Interpretation and Evaluation of Electrical Lighting in Plant Factories with Ray-Tracing Simulation and 3D Plant Modeling

: In plant factories, light is fully controllable for crop production but involves a cost. For e ﬃ cient lighting, light use e ﬃ ciency (LUE) should be considered as part of light environment design. The objectives of this study were to evaluate and interpret the light interception, photosynthetic rate, and LUE of lettuces under electrical lights using ray-tracing simulation. The crop architecture model was constructed by 3D scanning, and ray-tracing simulation was used to interpret light interception and photosynthesis. For evaluation of simulation reliability, measured light intensities and photosynthetic rates in a growth chamber were compared with those obtained by simulation at di ﬀ erent planting densities. Under several scenarios modeling various factors a ﬀ ecting light environments, changes in light interception and LUE were interpreted. The light intensities and photosynthetic rates obtained by simulation showed good agreement with the measured values, with R 2 > 0.86. With decreasing planting density, the light interception of the central plant increased by approximately 18.7%, but that of neighboring plants decreased by approximately 5.5%. Under the various scenarios, shorter lighting distances induced more heterogenetic light distribution on plants and caused lower light interception. Under a homogenous light distribution, the light intensity was optimal at approximately 360 µ mol m − 2 s − 1 with an LUE of 6.5 g MJ − 1 . The results of this study can provide conceptual insights into the design of light environments in plant factories.


Introduction
Light is one of the most important environmental factors driving photosynthesis and growth. In this respect, full control of the light environments of plant factories with electrical lights (PFELs) has the advantages of stable year-round crop production, along with high productivity and quality [1][2][3][4]. Meanwhile, despite the continuous increase in the luminous efficacy of light sources such as LEDs [5], electrical energy consumption for lighting is a major burden for operating commercial PFELs. Electrical energy occupies the largest part of the operation cost, and most of the electrical energy consumption comes from lighting rather than other energy loads, such as heating, cooling, or dehumidification, in PFELs [6,7].
One solution for improving light use efficiency (LUE) is to optimize the light environment to maximize crop photosynthesis. To achieve this purpose, the light distribution in cultivating areas in PFELs can be modified by changing the spatial disposition of the light source when using the same light source or the same usable energy. Targeted lighting by adjacent LED positioning [8] and For alternatives for light interception that cannot actually be measured, light intensities at several points were used as an indirect index to describe the accuracy of estimated canopy light interception. PPFD was set at 200 μmol m −2 s −1 , and light intensity was measured by a light meter (LI-250A, LI-COR, Lincoln, NE, USA) in both the empty and canopy-arranged growth chamber at fixed points. To investigate whether the lighting power and distribution were well set in the simulation, light intensities were first compared in an empty chamber without plant models at 16 different positions with 3 height-levels from the floor. With the lettuce plants in the chamber, light intensities were only measured on the floor because the measurement through the plant canopy can cause disaccord with simulation by touching.
The net photosynthetic rate (Pn) of the whole canopy was measured by a gas analyzer (LI-840A, LI-COR, Lincoln, NE, USA) connected to the growth chamber. To obtain the Pn, the growth chamber was enclosed, the change in CO2 concentration was monitored every second from 800 to 400 μmol mol −1 , and the difference in CO2 concentration averaged over 3 min was used to calculate the whole canopy photosynthetic rate. PPFD was set at 100, 200, and 300 μmol m −2 s −1 . The temperature was set to 22 °C, and the range of relative air humidity was 60%-80% in the growth chamber. Air leakage from the growth chamber was measured at CO2 concentrations above 1000 μmol mol −1 , and the number of air exchanges was 0.0016 h −1 , which was used to calibrate the photosynthetic rate.

