# A tuneable wavelength reference for chip-scale laser cooling

S. Dyer  SUPA and Department of Physics, University of Strathclyde, G4 0NG,
Glasgow, United Kingdom  K. Gallacher  James Watt School of Engineering,
University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow, G12 8LT,
U.K.  U. Hawley  James Watt School of Engineering, University of Glasgow,
Rankine Building, Oakfield Avenue, Glasgow, G12 8LT, U.K.  A. Bregazzi  SUPA
and Department of Physics, University of Strathclyde, G4 0NG, Glasgow, United
Kingdom  P. F. Griffin  SUPA and Department of Physics, University of
Strathclyde, G4 0NG, Glasgow, United Kingdom  A. S. Arnold  SUPA and
Department of Physics, University of Strathclyde, G4 0NG, Glasgow, United
Kingdom  D. J. Paul  James Watt School of Engineering, University of Glasgow,
Rankine Building, Oakfield Avenue, Glasgow, G12 8LT, U.K.  E. Riis  SUPA and
Department of Physics, University of Strathclyde, G4 0NG, Glasgow, United
Kingdom  J. P. McGilligan  SUPA and Department of Physics, University of
Strathclyde, G4 0NG, Glasgow, United Kingdom

###### Abstract

We demonstrate a tuneable, chip-scale wavelength reference to greatly reduce
the complexity and volume of cold-atom sensors. A 1 mm optical path length
micro-fabricated cell provides an atomic wavelength reference, with dynamic
frequency control enabled by Zeeman shifting the atomic transition through the
magnetic field generated by the printed circuit board (PCB) coils. The dynamic
range of the laser frequency stabilization system is evaluated and used in
conjunction with an improved generation of chip-scale cold atom platforms that
traps 4 million 87Rb atoms. The scalability and component consolidation
provide a key step forward in the miniaturization of cold atom sensors.

††preprint: APS/123-QED

##  I Introduction

The miniaturization of cold atom platforms for remote sensing and portability
has tantalising prospects for next-generation quantum technology [1, 2, 3, 4,
5]. Owing to the long interrogation times achievable with laser cooling, the
development of on-chip cold-atom platforms could improve the stability of
current thermal atomic sensors to the benefit of applications in navigation,
geological surveying, communication and precision timing, driving towards
fully integrated atomic systems.

Recent research has demonstrated drastic improvements in the scalability of
critical components at the heart of atomic sensors. While initially focused on
the scalability of thermal atom packages, the micro-fabrication of core
components revolutionized the scalability in a plethora of instruments,
including atomic clocks [6, 7, 8], magnetometers [9, 10, 11], and wavelength
references [12, 13]. At the heart of many of these devices is a micro-electro-
mechanical systems (MEMS) vapor cell. Typically formed from a glass-silicon-
glass wafer stack, the on-chip thermal vapor system offers a simplicity and
design versatility that complements its application in precision spectroscopy
[14, 15, 16, 17].

The miniaturization of thermal atom packages has also driven forward the
scalability of cold-atom sensors. Recent studies have demonstrated cold-atom
sensor scalability through the coupling of photonic integrated circuits [18,
19, 20], meta-surfaces [21, 22], diffractive optics [23, 24, 25], planar coil
systems [26] and micro-fabricated alkali sources [27, 28]. More recently, MEMS
vapor cells capable of sustaining ultra-high-vacuum (UHV) have been shown in
conjunction with micro-fabricated grating chips as an on-chip platform for
cold-atoms [29]. Parallel avenues of research have aimed to address the
miniaturization and simplicity of cold atom systems through the development of
plug-and-play interfaces, making use of conventional off-the-shelf optics [30,
31]. Many of these cold-atom systems, however, have focused on individual
component development, such that a fully integrated cold-atom platform has
remained elusive.

In this Article, we demonstrate a tuneable wavelength reference at 780 nm that
complements chip-scale laser cooling of Rb atoms. A single optical package
enables laser frequency tuning and stabilization in a micro-fabricated vapor
cell, sandwiched between a printed-circuit-board (PCB) coil pair. The dynamic
range of the chip-scale package is evaluated as a viable replacement to
standard larger components used for real-time frequency control, such as
acousto-optical modulators. The wavelength reference is coupled with a chip-
scale cold-atom platform to demonstrate device simplicity and compatibility
for laser-cooling applications. Finally, the combined apparatus demonstrates
laser cooled atom numbers $>10^{6}$ in thick silicon MEMS vacuum cells. The
union of such components provides a key step in the scalability and mass
production of cold-atom systems.

##  II Experimental set-up

The experimental apparatus used for the wavelength reference and chip-scale
laser cooling platform are shown in Fig. 1 (a) and (b) respectively. The light
source is provided from a butterfly packaged volume-Bragg reflector (VBR)
laser centred at 780 nm. The light from the VBR is incident through a 5 mm
polarizing beam splitter (PBS), with one arm coupled into our chip-scale
wavelength reference.

Figure 1:  A schematic diagram overview of the chip-scale wavelength and
cooling platforms. (a): A MEMS cell based wavelength reference using saturated
absorption spectroscopy. PCB-HC: Printed-circuit-board Helmholtz coils. PBS:
Polarizing beam splitter. SMR: Surface mounted resistor. (b): MEMS cell-GMOT
incorporated laser cooling platform with planar coils. GMOT: Grating magneto-
optical trap. PCB-AHC: Printed-circuit-board anti-Helmholtz coils.(c):
Microscope image of the MEMS cell in the wavelength reference package. (d):
Layer structure for the wavelength reference MEMS cell stack. BSG:
Borosilicate glass. Si: Silicon. (e): Layer structure for the UHV-MEMS cell
stack. ASG: Aluminosilicate glass. (f): Example image of the cold-atom sample
formed from the combined chip-scale platforms.

