With the rapid advancement of modern science and technology, illumination systems have become an indispensable part of daily life. In fields such as road, medical, and industrial applications, a well-designed illumination system can significantly enhance safety. Therefore, designing an illumination system with a distributed light pattern that meets human needs has become a key focus in the lighting industry. Light emitting diodes (LEDs), with their advantages of environmental friendliness, energy efficiency, and high performance, have gradually replaced traditional light sources and are now the dominant light solution in the market. However, LEDs often require secondary optical design to achieve more uniform and efficient illumination, meeting the specific lighting needs of different environments and improving overall lighting quality and experience. In this paper, we propose a new method for designing a uniform lighting lens in the context of illumination engineering.

In light of the luminous characteristics of LED light sources, a novel hypothesis is proposed for designing extended LED light sources, treating the extended light source as a collection of infinite point sources. The divergence half-angle limit for each small point source is strictly defined, and a uniform internal freeform surface is designed to serve as a secondary light source. The external freeform surface then maps the uniform secondary source to the target surface, a method called the hypothetical point source ensemble (HPE). Based on the inner freeform surface, the outer surface is designed by analyzing the point-to-point energy mapping from the light source to the illuminated plane using the source-target mapping method. We derive the corresponding theoretical model and a new formula for calculating the emitted light angle. The point convergence of the outer freeform surface is calculated using Snell’s law in vector form and the tangent iteration method. The discrete point cloud data of the double freeform lens are then obtained and imported into the 3D modeling software to create the final lens design.

Using the proposed method, we design uniform illumination lenses for various applications. For example, with a light source diameter of 1 cm and a distance-to-height ratio of 1, the initial lens design achieves 88% uniformity (Fig. 9). After polynomial fitting and optimization of the lens profile, the final energy utilization rate is 80%, and the illumination uniformity is improved to 97.7%, demonstrating the high uniformity capabilities of our lens. To verify that the illumination lens designed using the point source ensemble method is not limited to a single illumination distance, simulations are conducted for both far-field illumination at distances of 2 and 10 m, and near-field illumination at 50 and 100 mm, all with a distance-to-height ratio of 1, as shown in Fig. 11. The results confirm that the illumination uniformity on the target surface exceeds 97%. To test the method’s flexibility, a lens is designed with a distance of 1 m and a lighting plane radius of 1.5 m. Simulation results shown in Fig. 12 indicate 95% uniformity. Additional simulations with a rectangular light source (1 cm side length) and a lighting distance of 1 m, as shown in Fig. 13, achieve 94.8% uniformity. A lens for a circular LED light source with a 2 mm diameter is also tested (Fig. 14), yielding 94.44% energy utilization and 99% uniformity. The far-field illumination lens, designed for a point source, achieves 94.6% energy utilization and 99% uniformity. These simulation results, across five different application conditions, verify the simplicity, high uniformity, energy utilization, and broad applicability of the proposed HPE method.

To address the issue of uneven illumination from Lambertian light sources, we propose a new hypothetical point source ensemble method for uniform illumination in lighting engineering. We outline a complete design and optimization process for uniform illumination lenses. By treating the extended light source as a set of point light sources, mathematical models are developed to solve for the inner and outer freeform surfaces of the lens, based on the illumination square law and the principle of energy conservation. Through point-by-point construction and tangent iterative calculation, a compact, high-energy utilization lens with uniform illumination is designed. The simulation results demonstrate that the method is applicable not only to circular light sources but also to rectangular ones. Compared with existing methods, the HPE method is simpler and more versatile, working for both extended and point light sources. The designed extended light source lens achieves 97.7% uniformity, while the point source lens achieves 99% uniformity and 94.6% energy utilization. This demonstrates that the HPE method makes a significant contribution to uniform illumination in lighting engineering. Future research will focus on the fabrication of lenses designed using this method and their application to off-axis lighting.