot can lead to water leakage. The artifacts are mainly caused by sample preparation errors, but
measurement failures with missing signal amplitudes and interface regions with different behaviors
can also be identified, if they happen or exist. This makes the hyperspectral setup a great
measurement tool for critical and nonhomogeneous samples, and reduces fault analysis and
interpretations. Additionally, because unwanted areas are taken out of consideration, the pixels can
be classified, and common sample areas can be combined for further analysis in the MATLAB
environment, for example. This analysis could reveal a typical spectral response or indicate that a
more complex situation exists. Furthermore, the statistically confirmed results can be compared with
the simulation results in the future. Nevertheless, the visualization of the spectral result often enables
a quick interpretation of the situation; for example, water added the offset in the frequency range.
This does not mean that a single frequency is sufficient for analyzing this behavior because scattering
still dominates the amplitude of each frequency.
5. Conclusion
THz hyperspectral imaging provides all of the advantages of normal light hyperspectral imaging
but enables transmission mode analyses of difficult samples. Here the transillumination of cm thick
samples is possible, and the optical resolution could be up to 2 mm. The energy of THz radiation is
not high enough to change the energetic states of atoms or molecules, but the physical scattering and
dielectric constant still produce contrasts in the THz images. Organic content in soil samples could
Figure 25. This figure shows the five spectra indicated in Figure 24.
4. Discussion
THz hyperspectral imaging enables transmission mode analyses of difficult samples, but is
strongly influenced by Mie scattering. Thus, all of the scattering along the beam pathway disorders the
beam and causes image distortion. Therefore, the imaging of soil samples is extremely difficult and
not possible if the sample is dominated by large sand particles of approximately 1 mm. Conversely,
the amount of scattering indicates the particle size fraction and could be an important measurement
tool for soil samples. The analysis of the setup demonstrates a local resolution of approximately 2 mm,
which is reasonably good for an emitter with a wave guide and horn antenna. Therefore, even images
with smaller pixel sizes are blurred in that range. However, with respect to the soil samples, scattering is
the dominant factor that causes image distortion. Looking at image “p” in Figure 21, the scattering
blurs the image of the carrot letter “A”. The image looks like noise, but is not noise; it is reproducible
scattering. The multiple images for each frequency step enable statistical analysis in the MATLAB
environment. For example, the image of the mean value clearly reproduces the letter “A”.
The imaging helps the user to identify local artifacts and therefore avoid taking these pixels
into account in further statistical analyses of this sample region. For example, the mechanical stress
on the carrot can lead to water leakage. The artifacts are mainly caused by sample preparation
errors, but measurement failures with missing signal amplitudes and interface regions with different
behaviors can also be identified, if they happen or exist. This makes the hyperspectral setup a
great measurement tool for critical and nonhomogeneous samples, and reduces fault analysis and
interpretations. Additionally, because unwanted areas are taken out of consideration, the pixels
can be classified, and common sample areas can be combined for further analysis in the MATLAB
environment, for example. This analysis could reveal a typical spectral response or indicate that a
more complex situation exists. Furthermore, the statistically confirmed results can be compared with
the simulation results in the future. Nevertheless, the visualization of the spectral result often enables
a quick interpretation of the situation; for example, water added the offset in the frequency range.
This does not mean that a single frequency is sufficient for analyzing this behavior because scattering
still dominates the amplitude of each frequency.
5. Conclusions
THz hyperspectral imaging provides all of the advantages of normal light hyperspectral imaging
but enables transmission mode analyses of difficult samples. Here the transillumination of cm thick
samples is possible, and the optical resolution could be up to 2 mm. The energy of THz radiation is
not high enough to change the energetic states of atoms or molecules, but the physical scattering and
dielectric constant still produce contrasts in the THz images. Organic content in soil samples could
add about 50 dB signal damping, as demonstrated in Figure 19. The reduced resolution compared to
Sensors 2020,20, 5660 21 of 22
optical measurements does not enable the analysis of single particles in an aggregation, but enables
measurements in the volume. The average of multiple pixels generates a common result of a sample.
Figure 23 demonstrates the sensitivity of the setup for particle size of about 10 dB/100
µ
m for quartz
sand. Additionally, the results for the mean value and the DF in Figure 23 show different trends for the
particle size and could be good input candidates for future machine learning approaches. Additionally,
both parameters are influenced by water damping of organic material such as carrot. Therefore,
THz hyperspectral imaging is a valuable tool for analyzing difficult samples such as soil samples.
Author Contributions:
B.M. and V.D. conceived and designed the experiments; B.M. and V.D. performed the
experiments; B.M., C.W., J.S. and V.D. analyzed the data; B.M., R.G. and J.S. contributed analysis tools; C.W., V.D.
and R.G. wrote the paper. All authors have read and agreed to the published version of the manuscript.
Funding:
This research is part of the BonaRes project Integrated System for Site-Specific Soil Fertility Management
(I4S) and is funded by the German Federal Ministry of Education and Research, grant 031B0513A.
Acknowledgments:
The companies ELVA-1 and Semic RF are gratefully acknowledged for developing the setup
and for support in improving the measurement conditions.
Conflicts of Interest:
The authors declare no conflict of interest. The founding sponsors had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision
to publish the results.
Abbreviations
The following abbreviations are used in this manuscript:
Vis-NIR Visible to Near-Infrared
DF Dynamic factor
HDPE high-density polyethylene
THz Terahertz
GHz Gigahertz
TX Transmitter
RX Receiver
GUI Graphical user interface
CW Continuous wave
PC Personal computer
FWHM Full width half maximum
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