The laser wavelength reference is provided by saturated absorption
spectroscopy through a 2 mm thick MEMS cell, shown at the centre of Fig. 1
(a). The MEMS spectroscopy cell, shown in Fig. 1 (c), is composed of a 1 mm
thick silicon frame anodically bonded at both interfaces to 0.5 mm thick
borosilicate glass wafers, as highlighted in Fig. 1 (d). The silicon frame is
deep reactive-ion etched using an anisotropic Bosch process [32] to form a
two-chamber cell connected via 650$\,\mu$m wide, non-line-of-sight channels.
The first chamber houses a micro-pill based alkali vapor source (SAES
Rb/AMAX/Pill1-0.6). The second chamber acts as the spectroscopy region with a
2 mm diameter aperture. The cell is mechanically diced to dimensions of
$10\,$mm$\times 10\,$mm$\times 2\,$mm and a surface-mounted resistor is
adhered to the side of the silicon frame to provide heating. Prior to the
implementation of the MEMS cell in the apparatus, the pill is laser activated
with 1 W of 1070 nm laser light focused onto the pill surface for 10 s [33].

The MEMS cell is sandwiched between a pair of PCB Helmholtz coils. Each 1 mm
thick PCB is double-side printed and electrically connected via a circuit
through-hole to increase the number of turns over the given board volume. The
coil is formed of 35 $\mu$m thick copper layer wires with 170$\,\mu$m width
deposited on the surfaces of the board to form a total of 14 turns, with a
mean radius of 3.3 mm ($R_{min}=2.2\,$mm, $R_{max}=4.5\,$mm). The centre of
the coil has a 1.5 mm radius aperture that is aligned for optical
interrogation of the MEMS cell through the spectroscopy region. The coils and
cell are held firmly in location within a 3-D printed mount, to ensure a
robust alignment. The laser is frequency modulated at 250 kHz via current
dithering. The output from the laser is passed through a PBS, circularly
polarized with a $\lambda/4$ wave-plate before the MEMS cell and reflected by
a dielectric reflector, mounted to the back of the MEMS cell. The output
transmission from the spectroscopy system is directed through the PBS to a
photodiode, where the absorption signal is passed to external electronics for
demodulation and the resulting error signal is used to electronically feed-
back to the VBR current for frequency stabilization.

The remaining light is passed through an electro-optical-modulator (EOM)
driven at 6.5 GHz to generate 5$\,\%$ side-bands for hyperfine re-pumping in
the laser cooling process. The light is then fibre coupled and expanded in
free-space to the cold-atom system. The light is circularly polarized with a
$\lambda/4$ wave-plate before being incident through the UHV-MEMS cell. The
UHV-MEMS cell, shown in Fig. 1 (b), is composed of a 6 mm thick silicon frame,
fabricated with water-jet processing to achieve the deep silicon cut [34]. The
silicon wafer is anodically bonded at the upper and lower surfaces to 700
$\mu$m thick aluminosilicate glass wafers, as highlighted in Fig. 1 (e). The
upper glass wafer is connected to an ion pump and resistively-heated alkali
dispenser through a copper pinch-off tube adhered over a mechanically drilled
glass through-hole. The UHV-MEMS cell outer dimensions are 70 mm$\,\times
34\,$mm$\,\times 7.4\,$mm with a 20 mm$\times 20\,$mm$\times 6\,$mm laser
cooling region, which accommodates the surface area of the grating chip. The
3-segment grating chip is fabricated with a 1100 nm period over the 2
cm$\times\,$2 cm surface area of the chip. At the center of the grating, a 2
mm diameter hole has been laser cut for optical access and imaging [35]. The
grating chip is placed immediately below the UHV-MEMS cell lower window to
ensure a maximum optical overlap volume exists within the UHV-MEMS cell vacuum
volume. A 30 mm$\times\,$8 mm channel in the cell from the pinch-off region
leading to the cooling region was designed to aid fluorescence imaging of the
cold-atoms by allowing a low angular displacement between the cell and imaging
system. The low incident angle for imaging avoids diffracted orders from the
grating chip and greatly reduces the surface scatter from the cell walls,
glass and grating. An example of this imaging axis is shown in Fig. 1 (f). The
UHV-MEMS cell and grating are sandwiched by a PCB anti-Helmholtz pair (PCB-
AHC). These PCB coils are of the same thickness and wire properties as the
previously described Helmholtz PCBs. Each PCB-AHC, however, is formed of 30
turns, 15 on each side, with a mean radius of 12.5 mm ($R_{min}\,=\,10.2\,$mm,
$R_{max}=14.9\,$mm).

To enable miniaturization of the cold-atom optical system, the bulky optical
and electronic system required for the acoustic optical modulator (AOM) was
replaced with the tuneable Zeeman lock [36]. The laser is locked directly to
the $F=2\rightarrow F^{\prime}=3$ cooling transition, and a frequency offset
is provided from the PCB Helmholtz coils, with the magnetic field orientation
illustrated in Fig. 2 (a). The magnetic field is simulated from a numerical
solution to the Biot-Savart law, for parameters meeting that of the PCB. The
offset mechanism uses a bias magnetic field along the axis of the beam, which
induces a shift to the Zeeman sub-levels. Circularly polarized light is used
to optically pump the atoms into the stretched states. As such, the
magnetically sensitive sub-Doppler features can be exploited to tune the laser
lock frequency while avoiding the optical losses typical of a double passed
AOM setup [37]. To determine the versatility of the frequency offset, a beat-
note was measured against an external-cavity diode-laser (ECDL), which was
stabilized to the $F=2\rightarrow F^{\prime}=2,3$ cross-over transition of
87Rb using saturated absorption spectroscopy on a separate reference cell. The
beat-note signal was obtained by overlapping light from each laser onto a fast
photodiode and the output frequency was tracked on a frequency counter.

##  III Results

The induced frequency shift for weak magnetic fields was found to be $1.42\pm
0.12\,$MHz/G in agreement with the expected shift for the
$F=2,m_{F}=2\rightarrow F^{\prime}=3,m_{F}=3$ transition, indicating
stretched-state optical pumping. For stronger magnetic fields, the error
signal is deformed due to lineshape broadening from magnetic field
inhomogeneities, placing a limit on the frequency tuning range of
$\approx\pm$30 MHz. However, this range is sufficient to achieve a red-detuned
lock for the magneto-optical trap, where the trapped atom number is typically
optimum in Rb for a detuning between $\Delta=-\Gamma\rightarrow-2\Gamma$,
where $\Gamma$ is the natural linewidth of the excited state
($\Gamma_{\textrm{D${}_{2}$}}=2\pi\times 6.1$ MHz) [38]. Over this detuning
range, the PCB-HC coil pair require $<$ 0.7 W of electrical power. The error
signal from the MEMS cell, shown for $\Delta=12$ MHz in Fig. 2 (c) with a
black line, has no significant amplitude or linewidth degradation compared to
the resonant signal, shown in gray. The detuning range here could also prove
beneficial to the frequency detunings typical of optical molasses.

