Cucumber plants (Cucumis sativus, cv. Saladin F1, Philipp Klein GmbH, Fürth, Germany) were cultivated in individual pots (7 x 7 x 8 cm) under a 16-hour photoperiod using white horticultural LEDs (Luxeon SunPlus 2835, 250 ±50 µmolm⁻² s⁻¹). Germination occurred in a growth tray and plants were transferred after 8–10 days to an automated drip irrigation system supplying each plant with 20mL nutrient solution twice daily. The nutrient solution comprised demineralized water enriched with calcium-magnesium supplements (CalMag, Plagron, Weert, Netherlands) and hydroponic fertilizers (Hydro A+B, Plagron, Weert, Netherlands). Plants were utilized at the five-leaf developmental stage, approximately 30 days post-sowing. Leaves were numbered according to their date of first appearance, starting from the first one labeled as order one to the fifth, labeled as order five.

Leaf spectral reflectance measurements were conducted using an integrating sphere (ISP-REF, Ocean Optics, USA) coupled to a spectrometer (Ocean HDX, Ocean Optics, USA), see Figure 1, providing a spectral range of 200nm to 1100nm with a resolution of approximately 0.75nm to 1.2nm. Measurements were calibrated for instrument nonlinearities and dark- current correction according to manufacturer specifications. Illumination was provided by a deuterium-halogen lamp (DH-2000, Ocean Optics, USA) guided via fiber optics into the integrating sphere. Stray light and back-reflections were minimized using a custom-built black light trap lined with highly absorptive Musou Black felt (Koyo Orient, Japan; absorbance > 99.9%). Reflectance spectra were normalized relative to a Spectralon white reference standard (99% reflectance), with integration times dynamically adjusted to maintain optimal detector utilization (approximately 90% of detector saturation).

Final reflectance values were calculated as in Equation 1:

with the spectral radiant flux of the leaf probe ϕprobe(λ), the one of the white reference standard ϕwhite(λ), the dark spectral radiant flux ϕdark(λ) and the spectral reflectance of the whitestandard ρwhite(λ). Spectral measurements were limited to the range from 440 nm to 850 nm.

The analysis revealed that using five sampling points per leaf reduced the standard error of integrated reflectance from 6.9% at one point to 3.1% at five points, further decreasing to 2.1% when using ten points and reaching a minimum of 1.6% at twenty points. The sampling density of five points provided a practical balance between measurement speed and precision. Consequently, all subsequent leaf-level spectral measurements were performed using five representative points per leaf, in total 34 plants. All measured spectral reflectance data is available in the Supplementary Data. In cucumber leaves, which are larger than those of e.g. tomato or basil, pigment inhomogeneities can affect measurement results. Smaller leaves tend to average out such variation across the field of view, but for larger leaves, increased sampling density improves accuracy. This should be considered when performing similar measurements with different species.

To evaluate whether the optical properties of cucumber leaves vary systematically with leaf order, a set of established vegetation indices originally developed for remote sensing applications was calculated from adaxial reflectance spectra. These indices were not specifically designed for greenhouse crops such as cucumber, but are commonly used to estimate parameters such as chlorophyll and anthocyanin content, leaf area index (LAI), leaf mass, water status, or senescence stage (Coops and Stone, 2005). Their definitions and target variables are summarized in Table 1.

The simplest metrics are the reciprocal-reflectance indices (RR), where the inverse of reflectance at a given wavelength is used as a proxy (e.g., RR₅₃₀, RR₅₅₀, RR₇₀₀) to relate to chlorophyll (Gitelson et al., 2003). To reduce the influence of non-photosynthetic/background effects, ratio-type metrics have been introduced. The modified simple ratio (MSR) enhances sensitivity relative to simple ratios and compresses dynamic range (Chen, 1996; Chen et al., 2013). Chlorophyll index (CI) variants (Carter’s CI, Datt’s CI, and the Gitelson & Merzlyak forms) use red/red-edge (Horler et al., 1983) and NIR bands to estimate chlorophyll concentration (Carter, 1994; Datt, 1999; Gitelson and Merzlyak, 1994).

The modified and transformed chlorophyll absorption ratio indices (MCARI, TCARI) quantify absorption features around 670nm to 700nm while incorporating a reference at 550nm, thereby reducing structural/background influences (Daughtry, 2000; Wu et al., 2008). The modified normalized difference (MND) minimizes structural effects by including a structurally insensitive band near 445nm (Sims and Gamon, 2002). The red-edge vegetation stress index (RVSI) exploits reflectance differences around the red-edge region as a stress-sensitive proxy (Merton, 1999).

