Non-Contact Monitoring of Plant Leaf Water Status Using Terahertz Waves

The water status of a plant is one of the key physiological metrics reflecting its growth and productivity. A rapid and quantitative evaluation of the plant water content is thus of significance for irrigation management, disease prevention, and yield enhancement [1]. Conventional approaches to estimating plant leaf water content, such as gravimetric and thermogravimetric measurements [2], provided accurate evaluations. However, they cannot offer real-time characterization due to their time-consuming processes and therefore are not suitable for in situ field applications. Moreover, they are not feasible for long-term monitoring of leaf water content of the same plant due to their destructive nature. Alternatively, sensor arrays [3] can be employed to monitor leaf moisture levels. However, they require physical contacts with leaves and thus resulting in relatively low measurement efficiency. In order to non-invasively monitor the plant water content, various approaches were presented, including the employment of ultrasound waves to correlate leaf transmission coefficients with its water content [4], and microwaves to build a link between leaf reflectivity and its moisture level [5]. However, the use of ultrasound waves requires advanced deep learning algorithms and a substantial amount of measurements to train the water content estimation model. On the other hand, the complex permittivity (\(\epsilon = \epsilon _\text {r} - j\epsilon _\text {i}\)) of a plant leaf at microwave frequencies is significantly influenced by the dissolved salts inside. As an alternative, the plant water content can be accurately and non-destructively evaluated using terahertz waves.

The terahertz spectral frequency range spans from 0.1 to 10 THz and possesses a myriad of unique properties [6‐8]. For instance, terahertz waves couple strongly with, and as such are highly sensitive to, hydrogen bonds in water [9, 10]. Moreover, the effect of water salinity on the leaf permittivity at terahertz frequencies is negligible [11]. These distinctive features make terahertz waves particularly useful in quantitatively assessing the water status of living leaves. However, evaluating water status based on reflections from the leaf is vulnerable to the incident angles of terahertz waves. In order to alleviate the influence of wave incident angles on the accuracy of plant water status assessment, various approaches [11‐16] were presented to evaluate the leaf water content using its transmission coefficients. However, some of them [13] acted as plant water status indicators that only revealed the plant moisture variations and cannot provide quantitative evaluations. To quantify the relative water content in leaves, an analytical model based on radiative transfer theory [11] was implemented to correlate leaf transmissivity with its relative water content. However, the model required characterization of leaf reflectivity that added measurement complexity, while the inherent inaccuracy associated with the model led to significant deviations between the calculated and measured results. Moreover, an effective medium theory [17, 18] was introduced to accurately describe the dielectric function of a plant leaf from 0.3 to 1.8 THz. However, it required mechanically pressing the dry leaf to determine the complex permittivity of leaf solid tissues, while different pressures lead to varied permittivities. On top of that, additional measurements were needed to determine the leaf area, surface roughness profiles, and the relative volumetric proportions of the leaf composition, making the approach less suitable for field applications. In [19], the effective medium theory was further developed to quantify leaf water status without measuring leaf area or surface roughness. However, it still required measuring the complex permittivity of dry leaf tissues, transmission coefficients of leaves with different known relative water contents, and relative volumetric fractions of each leaf component. To further simplify measurements, an iterative optimization approach was developed to estimate the relative volumetric fractions of each leaf component by fitting measured transmission coefficients, while assuming the leaf surface roughness and the complex permittivity of each component are known [20‐22]. This method has enabled three-dimensional water mapping in an Agave leaf [22] and allowed investigations into water retention strategies and hydration dynamics in Agave striata.

In this work, we present a study to accurately correlate the relative water content and water potential of a plant leaf with the non-destructively extracted complex permittivity measured with terahertz waves in transmission. The real part of the complex permittivity affects the propagation speed of terahertz waves transmitting through the leaf, while the imaginary part denotes wave attenuation. We found that the real part is collectively determined by the leaf water content and solid tissue density, while the solid tissue density experiences variation during leaf dehydration. Differently, the imaginary part is predominantly set by the leaf water content. As such, the imaginary part of complex permittivity is correlated with the leaf relative water content and water potential. The presented study suggests that terahertz probing can overcome some key limitations of existing methods, such as being destructive, contacting, or qualitative. It provides a direct quantitative analysis of leaf water status in a non-contact manner. It facilitates terahertz technology in field applications by establishing direct correlations among leaf complex permittivity, relative water content, and water potential through simplified measurement and data processing. Once the leaf complex permittivity is contactlessly extracted, its corresponding relative water content and water potential can be readily determined based on the correlations. This study focuses on contactless measurements at leaf regions without major veins and avoids leaf tilting and lateral or axial movements, so as to minimize measurement inaccuracies. Additionally, the presented study also introduces single-frequency empirical models that support the use of high-power narrowband sources with improved practicality for field deployments.