Figure 2:  (a): Printed-circuit-board generated Helmholtz magnetic field
orientation through the 2 mm thick MEMS cell. (b): Measured frequency shift as
a function of the applied magnetic field, as calculated from the coil
properties. (c): The Zeeman shifted error signal at 12 MHz detuning (black)
and on resonance (gray) with 16 averages. Figure 3:  (a): Printed-circuit-
board generated anti-Helmholtz magnetic field orientation through the 6 mm
thick UHV-MEMS cell. (b): Measured atom number as a function of laser lock
frequency, provided by the MEMS wavelength reference. (c): Overlapping Allan
deviation of the beat-note signal when the VBR laser is stabilised to the
tuneable MEMS wavelength reference and a 7 cm reference cell, shown in red
squares and blue circles respectively. (d): Simultaneously measured atom
number stability from the MEMS-GMOT platform.

To demonstrate the applicability of the wavelength reference to cold-atom
sensors, the VBR was locked to the cooling transition, and coupled into the
chip-scale cold-atom platform. To aid further miniaturization, traditionally
large wire-wound anti-Helmholtz coils have been replaced in favour of a PCB
solution. Each double-sided PCB anti-Helmholtz coil used in the cold-atom
system has a resistance of 10 $\Omega$ and draws 1 A of current to achieve 20
G/cm, with the field orientation relative to the other system components shown
in Fig. 3 (a).

The increased vacuum cell volume of the UHV-MEMS cell, compared to previous
work, has been made possible from the recently demonstrated water-jet cutting
of silicon wafers [34]. The improved cell volume now enables $\approx 93$ $\%$
of the GMOT optical overlap volume to coincide within the MEMS cell [35]. Due
to this, an optimum atom number of 4$\times$106 atoms is obtained in the chip-
scale platform for a detuning of 11 MHz, as demonstrated in Fig. 3 (b),
agreeing well with previous GMOT work [23]. It was observed that with an
incident intensity of $\approx$ 13 mW/cm2, the atom number would reach a
maximum at 20 G/cm.

Finally, the frequency fluctuations of the chip-scale wavelength reference
were temporally measured, with the impact on the measured atom number from the
cold-atom platform simultaneously tracked. During this measurement the
detuning was set to 12 MHz, which produced an atom number of $\approx\,3\times
10^{6}$. The relative stability of the wavelength reference is illustrated in
Fig. 3 (c). The observed relative frequency stability is on the order of 10-11
for all integration windows. While this stability does not meet the
performance of state-of-the-art on-chip wavelength reference [12], it is
suitable for keeping the laser drift well below the 6 MHz linewidth of the
cooling transition to satisfy the miniaturization of the cold-atom apparatus.
Further to this, when the tuneable wavelength reference is replaced with a 7
cm reference cell, a similar stability was observed, as demonstrated in Fig. 3
(c), indicating that the stability is not limited by the MEMS cell package.
The simultaneously measured atom number stability, shown in Fig. 3 (d),
integrates down with a slope of $\tau^{-1/2}$, demonstrating that the
frequency fluctuations of the wavelength reference have no contribution to the
stability of the trapped atom number.

The amalgamation of these on-chip technologies has successfully demonstrated a
significant scalability in cold-atom technology, while offering a simplified
optical system comprised of planar components.

##  IV Conclusion

We have demonstrated an on-chip solution for wavelength referencing in cold-
atom systems. The simple architecture and mass producible components are
suitable for implementation in a wide range of quantum technologies, with a
detuning range of $\pm$30 MHz demonstrated in constant use, and increased
values possible for short time intervals. The amalgamation with the 6 mm thick
silicon based UHV-MEMS cell directly demonstrates the applicability of the
tuneable wavelength reference as a suitable replacement for traditionally
bulky cold-atom optical systems.

###### Acknowledgements.

The authors would like to thank R. Boudot for useful conversations. The
authors acknowledge funding from Defence Security and Technology Laboratory,
Engineering and Physical Sciences Research Council (EP/T001046/1), and Defence
and Security Accelerator. The authors would like to acknowledge support from
the INMAQS collaboration (EP/W026929/1). J. P. M gratefully acknowledges
funding from a Royal Academy of Engineering Research Fellowship and D. J. P.
from a Royal Academy of Engineering Research Chair in Emerging Technologies
(CiET2021$\backslash$123). A. B. was supported by a PhD studentship from the
Defence Science and Technology Laboratory (Dstl).

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1in1in1in1in

11institutetext: Idrees Zaman 22institutetext: Sustainable Communication
Networks, University of Bremen, Germany 33institutetext: Nandit Jain
44institutetext: Department of Chemical Engineering, Indian Institute of
Technology, Kanpur
44email<EMAIL_ADDRESS>55institutetext: Anna Förster 66institutetext:
Sustainable Communication Networks, University of Bremen, Germany
66email<EMAIL_ADDRESS>

* This is an extended version of I. Zaman, N. Jain and A. Förster, "Artificial Neural Network based Soil VWC and Field Capacity Estimation Using Low Cost Sensors," 2018 IFIP/IEEE International Conference on Performance Evaluation and Modeling in Wired and Wireless Networks (PEMWN), Toulouse, 2018.

