Mathematical Analysis and Freeform Surface Modeling for LED Illumination Systems Incorporating Diffuse Reflection and Total Internal Reflection
Year: 2025
Type: article
Abstract: Indirect lighting systems employing light-emitting diodes (LEDs) and diffuse reflective surfaces are prevalent in applications demanding stringent illumination uniformity. However, conventional diffuse reflection approaches exhibit inherent limitations (inevitable light loss from multiple diffuse reflections and trade-off between uniformity and efficiency). To overcome these constraints, we introduce a novel composite freeform surface illumination system that synergistically integrates total internal reflection (TIR) with diffuse reflection. This design leverages the inherent Lambertian radiation characteristics of LEDs and the properties of ideal diffuse reflectors. A rigorous mathematical model is derived based on the luminous intensity distribution of the LED chip, the prescribed illumination requirements on the target plane, the principle of energy conservation, and Snell’s law. The resulting system of nonlinear equations is solved to generate a series of two-dimensional profile curves, which are subsequently synthesized into an off-axis freeform surface. Simulated results demonstrate that the proposed system achieves higher optical efficiency and superior illumination uniformity compared to traditional diffuse reflector configurations. This universal and feasible methodology broadens the application potential of high-performance diffuse indirect lighting.
Source: Photonics
Authors: Xin Xu, Jianghua Rao, Xiaowen Liang, Zhenmin Zhu, Yuanyuan Peng
Institution: East China Jiaotong University
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
Awards: G5048843695, G6716001644
OpenAlex ID: W4415262977