Beyond chlorophyll, the structure insensitive pigment index (SIPI) targets the carotenoid-to-chlorophyll balance (Pen Uelas et al., 1995), and the red-to-green index (RGI) is linked to anthocyanin content (Gamon and Surfus (1999)). Variants of the normalized difference vegetation index (NDVI) use red or red-edge bands against a reference band (e.g. at 800nm) and are frequently related to canopy greenness and LAI (Katsoulas et al. (2016); Wu et al. (2008)). Finally, the plant senescence reflectance index (PSRI) is used as an indicator of leaf age and fruit ripening (Merzlyak et al. (1999)).

The relationship between spectral metrics and leaf order (as an indicator of leaf age) was analyzed through the following systematic approach:

1. Metric computation per leaf: Metric values (x_point) were computed at each measurement location. The leaf-specific mean value was derived from five replicate measurements per leaf as in Equation 2:

2. Within-plant centering: Leaf-averaged metric values were normalized per plant by subtracting the median (Equation 3): across all five leaves, removing plant-specific systematic offsets (Equation 4):

3. Statistical Correlation: The centered values were correlated with leaf order, where a lower order number indicates an older leaf. The Spearman order correlation coefficient was used to assess monotonic relationships without assuming linearity. All calculations were performed using the SciPy library (Virtanen et al., 2020).

No data points were excluded as outliers. Potential measurement noise and biological variability were accounted for statistically by averaging five replicate points per leaf (Equation 2) and by within-plant centering (Equation 4), which removed plant-specific offsets. Since the analysis relied on Spearman rank correlations, which are non-parametric and insensitive to absolute magnitude deviations, individual extreme values exert minimal influence on correlation strength or direction.

The mean adaxial and abaxial reflectance spectra of cucumber leaves exhibit characteristic patterns associated with chlorophyll-dominated absorption in the visible range and internal structural scattering in the near-infrared (Figure 2). Across all leaf orders and measurement points, adaxial surfaces reflected more light than abaxial ones, particularly below 700nm.

In the blue region (< 500nm), average reflectance was approximately 19% on the adaxial and 14% on the abaxial surface. A distinct local maximum occurred at 550nm, with values of 26% (adaxial) and 19% (abaxial). Reflectance dropped to a local minimum near 670nm, corresponding to the red chlorophyll absorption peak before rising again toward the red-edge (Horler et al., 1983). At 700nm, reflectance reached 26% (adaxial) and 20% (abaxial), respectively.

These side-dependent differences were consistent across samples and most pronounced in the green and red spectral regions. The standard deviation across biological replicates remained relatively constant across wavelengths, indicating stable measurement conditions and low within-group variability.

The higher reflectance on the adaxial surface is likely attributable to anatomical asymmetries, including differences in epidermal structure, wax layer thickness, or palisade cell orientation. These findings establish a baseline for subsequent analyses of order-dependent reflectance variation.

To statistically assess whether these spectral differences between leaf surfaces are significant, a two-sided Mann–Whitney U test was applied at each wavelength using the SciPy library in Python (Virtanen et al., 2020). The test compared the distributions of reflectance values from all adaxial and abaxial leaf samples, respectively.

As shown in Figure 3, over 90% of all wavelengths below 700nm yielded statistically significant differences between the two surfaces (p < 0.05). Above 700nm, these differences sharply declined, with significance observed in less than 10% of the spectral range. This confirms that reflectance is strongly dependent on leaf side throughout the photosynthetically active region and should be considered accordingly in optical sensor design.

The Spearman correlation coefficients between each index and leaf order were computed and are shown in Figure 4. Most indices exhibited strong absolute correlations (|r| > 0.6), especially those related to chlorophyll content, LAI, and biomass. Indices based on spectral ratios generally yielded stronger correlations than those based on inverse reflectance, such as RR₅₃₀.

The observed correlation between order and chlorophyll-sensitive indices suggests a relationship between chlorophyll content and leaf age. This is supported by results from Liu et al., who found systematic changes in chlorophyll concentration across different leaf ages in six plant species (Liu et al., 2009).

In contrast, the Plant Senescence Reflectance Index (PSRI), which targets age-related pigment degradation in senescing tree species, did not correlate in this study. This is consistent with expectations, as young cucumber plants do not exhibit the strong seasonal pigment shifts observed in deciduous species.

Among NDVI-based metrics, all but NDVI₄₉₀,₆₂₀ (which relates to water content) were negatively correlated with leaf order. NDVI₆₈₀,₈₀₀, which reflects LAI, showed the strongest correlation among them. This negative relationship indicates increasing leaf area with developmental progression, consistent with plant growth dynamics.