# Machine Learning based Soil VWC and Field Capacity Estimation Using Low Cost
Sensors

Idrees Zaman  Nandit Jain  Anna Förster

(January 2021)

###### Abstract

The amount of water present in soil is measured in terms of a parameter
commonly referred to as Volumetric Water Content (VWC) and is used for
determining the field capacity of any soil. It is an important parameter
accounting for ensuring proper irrigation at plantation sites for farming as
well as for afforestation activities. The current work is an extension to
already going on research in the area of wireless underground sensor networks
(WUSNs). Sensor nodes equipped with Decagon 5TM volumetric water content (VWC)
and temperature sensor are deployed underground to understand the properties
of soil for agricultural activities. The major hindrances in the deployment of
such networks over a large field are the cost of VWC sensors and the
credibility of the data being collected by these sensors. In this paper, we
analyze the use of low-cost moisture and temperature sensors that can either
be used to estimate the VWC values and field capacity or cross-validate the
data of expensive VWC sensors before the actual deployment. Machine learning
algorithms, namely Neural Networks and Random Forests are investigated for
predicting the VWC value from low-cost moisture sensors. Several field
experiments are carried out to examine the proposed hypothesis. The results
showed that low-cost moisture sensors can assist in estimating the VWC and
field capacity with a minor trade-off.

###### Keywords:

Volumetric Water Content Underground Sensors Artificial Neural Networks Random
Forest Machine Learning

##  1 Introduction

Substantial growth in the field of wireless sensor networks (WSN’s) has
empowered researchers to gather large amounts of data and to reveal the
sequestered information about the nature. This information helps to understand
the environment better and guides to take appropriate decisions. This
progression in WSN leads to the evolution of its applications that are not
only limited to above ground but can be extended to underwater wireless sensor
networks (UWSN), multimedia wireless sensor networks, mobile wireless sensor
networks and wireless underground sensor networks (WUSN). The current work
focuses on the challenges faced in agricultural monitoring in WUSN. WUSNs
generally follow the same communication principle as conventional WSNs but the
communication range decreases significantly because of the high permittivity
of the soil. Hence, the WUSN requires much dense deployment in order to cover
a larger area under observation. Also, the deployment and maintenance cost of
WUSN is much more than the terrestrial WSN. There are many applications of
WUSN b1 , including, but not limited to landslide monitoring b2 ,
infrastructural monitoring b3 , mines disaster management b4 , agricultural
monitoring b5 . The current work proposes enhanced sustainable agricultural
monitoring using WUSN. There are several factors like soil moisture, soil
temperature, soil composition, bulk air density, volumetric water content
(VWC), pH value, conductivity etc. that determine the suitability of a soil
for agricultural and other relevant activities. The most important factor
among all mentioned factors is the volumetric water content (VWC) of the soil.
The information about VWC at plants root zone level assists in taking
appropriate decisions for more efficient irrigation and reforestation. The VWC
is defined as the ratio of water volume to the soil volume and is being
measured using the dielectric permittivity of the soil. Soil VWC information
is of great use for providing irrigation solutions to the farmers as well as
its integration with wireless sensor networks allows monitoring of the remote
agricultural places and reforestation projects. A wide range of expensive VWC
sensors are available for monitoring the water content of a soil. The cost of
VWC sensors become a bottleneck for the farmers to opt the techniques of smart
agriculture to increase their crops productivity. The current work strives to
address the aforementioned issues regarding soil monitoring.
The current work is a part of the cooperation between the Sustainable
Communication Networks group at the University of Bremen in Germany and the
ReviTec b6 ,b7  project from the Center of Environmental Research and
Sustainable Technology (UFT) at the University of Bremen. The agricultural
fields in Ngaoundere, Cameroon where the project is aimed to be deployed are
often located in remote areas far away from settlements. In such regions,
vandalism is quite frequent from anti social elements. Also, there is a risk
of sensors and experiment being harmed by the farmer as well as wild animals.
Given such circumstances, it is advisable to use underground sensors with no
visible parts above the ground.
The aim of this work is to help ecologists to evaluate the performance of
their revitalization techniques and common farmers to adopt soil monitoring
techniques to better understand the nature of their agricultural fields. The
WUSN also helps farmers to pursue their normal agricultural field operations
without any hindrance as all the sensor nodes are buried underground. The
current work will also help in a much denser deployment of the sensors which
otherwise is not possible because of the expensive volumetric water content
sensors.

##  2 Related Work

Mainly, there are two methods for measuring the VWC of the soil i.e. aerial
sensing and underground sensing. The subsequent sections will highlight the
recent work carried out in both the approaches along with their advantages and
shortcomings.

###  2.1 Aerial Sensing

The process of aerial sensing requires satellite imaging or high altitude
aircraft imaging to get viable information for the ground soil. For the
purpose of VWC estimation, it is generally done through imaging or
electromagnetic (EM) waves. In this direction, NASA launched Soil Moisture
Active Passive (SMAP)b8  in 2015, that is an American environmental research
satellite. SMAP has been designed to measure soil’s moisture content over a
three-year period, every 2-3 days. The SMAP observatory consists of a
spacecraft mounted with instruments in a near-polar, Sun-synchronous orbit.
The SMAP consists of a radiometer (passive) instrument and a synthetic
aperture radar (active) instrument operating with multiple polarizations in
the L-band range. The project is aimed at developing global maps of soil
moisture for areas not covered by water or snow. In b9 , authors used Bayesian
Artificial Neural Network based approach has been proposed to extract soil’s
VWC information from high resolution imaging drone through an autonomous
unmanned aerial system (UAS), named AggieAir, equipped with visual, near-
infrared, and thermal cameras. The imaging was done at 0.15 m resolution for
the visible and near infrared bands and 0.6 m resolution for the thermal
infrared band. Multiple indices like red, green, blue, NIR, thermal, NDVI,
VCI, EVI, VHI, and field capacity were extracted from the images to train the
models. The study area was the 0.34 km2 agricultural field located in Scipio,
Millard County, in central Utah. Intensive ground sampling was carried out to
detect the ground truth. The model could estimate root zone’s VWC with a good
accuracy (RMSE = 0.05).
In b10 , the authors used the satellite data to obtain VWC data. The authors
use Global Vegetation Moisture Index (GVMI) to retrieve vegetation water
content. The index was created based on an analytical method using radiative
transfer models at leaf, canopy, and atmospheric levels, with an emphasis to
maximise sensitivity to vegetation water content and to minimize sensitivity
to other factors such as atmospheric perturbations and angular effects. The
index was validated on areas covered with four different vegetation types,
representing a vegetation gradient from open herbaceous (Shrub Steppe) to the
densely vegetated formation (Savannah Woodland). A linear correlation
coefficient of 0.93 was observed between GVWI derived VWC and field
measurements. The aerial sensing method is generally quite expensive, given
that satellites or aircrafts and high definition cameras are involved.
Usually, the aforementioned methods are used for estimating the VWC profile
over very large areas and are not feasible enough to be used by farmers for
their agricultural fields.

