Supplemental light is a fundamental driver of plant growth and a key variable in optimizing crop productivity in controlled environments. Light-emitting diodes (LEDs), operating across distinct spectral channels, are widely adopted for their efficiency and demonstrated benefits. However, conventional top-lighting often produces non-uniform distribution, with excessive interception at the upper canopy and insufficient penetration into lower leaves. Intra-canopy lighting has emerged as a promising solution, yet the absence of rigorous models for spatial and vertical light distribution continues to limit optimization of supplemental lighting. In this study, we present and validate a unified mathematical framework for modeling the propagation and transmittance of photosynthetic photon flux density (PPFD, μmol s−1 m−2) across the extended Photosynthetically Active Radiation (ePAR) spectrum (400–750 nm). The model accounts for individual spectral channels (blue, red, far-red, white) and their combinations, simulating three-dimensional spatial distribution and vertical PPFD profiles along tomato plants. Validation with multi-lamp experimental data demonstrated mean percentage errors below 1% in spatial top-canopy PPFD and below 2.5% in vertical PPFD transmittance, across all spectral channels. The proposed algorithm operates with low and linear computational overhead, achieving average execution times of 27 ± 10μs per PPFD point, ensuring scalability to large greenhouse systems. The proposed model enables precise PPFD monitoring and provides the basis for advanced supplemental lighting strategies, supporting the integration of real-time digital twins for adaptive light management in smart greenhouse environments.

DOI: 10.1016/j.compag.2026.111969