Abstract

To improve the optical performance of LED-based lighting devices, refractive optical elements are usually used. We propose a novel technique for the computation of free-form optical elements with two refractive surfaces generating the required illuminance or intensity distribution. The proposed approach makes it possible to control the balance of deflection angles between the inner and outer surfaces of the optical element. It has been proved that for the point light source, the maximal efficiency is obtained when each refractive surface performs exactly the half of the required ray deflection. As an example, a set of optical elements producing a uniformly illuminated square region is computed. Simulation of the computed designs with extended sources has shown that the most tolerant solutions to the size of the light source are obtained in the case when the inner surface performs 60–80% of the ray deflection, and the outer surface performs the remaining 20–40%. The influence of deflection balance on the size of the optical element is discussed.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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2015 (2)

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Y. Ma, H. Zhang, Z. Su, Y. He, L. Xu, X. Liu, and H. Li, “Hybrid method of free-form lens design for arbitrary illumination target,” Appl. Opt. 54(14), 4503–4508 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (6)

2012 (4)

2011 (1)

2004 (1)

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

1998 (1)

P. Guan and X.-J. Wang, “On a Monge-Ampere equation arising in geometric optics,” J. Differ. Geom. 48(2), 205–223 (1998).

1978 (1)

Bäuerle, A.

Benitez, P.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Benítez, P.

Blen, J.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Borisova, K. V.

M. A. Moiseev, L. L. Doskolovich, K. V. Borisova, and E. V. Byzov, “Fast and robust technique for design of axisymmetric TIR optics in case of an extended light source,” J. Mod. Opt. 60(14), 1100–1106 (2013).
[Crossref]

Bräuer, A.

Bruneton, A.

Byzov, E. V.

M. A. Moiseev, L. L. Doskolovich, K. V. Borisova, and E. V. Byzov, “Fast and robust technique for design of axisymmetric TIR optics in case of an extended light source,” J. Mod. Opt. 60(14), 1100–1106 (2013).
[Crossref]

Chaves, J.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Chen, H.-C.

Chiu, H.-Y.

Doskolovich, L. L.

M. A. Moiseev, L. L. Doskolovich, K. V. Borisova, and E. V. Byzov, “Fast and robust technique for design of axisymmetric TIR optics in case of an extended light source,” J. Mod. Opt. 60(14), 1100–1106 (2013).
[Crossref]

M. A. Moiseev and L. L. Doskolovich, “Design of TIR optics generating the prescribed irradiance distribution in the circle region,” J. Opt. Soc. Am. A 29(9), 1758–1763 (2012).
[Crossref] [PubMed]

Dross, O.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Duerr, F.

Elmer, W. B.

Falicoff, W.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Feng, Z.

Gan, Z.

R. Hu, Z. Gan, X. Luo, H. Zheng, and S. Liu, “Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses,” Optik (Stuttg.) 124(19), 3895–3897 (2013).
[Crossref]

R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012).
[Crossref] [PubMed]

Gong, M.

Guan, P.

P. Guan and X.-J. Wang, “On a Monge-Ampere equation arising in geometric optics,” J. Differ. Geom. 48(2), 205–223 (1998).

He, Y.

Hernandez, M.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Hu, R.

R. Hu, Z. Gan, X. Luo, H. Zheng, and S. Liu, “Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses,” Optik (Stuttg.) 124(19), 3895–3897 (2013).
[Crossref]

R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012).
[Crossref] [PubMed]

Huang, L.

Jin, G.

Li, H.

Lin, J.-Y.

Lin, K. Ch.

K. Ch. Lin, “Weighted least-square design of freeform lens for multiple point sources,” Opt. Eng. 51(4), 043002 (2012).
[Crossref]

Liu, S.

R. Hu, Z. Gan, X. Luo, H. Zheng, and S. Liu, “Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses,” Optik (Stuttg.) 124(19), 3895–3897 (2013).
[Crossref]

R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012).
[Crossref] [PubMed]

Liu, X.

Loosen, P.

Luo, X.

R. Hu, Z. Gan, X. Luo, H. Zheng, and S. Liu, “Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses,” Optik (Stuttg.) 124(19), 3895–3897 (2013).
[Crossref]

R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012).
[Crossref] [PubMed]

Ma, Y.

Meuret, Y.

Michaelis, D.

Minano, J. C.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Miñano, J. C.

Mohedano, R.

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Moiseev, M. A.

M. A. Moiseev, L. L. Doskolovich, K. V. Borisova, and E. V. Byzov, “Fast and robust technique for design of axisymmetric TIR optics in case of an extended light source,” J. Mod. Opt. 60(14), 1100–1106 (2013).
[Crossref]

M. A. Moiseev and L. L. Doskolovich, “Design of TIR optics generating the prescribed irradiance distribution in the circle region,” J. Opt. Soc. Am. A 29(9), 1758–1763 (2012).
[Crossref] [PubMed]

Oliker, V.