###  2.2 Underground Sensing

In the recent past, researchers have proposed several techniques to measure
the VWC of large agricultural fields using underground sensing. In G. Shan et
al. b11 , an underground mobile dielectric sensor is used to measure the VWC
of the tomato crop root zone in an experimental field sizing 240m2. The VWC is
logged twice a day continuously for a period of three months. A stepper and dc
motor are used to move the dielectric sensor in steps of 5cm in a buried PVC
tube of length 4m. The metal electrodes of the embedded sensor are firmly
adjoined to the PVC tube. The probes of the dielectric sensor generate a
fringing field that passes through the plastic PVC tube into the soil and
measures the dielectric permittivity of the soil. The mobile dielectric sensor
allows to cover a larger area with a single sensor. The data collected gives
useful insight in soil and plant water losses linked with evapotranspiration.
The data collected through the sensor is also cross-validated against the
estimated model of the root zone soil. Such setup requires high deployment and
maintenance cost.

In Mittelbach et al. b12 , the authors evaluate the performance of
commercially available expensive VWC sensors from Decagon Devices. The work
involved field measurements performed at two sites with different soil texture
and calibration techniques in Switzerland covering more than a year of
parallel measurements in several depths down to 120 cm. The authors observed
that the measurement accuracy of the 10HS sensor decreased considerably with
increasing VWC and became insensitive to variations of VWC above 40%, whereas
the 5TM sensor showed better sensitivity to higher VWC values. To the best of
our knowledge, no one has used the low cost soil monitoring sensors for
estimating the VWC value.

##  3 Soil Sensing

The volumetric water content (VWC) is one of the important parameter to
understand the feasibility of any soil for agricultural activities. The VWC is
then used to derive the field capacity of any soil, which is another parameter
to analyze the suitabitly of any soil for agriculture. However, measuring of
VWC require complex methods i.e. time domain reflectometry (TDR) and frequency
domain reflectometry (FDR). The sensing modules based on TDR and FDR are
usually quite expensive i.e. 5TM Decagon sensor b13 . Therefore, potential low
cost sensors that can estimate the VWC in place of TDR and FDR based methods
are analyzed.

###  3.1 Field Capacity

Soil is normally composed of three types of particles, i.e. sand, silt and
clay. The proportion of these particles in the soil dictate the suitability of
the soil for agricultural activities. The porosity of soil depends on the pore
size and pore density, that determines the field capacity of any soil. Field
capacity b14  is the remaining VWC in the soil after two to three days of a
rainfall, when most of the water is drained by the gravity. While determining
the field capacity, it is assumed that no water is used by plant roots or
evaporated. Therefore it is preferable to estimate the field capacity in
winter so that the chances of water evaporation are minimum. Field capacity
depends highly on the composition of particles in the soil. For example the
sandy soil has a much smaller field capacity than the soil with clay
particles, as the water gets drained much quickly in sandy soil than the soil
with clay particles.

###  3.2 Need for Alternate Sensors

The soil's VWC is a localized observation, and multiple nodes are needed to
analyze large areas. The cost of a single 5TM VWC sensor ranges from Euro 180
to Euro 220, depending on the vendor. It is not a practical solution to deploy
a large number of such expensive sensors in a large agricultural field.
Therefore, an investigation into alternate solutions is required to reduce the
deployment cost for agricultural monitoring. Table 1 shows all the soil
sensing sensors and the subsequent section explains the principal of these
sensors in detail.

Table 1: Sensor Details. Sensor Name | Measurement | Price
---|---|---
DS18S20 (OneWire)b15  | Temperature | €15.5b16
SHT10b17  | Temp & Humidity | €54b18
YL-69 | Moisture | €1.3b19
SEN13322b20  | Moisture | €4.9b21
5TM Decagonb13  | VWC | €180b23

###  3.3 5TM Decagon Sensor

5TM decagon is one of the most reliable and expensive sensors used for VWC
monitoring. The sensor uses the time domain reflectometry (TDR) method for
measuring the dielectric permittivity of the soil. It measures the time taken
by an electromagnetic pulse to go through a transmission line and return back.
This time taken is related to the dielectric permittivity $\kappa$ using
Equation 1 b24 .

$\kappa=(\frac{tc}{2L})^{2}$ (1)

where, $L$ is the length of the transmission line, $c$ is the speed of light
and $t$ is the time taken by the electromagnetic pulse.

The Topp's equation b25  is:

$VWC=4.3\cdot 10^{-6}*\varepsilon_{\mathrm{a}}^{3}-5.5\cdot
10^{-4}*\varepsilon_{\mathrm{a}}^{2}+2.92\cdot
10^{-2}*\varepsilon_{\mathrm{a}}-5.3\cdot 10^{-2}$

where $\varepsilon_{\mathrm{a}}$ is the dielectric permittivity value reported
by the 5TM sensor. The VWC values obtained by substituting the dielectric
permittivity values are considered as ground truth.

###  3.4 Alternate Sensors

YL-69 is a low cost sensor used to measure the moisture of the soil. The
sensor has both digital and analog outputs. The sensor measures the soil
resistivity by passing current between its two prongs. The increase in
moisture will offer less resistance, resulting in higher current and
eventually higher values at the output of the sensor.

SEN-13322 is also a moisture sensor and follows the same measurement principle
as the YL-69 moisture sensor. The SEN-13322 only gives an analog output which
can be used to calculate the moisture in the soil.

The SHT10 sensor measures the humidity and temperature. The sensor has an
inbuilt 14 bit A/D converter for temperature measurements and 12 bit A/D
converter for humidity measurements. The sensor has a serial interface that
can be connected to any microcontroller.