In order to establish relationships between the three metrics of the leaf, i.e., complex permittivity, relative water content, and water potential, in different hydration states, three indoor experiments on two living Cineraria (Senecio Cineraria) leaves are conducted simultaneously and under identical environmental conditions. The room temperature and humidity are controlled by the air conditioner, with the temperature varies from 22.3 to \(24.6^{\circ }\)C, while the relative humidity ranges from \(40.3\%\) to \(54.5\%\) over the duration of the experiment. The measured room lighting condition is \(7~\upmu \text {mol}/\text {(m}^{\text {2}}{\cdot}{\text {s}})\). Note that the Cineraria leaves are chosen as a proof-of-concept for extracting leaf key metrics; however, other types of plant leaves with different thicknesses can also be employed in the study. To minimize measurement uncertainty, leaf weight, thickness, and transmission coefficients are recorded using an accurate scale with a precision of 10 mg, a micrometre with a resolution of 1 \(\upmu \)m, and a high-accuracy characterization system, respectively. Note that instrument precisions are provided as reference values and do not represent actual measurement accuracy. Further evaluations demonstrate that the scale exhibits strong reliability and consistency, with a maximum weight measurement deviation of only \(0.05\%\) that has a negligible impact on the assessment of leaf relative water content. The characterization system consists of a Keysight vector network analyzer (VNA) and VDI extension modules (VNAX WR\(-\)3.4), and it demonstrates strong stability with transmission magnitudes remain unchanged and phase shifts less than \(9^{\circ }\) over a 20.7-h measurement period. The high-precision instruments eliminate the need of repeated experiments.

Figure 2 shows leaf 1 recorded weight variations over time, reflecting the dynamics of water diffusion from the leaf tissues and the resulting changes in hydration states. In accordance with the recorded leaf weights at different hydration states, their corresponding relative water contents can be characterized using [28]where \(w_r\) is the recorded leaf weights at different instants, while \(w_d = 0.08~\text {g}\) and \(w_t = 1.79~\text {g}\) are the dry and turgid weights, respectively. Note that the relative water content is directly determined by leaf weights, and it is not extracted from transmission coefficients. Figure 2 also illustrates the dehydration of leaf over time, measured by its relative water content. The Cineraria leaf exhibits a high rate of water evaporation in its turgid state, with its relative water content decreased to \(90.7\%\) at the start of the experimental characterization of \(t_\text {meas}=0\). This rapid water loss can be attributed to the high vapour pressure within the leaf when it is fully hydrated, which creates a significant gradient for water diffusion and evaporation [29, 30].

To accurately extract the complex permittivities of leaf 1 in various hydration states, it is essential to determine the corresponding thicknesses. Directly measuring the leaf’s thickness regularly can shift the leaf out of the focal plane of terahertz waves, leading to inaccuracies in measured transmission coefficients. Additionally, multiple measurements with applied pressure to the leaf may artificially alter its thickness. Alternatively, the leaf thickness variations can be estimated based on a relationship between the leaf weight and thickness shown in Fig. 3. It is noted that such a weight-thickness relationship is used only for establishing accurate correlations among the leaf complex permittivity, relative water content, and water potential. Leaf weight measurement is not required for field applications. The exponential relationship [11] between them can be explained by the varying rate of water evaporation in different hydration states. In the leaf turgid state, a high rate of water evaporation leads to cell collapse and thus a significant decrease in its thickness. However, as the leaf continues to lose water, the remaining moisture becomes tightly bound within the leaf cell walls and intracellular spaces [31], resulting in a less pronounced reduction in thickness. Accordingly, the leaf thickness at a specific hydration state can be mapped from its corresponding weight using Fig. 3.