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Qin, Z.

Rubinstein, J.

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Schreiber, P.

Stollenwerk, J.

Su, Z.

Thienpont, H.

Wang, X.-J.

P. Guan and X.-J. Wang, “On a Monge-Ampere equation arising in geometric optics,” J. Differ. Geom. 48(2), 205–223 (1998).

Wester, R.

Wolansky, G.

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Wu, B.

Wu, R.

Xu, L.

Zhang, H.

Zhang, Y.

Zheng, H.

R. Hu, Z. Gan, X. Luo, H. Zheng, and S. Liu, “Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses,” Optik (Stuttg.) 124(19), 3895–3897 (2013).
[Crossref]

R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012).
[Crossref] [PubMed]

Adv. Appl. Math. (1)

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Appl. Opt. (2)

J. Differ. Geom. (1)

P. Guan and X.-J. Wang, “On a Monge-Ampere equation arising in geometric optics,” J. Differ. Geom. 48(2), 205–223 (1998).

J. Mod. Opt. (1)

M. A. Moiseev, L. L. Doskolovich, K. V. Borisova, and E. V. Byzov, “Fast and robust technique for design of axisymmetric TIR optics in case of an extended light source,” J. Mod. Opt. 60(14), 1100–1106 (2013).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

K. Ch. Lin, “Weighted least-square design of freeform lens for multiple point sources,” Opt. Eng. 51(4), 043002 (2012).
[Crossref]

P. Benitez, J. C. Minano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernandez, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Optik (Stuttg.) (1)

R. Hu, Z. Gan, X. Luo, H. Zheng, and S. Liu, “Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses,” Optik (Stuttg.) 124(19), 3895–3897 (2013).
[Crossref]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 2003).

V. I. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, F. Tomi, eds. (Springer, 2003).

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Figures (5)

Fig. 1
Fig. 1 Working principle of collimator with two refractive surfaces.
Fig. 2
Fig. 2 The dependence of collimator integrated efficiency on the coefficient k.
Fig. 3
Fig. 3 The cross-sections of the designed optical elements.
Fig. 4
Fig. 4 Optical elements with different values of k and simulation results.
Fig. 5
Fig. 5 Dependence of Fresnel transmission coefficient at the single refractive surface on the ray rotation angle.

Equations (12)

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d R ( ψ ) d ψ = R ( ψ ) sin ( ψ γ ( ψ ) ) 1 / n cos ( ψ γ ( ψ ) ) .
R = R 0 ( n 1 n cos ( ( 1 k ) ψ ) 1 ) 1 1 k ,
R 0 + n l 0 = R ( ψ ) + n l ( ψ ) + ( R 0 + l 0 R ( ψ ) cos ψ l ( ψ ) cos γ ( ψ ) ) ,
l ( ψ ) = l 0 ( n 1 ) R ( ψ ) ( 1 cos ψ ) n cos k ψ .
R ( ψ ) = R ( ψ ) s 0 , r ( ψ ) = R ( ψ ) + l ( ψ ) s 1 ,
R ( s 0 ) = R ( s 0 ) s 0 , r ( s 0 ) = R ( s 0 ) + l ( s 0 ) s 1 ( s 0 ) , R ( s 0 ) = R 0 ( n 1 n cos ( ( 1 k ) arc cos ( s 0 , p ) ) 1 ) 1 1 k , l ( s 0 ) = l 0 ( n 1 ) R ( s 0 ) ( 1 ( s 0 , p ) ) n ( s 1 ( s 0 ) , p ) .
Φ i = δ Ω i I ( p ) d Ω , p i = δ Ω i p I ( p ) d Ω Φ i .
R p ( s 0 ) = R i ( s 0 ) s 0 , i = argmin R j ( s 0 ) , R j ( s 0 ) = R 0 j ( n 1 n cos ( ( 1 k ) arc cos ( s 0 , p j ) ) 1 ) 1 1 k .
r ( s 0 ) = R ( s 0 ) + l i ( s 0 ) s 1 ( s 0 ) , i = arg min l j ( s 0 ) , l j ( s 0 ) = l 0 j ( n 1 ) R ( s 0 ) ( 1 ( s 0 , p j ) ) n ( s 1 ( s 0 ) , p j ) .
I ( p ) = E ( x , y ) x 2 + y 2 + f 2 p z ,
T T ( α ) = T ( α ) T ( δ α ) T ( α ) T ( δ α ) = 0.
T T ( α ) | δ / 2 = 2 T ( δ / 2 ) T ( δ / 2 ) 2 T ( δ / 2 ) 2 .

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