In Figure 1, a plant leaf cut scheme is shown where it can be noticed that the different plant tissues (parenchyma, mesophyll and guard cells) which have low CO₂ contents and a high amount of water. The atmosphere, presented as a gray cloud constitutes a relatively dry environment that can eventually dehydrate or even kill the entire plant if the environmental conditions are not adequate [1]. The stomata guard cells which are the orange ones in Figure 1, are the plant system that controls the stomatal pores open and close process to balance the CO₂ and water fluxes between the plant and its environment. Here r_b is the boundary resistance and r_s is the stomatal resistance.

As was aforementioned, E is a function that depends primarily on the difference between e_i and e_o. However, primary humidity sensors provide relative humidity measurement values [6] and need to be converted into e_i and e_o. First, it is necessary to determine e_s in order to know the maximum amount of water that air can contain at a specified T_a by using vapor curves in the Mollier thermodynamic diagrams [2] or by using the simplified equation (1) as was previously reported [19]. Then e_i and e_o can easily be obtained with (2) and (3), where RH_i is air input RH and RH_o is leaf chamber output RH. (1) e s = 6.13753 × 10 − 3 exp ( T a 18.564 − T a 254.4 T a + 255.57 ) (2) e i = ( RH i ) ( e s ) 100 (3) e o = ( RH o ) ( e s ) 100

In order to estimate E; it is necessary to calculate another important factor, W which is the mass flow rate per leaf area, expressed in mol/m²/s for open flow systems. W equation is stated in (4), where P is the atmospheric pressure in Bar, V is the volumetric air flow in liters per minute (lpm), T_aK is air temperature in Kelvin (K) and A is leaf area in cm², which is often used the effective leaf chamber area in transpiration and photosynthesis measurement systems [19]. The 2005.39 constant is an adjusted coefficient to change mass units to mol, surface to m² and time from minutes to seconds: (4) W = ( 2005.39 ) ( V ) ( P ) ( T a K ) ( A )

Once e_i, e_o and W were estimated, E can be calculated as established in (5) and expressed in mg/m²/s: (5) E = ( W ) ( 1000 ) ( 18.02 ) ( e o − e i ) ( P − e o )

Stomatal conductance is another important transpiration dynamic variable that represents the guard cells vapor conductivity [1,2,5]. It can be estimated from primary temperature and RH sensors data. The first step is to calculate the leaf saturation vapor pressure e_leaf as a function of T_leaf. For this purpose, (1) can be used to calculate e_leaf substituting T_a by T_leaf to obtain (6). r_b is considered a constant of 0.3 m²s/mol. Once e_leaf is obtained, stomatal conductance (C_leaf) can be calculated by using (7), expressing the result in mmol/m²/s as was previously utilized [19]: (6) e leaf = 6.13753 × 10 − 3 exp ( T leaf 18.564 − T leaf 254.4 T leaf + 255.57 ) (7) C leaf = W ( e leaf − e o e o − e i ) ( P − e o P − R b W ) ( 1000 )

VPD is a variable that represents the margin between air vapor pressure and air saturation vapor pressure. If air RH is low, VPD has a large margin; but if RH is high VPD is low and it is easy to get undesirable condensation conditions [6]. To calculate VPD it is necessary to subtract e_i from e_s. The most common units to represent VPD are kPa [2]: (8) VPD = e s − e i

Transpiration smart sensing cycle methodology is shown in Figure 3. Here, the green blocks represent the open leaf chamber stages and red blocks represent the closed leaf chamber; therefore, isolating the plant leaf. Each measurement starts with the activation of the air vacuum pump and closing the leaf chamber by the servomotor controller to isolate the plant sample. The smart sensor performs a 1 min delay to wait pneumatic line flow steady state. After that, the data acquisition starts by measuring cycles of 1 Hz sampling frequency from the five primary sensors. This process is repeated to acquire 64 samples from each sensor in each transpiration measurement cycle. Once sufficient data has been acquired, the computation of transpiration dynamics are performed, data can be transferred, the leaf chamber is opened and vacuum pump is turned off to save energy. Finally, another delay is carried out to complete the 15 min duration of the entire transpiration smart sensing process. This measurement period was selected because in commercial equipment, the fastest acquisition period is 15 min and this is necessary to establish the same sampling frequency to compare both sensing techniques.