DS18S20 sensor is used to measure the temperature of the soil. The use of a
standalone temperature sensor allows to cross validate the data from other
sensors used for soil monitoring. DS18S20 also has a built-in 9 bit A/D
converter and uses a 1-wire protocol to communicate with any microcontroller.

##  4 Experimentation Setup

In order to cross validate the proposed hypothesis, an experiment was
performed at the ReviTec site b6 . Although the experimental field is only
composed of sand particles but any soil type can be used for the experiment as
it will only affect the slope of rising and falling values in VWC. The
experiment was carried out from June 29, 2017, to July 10, 2017 when the
weather conditions were feasible for the field capacity estimation. A total of
7262 observations were recorded.
The low cost sensors as well as a Decagon 5TM-VWC-Temperature sensor mentioned
in Section 1 are attached to our MoleNetb27  sensor node and are placed inside
a waterproof box.

Figure 1: Experimental setup for gathering soil data

The sensor node samples the data from all the sensors every two minutes and
sends the information to the base station.

Two MoleNet sensor nodes equipped with all the mentioned sensors are buried at
a depth of 30cm. The internodal distance between the buried nodes is kept
relatively small (1m) to have similar kind of data to be used for the ground
truth later on. An aboveground base station is used for receiving the packets
from buried sensor nodes.

###  4.1 Observations

During the experimentation period, it rained multiple times. The actual
rainfall data for the experimentation period is taken from a weather station,
located 1.5km away from the experimental field. Figure 4.1 shows the data from
the VWC sensor against the rainfall data during the experiment. The rainfalls
and the dry period in between allowed precise field capacity estimation. The
initial peaks in the graph validate the heavy rainfall after the initial
deployment of the sensor nodes. The last peak in VWC data does not perfectly
reflect the amount of rain shown in the graph. One possible reason can be the
location of the weather station that is approximately 1.5km away from the
experimental field.

Figures 4.1, 4.1 and 4.1 show the temperature, moisture and humidity data
against the VWC data respectively. The reason for the dissimilar values of the
deployed moisture sensors in Figure 4.1 is the different measuring principle
of both sensors. Therefore raw sensor values are used instead of converting
them into respective moisture values. The data from all the low cost sensors
is then used for regression modeling.

Figure 2(()): 5TM VWC Sensor and rainfall data

Figure 2(()): Temperature and 5TM VWC Sensor data

Figure 3(()): Moisture and 5TM VWC Sensor data

Figure 3(()): SHT10 Humidity and 5TM VWC Sensor data

###  4.2 Estimated Field Capacity

Figure 4.1 shows that, after the first rainfall, there was no rain till July
2nd, 2017. Although the experiments are performed in summer, Figure 4.1 shows
that the temperature after the rain remained below 20°C until the next
rainfall and also there is not much vegetation on the experimental field.
Therefore, it can be assumed that most of the water is drained by gravity. The
field capacity of the experimental field is approximately 5.5%.
In the subsequent section, the data collected from all low cost sensors is
used to predict the VWC data and eventually the field capacity of the
experimental field.

##  5 Model Fitting

Regression based model fitting is used to find a relationship between a
response variable i.e. volumetric water content (VWC) against one or more
predictor variables i.e. temperature, humidity and moisture sensor values. In
current work, Support Vector Machine Regression (SVR), Random Forests and
Artificial Neural Networks (ANNs) are used for regression based model fitting.
K-fold cross validation is used for the validation of the predicted model over
the test data. Root mean square error (RMSE), mean absolute error and Pearsons
Coefficient R parameters are used. The subsequent section will briefly explain
these performance evaluation parameters.

###  5.1 Performance Evaluation Parameters

Root mean square error (RMSE) and mean absolute error (MAE) are the two most
used parameters to determine the accuracy of the predicted model to the actual
model. RMSE calculates the square root of the average of square differences
between the predicted data and actual data. Equation 2 shows how to calculate
the RMSE.

$RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(x_{i}-\hat{x_{i}}\right)^{2}}$ (2)

where $x_{i}$ is the actual data and $\hat{x_{i}}$ is the estimated data.
Whereas, MAE calculates the average magnitude of the error in the estimated
dataset. Equation 3 shows how to calculate the MAE.

$MAE=\frac{1}{n}\sum_{i=1}^{n}|x_{i}-\hat{x_{i}}|$ (3)

Pearson correlation coefficient (R) measures the correlation between two
datasets, in our case the actual dataset and the predicted dataset. A value of
R equal to 1 indicates a strong correlation between the actual and predicted
dataset, while a value equal to zero indicates no correlation between two
datasets. Equation 4 shows how to calculate R.

$R=\frac{n\left(\sum x\hat{x}\right)-\left(\sum
x\right)\left(\sum\hat{x}\right)}{\sqrt{\left[n\sum x^{2}-\left(\sum
x\right)^{2}\right]\left[n\sum\hat{x}^{2}-\left(\sum\hat{x}\right)^{2}\right]}}$
(4)

###  5.2 Support Vector Regression (SVR)

Support vector regressors (SVRs) are a class of machine learning algorithms
which is based on the functions of the kernel based learning. The Support
Vector Regression (SVR) follows the same principles for the regression as the
support vector machine (SVM) does for the classification of the dataset.
However, in case of regression the possibilities are infinite in the output
class. Therefore, a tolerance error (epsilon) is introduced in order to
approximate the SVM. SVR strives to minimize the generalization error bound
rather than minimizing the observed training error which results in better
generalized performance b28 .
SVR uses different kernel functions i.e. polynomial, radial base function
(RBF)b29  and sigmoid. Equation 5 shows the gausian radial basis function. The
kernel functions in SVR transform the data into a higher dimensional feature
space in order to perform the linear separation.

$K(x_{i},\hat{x_{i}})=exp\big{(}-\frac{{||x_{i}-\hat{x_{i}}||}^{2}}{2\sigma^{2}}\big{)}$
(5)

#### Results

Support vector machine regressor (SVR) uses the input from all the low cost
senors i.e. DS18S20 temperature, SHT10 humidity, SHT10 temperature, YL-69
moisture and SEN13322 moisture sensor, in order to predict the volumetric
water content (VWC) and field capacity of the soil under observation. Radial
basis function kernel is used to train the SVM.

