3.2. Evaluation of Ray-Tracing Simulation and Photosynthesis Estimation
In the empty growth chamber without plants, the measured and simulated light intensities corresponded well to the 1:1 line with an R
2 of 0.979 and RMSE of 0.7048 (
Figure 4A). When the plants were positioned in the growth chamber, the simulation result also reflected the measured light intensities well, with an R
2 of 0.864 and RMSE of 0.7048, but the accuracy was slightly decreased compared with that of the empty chamber (
Figure 4B).
A decreased accuracy of simulated light intensity by introduction of the plant canopy was found in previous studies that conducted the simulation using a chamber with electrical lights and plant models [
23,
28]. From our perspective, the lower R
2 value of light intensities with the plant canopy was attributed to the complexity and denseness of the plants, which can cause some errors between measurement and simulation by touching or misplacement. Because most electrical lights have the feature of direct light, light intensities between shaded and lighted areas are apparently different under light sources. Additionally, small changes in sensor position or angle can induce large differences in measured values.
At different levels of PPFD and CO
2 concentration, the measured and estimated values of canopy
Pn per unit leaf area were well matched, with an R
2 of 0.986. However, at the measurement points of low
Pn, which were measured and calculated at low PPFDs, the simulation underestimated
Pn by approximately 29% (
Figure 5).
In this study, leaf photosynthetic rates measured in the PPFD range of 0 to 1200 μmol m−2 s−1 were used to obtain the parameters of photosynthesis models (e.g., Vcmax, Jmax), whereas the canopy Pn was measured below a PPFD of 300 μmol m−2 s−1. Thus, the model parameters that can be applied for wide PPFD ranges might underestimate the canopy photosynthetic rate at low levels of PPFDs.
3.3. Quantification of Light Interception in the Growth Chamber Environment
The distributions of intercepted light at different planting densities are visually described by a color gradient along with simulation results in
Figure 6. Overall, light interception was evidently heterogeneous at each part of the canopy. In particular, in a leaf, light interception was dramatically decreased at marginal areas due to its convex curvature. In many studies using plant models and optical simulation, most structural elements, such as the angle, size, and geometrical dimensions of plant organs, were generally well considered [
13,
14,
15,
29], but detailed morphological features, such as leaf curvature, are often overlooked, which are hard to measure and digitize. However, because the exclusion of some morphological features can lead to misestimations [
18], the importance of reflecting morphological details on plant models should be emphasized.
When the planting density was changed from HD to LD, the light interception of the central plant was increased at the middle canopy height, but those of the outer plants decreased at the high canopy height by receding from the center of the light source (
Figure 7A). Consequently, the average light interception increased by approximately 18.7% at the central plant but decreased by approximately 5.5% at the outer plants; thus, the total light interception was larger for HD by approximately 2.2% (
Figure 7B).
Under natural light, planting density and canopy arrangement are the main considerations for efficient light interception because natural light is assumed to be a surface light source, uniform in illuminating areas, and uncontrollable. However, under electrical lights, changing the canopy arrangement affects not only the mutual shading between plants but also the incident light environment due to the physical light distribution [
30]. When the planting density was changed from HD to LD, light interception of the central plant was evidently expected to be increased by reduction of mutual shading, but those of the outer plants were unpredictable. In this case, the decrement in light interception by receding from the center of the light source was larger than the increment by diminished mutual shading for border plants, and consequently, whole canopy light interception was decreased for LD.
3.4. Scenario
The nature of light interception on the canopy surface was obviously changed under different light source arrangements and lighting distances (
Figure 8). For the low lighting distance, the light interception was focused on the leaves directly under the light source and was near zero on the other leaves. Meanwhile, for lighting distances over 30 cm, the light interceptions were less influenced by the light source arrangement and were overall uniformly distributed on the canopy, but some decrements in uniformity were again observed at lighting distances over 35 cm, which resulted in the lowest CV
LI at 30 cm (
Figure 8). The effect of reflective material on canopy light interception also varied between different lighting distances and arrangements (
Figure 9). On BP, the increment in light interception showed U-shaped patterns according to lighting distance, which was largest at 20 cm, with 3.13 μmol m
−2 s
−1, and lowest at 30 cm, with 2.54 μmol m
−2 s
−1. Conversely, the increment tended to be larger at long lighting distances on VAP—largest at 35 cm, with 3.06 μmol m
−2 s
−1. On average, the light interception was increased by approximately 3.6% by introducing the reflective material. As a result, the total light interception was larger on VAP than BP and was larger at 30 cm between several lighting distances in most cases (
Figure 10A). The estimated
Pn showed similar patterns with light interception (
Figure 10B), but was reversed in some cases (e.g., VAP-NR) due to low LUE
I at short lighting distances (
Figure 10C).
