The block diagram of the experimental setup in the laboratory is presented in Figure 1 . It consists of four units: the power unit, sensing unit, processing unit, and display unit. The power unit includes a direct current power supply, specifically the GWINSTEK GPS-4303C model, which is crucial for powering other essential system elements. The sensing unit comprises an optical sensor, detailed in the block diagram in Figure 2 . As shown, the sensor is made up of two sub-units: the transmission and detection units. The transmission unit contains LEDs,

while the detection unit includes a photodiode. Specifically, the LEDs used are infrared, red, and blue, which detect the concentrations of Nitrogen, Phosphorus, and Potassium, respectively, due to their corresponding optical features (same absorption wavelengths) as specified in Table 1 . These LEDs emit visible and infrared optical radiation to experimental samples. The photodiode in the detection unit absorbs light reflected from the experimental samples, producing an output voltage proportional to the reflected light. To minimize the impact of ambient-light interference, all experiments were conducted inside a dark, enclosed box specifically designed to eliminate external light sources. Additionally, to ensure accurate sensor readings, each measurement was performed three times under varying environmental conditions, and the average of these replicates was used in the analysis.

The processing unit, primarily consisting of an ESP32 microcontroller, processes data from the sensor (reflected voltage) using sensor’s models incorporated into the program codes loaded onto the microcontroller. The models for determining the concentrations of Nitrogen, Phosphorus, and Potassium are specified in Equations (1)-(3), respectively. These models derived from calibration experiments conducted on multiple experimental samples with varying NPK concentrations. The flowchart diagram for the program code is shown in Figure 3 . As shown in the flowchart, the initial step of the program involves receiving an input signal from the sensor. These signals correspond to different optical radiation, as detailed in Table 1 . When infrared radiation is received, the model in Equation (1) is used

to determine the concentration of N in soil. If the detected optical radiations are red and blue, the models specified in Equations (2) and (3) are used to calculate the concentrations of P and K, respectively. The display unit is made up of an LCD 16 × 2, whose main purpose is to display results from the processing unit, specifically the concentration of macronutrients.

$y=18482x^2-8720.8x+1027.4$ (1)

$y=10573x^2-4042.5x+386.29$ (2)

$y=-4496x^2+20834x-2397.9$ (3)

where y is the concentration of macronutrient (N, P, or K) in percentage (%), and x is the reflected voltage in volts

One of the main factors to consider when determining the geometric parameters of optical sensors is the alignment of the different elements constituting the sensor. Since optical sensing involves the transmission of sensed signals in the form of light rays, improper alignment of the sensor elements can lead to significant external light interference [18] . By considering the alignment of sensor elements as key factors in determining the sensor’s geometric parameters, the law of reflection, which states that the angle of reflection equals the angle of incidence, can be used to determine the specific geometric parameters.

These specific parameters include optimal path length (x), angle of incidence (θi) and angle of reflection (θr), and distances between various components (d1, d2, and D). Figure 4 provides an illustrative diagram of our sensor with labelled geometric parameters. The θi was systematically varied within the range 0˚ < θi < 90˚. At 0˚, the LED points directly at the photodiode, resulting in minimal reflection, which makes accurate measurements challenging. Similarly, at 90˚, the LED points directly at the reflector (sample plate), and the photodiode aligns with the

reflector, minimizing reflected light detection due to the incident light reflecting along its original path. Therefore, angles of 0˚ and 90˚ were avoided. For each angle (30˚, 45˚, 60˚, 75˚) the corresponding x, d1, d2, and D were determined, as detailed in Table 2 .

The sample used in this experimental procedure was composed of NPK fertilizer and black soil, as illustrated in Figure 5 . Initially, the experimental sample was air-dried to remove moisture content and then pulverized into a fine powder using a blender. Afterward, the powdered sample was sifted through a sieve to eliminate any sizable particles that might disrupt measurements. Finally, the sample was chemically analysed to determine the exact concentrations (also known as reference concentrations) of Nitrogen, Phosphorus and Potassium as detailed in Table 3 . Nitrogen analysis involved combusting the analytical samples at 10,500˚C in a helium and oxygen atmosphere. The nitrogen content was converted into

various nitrogen oxides, which were subsequently reduced to molecular nitrogen. Quantification of nitrogen was performed using a thermal conductivity detector. For phosphorus and potassium analysis, Laser-Induced Breakdown Spectroscopy (LIBS) was employed, utilizing the reference material “Monta CRM2710 floor”. LIBS is a rapid and cost-effective technique for analyzing phosphorus and potassium in fertilizers. It works by focusing a laser onto the sample’s surface to create plasma, which is then analyzed to determine the elemental composition. These experiments were conducted at the ISA (Institute of Analytical Sciences) UMR5280, Université Claude Bernard Lyon 1.