Construction of 3D-Scanned Plant Models
The lettuces used for the above measurements were directly scanned to reconstruct a 3Dscanned plant model (3D-SPM, Figure 1A) with a high-resolution portable 3D-scanner (GO! SCAN50TM, Creaform, Lévis, Quebec, Canada). The resolution of the scanner was set at 2 mm. Because inner and overlapping leaves are difficult for the 3D scanner to recognize, each leaf was For alternatives for light interception that cannot actually be measured, light intensities at several points were used as an indirect index to describe the accuracy of estimated canopy light interception. PPFD was set at 200 µmol m −2 s −1 , and light intensity was measured by a light meter (LI-250A, LI-COR, Lincoln, NE, USA) in both the empty and canopy-arranged growth chamber at fixed points. To investigate whether the lighting power and distribution were well set in the simulation, light intensities were first compared in an empty chamber without plant models at 16 different positions with 3 height-levels from the floor. With the lettuce plants in the chamber, light intensities were only measured on the floor because the measurement through the plant canopy can cause disaccord with simulation by touching.
The net photosynthetic rate (P n ) of the whole canopy was measured by a gas analyzer (LI-840A, LI-COR, Lincoln, NE, USA) connected to the growth chamber. To obtain the P n , the growth chamber was enclosed, the change in CO 2 concentration was monitored every second from 800 to 400 µmol mol −1 , and the difference in CO 2 concentration averaged over 3 min was used to calculate the whole canopy photosynthetic rate. PPFD was set at 100, 200, and 300 µmol m −2 s −1 . The temperature was set to 22 • C, and the range of relative air humidity was 60%-80% in the growth chamber. Air leakage from the growth chamber was measured at CO 2 concentrations above 1000 µmol mol −1 , and the number of air exchanges was 0.0016 h −1 , which was used to calibrate the photosynthetic rate.

Construction of 3D-Scanned Plant Models
The lettuces used for the above measurements were directly scanned to reconstruct a 3D-scanned plant model (3D-SPM, Figure 1A) with a high-resolution portable 3D-scanner (GO! SCAN50TM, Creaform, Lévis, Quebec, Canada). The resolution of the scanner was set at 2 mm. Because inner and overlapping leaves are difficult for the 3D scanner to recognize, each leaf was scanned separately. A total of nine lettuces were scanned, and leaves smaller than 2 cm in length were neglected. After scanning, scan data were incorporated into the original plant structure based on positioning information using scan software (Vxelement, Creaform, Lévis, Quebec, Canada). The holes and noises of the 3D mesh data were fixed, and the 3D mesh was reconstructed to the surface model by reverse engineering software (Geomagic Design X, 3D Systems, Rock Hill, SC, USA) to perform ray-tracing simulations.
To determine the model's validity, leaf areas from scanned data were compared with measured samples. Leaf areas of a lettuce (14 in total) were photographed and quantified with ImageJ software (National Institutes of Health, Bethesda, MD, USA).

Ray-Tracing Simulation
To set the optical properties in ray-tracing simulation, the transmittance and reflectance of the leaf and chamber surface were measured with a spectroradiometer (BLUE-Wave Spectrometer, StellarNet Inc., Tampa, FL, USA) ( Figure 2). Because leaf optical properties for different ages or positions showed no differences, the average value of three points was used. The transmittance of the black board was neglected, and the ceiling of the chamber was set as a fully permeable material. Optical properties in the range of 400 to 700 nm were applied in the simulation, considering the spectrum range of the LED used.

Ray-Tracing Simulation
To set the optical properties in ray-tracing simulation, the transmittance and reflectance of the leaf and chamber surface were measured with a spectroradiometer (BLUE-Wave Spectrometer, StellarNet Inc., Tampa, FL, USA) ( Figure 2). Because leaf optical properties for different ages or positions showed no differences, the average value of three points was used. The transmittance of the black board was neglected, and the ceiling of the chamber was set as a fully permeable material. Optical properties in the range of 400 to 700 nm were applied in the simulation, considering the spectrum range of the LED used.
To perform ray-tracing simulation, the virtual growth chamber and LED plate were reconstructed ( Figure 1B) based on the dimensions measured by 3D computer-aided design software (Solidworks, Dassault Systèmes, Vélizy-Villacoublay, France). A total of 640 red LED chips and 96 blue LED chips were mounted on the LED plate, considering dimensions and patterns. For each LED chip, spectral distributions of red and blue LEDs were measured with a spectroradiometer at 1-nm intervals for spectral power distribution (SPD) settings, and for physical light distribution (PLD), a Lambertian distribution with an angle of 60° was set.
After virtual growth chamber setting, 3D-SPMs were placed in the virtual growth chamber to perform ray-tracing simulation ( Figure 1B) with the observed rotation angle and position. To compare the measured light intensity with the simulated light intensity, virtual light sensors were placed on the light measurement points.
The ray-tracing simulation was performed using ray-tracing software (OPTISWORKS, OPTIS Inc., La Farlède, France). The total number of rays emitted was set to 200 million, considering the model size. To match the PPFD in the virtual growth chamber with the actual environment, a cylinder-shaped detector was modeled based on the quantum sensor dimension and placed on the datum point. LED outputs were set to 0.009, 0.018, and 0.027 W for red LED chips and 0.02175, 0.0435, and 0.06525 W for blue LED chips, representing PPFDs of 100, 200, and 300 μmol m −2 s −1 , respectively. The total photosynthetic photon fluxes emitted were 79.3, 158.6, and 237.9 μmol s −1 , respectively.  To perform ray-tracing simulation, the virtual growth chamber and LED plate were reconstructed ( Figure 1B) based on the dimensions measured by 3D computer-aided design software (Solidworks, Dassault Systèmes, Vélizy-Villacoublay, France). A total of 640 red LED chips and 96 blue LED chips were mounted on the LED plate, considering dimensions and patterns. For each LED chip, spectral distributions of red and blue LEDs were measured with a spectroradiometer at 1-nm intervals for spectral power distribution (SPD) settings, and for physical light distribution (PLD), a Lambertian distribution with an angle of 60 • was set.