Light uniformity in PFELs is crucial not only for even growth between plants [
31] but also for efficient photosynthesis due to the convex shape of the light-response curve [
32]. The light concentration and overlapping on leaves derived from the emitting distribution of light sources was found in this scenario (
Figure 8), and the lack of uniformity was connected to low LUE
I, especially for intact lighting (
Figure 10C). The use of reflective material on the floor distinctly improved the light interception, but it is shown not to be the prior factor for designing a light environment because the large amount of increased light by reflection was not mostly connected to the increment in total light interception (
Figure 9,
Figure 10A). The emitting distribution affected the differences in light interception between VAP and BP, which is related to the plant structure. The lettuce is a rosette-type plant with no petiole, so the angle of the leaf surface is positive, that is, the light incidence angle is near perpendicular for VAP and near horizontal for BP. On the leaf level, light interception is highly differentiated by incidence angle and is larger for vertically emitted light [
15,
18], which results in larger light interception for VAP. In this respect, other types of plants were not simulated, but some plants having negative leaf angles can induce the opposite results under different light source arrangements.
Finally, for all scenarios, the PPFD
opt for achieving LUE
E,max was found (
Figure 11). The range of PPFD
opt was between 300 and 380 μmol m
−2 s
−1 and was mainly distributed at approximately 360 μmol m
−2 s
−1 for homogeneously intercepted cases. In this scenario, LUE
E,max was the largest at a 30-cm lighting distance with VAP-HR, and both PPFD
opt and LUE
E,max were relatively low at a 20-cm lighting distance; thus, the maximum LUE
E,max was approximately 20.3% larger than the minimum. In all cases, a larger LUE
E,max was achievable at a low PPFD
opt for HR when comparing NR and HR.
When light intensities were increased, the change pattern of LUE was similar to quadratic functions that increase to a certain light intensity point and decrease afterwards. Between the scenario variables, the high level of light interception and low level of CV
LI were connected to the high LUE
E,max, indicating that the high light-intercepting efficiency (LI
e) is related to the potentially achievable LUE
E,max. In particular, in the case of a lighting distance of 20 cm, which showed a low LI
e, the PPFD
opt was relatively low, at approximately 310 μmol m
−2 s
−1, due to their heterogenetic light distribution on leaves. Additionally, the overall increment in light interception by reflective material induced the higher LUE
E,max at a relatively low level of PPFD. It is difficult to directly compare this result with others because there were no cases analyzing LUE in PFELs with the simulation. When compared with normal LUE in greenhouse cases, the LUE
E,max in this study is approximately 1.8 times higher [
15]. Additionally, compared with generally adopted PPFD levels for research or cultivation with less than 200 μmol m
−2 s
−1 [
9,
10,
33,
34], this result suggests that the larger range of PPFD can be efficient for improving LUE.
3.5. Applicability and Limitations
Previous studies that applied methods similar to those of this study under natural light mainly focused on the analysis of the light environment with diurnal or seasonal changes, which can be affected by climatic and weatherly factors. The light environment in PFELs is determined by controllable light sources, so the potential for application of simulation methods is thought to be larger. In particular, because electrical lighting in PFELs consumes electrical power, which incurs additional costs, simulation studies are important not only for analyzing the light interception of plants but also for improving energy use efficiency. By introducing some variables related to the light environment to the simulation, we analyzed their effects on light interception, photosynthesis, and LUE, and this result could support the optimal light design in PFELs. Additionally, to our knowledge, this is the first study to adopt the optimal light intensity for achieving the maximum LUE, which can support efficient electrical energy management. It is expected that further studies on various types of crops, types of lights, and lighting methods can expand the applicability of our findings for user purposes. Meanwhile, the method for constructing structurally accurate plant models should be improved. Because cultivated crops in PFELs mainly have small and dense canopies, 3D-scanned or image-based plant modeling methods have limitations in describing the whole canopy without destruction. Additionally, compared with rule-based plant models, the description of model continuity in time series is difficult. Nevertheless, because structural accuracy in the plant model is important for precise light analysis, as described above, methods to combine the advantages of different modeling methods should be developed.