Bild vergrößern

Bild vergrößern

An iterative approach [32] is implemented to extract the measured complex permittivities of leaf in various hydration states based on its transmission coefficients and measured thicknesses. Further measurements and analysis reveal that the iterative approach can estimate both thickness and complex permittivity for electrically thick samples relying on the Fabry-Perot effect. However, it cannot accurately estimate thickness for electrically thin samples such as plant leaves especially in a limited frequency range. Therefore, the leaf thickness at a specific hydration state is estimated based on its recorded weight at that state and the weight-thickness relationship in Fig. 3. A leaf can be considered a mixture of water, air, and solid tissues [20]. The real part of leaf permittivity is influenced by both water content and tissue density. The real part of the complex permittivity for water [33] at room temperature is approximately 5.51 from 220 to 330 GHz, and it is typically higher than that of solid tissues. During dehydration, the leaf loses bulk water, followed by changes in its cellular structure, such as cell collapse and the breakdown of cell membrane integrity [34]. Water loss leads to a decrease in the real part of the permittivity, while structural alternations enhance the density of solid tissues and thus increase the real part of the permittivity. Consequently, the opposing effects result in fluctuations in the real part of the leaf permittivity during dehydration as shown in Fig. 4. Specifically, as the leaf loses water, the real part of the complex permittivity at 220 GHz decreases from 3.2 at \(t_\text {meas} = 0~\text {h}\) to 1.0 at \(t_\text {meas} =8.6~\text {h}\) as shown in Fig. 4a, corresponding to a reduction in leaf relative water content from \(90.7\%\) to \(35.6\%\) in Fig. 2. Note that a value higher than 1.0 is expected for the real part of the complex permittivity, due to the presence of bound water and solid tissues in the leaf during its entire hydration process. The real part of leaf complex permittivity equals 1.0 at \(t_\text {meas} =8.6~\text {h}\) can be attributed to discrepancies in the estimated thickness. Eventually, the real part of the complex permittivity at 220 GHz increases to 1.9 due to the enhanced tissue density. The real part of the leaf complex permittivity at other frequencies share a similar trend as that at 220 GHz, as evidenced in Fig. 4b and c. On the other hand, the imaginary part of the leaf complex permittivity at 220 GHz in Fig. 4a exhibits an overall decreasing trend over time during dehydration, interspersed with minor fluctuations at around \(t_\text {meas} = 10.4~\text {h}\). The minor fluctuations result from the ripples in the recorded weight in Fig. 2, which propagate to the thickness through the weight-thickness correlation, and eventually affecting the extracted complex permittivity. The imaginary part at 220 GHz ultimately reaches a value close to 0, indicating negligible wave absorption by the leaf solid tissues. Similar variations in the imaginary part are observed at 275 GHz and 330 GHz as presented in Fig. 4b and c, respectively. Importantly, the leaf relative water content in Fig. 2 and the imaginary part of the complex permittivity in Fig. 4 exhibit a consistent behaviour, allowing for the establishment of a one-to-one correlation between them.

The leaf water potential \(\Psi _\text {leaf}\) provides crucial mechanistic insight into the forces driving water movement within leaves. It enables the quantification of the balance between osmotic and turgor pressures, while also facilitating accurate estimation of hydraulic conductance [35]. Results from continuous thermocouple psychrometer measurements of \(\Psi _\text {leaf}\) are shown in Fig. 5. The initial rise in \(\Psi _\text {leaf}\) is typical during the equilibration phase of psychrometry, as the sensor establishes a robust contact with the leaf and a hermetic seal. The highest measured \(\Psi _\text {leaf}\) is \(-1.5\) MPa that appears at \(t_\text {meas} = 1.2~\text {h}\), marking the beginning of the leaf’s dry-down phase (via excision). At \(t_\text {meas} = 6.7~\text {h}\), the leaf reaches its lowest \(\Psi _\text {leaf}\) of \(-6.4\) MPa, which is the measurement limit of the psychrometer instrument. The decline in \(\Psi _\text {leaf}\) is faster than the leaf dehydration rate presented by the relative water content in Fig. 2, indicating a weak stomatal response or low sensitivity to drying for this species.

Bild vergrößern

Bild vergrößern

Based on the synchronized measurements on the leaf relative water content, complex permittivity, and water potential across different hydration states, direct correlations between them can be established as shown in Fig. 6. As such, both the leaf water potential and relative water content can be readily evaluated from the permittivity extracted using terahertz waves at any single frequencies between 220 and 330 GHz. The established correlations enable real-time plant water status monitoring for field applications.

