Optimizing freeform lenses for extended sources with algorithmic differentiable ray tracing and truncated hierarchical B-splines

The generation of a specific laser beam profile on the work surface is key to various laser beam shaping tasks, relying heavily on diffractive optical elements (DOEs). Most beam-shaping DOEs are designed using iterative Fourier transform algorithms (IFTAs), which generally have slow convergence and prone to stagnate at local minima. Moreover, the microreliefs generated by IFTAs tend to be irregular, complicating manufacturing and causing uncontrolled scattering of light. We propose a differentiable DOE design method that applies a phase-smoothness constraint using multi-level B-splines. A multi-scale gradient-descent optimization strategy, naturally linked with the multi-level B-splines, is employed to robustly determine the optimized phase distribution that is fully continuous. This, in turn, can lead to more regular DOE microreliefs, which can simplify the fabrication process and be less sensitive to changes in wavelength and working distance. Furthermore, our method can also design a fully continuous freeform lens, distinguished from most freeform lens design approaches by its foundation in physical optics rather than geometrical optics. Simulation and experimental results of several design tasks demonstrate the effectiveness of the proposed method.

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Differentiable design of a double-freeform lens with multi-level radial basis functions for extended source irradiance tailoring

Tang,

Li,

Feng

et al. 2024

Optica

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Freeform optics are key for generating prescribed illumination patterns from given sources, which are crucial for solid-state lighting and machine vision illumination. There is an increasing demand for compact freeform optics, which presents a substantial challenge for current design methods since the source dimensions must be considered. Most current extended-source design methods, although requiring profound knowledge of optics and mathematics, focus on the modest goal of obtaining uniform irradiance distributions. We address a more challenging design problem of generating an irradiance distribution of arbitrary shape through a double-freeform lens that can fully encompass the extended source. We propose a differentiable design method whose uniqueness lies in the representation of the double-freeform surfaces using multi-level spherical radial basis functions, which has a natural link to a multi-scale optimization technique. In addition, we employ a sequential unconstrained minimization technology complemented with Lagrange multipliers that add key feasibility constraints on lens shape and size. The proposed method is flexible, general, and efficient in designing highly compact freeform lenses for generating both simple and complex irradiance distributions, as demonstrated through the design examples. This could enable a universal solution to the extended-source design problem.

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Optimizing freeform lenses for extended sources with algorithmic differentiable ray tracing and truncated hierarchical B-splines

Cited by 3 publications

References 27 publications

Differentiable freeform lens design for irradiance tailoring on tilted target plane

Differentiable freeform lens design for irradiance tailoring on tilted target plane

Differentiable design of freeform diffractive optical elements for beam shaping by representing phase distribution using multi-level B-splines

Differentiable design of a double-freeform lens with multi-level radial basis functions for extended source irradiance tailoring

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