Precision Control of Freeform Illumination Lenses: The Triumph of Triangle Mesh Method


In non-imaging optics, the quest for precision in controlling light energy distribution for illumination purposes has led to the emergence of freeform illumination optics. These optical systems are highly sought after due to their ability to provide additional degrees of freedom in shaping light beams. The design of such optics poses a unique challenge, involving the solution of an inverse problem that maps the power distribution of a light source to the desired irradiance distribution at the target. At the heart of freeform illumination optics lies the second law of thermodynamics, which establishes a fundamental trade-off between the etendue of the source and the level of information contained in the irradiance field. Consequently, numerous design methods have been devised to address well-posed inverse problems that involve zero-etendue sources and irradiance distributions rich in detail. However, many of these methods primarily focus on achieving uniform illumination fields with symmetric shapes for extended sources. This approach can be limiting when dealing with non-uniform irradiance fields, especially those featuring discontinuous distributions and boundaries. In a new study published in the peer-reviewed Journal Optics Letters, written by Mr. Linpei Li and Professor Xiang Hao from Zhejiang University, reported an innovative approach to precise light energy control in freeform illumination lenses.

In their study, the authors extended the application of the piece-wise smooth triangle mesh approach. Previously, this local approximation strategy was used only in the middle of the optimization process. However, the researchers now propose using the triangle mesh method to provide a precise definition throughout the entire freeform surface. This innovation is particularly noteworthy because it overcomes the need for extensive Monte Carlo (MC) analysis, even when dealing with extended light sources.

To demonstrate the effectiveness of their approach, the researchers compared the Triangle Mesh Method with the supporting quadric method and evaluated the results against those generated by the widely used LightTools Freeform Lens Design Feature. The authors introduced a freeform illumination model based on ray optics. This model considers an extended light beam with non-zero etendue entering the lens through a planar front surface, undergoing modulation by refraction at the exiting freeform surface. The design objective is to achieve a prescribed non-uniform irradiance distribution at a specific target region on a receiving plane.

The incident light beam in the model simulates a setup collimating an incoherent flat disk source, characterized by both lateral and angular extensions. At each point on the surface, a cone of rays is considered instead of a single ray. This cone’s properties remain consistent, differing only in translational positions, leading to shift-invariant behavior in ray tracing. To achieve this shift-invariant behavior, Mr. Linpei Li and Professor Xiang Hao proposed forcing the neighborhood normal of the surface to be constant, leading to the use of planar facets. These polygonal facets enable a reduction in the dimensions of the light beam representation. Each facet is associated with a transform matrix, and the light spot corresponding to the facet is calculated as a convolution between the geometric projection and the cone section distribution.

One of the key challenges in freeform illumination design is the computational complexity of convolution calculations, especially when dealing with a large number of facets. To address this challenge, the authors used a proxy strategy that provides an analytical approximation for the entire convolution, thus reducing computational overhead. Moreover, they outlined a comprehensive optimization model with defined mathematical expressions. The optimization process minimizes an objective function that includes terms controlling surface roughness, energy conservation, and similarity to the target irradiance distribution. The weights associated with these terms are manually tuned.

The researchers conducted numerical experiments to validate their approach. These experiments involved the design of a freeform lens for D-light using the Triangle Mesh Method and the LightTools Freeform Lens Design Feature. The results demonstrated the effectiveness of their method in achieving precise irradiance control. They utilized Pytorch for the implementation of the proposed model. Additionally, the researchers fabricated the optimized lens using a 3-axis slow tool-servo machine. The results from the physical lens were compared with simulation data, further confirming the accuracy of their approach.

In summary, the study led by Professor Xiang Hao and Mr. Linpei Li from Zhejiang University introduced a novel approach to precise light energy control in freeform illumination lenses. By extending the application of the Triangle Mesh Method and introducing a proxy strategy, the researchers have demonstrated the effectiveness of their method in achieving precise irradiance control, as evidenced by both simulation and experimental results. This innovative approach opens new possibilities for the design and fabrication of freeform illumination optics, with potential applications in a wide range of fields.


This work was financially supported by “Leading Goose” R&D Program of Zhejiang (2022C01077); National Natural Science Foundation of China (92050115); Natural Science Foundation of Zhejiang Province (LZ21F050003); Fundamental Research Funds for the Central Universities (2022QZJH29); National Key Research and Development Program of China (2022YFB3206000).


Li L, Hao X. Optimizing triangle mesh lenses for non-uniform illumination with an extended source. Opt Lett. 2023 ;48(7):1726-1729. doi: 10.1364/OL.485874.

Go to Opt Lett.

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