Calculation of Photosynthetic Rate from Simulation Results
After virtual growth chamber setting, 3D-SPMs were placed in the virtual growth chamber to perform ray-tracing simulation ( Figure 1B) with the observed rotation angle and position. To compare the measured light intensity with the simulated light intensity, virtual light sensors were placed on the light measurement points.
The ray-tracing simulation was performed using ray-tracing software (OPTISWORKS, OPTIS Inc., La Farlède, France). The total number of rays emitted was set to 200 million, considering the model size. To match the PPFD in the virtual growth chamber with the actual environment, a cylinder-shaped detector was modeled based on the quantum sensor dimension and placed on the datum point. LED outputs were set to 0.009, 0.018, and 0.027 W for red LED chips and 0.02175, 0.0435, and 0.06525 W Agronomy 2020, 10, 1545 5 of 14 for blue LED chips, representing PPFDs of 100, 200, and 300 µmol m −2 s −1 , respectively. The total photosynthetic photon fluxes emitted were 79.3, 158.6, and 237.9 µmol s −1 , respectively.

Calculation of Photosynthetic Rate from Simulation Results
Based on the ray-tracing simulation results, P n was calculated by the absorbed PPFD and photosynthesis model. For the photosynthesis model, the modified Faquhar, von Caemmerer, and Berry (FvCB) model by Qian [24] was used. To obtain FvCB model parameters, the photosynthetic rate was measured for the upper and lower canopies by a portable photosynthesis system (LI-6400, LI-COR, Lincoln, NE, USA) with 4 different CO 2 concentrations (100, 400, 800, and 1200 µmol mol −1 ) and 8 different light intensities (0, 50, 100, 200, 400, 600, 900, and 1200 µmol m −2 s −1 ). The leaf temperature was set to 22 • C, and the relative humidity ranged from 60% to 70%.
The dark respiration rate (R d ) was fixed at the measured photosynthetic rate under a PPFD of 0 µmol m −2 s −1 , and these were 0.75 and 0.41 µmol CO 2 m −2 s −1 for the upper and lower canopies, respectively. The V cmax and J max values were obtained by nonlinear regression using measured leaf photosynthesis data and equations of Qian [24], and were 68.324 and 139.851 for the upper canopy and 46.423 and 52.898 for the lower canopy, respectively. The CO 2 compensation points (Γ * ) were obtained by nonlinear regression using measured leaf photosynthesis data and the following Equation (1): where P leaf is measured leaf photosynthetic rate and C i is intercellular CO 2 concentration. a, b, and c are equation coefficients. Resultingly, Γ * values were 42.897 and 16.923 for the upper and lower canopies, respectively. The efficiency of light energy conversion (α) and curvature value (θ) were fixed at empirical values of 0.18 mol (electron) mol −1 (photon) and 0.7, respectively [25,26].
The simulation results included the point cloud of the 3D-SPM (x, y, and z coordinates) and the absorbed light energy (W) that was converted to absorbed PPFD by a conversion coefficient of 5.013, considering the spectral distribution of the LEDs used. The photosynthetic rate on the i-th point cloud (P i , µmol m −2 s −1 ) was calculated by Equation (2): where A c,i and A j,i are the net photosynthetic rate (µmol m −2 s −1 ) limited by rubisco activity and the electron transfer rate of the i-th point cloud, respectively. P n was calculated by Equation (3): where OA i (m −2 ) is the occupied area of a point cloud and was normalized to 1 × 10 −6 m −2 for calculation. n and LA indicate the total point number and total leaf area (m −2 ), respectively, and these values varied depending on the size of the 3D-SPM. P n was calculated in various environments with three different light intensities (100, 200, and 300 µmol m −2 s −1 ), three different CO 2 concentrations (500, 600, and 700 µmol mol −1 ) and two different planting densities (HD and LD) for comparison with the measured values.