The prediction results from the Support Vector Machine based regression
modeling are shown in Table 2. The predicted values in Figure 4 show
significant variation even during the stable phase of the VWC data. Therefore,
estimation of field capacity is not possible using Random forests.

Figure 4: SVR based VWC Prediction using all inputs Table 2: Performance indicators for SVR based VWC prediction Sensor Cost | 75.7€
---|---
Algorithm | SVR
Training Input |  | DS18S20 and SHT10 (Temperature),
---
YL-69 and SEN13322 (Moisture),
SHT10 (Humidity)
RMSE | 0.00927354
MAE | 0.00564785
Pearson's R | 0.40901482

###  5.3 Random Forests

Random Forest is an ensemble based machine learning algorithm and is a
combination of multiple decorrelated decision trees.

In case of the regression based tree, the target is a real number instead of a
class and the leaf node corresponds to a real number. A Random Forest model
trains multiple decision trees simultaneously where each training strives to
minimize a cost function i.e. mean square error or mean absolute error in case
of regression modeling.

Figure 5: Random forest based VWC Prediction using all inputs

For the purpose of training Random Forest model, the Scikit-Learn b30
learning method is used. Initially all the input variables i.e. DS18S20
temperature, SHT10 humidity, SHT10 temperature, YL-69 moisture and SEN13322
moisture are used for training the model. All the inputs are normalized and
the mean and standard deviation of all the parameters of the training and
testing sets are calculated. Table 3 shows the configuration parameters used
for training the Random Forest based regression model.

Table 3: Configuration Parameters for Random Forest Parameter | Value
---|---
Number of Estimators | 24
Number of Leaf Nodes | 30
Maximum Depth | 7

Root mean squared error (RMSE), mean absolute error (MAE) and Pearson's
correlation coefficient (R) are used as the performance evaluation parameters
for the learned model. In order to avoid overfitting of the learned model over
the training dataset, five fold cross validation method is used. The entire
dataset is divided into 5 equal subsets. One subset is held out while the
remaining four subsets are used to train the regression model and the
resultant model is used to make predictions over the held out subset. The
whole process is repeated five times, once for each of the five subsets.

#### Results

The prediction results from the Random Forest based regression modeling are
shown in Table 4. The predicted values in Figure 5 show significant variation
(even more than SVR) even during the stable phase of the VWC data. Therefore,
estimation of field capacity is very difficult using Random forests.
In case of decision trees and Random Forests, the predictions are a limited
number of discrete values, depending on the number of leaf nodes. Therefore,
the only axis aligned separation is possible with Random Forests, as visible
from the horizontal lines in the 'Predicted Value' curve. For improved
regression modeling using Random Forests, the number of leaf nodes should be
increased manifolds which further would increase the complexity of the model
significantly.

Table 4: Performance indicators for Random Forest based VWC prediction Sensor Cost | 75.7€
---|---
Algorithm | Random Forest
Training Input |  | DS18S20 and SHT10 (Temperature),
---
YL-69 and SEN13322 (Moisture),
SHT10 (Humidity)
RMSE | 0.00907407
MAE | 0.00621031
Pearson's R | 0.47870054

###  5.4 Gradient Boosting Regression

In order to improve the prediction results of the random forests over the
stable area of the volumetric water content, gradient boosting regression
technique is used. Gradient boosting is an ensemble technique in which
predictions are made based on the weak predictions of a regression technique
i.e. decision trees. Table 5 shows the configuration parameters for our
gradient boosting regression model.

Table 5: Configuration Parameters for Gradient Boosting Regression Parameter | Value
---|---
Random State | 0
Number of Estimators | 100
Maximum Leaf Nodes | 25
Maximum Depth | 3

#### Results

Figure 6 shows the results of gradient boosting regression. The model improves
the predicted values in the stable regions of the volumetric water content as
compared to predictions based only on Random Forests. The pearson constant in
table 6 also shows improvement in the Pearson's R coefficient value, hence
validating the improvement in the predictor as compared to Random Forests
regression modeling. However, the results in the stable region of the
volumetric water content are dissimilar to the actual values of the volumetric
water content making it difficult to accurately estimate the field capacity of
the soil.

Figure 6: Gradient Boosting Regression based VWC Prediction using all inputs Table 6: Performance indicators for Gradient Boosting Regression based VWC prediction Sensor Cost | 75.7€
---|---
Algorithm | Gradient Boosting Regression
Training Input |  | DS18S20 and SHT10 (Temperature),
---
YL-69 and SEN13322 (Moisture),
SHT10 (Humidity)
RMSE | 0.00860634
MAE | 0.00559653
Pearson's R | 0.53127975

###  5.5 Artificial Neural Networks (ANNs)

Artificial Neural Networks (ANNs) are a class of machine learning algorithms
that can also be used for classification as well as regression modeling.

In the current work, the back-propagation algorithm is used for training the
ANN. A neural network is initialized with random weights and then iteratively,
based on the prediction error, gradient flows backward and corrects the
randomly initialized weights till the model gives predictions with acceptable
accuracy.

In current work, Keras b31  with Tensorflow b32  backend is used to train the
ANN. An ANN with 9 hidden layers (higher number of layers led to insignificant
increase in performance) is used for regression based model fitting. All the
inputs are normalized in the same way as it is done for the Random Forests.
Exponential Linear Unit (ELU) b33  is used as the activation function.

The weights of an ANN are initialized to non zero values to break the
symmetry. He normal b34  initializer is used to initialize the kernel.
According to He normal initialization, the weights should be drawn from a
truncated normal distribution centered on 0 with $\sigma=sqrt(2/n)$ where $n$
is the number of input units. The advantage of using this initialization is
that it ensures that all neurons in the network initially have approximately
the same output distribution and this improves the rate of convergence. In the
current configuration, biases are set to zero. L2 regularization is used to
avoid the overfitting problem. It penalizes the squared magnitude of all
parameters directly in the loss function.

