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Feng Z X, Cheng D W, Wang Y T. Iterative freeform lens design for prescribed irradiance on curved target. Opto-Electron Adv 3, 200010 (2020). doi: 10.29026/oea.2020.200010
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Original Article Open Access
Iterative freeform lens design for prescribed irradiance on curved target
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Abstract
Current freeform illumination optical designs are mostly focused on producing prescribed irradiance distributions on planar targets. Here, we aim to design freeform optics that could generate a desired illumination on a curved target from a point source, which is still a challenge. We reduce the difficulties that arise from the curved target by involving its varying z-coordinates in the iterative wavefront tailoring (IWT) procedure. The new IWT-based method is developed under the stereographic coordinate system with a special mesh transformation of the source domain, which is suitable for light sources with light emissions in semi space such as LED sources. The first example demonstrates that a rectangular flat-top illumination can be generated on an undulating surface by a spherical-freeform lens for a Lambertian source. The second example shows that our method is also applicable for producing a non-uniform irradiance distribution in a circular region of the undulating surface. -
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References
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Feng Z X, Cheng D W, Wang Y T. Iterative freeform lens design for prescribed irradiance on curved target. Opto-Electron Adv 3, 200010 (2020). doi: 10.29026/oea.2020.200010
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Figure 1.
Sketch of the design geometry.
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Figure 2.
The rectangular (u, v) grid (a) is transformed into a circular (u', v') grid (b) which is used as the stereographic coordinates (c).
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Figure 3.
The flow diagram of the new IWT procedure for a curved target.
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Figure 4.
The desired curved target.
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Figure 5.
(a) The (u′, v′) grid corresponding to a uniform (u, v) grid on Ω={(u, v)|-0.94≤u≤0.94, -0.94≤v≤0.94} and (b) the final target grid for the first design (only showing 64×64 grid points for better visualization); (c) The final 3D freeform lens model and (d) its simulation results for a point like source (size: 10-3 mm×10-3 mm). (The unit of the irradiance: W/mm2)
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Figure 6.
(a) The (u′, v′) grid corresponding to a uniform (u, v) grid on Ω={(u, v)|-0.8≤u≤0.8, -0.8≤v≤0.8} and (b) the final target grid for the second design (only showing 64×64 grid points for better visualization); (c) The final 3D freeform lens model and (d) its simulation results for a point like source (size: 10-3 mm×10-3 mm). (The unit of the irradiance: W/mm2)
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Figure 7.
Simulated irradiance distributions for the first lens design when the source size is changed into (a) 1 mm× 1mm and (b) 2 mm× 2 mm respectively; simulated irradiance distributions for the second lens design when the source size is changed into (c) 1 mm × 1mm and (d) 2 mm × 2 mm respectively.
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Figure 8.
Simulated irradiance distributions for the first lens design when the source-lens system is (a) 5 mm and (b) 10 mm closer to the target. Simulated irradiance distributions for the second lens design when the source-lens system is (c) 5 mm and (d) 10 mm closer to the target.