Scenarios
Based on the constructed plant models and explained processes, scenarios were conducted to examine the effect of lighting manipulation on light interception and photosynthesis. Nine 3D-SPMs were isotropically arranged at a planting density of 25 plants m −2 , and the central one was selected for the light environment analysis. In addition, 8 or 9 LED bars that were 1.5 m long, which were oversized compared to the canopy size, were only used to find the impact of selected scenario variables, ignoring the decay of light intensity at marginal illuminating areas. Three variables were considered for the scenarios: (1) LED bars were arranged vertically above the center of the plant (VAP) or between the plant (BP); (2) lighting distances were set from 20 to 40 cm with an interval of 5 cm, based on the distance between the floor and the bottom of the LED bars; and (3) floor surface properties were set for nonreflective material (NR, 0% reflectance) or high-reflective material (HR, 100% reflectance). These three variables were independently changed, and thus a total of 40 cases were simulated. For all cases, the power of LED bars was set to represent an average PPFD of 200 µmol m −2 s −1 on the area occupied by the central 3D-SPM (20 × 20 cm).
For evaluation of the light environment according to the scenarios, the coefficient for variance of light interception (CV LI ), LUE, light interception, and photosynthetic rate were calculated. The CV LI was calculated by the ratio of the standard deviation of intercepted light to the total mean light interception, and the LUE was calculated by the ratio of the net photosynthetic rate per plant to the emitted photosynthetic photon flux (PPF) from the light source (LUE E ) or intercepted PPF (LUE I ). The change in LUE E was calculated according to light intensity to obtain the maximal LUE E (LUE E,max ), and the light intensity at LUE E,max was described as an optimal PPFD (PPFD opt ).

Statistical Analysis
To compare the simulated light intensity and photosynthesis with the measured ones, the R 2 and root mean square error (RMSE) were calculated using statistical programs (R, The R foundation, Vienna, Austria).

D-scanned Plant Model
The leaf areas of the scanned data were approximately 12% larger than those of the measured data ( Figure 3). This result conflicts with previous studies that found that the image-based model of plant leaves was well matched to actual ones [18,22]; nevertheless, from our perspective, leaf area acquired by 3D scanning was more adjacent to actual values in this case. Leaf area is generally measured from projection area, and this assumes that leaves have flat structure. However, leaf morphology tends to be curled under LED lights with high blue content [27], and the lettuces used in this study also had convex and curled leaf shapes ( Figure 1A), indicating that the projection area underestimated the actual leaf area in this case. Meanwhile, the 3D scanner collects the coordinates of the leaf surface converted to a 3D mesh, which can accurately reflect the leaf curvature and structure. Therefore, further analysis and calculation of light interception and photosynthesis were conducted using scanned leaf areas.
Agronomy 2020, 10, x FOR PEER REVIEW 6 of 15 properties were set for nonreflective material (NR, 0% reflectance) or high-reflective material (HR, 100% reflectance). These three variables were independently changed, and thus a total of 40 cases were simulated. For all cases, the power of LED bars was set to represent an average PPFD of 200 μmol m −2 s −1 on the area occupied by the central 3D-SPM (20 × 20 cm). For evaluation of the light environment according to the scenarios, the coefficient for variance of light interception (CVLI), LUE, light interception, and photosynthetic rate were calculated. The CVLI was calculated by the ratio of the standard deviation of intercepted light to the total mean light interception, and the LUE was calculated by the ratio of the net photosynthetic rate per plant to the emitted photosynthetic photon flux (PPF) from the light source (LUEE) or intercepted PPF (LUEI). The change in LUEE was calculated according to light intensity to obtain the maximal LUEE (LUEE,max), and the light intensity at LUEE,max was described as an optimal PPFD (PPFDopt).