In order to calculate plant transpiration E, an FPGA-based signal processing methodology is proposed and described in Figure 4. Average decimation filters of 64th order are applied to all the primary sensors signals T_a, RH_i, and RH_o in order to reduce undesired quantization noise as stated in (9), (10), and (11) and presented by [14]. Once T_{a os}, RH_{i os}, and RH_{o os} were estimated, a 1st order IIR low-pass filter (LPF) with cut-off frequency (f_c) of 1/3600 Hz is applied to obtain the filtered versions of the decimated signals known as T_{a osf}, RH_{i osf}, and RH_{o osf}. To gather E, equations (1) to (5) are computed from the filtered signals as presented in Figure 4. (9) T a os ( k 64 ) = 1 64 ∑ i = 0 64 − 1 T a ( k − i ) (10) RH i os ( k 64 ) = 1 64 ∑ i = 0 64 − 1 RH i ( k − i ) (11) RH o os ( k 64 ) = 1 64 ∑ i = 0 64 − 1 RH o ( k − i )

Stomatal conductance is advantageous because it utilizes certain factors previously calculated in the transpiration stage. A FPGA-based signal processing methodology is proposed and described in Figure 5.

Average decimation filters of 64^th order are applied to T_leaf sensor signals to reduce undesired quantization noise in the same manner as the previous stage according to (12). Once T_{leaf os} was estimated, a 1st order IIR low-pass filter (LPF) stage with f_c = 1/3600 Hz is applied to obtain its filtered version T_{leaf osf}. Consequently, e_leaf is calculated as stated in (6) and introduced in (7) to obtain C_leaf : (12) T leaf os ( k 64 ) = 1 64 ∑ i = 0 64 − 1 T leaf ( k − i )

VPD estimation is very simple once e_s and e_i are calculated in the transpiration calculation stage. VPD is obtained from the subtraction stated in (13). VPD implementation can be noted in Figure 6: (13) VPD = ( 100 ) ( e s − e i )

LATD calculation requires subtracting the filtered air temperature and filtered leaf temperature. As occurred in previous calculation stages, once T_{a osf} and T_{leaf osf} was calculated, LATD computation is simple by using (14), as demonstrated in Figure 6: (14) LATD = T a osf − T leaf osf

To measure ambient light in a smoother signal manner, the same average decimation filter (15) plus 1st order IIR LPF with f_c = 1/3600 Hz was applied to the signal light in order to obtain its improved version light_osf: (15) light os ( k 64 ) = 1 64 ∑ i = 0 64 − 1 light ( k − i )

The experimental setup can be seen in Figure 7, which shows the development of a smart sensor setup and the commercial Phytech PTM-48M, see Figure 7a and Figure 7b used for performance comparisons. For this experiment, tomato (Lycopersicon esculentum) plants were chosen as biological material to measure transpiration responses in the proposed smart sensor testing. The proposed smart sensor consists on an instrumentation platform capable of measuring T_a, T_leaf, RH_i, RH_o and Light. To measure temperature readings, Honeywell Pt1000 RTD primary sensors were used which have a measurement range from −200 °C to 540 °C, but are configured for a 0 to 65 °C range with an accuracy rate of ±0.3 °C considered suitable for plant temperature ranges [10]. A RTD-signal conditioning system was developed to convert the resistance variation into a 0 to 5 volt format. For RH measurements, Honeywell HIH-4000 capacitive RH sensors with a range from 0 to 95% RH and accuracy of ±2.5% were selected and connected through a developed RH-signal conditioning system [11]. Ambient light measurement is achieved by using an OSRAM SFH-5711 light sensor with range from 0 to 100,000 lux and an accuracy of ±0.04% of its measured value, providing a 0 to 50 μA current signal [25], converted into 0 to 5 V by a designed light-signal conditioning system. The results are suitable in order to measure light intensities in rooms from total darkness to complete sunlight. Each primary sensor reading passes through a 2nd order analog anti-alias LPF with 20 Hz cut-off frequency embedded in the proposed smart sensor. An eight channel 12-bit data acquisition system based on the Burr Brown ADS7844 analog to digital converter instrumentation platform was developed to read the primary sensors [26]. An FPGA based hardware digital signal processing unit was utilized to compute the transpiration response variables from the primary sensors readings based on an Altera Cyclone III EP3C16F484C6N device with 16,000 LE [27]. For the open/close leaf chamber mechanism, a miniature servomotor model E-Sky 000155 was utilized because of its low power consumption. The air flow was induced using a dc-motor piston based vacuum pump. The FPGA IP core was implemented in VHDL language, integrating the DAS driver, leaf chamber motors control, signal processing unit and communications blocks.

