• Infrared and Laser Engineering
  • Vol. 50, Issue 2, 20200183 (2021)
Tiantian Hu1、2, Chunmei Zeng1、2, Congshan Rui1、2, Yang Hong1、2, and Suodong Ma1、2
Author Affiliations
  • 1School of Optoelectronic Science and Engineering, Soochow University, Suzhou 215006, China
  • 2Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China
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    DOI: 10.3788/IRLA20200183 Cite this Article
    Tiantian Hu, Chunmei Zeng, Congshan Rui, Yang Hong, Suodong Ma. Optical design of freeform Fresnel TIR lens for LED uniform illumination[J]. Infrared and Laser Engineering, 2021, 50(2): 20200183 Copy Citation Text show less

    Abstract

    A new design of total internal reflection (TIR) lens was presented which had a freeform Fresnel surface in the central part of the front to improve the heat dissipation capability. Snell's law and the reflection law were applied to construct the freeform refractive surface and the freeform reflective surface for the TIR lens. The freeform refractive surface was transformed into the freeform Fresnel surface with universal design method of Fresnel lens. The simulation result for the freeform Fresnel TIR lens obtained by Monte Carlo ray tracing shows that the far field illumination uniformity of 82.0% and the luminous efficiency of 96.6% are achieved for the light source size of 2 mm×2 mm, in the meanwhile the lens weight is only 21.94 g. The freeform Fresnel TIR lens has nearly 20% reduction in lens weight and volume, only a 2% reduction in luminous efficiency, and no reduction in illumination uniformity compared to the TIR lens without the Fresnel surface. The result indicates that the Fresnelization for freeform surface of TIR lens can significantly reduce the volume and weight of TIR lens and shorten the optical path length, thus effectively improve its heat dissipation efficiency and service life while maintaining a high performance.
    $ {\int }_{{\theta }_{\rm{i}}}^{{\theta }_{i+1}}{I}_{\theta } \varOmega ={\int }_{{S}_{i}}^{{S}_{i+1}}E{\rm{d}}S $(1)

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    $ {\varphi }_{\rm{t}}=2\pi {\int }_{0}^{\frac{\pi }{2}}{I}_{\theta }{\rm{sin}}\theta {\rm{d}}\theta $(2)

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    $ 2{\rm{\pi }}{\int }_{{\theta }_{\rm{i}}}^{{\theta }_{i+1}}{I}_{\theta }{\rm{sin}}\theta {\rm{d}}\theta =\dfrac{{\varphi }_{\rm{t}}}{N}=\dfrac{2\pi }{N}{\int }_{0}^{\frac{\pi }{2}}{I}_{\theta }{\rm{sin}}\theta {\rm{d}}\theta $(3)

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    $ {S}_{0}=\pi {r}_{i+1}^{2}-\pi {{r}}_{i}^{2}=\dfrac{\pi {R}^{2}}{N} \left( {i = 0,1,\;2,\;3,\;\cdots N - 1} \right) $ (4)

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    $ {\left[1+{n}^{2}-2n\left({{O}} \cdot {{I}}\right)\right]}^{1/2} \cdot {{N}}={{O}}-n{{I}} $(5)

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    $ \sqrt{2-2\left({{O}} \cdot {{I}}\right)} \cdot {{N}}={{O}}-{{I}} $(6)

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    $ {y}_{1i+1}=h $(7)

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    $ {x}_{1i+1}=h×\tan\left({A}_{i+1}\right) $(8)

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    $ {x}_{2i+1}=\dfrac{{y}_{2i}-{y}_{1i+1}+{\rm{cot}}\left({P}_{i+1}\right){x}_{1i+1}-{k}_{2i}{x}_{2i}}{{\rm{cot}}\left({P}_{i+1}\right)-{k}_{2i}} $(9)

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    $ \begin{array}{l} {y}_{2i+1}=\dfrac{{k}_{2i}[{y}_{2i}-{y}_{1i+1}+{\rm{cot}}\left({P}_{i+1}\right){x}_{1i+1}-{k}_{2i}{x}_{2i}]}{{\rm{cot}}\left({P}_{i+1}\right)-{k}_{2i}}-\\ \;\;\;\;\;\;\;\;\;\;\;\;{k}_{2i}{x}_{2i}+{y}_{2i} \end{array}$(10)

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    $ {k}_{2i}=\dfrac{\dfrac{{(x}_{4i}-{x}_{2i})}{\sqrt{{({x}_{4i}-{x}_{2i})}^{2}+{({y}_{4i}-{y}_{2i})}^{2}}}-\dfrac{n({x}_{2i}-{x}_{1i})}{\sqrt{{{x}_{2i}}^{2}+{{y}_{2i}}^{2}}}}{\dfrac{n({y}_{2i}-{y}_{1i})}{\sqrt{{{x}_{2i}}^{2}+{{y}_{2i}}^{2}}}-\dfrac{({y}_{4i}-{y}_{2i})}{\sqrt{{({x}_{4i}-{x}_{2i})}^{2}+{({y}_{4i}-{y}_{2i})}^{2}}}} $ (11)

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    $ {x}_{4,t+1}=\dfrac{{-y}_{4,t}+{y}_{3,t+1}-{m}_{3,t+1}{x}_{3,t+1}+{p}_{4,t}{x}_{4,t}}{{p}_{4,t}-{m}_{3,t+1}} $(12)

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    $ {y}_{4,t+1}={p}_{4,t}\left({x}_{4,t+1}-{x}_{4,t}\right)+{y}_{4,t} $(13)

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    $ {m}_{3,t+1}=\dfrac{{y}_{4,t+1}-{y}_{3,t+1}}{{x}_{4,t+1}-{x}_{3,t+1}} $(14)

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    $ {p}_{4,t}=\dfrac{\dfrac{({x}_{4,t}-{x}_{3,t})}{\sqrt{{({x}_{4,t}-{x}_{3,t})}^{2}+{({y}_{4,t}-{y}_{3,t})}^{2}}}}{\dfrac{({y}_{4,t}-{y}_{3,t})}{\sqrt{{({x}_{4,t}-{x}_{3,t})}^{2}+{({y}_{4,t}-{y}_{3,t})}^{2}}}} $(15)

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    $ \Delta R={R}_{j+1}-{R}_{j}=d(0\leqslant j\leqslant N) $(16)

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    $ \Delta r=d/M $(17)

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    $ {R}_{j}= j\times d $(18)

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    $ {r}_{ji}={R}_{j}+i\Delta r(0\leqslant i \leqslant M) $(19)

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    $ {{U}}=\dfrac{{E}_{{\rm{max}}}+{E}_{\min}}{2\cdot {E}_{{\rm{max}}}}=\dfrac{1}{2}+\dfrac{{E}_{\min}}{{2\cdot E}_{{\rm{max}}}} $(20)

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    Tiantian Hu, Chunmei Zeng, Congshan Rui, Yang Hong, Suodong Ma. Optical design of freeform Fresnel TIR lens for LED uniform illumination[J]. Infrared and Laser Engineering, 2021, 50(2): 20200183
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