Statistical Analysis
To compare the simulated light intensity and photosynthesis with the measured ones, the R 2 and root mean square error (RMSE) were calculated using statistical programs (R, The R foundation, Vienna, Austria).

D-scanned Plant Model
The leaf areas of the scanned data were approximately 12% larger than those of the measured data ( Figure 3). This result conflicts with previous studies that found that the image-based model of plant leaves was well matched to actual ones [18,22]; nevertheless, from our perspective, leaf area acquired by 3D scanning was more adjacent to actual values in this case. Leaf area is generally measured from projection area, and this assumes that leaves have flat structure. However, leaf morphology tends to be curled under LED lights with high blue content [27], and the lettuces used in this study also had convex and curled leaf shapes ( Figure 1A), indicating that the projection area underestimated the actual leaf area in this case. Meanwhile, the 3D scanner collects the coordinates of the leaf surface converted to a 3D mesh, which can accurately reflect the leaf curvature and structure. Therefore, further analysis and calculation of light interception and photosynthesis were conducted using scanned leaf areas.

Evaluation of Ray-Tracing Simulation and Photosynthesis Estimation
In the empty growth chamber without plants, the measured and simulated light intensities

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).
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 CO2 concentration, the measured and estimated values of canopy Pn per unit leaf area were well matched, with an R2 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. 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 P n per unit leaf area were well matched, with an R 2 of 0.986. However, at the measurement points of low P n , which were measured and calculated at low PPFDs, the simulation underestimated P n 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., V cmax , J max ), whereas the canopy P n 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.

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. Figure 5. Comparison between measured and estimated canopy photosynthetic rates (P n ) in the growth chamber. The PPFD was set to 100, 200, and 300 µmol m −2 s −1 , and the CO 2 concentration was set to 500, 600, and 700 µmol mol −1 . Nine lettuce plants at DAT 21 were used.

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.

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 CVLI 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 LUEI 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

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 P n 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.
Agronomy 2020, 10, x FOR PEER REVIEW 10 of 15 found in this scenario (Figure 8), and the lack of uniformity was connected to low LUEI, 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.   found in this scenario (Figure 8), and the lack of uniformity was connected to low LUEI, 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 PPFDopt for achieving LUEE,max was found ( Figure 11). The range of PPFDopt 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, LUEE,max was the largest at a 30-cm lighting distance with VAP-HR, and both PPFDopt and LUEE,max were relatively low at a 20-cm lighting distance; thus, the maximum LUEE,max was approximately 20.3% larger than the minimum. In all cases, a larger LUEE,max was achievable at a low PPFDopt 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 CVLI were connected to the high LUEE,max, indicating that the high light-intercepting efficiency (LIe) is related to the potentially achievable LUEE,max. In particular, in the case of a lighting distance of 20 cm, which showed a low LIe, the PPFDopt 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 LUEE,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 LUEE,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. Floor surface was set at non-reflective (NR) or highly-reflective (HR) material.

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 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.

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.

Conclusions
Light use efficiency (LUE) is an important factor in designing the light environment in plant factories with electrical lights (PFELs). To analyze LUE, 3D-scanned plant models (3D-SPMs) for lettuces and ray-tracing simulation were used. The leaf areas of 3D-SPMs were slightly larger compared with the measured data, but considering the curled and convex structure of leaves, those of 3D-SPMs are thought to be more adjacent to actual ones. Additionally, in a growth chamber with an LED source, the simulation results were well matched with the measured light intensities and photosynthesis. When planting density decreased, the light interception of the central plant was increased due to a decrease in the mutual shading effect, but that of border plants was decreased by receding from the center of the light source. Different lighting distances, light arrangements, and floor reflectances also affected light interception, and the results indicated that cases with lower deviations in intercepted light showed larger light interception and LUE. The optimal photosynthetic photon flux density (PPFD) level for achieving maximal LUE was able to be obtained, which can support the control of light sources. Our study suggests a basic insight into designing the light environment in PFELs for maximization of LUE.