Geometric parameters were varied (as specified in Table 2 ) and their effects on detected soil macronutrients concentration were evaluated. Figure 6 displays how the measured concentration of NPK varied with changes in the optical path length (x) and incidence angle (θ_i). Results gotten showed that these geometric parameters significantly impact measurement accuracy and sensor reliability. The variation in these parameters influences how external light interacted with the sensor,

hence affecting the signal quality and measurement precision of the sensor. Therefore, understanding these effects or change in variations is crucial for optimizing the sensor design, hence ensuring that macronutrients are detected accurately and efficiently in agricultural farmlands.

For all optical radiation, we noticed significant changes in the concentration of macronutrients (NPK) to changes in optical path length and angle of incidence. As the optical path length increased, the detected macronutrient concentration deviated from the reference concentration. This deviation is mainly due to increased light attenuation along extended optical paths, which leads to signal degradation, hence reduce accuracy. Longer optical paths amplify scattering effects, decreasing sensitivity and complicating nutrient quantification (Li et al. [19] and Alem et al. [20] ). Masrie et al. [14] and Yusof et al. [16] further emphasized the negative impact of extended optical paths, highlighting that excessive attenuation reduces the ability of the sensors to detect soil nutrients effectively.

The angle of incidence also exhibited a significant influence on sensor accuracy. Increase in angle of incidence led to greater reflection losses, decreasing the amount of transmitted light that reached the detector. This observation supports the results presented by Ahmed et al. [21] and Liu et al. [22] , which demonstrated that optimizing angle of incidence enhances the measurement stability by balancing absorbed and reflected light intensity with light transmission efficiency. These findings indicate that geometric parameter optimization is vital for improving sensor performance and ensuring reliable macronutrient detection in precision agriculture.

To determine the optimal geometric parameters, root mean square error (RMSE) values were computed for different path lengths and angle of incidence as shown in Figure 7 . The optimal optical path length and angle of incidence were determined to be 2 cm and 60˚, respectively. These optimal parameters provided the most accurate results with the least RMSE, compared to other tested conditions, hence demonstrating their effectiveness in enhancing sensor precision.

As shown in Figure 6 , the difference in macronutrient concentrations at x = 2 cm compared to the reference concentration was minimal when compared to the differences at x = 4 cm, x = 6 cm, x = 8 cm, and x = 10 cm, making x = 2 cm the optimal value. Hence larger path length resulted in significantly higher RMSE values, and this is primarily due to excessive signal attenuation and scattering effects. Prior studies by Masrie et al. [14] and Yusof et al. [16] , confirm that extended optical path lengths increase light dispersions, adversely affecting nutrient detection. It is therefore essential to select the appropriate optical path length to maintain accuracy and minimize measurement inconsistencies and error.

Similarly, an angle of incidence of 60˚ provided the highest measurement accuracy with a lower RMSE when compared to RMSE values gotten at 30˚, 45˚, and 75˚, as it optimized the balanced between reflected and transmitted light. These findings align with the observations from Ahmed et al. [21] and Liu et al. [22] , who demonstrated that optimizing the angle of incidence leads to enhanced sensor efficiency and reliability. By refining these geometric parameters, optical sensors can be more effectively tailored for agricultural applications, ensuring excellent performance across varying environmental conditions.

With the optimal path length and angle of incidence established, further analysis was conducted to assess how these parameters influence sensor accuracy and mitigate external interference in detection of soil macronutrients.

It was observed that Phosphorus exhibited a significantly lower RMSE compared to Nitrogen and Potassium. This suggests that the spectral absorption characteristics of Phosphorus aligns more effectively with the emission spectrum of the optical sensor, making its detection less susceptible to geometric variations. The least RMSE for Phosphorus supports findings presented by Kato and Nishimura [23] , who demonstrated that phosphorus is more accurately predicted in soil compared to Nitrogen and Potassium. This observation highlights an advantage in Phosphorus detection, indicating that future sensor designs may further need modified calibration methods to maximize accuracy for the detection of Nitrogen and Potassium. Additionally, percentage error calculations performed between experimental macronutrient concentrations at optimal geometric parameters and reference chemical analysis values (shown in Figure 8 ) confirmed minimal errors in Phosphorus detection. This finding is also consistent with studies conducted by Fang et al. [24] , where sensor geometry optimization was carried out to enhance target localization and nutrient measurement precision.

While the optimal geometric parameters significantly improve sensor accuracy, several challenges must be considered for real-world implementation. First, maintaining precise geometric alignment in field conditions may be difficult due to mechanical disturbances, uneven terrain, or sensor degradation over time [25] . Second, soil composition, texture, and moisture content vary across regions and can influence optical interactions with the sensor. Studies by Kato and Nishimura [23] confirm that changes in soil properties (specifically soil moisture content) significantly affect sensor readings, with dry soil exhibiting lower accuracy compared to wet soil. To address these challenges; calibration models may need to be localized or dynamically adjusted and robust sensor housing and auto-alignment mechanisms may be necessary, along with localized calibration models tailored to regional soil characteristics.