Indices based on inverse reflectance at 530nm, 550nm, and 700nm had moderate negative correlations around r ≈ −0.45, which were notably lower than those of NDVI-type metrics targeting chlorophyll content. The SIPI, which combines chlorophyll and carotenoid sensitivity, showed a weaker correlation of r = 0.27. The RGI, associated with anthocyanin content, reached r = −0.53, similar to inverse single-band metrics.

In summary, most indices linked to chlorophyll, anthocyanin, and LAI showed significant correlations with leaf order, while indices associated with water or nitrogen content showed weaker relationships. Interestingly, the only metric designed specifically to estimate leaf age, PSRI, did not correlate in this context, likely due to the limited pigment variation in young cucumber foliage compared to autumn leaves of trees.

These findings suggest that several established reflectance indices may be useful for in situ estimation of leaf developmental stage. However, many of them incorporate spectral bands outside the 440nm to 740nm range. For use in sensor-based plant monitoring systems, particularly with simplified multispectral hardware, further investigations on more metrics will be required.

Beyond index-based metrics, we examined how spectral reflectance at discrete wavelengths correlates with leaf order. Spearman correlation coefficients were calculated in 20nm increments across the measured spectrum, results are shown in Figure 5.

On the abaxial leaf surface, reflectance generally decreases with increasing leaf order (i.e., younger leaves). Correlation coefficients were consistently negative and reached values below r = −0.5 across most parts of the spectrum. The strongest correlations were observed in the blue and red regions, with a minimum of r = −0.87, indicating pronounced age-related spectral changes on the abaxial side.

In contrast, reflectance on the adaxial surface exhibited weaker and more wavelength-dependent correlations. In the blue (<500nm) and red absorption bands (640nm to 680nm), no significant correlation was detected. Slight positive correlations were observed in the green spectral range between 520nm and 620nm, with a maximum of r = 0.43 around 540nm. A minor negative correlation also appeared near 740nm. These results suggest that adaxial reflectance shows only a weak association with leaf age, primarily in the green spectral region.

Figure 5 highlights the spectral intervals where statistically significant correlations (p < 0.01) were found. In particular, the ranges around 520nm to 580nm and near 700nm yielded the most consistent relationships with leaf order.

Overall, the analysis demonstrates that reflectance–order correlations are wavelength-dependent and leaf-side specific. While the abaxial side exhibits stronger monotonic trends, especially in pigment-absorbing bands, the adaxial side provides localized but weaker correlations. These findings further support the selection of narrowband spectral regions for sensor-based leaf age monitoring.

Several established vegetation indices yielded strong correlations with leaf order when computed from adaxial reflectance data. However, many of these indices include wavelengths above 740nm, which are outside the PAR spectral range and could not be present in solely artificial lighting cultivation systems. In addition, the previous spectral analysis showed that reflectance-based metrics in the PAR region can still exhibit informative correlations with leaf order.

To systematically evaluate which spectral combinations carry the strongest ontogenetic signals, we computed pairwise reflectance ratios for all measured wavelengths between 440nm and 740nm in 20nm increments. The general formula for spectral ratios is:

Here, λ_num and λ_den denote the wavelengths at which reflectance ρ(λ) is evaluated for the numerator and denominator of the ratio, respectively.

Spearman correlation coefficients between each spectral ratio and leaf order were calculated. The resulting correlation maps are shown in Figures 6, 7 for abaxial and adaxial reflectance, respectively. Note that the visualizations differ from conventional correlation matrices: axes represent numerator and denominator wavelengths instead of distinct variables.

Figure 6 shows that several abaxial spectral ratios exhibit strong correlations with leaf order, particularly when the numerator or denominator includes 440nm, 720nm, or 740nm. The strongest absolute correlation (r = −0.835) was observed for the ratio ρ(720nm)/ρ(640 nm), although this value remained below the correlation achieved by the pure reflectance at 440nm alone.

In contrast to the direct reflectance values shown previously, spectral ratios from adaxial reflectance produced significantly higher correlation coefficients (Figure 7), reaching up to r = 0.741, compared to a maximum of r = 0.433 for single wavelengths. On the adaxial side, however, the specific wavelength combinations had a greater influence on correlation strength. For example, ratios involving 720nm yielded strong correlations only when paired with 540nm or 560nm.

These results suggest that appropriately chosen spectral ratios can enhance sensitivity to leaf ontogeny, especially for adaxial reflectance. While single-wavelength metrics may suffice in some cases, ratio-based metrics allow for improved robustness and potentially better sensor integration within the 440nm to 740nm range.