Dynamic mapping and optimized design of LED lens for curved surface illumination (<italic>invited</italic>)

ObjectiveWith the rapid development and expanding application range of Light Emitting Diode (LED) technology, secondary optical design, as a key technology for achieving efficient and precise lighting, has become increasingly important. In the field of planar illumination, significant progress has been made in related research, and various optical design methods based on freeform surfaces and microstructures have been proposed, which adequately meet the requirements of most conventional lighting scenarios. However, when facing complex lighting targets such curved surfaces, existing light distribution design methods still have certain limitations. To address this, this paper proposes an LED lens design method for curved targets. Under a double projection coordinate system, the method establishes an energy mapping relationship from the light source to the target curved lighting surface through surface integration, and uses a point-by-point iterative numerical algorithm to solve the initial lens model. On the basis of the initial configuration, a closed-loop correction mechanism is constructed and combined with ray tracing programs, enabling the iterative optimization of the lens surface shape., thereby improving the light distribution accuracy and optical efficiency. Simulation results show that the proposed method can be applied to illuminate curved targets of different shapes. Taking wavy and saddle surfaces as examples, the irradiation uniformity is improved by 19.00% and 15.92%, respectively, and the system energy efficiency is increased by 3.05% and 3.37%, respectively. In addition, the obtained light spot contours match significantly better with the desired targets, and the designed lens is compact in structure, with the total size controlled within 20 mm, demonstrating good potential for practical applications.MethodsA design method for LED lenses achieving uniform illumination on curved surfaces is presented, following a systematic design procedure. Firstly, an iterative solution for the lens surface profile is established in the Cartesian coordinate system based on the law of refraction (Fig.2). Subsequently, surface integration is introduced in the double projection coordinate system (Fig.3) under the principle of étendue conservation to construct an energy mapping between the light source and target illumination surface. Finally, closed-loop feedback optimization (Fig.5) is employed to continuously refine lens parameters through comparison between simulated outcomes and design targets, progressively optimizing optical performance.Results and DiscussionsThe proposed design method utilizes the Jacobian matrix to transform the luminous intensity distribution of the spherical coordinate-based LED into the double projection coordinate system. The light energy of the source is then partitioned in this coordinate system, establishing an energy mapping between the source and the target illuminated surface (Fig.4). The introduction of surface integrals significantly reduces the computational complexity of the process. After obtaining the initial lens design, the mapping between the source and the target surface is refined based on simulation results (Fig.5), thereby improving the accuracy of the lens design. This optimization process compensates for the limitations of manual source partitioning and mapping construction. The method is applicable to both planar and non-planar target surfaces. Its feasibility is validated through two case studies involving an undulating surface and a saddle surface (Fig.6). Simulation results (Fig.9-Fig.10) indicate that the initial lens exhibits limited control over light distribution, resulting in a noticeable bright spot in the central region of the illumination pattern. However, after optimization, the performance improves significantly. Moreover, while emphasizing illumination uniformity, the optimization also enhances both the contour fidelity of the light spot (Fig.11-Fig.12) and the overall energy efficiency.ConclusionsThe designed lens features a biconvex surface configuration, where this double-surface architecture effectively suppresses total internal reflection during light refraction, thereby enhancing the lens's capability to precisely control light distribution from the source. Simulation results from two application cases demonstrate that while the initial lens design yields suboptimal illumination patterns, the optimized version achieves remarkable performance under consistent conditions—using a 1 mm diameter LED and maintaining a compact lens size below 20 mm. Both cases exhibit illumination uniformity exceeding 85%, energy efficiency reaching 90%, and light spot contours that closely match the intended patterns. These outcomes validate the feasibility of the feedback-based optimization strategy for refining the source-target mapping, confirming the applicability of the proposed method in designing secondary optical LED lenses for uniform illumination on curved surfaces.