The experiment was designed to monitor transpiration variables every 15 min to compare the proposed smart sensor with a Phytech PTM-48M photosynthesis and transpiration monitor configured at its fastest sampling period which is 15 min [18]. Both were connected to the same tomato plant to prove the effectiveness of the proposed smart sensor. The experiment ran for 24 hours beginning at 12:00AM and finishing at 12:00AM of the next day. It permits the acquisition of four measurement cycles per hour for a total of 96 measurements every 24 h. As was aforementioned, each measurement cycle acquires 64 samples from each primary sensor at a sampling frequency of 1 Hz to apply the 64th averaging decimation filters. The data can be sent to a data server for massive storage via an Analog Devices ADM3232 RS232 transceiver [28].

In this subsection, a comparison between the T_a and RH_i readings from the proposed smart sensor and the commercial PTM-48M is presented. Figure 8 illustrates this comparison where blue signals correspond to PTM-48M readings and red ones to the proposed smart sensor primary readings. Here, it can be noted that a similar tendency occurs for both measurements, but a lower amount of noise in the red signals is present due to the 64-sample average decimation filters and 1st order IIR filters that reduces undesirable variations. In this manner, the filtering advantages of the smart-sensor signal processing can be clearly noticed. RH_o, T_leaf, and Light readings are not compared because PTM-48M does not provide RH_o measurement in the data output table and does not have T_leaf and Light sensors.

This subsection shows a comparison between the proposed smart sensor transpiration estimation and the reference PTM-48M. In Figure 9, this comparison is represented by using blue for the PTM-48M transpiration signal and red for the smart-sensor transpiration estimation signal. Here, it is noteworthy that a similar transpiration signal behavior between both instruments occurs.

The proposed smart sensor fuses T_a, T_leaf, RH_i, Rh_o and Light measurements in a single device which is considered highly desirable for precision agriculture applications to be able to monitor different environmental factors that can affect the crops. In Figure 10, the monitoring results of the primary sensors in this experiment are presented. All of these were previously oversampled 64 times for the average filtering process and passed through an IIR 1st order LPF with a cut-off frequency of f_c = 1/(3600). As it can be seen, the amount of noise in these primary signals is very low.

In Figure 11, transpiration dynamics response variables (E, C_leaf, LATD, and VPD) can be observed. These parameters share a similar dynamic behavior because they are related to the entire photosynthesis and transpiration processes which involve different phenomena.

The computation of the required equations to obtain these results is achieved using FPGA reconfigurability and open architecture that permits implementation of any digital system such as data acquisition, memory management, signal processing, and data communication. The developed smart sensor fuses five primary sensors and can measure the necessary environmental variables to calculate transpiration dynamics and permits the user to observe and record different primary and response measurements at the same time and the relationship between these. This is very useful in precision agriculture in order to detect abnormal conditions. In contrast, commercial equipment as noted in [18,19] can measure time series of transpiration information; however, they do not provide the readings for all the primary sensors. In some cases, they are not equipped with the necessary sensors. The FPGA-based unit permits improvements of the primary sensor signals by oversampling and digital filtering that is consequently reflected in superior accuracy, and overall transpiration variables signal quality. The integration of these elements merge different variables at the same time that can be acquired and used to take specific control actions by communicating these transpiration measured values to other systems via RS232 interface like PC data servers, an irrigation controller, or a climatic control unit due to the online processing and remote communications capabilities of the proposed smart sensor. Taken together they constitute a smart sensor solution to monitor transpiration variables in precision agriculture applications by using a single FPGA-based system.