Bild vergrößern

Empirical models can be developed to describe the relationships between the three metrics at a specific frequency, enabling the use of high-power narrowband sources in field applications that are more portable and robust than broadband systems. As an example, Fig. 7 shows the empirical models at 220, 275, and 330 GHz. Specifically, both the relative water content and the imaginary part of the complex permittivity exhibit exponential decay during leaf dehydration, caused by non-uniform water loss over time across tissues. A simplified mathematical derivation suggests the use of third-order polynomial empirical models to effectively capture the asymmetric patterns in Fig. 7a–c, maintain model simplicity, and avoid overfitting the noise propagated from external scale vibrations in Fig. 2. The average deviations between measured and estimated relative water content at 220, 275, and 330 GHz are \(2.6\%\), \(3.1\%\), and \(3.2\%\), respectively. In the relative water content range of \(60\%\) to \(70\%\) where wilting typically occurs, the detection accuracy is \(1.4\%\). The accuracy is set by the measurement time interval rather than the iterative approach. While shortening the interval can further enhance the accuracy, it cannot surpass the inherent accuracy of each individual measurement that is collectively set by the instrument precision and experimental alignment. Further evaluations based on the measured data at 275 GHz reveal that \(\pm 10\%\) (\(\pm 20\) \(\upmu \)m) deviations from the measured thickness, potentially caused by leaf movement in the xy-plane in Fig. 1a or thickness measurement errors, can lead to a relative water content discrepancy of up to \(2.8\%\). Nonetheless, this level of accuracy is sufficient for field applications.

The measured water potential decreases nearly linearly during dehydration, and thus exponential empirical models describing the water potential as a function of the imaginary part of the complex permittivity at 220, 275, and 330 GHz are established in Fig. 7d–f, where the averaged discrepancy between measured and evaluated water potentials is merely 0.12, 0.12, and 0.15 MPA, respectively. It should be noted that the developed empirical models validate only at at a single frequency, as they rely on measured data specific to that frequency. Empirical models for other frequencies can be established accordingly using curve fitting.

It is worth noting that the presented empirical models are based on the principle that imaginary part of leaf permittivity reflects terahertz wave attenuation and is monotonically related to leaf water content. The models are frequency-specific as leaf permittivity is inherently frequency dependent. While the monotonic relationship holds across frequencies, the fitting parameters vary and need to be fitted individually at each frequency. These empirical models operate fundamentally different from effective medium theory [19, 20] and dielectric relaxation models [36] used to determine leaf water status. Specifically, the former treats the leaf as a mixture of water, air, and solid tissues, and it requires labour-intensive measurements to determine the complex permittivity and volumetric fractions of each leaf component. The latter relies on broadband frequency-dependent permittivity to capture the distinct relaxation behaviours of free and bound water in plant tissues. In contrast, the developed empirical models involve simplified measurements and support the use of high-power narrowband sources for field deployment. Importantly, as the monotonic relationship between imaginary part of leaf permittivity and water content is generally valid, the empirical models are appliable across various plant types, with frequency-specific fitting parameters reflecting the combine influence of plant structure and terahertz frequency.

To further illustrate the superiority of the presented work, Table 1 compares its performance with representative non-destructive methods used for assessing plant water status. Compared to the existing methods [37‐41] that primarily measure the leaf’s surface-level moisture, the presented work employs terahertz waves with longer wavelengths that can penetrate through the entire cross-section of the leaf to evaluate its overall water status. Additionally, the presented work exhibits improved robustness to environmental variations than the representative methods, making it well-suited for field applications.

The presented work has three associated challenges. First, the leaf under test should be placed in the focal plane of the focused terahertz beam. Despite this is a widely adopted method for leaf characterization [16, 42], a position deviation along the z-axis beyond the Rayleigh range can lead to inaccuracies in the measured transmission coefficients. In the presented experimental setup in Fig. 1a, the Rayleigh range equals 0.58 mm at 220 GHz [43, 44], and it can be increased by using a lens with a larger focal spot. However, the setup is intended to establish correlations among three key metrics and is not directly applicable to field applications. In field tests, collimated terahertz beam can be used for leaf water status evaluation, so as to make the measurement less sensitive to leaf positions. Second, the focused beams cover a measurement area of \(0.79~\text {mm}^{2}\), making real-time mapping of water distribution across a large leaf infeasible due to the single-pixel measurement. Third, the employed iterative approach for extracting the leaf complex permittivity is applicable to a single leaf characterization, limiting the efficiency in field applications. It can be envisaged that the water status of multiple overlapping leaves could be evaluated by incorporating transmission-line theory and network analysis [45, 46] into the iterative approach.

A quantitative analysis of the leaf water status using terahertz waves is conducted. The presented study correlates the leaf permittivity with the relative water content and water potential. This correlation can be used to quantify the leaf water status from terahertz imaging. Compared to the existing methods using terahertz waves, the presented study employs simplified experimental setup and data processing, facilitating the terahertz technology for field applications. The presented work can be further developed by involving a transmission-line theory and network analysis to rapidly quantify the water status of both exposed and occluded leaves. However, advanced algorithms are needed to account for leaf shifting and tilting in practical scenarios, which are not covered in the presented work. The agricultural sectors will benefit from the presented study with improved water status quantification feasibility and accuracy.