Abstract:Classroom lighting profoundly affects students’ visual health, learning efficiency, and psychological comfort, yet conventional design standards based on illuminance and correlated color temperature (CCT) overlook the critical role of spatial luminance distribution. Since luminance directly stimulates the retina, it better represents actual visual experience, but existing studies rarely quantify how luminance distribution features interact with CCT to shape subjective atmosphere preference. This study addresses this gap by systematically investigating the combined effects of spatial luminance gradients, mean luminance, and CCT on preference ratings under static self-study tasks, aiming to develop a predictive model that supports refined classroom lighting design. A controlled experiment was conducted in a variable-space chamber configured as a 12×6×4 m classroom. Eighteen LED luminaires with tunable CCT (2 700-6 000 K) and dimmable output were installed, and wall reflectances were varied using replaceable curtain fabrics. Thirty-six experimental conditions were generated by combining three CCT levels (3 000, 4 300, 5 500 K), three desk illuminance levels (300, 500, 1 000 lx), and four wall reflectance coefficients (0.6-0.9). Luminance distributions were captured at a seated student’s eye height using a Konica CA-2000 color luminance meter. After preprocessing with a region-growing algorithm, the visual field was divided into a 5×5 grid, yielding 25 regional mean luminances. From these, 16 directional luminance gradients (D11 to D82) were defined along eight radial directions at two distance steps, together with mean luminance (Lm), central luminance (Lc), and standard deviation (Ld), resulting in 20 candidate physical variables plus CCT. Subjective preference data were collected from 16 healthy university students (8 male, 8 female, aged 22-26) using a 5-point Likert scale after a 10-minute simulated reading task. Each participant evaluated all 36 conditions in random order, producing 576 valid responses. To identify the most influential predictors, both Pearson correlation and maximal information coefficient (MIC) were applied. Pearson correlations showed no significant linear relationships (p> 0.05), whereas MIC values revealed strong nonlinear associations: CCT ranked highest (MIC=0.92), followed by several gradients (D31, D41, D52, D62 at 0.53) and Lm (0.46). This clear discrepancy confirmed that the relationship between physical parameters and psychological preference is inherently nonlinear. To reduce multicollinearity among luminance features—inevitable due to global dimming—hierarchical clustering was performed on the 19 non-CCT variables using average linkage. The dendrogram identified three major clusters; after eliminating redundant members, four core variables were retained: CCT, Lm, the forward luminance gradient (D31, center-to-front-background difference), and the lower-left peripheral gradient (D82). These variables capture the dominant baseline effect of CCT, the overall brightness level, the spatial contrast in the primary viewing direction, and a secondary peripheral correction, respectively. Visualization of the data revealed strong interactive effects. Under 3 000 K, preference ratings increased nearly linearly with L? from 40 to 100cd/cm2, indicating that higher luminance compensates for the low-CCT induced drowsiness. However, under 4 300 K and 5 500 K, preference peaked at L? ≈ 70-80 cd/cm2 and then flattened or declined, demonstrating saturation and diminishing returns. Similarly, the effect of D?? reversed with CCT: positive under 3 000 K (enhancing spatial layering), neutral under 4 300 K, and negative under 5 500 K when D31 exceeded 80 cd/cm2, suggesting that high CCT combined with strong gradients increases visual stress. These patterns confirm that luminance features do not act independently but are deeply modulated by the CCT context. To quantitatively model these nonlinear and interactive relationships, a polynomial regression was formulated with centered CCT (to reduce collinearity), quadratic CCT2 term, linear Lm, D31, and D82, and an interaction term CCTadj×D31. The fitted model achieved excellent performance: R2= 0.912 (adjusted R2=0.894), with overall F-test p < 0.001. The negative coefficient for CCT2 confirmed the inverted-U shape, while the significant negative interaction coefficient (p <0.001) quantitatively proved that the contribution of D31 diminishes as CCT increases. The final equation provides a practical tool for predicting atmosphere preference from easily measurable or designable variables. The model also enables a clear mapping from design parameters to environmental features. CCT is primarily set by light source selection, with 4 300 K recommended as the optimal baseline. L? is controlled via dimming and luminaire count, with a saturation point around 70-80 cd/cm2 under neutral/cool CCTs. D31 is adjusted through front wall reflectance and luminaire optics: moderate enhancement under low CCT to improve spatial depth, but smoothing under high CCT to avoid glare and discomfort. D82, as a secondary factor, can be managed via side-wall materials. This mapping establishes a quantitative design workflow from inputs to predicted preference, enabling iterative optimization. In conclusion, this study demonstrates that classroom lighting preference is governed by strong nonlinear interactions between CCT and spatial luminance distribution, not by any single linear factor. The proposed model, with 91.2% explanatory power, successfully integrates these complexities and offers a scientific basis for intelligent, human-centric lighting control. The findings advocate for moving beyond uniform illuminance standards toward adaptive strategies that tailor luminance gradients according to CCT, ultimately enhancing visual comfort and well-being in educational environments.