Batch Normalization b35  is applied immediately after all fully connected
layers at the beginning of the training, forcing the activations throughout
the network to take on a unit Gaussian distribution. Batch Normalization makes
Neural Networks significantly more robust against bad initializations. The
mean squared error loss function is used to quantify the error for training
the model. The Adam b36  learning rate rule, which is an adaptive learning
rate method, is used to further increase the convergence rate.

In the adaptive learning rate method, weights that receive higher gradients
have their effective learning rate reduced, while weights that receive small
updates have their effective learning rate increased. Each model is trained
for 150 epochs and in batch sizes of 128 samples with overlapping samples in
subsequent batches..

#### Results using all sensors

Initially, the data collected from all the low cost sensors i.e. DS18S20
temperature, SHT10 humidity, SHT10 temperature, YL-69 moisture and SEN13322
moisture is used to train the ANN. Figure 7 shows the results for the
predicted value against the actual VWC value and Table 7 shows the performance
indicators for the same classifier. The Pearson's correlation coefficient R is
0.224, that is significantly small even compared to the regression based model
generated by Random Forests. One reason can be the presence of DS18S20 and
SHT10 temperature sensors data in the input because they have the least
correlation with the VWC data. But the predicted value shows better
correlation than Random Forests during the stable phase of the actual VWC
data. Therefore field capacity can still be estimated from the predicted VWC
data. The predicted VWC yields a field capacity of approximately 5.8%.

Figure 7: ANN based VWC Prediction using all inputs Table 7: Performance indicators for Neural Networks based VWC prediction Sensor Cost | 75.7€
---|---
Algorithm | Neural Networks
Training Input |  | DS18S20 and SHT10 (Temperature),
---
YL-69 and SEN13322 (Moisture)
SHT10 (Humidity),
RMSE | 0.01128973
MAE | 0.00691554
Pearson's R | 0.22410135

#### Results without temperature sensor

To cross validate this, temperature sensors data is discarded while training
the ANN. The data from all the other low cost sensors is used for training the
ANN. Figure 8 shows the predicted value against the actual VWC value and Table
8 shows the value for different performance indicators. The Pearson
correlation coefficient R increases from 0.224 to 0.4857 and the approximated
field capacity is 5.7%.

Figure 8: ANN based VWC Pediction using all sensors except DS18S20 Table 8: Performance indicators for Neural Networks based VWC prediction Sensor Cost | 60.2€
---|---
Algorithm | Neural Networks
Training Input |  | SHT10 (Temperature),
---
YL-69 and SEN13322 (Moisture)
SHT10 (Humidity)
RMSE | 0.01049934
MAE | 0.00650796
Pearson's R | 0.48575855

#### Results using only moisture sensors

Finally, only the data from the moisture sensor YL-69 and SEN13322 is used as
an input for training the ANN. Figure 9 shows the predicted value against the
actual VWC value and the performance indicators in Table 9 show significant
improvement for the aforementioned configuration of inputs. The Pearson's
correlation coefficient R for this configuration is equal to 0.7305 and shows
maximum correlation among all the earlier configurations between the predicted
and actual value for the VWC. The predicted value not only shows better
correlation during the transient phase of the actual VWC data but also shows
significantly less variation in the field capacity measuring region. The
estimated field capacity from the predicted VWC data is approximately 5.6%.
Table 10 shows the summarized comparison of all the algorithms with different
configuration of inputs. Regression based on ANNs with only moisture sensors
not only reduces the overall cost of the sensors, but also improves the
estimation accuracy of the field capacity as compared to all other
configurations.

Figure 9: ANN based VWC Prediction using moisture sensor YL-69 and SEN13322 Table 9: Performance indicators for Neural Networks based VWC prediction Sensor Cost | 6.2€
---|---
Algorithm | Neural Networks
Training Input | YL-69 and SEN13322 (Moisture)
RMSE | 0.00853104
MAE | 0.00566044
Pearson's R | 0.73053613

##  6 Conclusion

The proposed method allows much more dense deployment of the sensor nodes and
hence better field capacity profile estimation of the agricultural fields.
Using low cost sensor i.e. YL-69 and SEN13322 moisture sensors, the VWC and
field capacity of the soil can be estimated. Hence, the cost of the sensors
used for soil monitoring can be significantly reduced, that can help the
common farmers to use soil monitoring approaches in their agricultural fields
for better crop production. Also the current approach with extended
observation datasets will help the farmers and researchers to estimate,
predict and better understand the behaviour of different soils under
observation.

|  | DS18S20
---
(T)
| SHT10
---
(T)
| YL-69
---
(M)
| SEN13322
---
(M)
| SHT10
---
(H)
| Sensors
---
cost (€)
RMSE | MAE | Pearson's R |  | Field Capacity
---
Actual/Estimated
| Support Vector
---
Regression (SVR)
✓ | ✓ | ✓ | ✓ | ✓ | 75.7 | 0.00927354 | 0.00564785 | 0.40901482 | Not Possible
| Random Forests
---
Algorithm
✓ | ✓ | ✓ | ✓ | ✓ | 75.7 | 0.00907407 | 0.00621031 | 0.47870054 | Not Possible
| Gradient Boosting
---
Regression
✓ | ✓ | ✓ | ✓ | ✓ | 75.7 | 0.00860634 | 0.00559653 | 0.53127975 | Not Possible
| Artificial Neural
---
Network (ANN)
✓ | ✓ | ✓ | ✓ | ✓ | 75.7 | 0.01128973 | 0.00691554 | 0.22410135 | 5.5% / 5.8%
| Artificial Neural
---
Network (ANN)
✗ | ✓ | ✓ | ✓ | ✓ | 60.2 | 0.01049934 | 0.00650796 | 0.48575855 | 5.5% / 5.7%
| Artificial Neural
---
Network (ANN)
✗ | ✗ | ✓ | ✓ | ✗ | 6.2 | 0.00853104 | 0.00566044 | 0.73053613 | 5.5% / 5.6%
Table 10: Performance comparison of all the algorithms (T = Temperature, M =
Moisture, H = Humidity)

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