Abstract

A feedback method combined with fitting technique based on variable separation mapping is proposed to design freeform optical systems for an extended LED source with prescribed illumination patterns, especially with uniform illuminance distribution. Feedback process performs well with extended sources, while fitting technique contributes not only to the decrease of pieces of sub-surfaces in discontinuous freeform lenses which may cause loss in manufacture, but also the reduction in the number of feedback iterations. It is proved that light control efficiency can be improved by 5%, while keeping a high uniformity of 82%, with only two feedback iterations and one fitting operation can improve. Furthermore, the polar angle θand azimuthal angleφis used to specify the light direction from the light source, and the (θ,φ)-(x,y) based mapping and feedback strategy makes sure that even few discontinuous sections along the equi-φplane exist in the system, they are perpendicular to the base plane, making it eligible for manufacturing the surfaces using injection molding.

© 2013 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2012

2011

2010

2009

2008

2007

2005

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5924, 594207, 594207-12 (2005).
[CrossRef]

2004

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

2002

1998

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).

Benitez, P.

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

Blen, J.

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

Cassarly, W. J.

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation usingsource-target maps,” Opt. Express18(5), 5295–5304 (2010).
[CrossRef] [PubMed]

W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE7652, 76522L, 76522L-9 (2010).
[CrossRef]

Chaves, J.

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

Chen, F.

K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express17(7), 5457–5465 (2009).
[CrossRef] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
[CrossRef]

Ding, Y.

Dross, O.

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

Falicoff, W.

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

Feng, Z.

Fournier, F. R.

Gan, Z.

Gu, P. F.

Han, Y.

Hernández, M.

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

Hu, R.

Kim, J. K.

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

Li, H.

Liu, S.

Liu, X.

Liu, Z. Y.

K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express17(7), 5457–5465 (2009).
[CrossRef] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
[CrossRef]

Luo, X.

Luo, X. B.

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
[CrossRef]

Luo, Y.

Miñano, J. C.

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

Mohedano, R.

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

Muschaweck, J. A.

Oliker, V.

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5924, 594207, 594207-12 (2005).
[CrossRef]

Parkyn, W. A.

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).

Qian, K. Y.

Qin, Z.

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. Express20(13), 13727–13737 (2012).
[CrossRef] [PubMed]

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
[CrossRef]

Ries, H.

Rolland, J. P.

Schubert, E. F.

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

Situ, W.

Wang, K.

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
[CrossRef]

K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express17(7), 5457–5465 (2009).
[CrossRef] [PubMed]

Wang, L.

Wu, B.

Xiang, H.

Xu, L.

Zheng, H.

Zheng, Z. R.

Zhenrong, Z.

Appl. Opt.

J. Opt. A, Pure Appl. Opt.

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

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

Opt. Express

Proc. SPIE

W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE7652, 76522L, 76522L-9 (2010).
[CrossRef]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5924, 594207, 594207-12 (2005).
[CrossRef]

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).

Science

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

Other

L. Caffarelli and V. Oliker, “Weak solutions of one inverse problem in geometric optics,” J. Math. Sci. 154(1), 37–46 (2008, Preprint, 1994).

A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting.(John Wiley & Sons, 2002).

Florian Fournier, “Freeform reflector design with extended sources”, A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in CREOL, the College of Optics and Photonics at the University of Central Florida Orlando, Florida, 2010.

J. D’Errico, “Surface Fitting using gridfit,” (MATLAB CENTRAL File Exchange, 11 Nov 2005, Updated 29 Jul 2010). http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit .

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Figures (10)

Fig. 1
Fig. 1

Discontinuous section direction and injection molding difficulty (a) discontinuous sections are not perpendicular to the base plane (b) discontinuous sections are perpendicular to the base plane.

Fig. 2
Fig. 2

General Process of the method combined with feedback process and fitting technique.

Fig. 3
Fig. 3

Divide the target plane into cells (Only two equi- φ lines and equi- θ lines are drawn. Points are equally spaced on either axis).

Fig. 4
Fig. 4

( θ,φ )-x coordinate system before(black solid dots) and after(colored surface) fitting technique.

Fig. 5
Fig. 5

A schematic of the target point distribution before and after fitting technique. The figure only shows the right top corner of first quadrant. It can be observed that points are converged inside (green points are clearly denser in the inner part and sparse on the edge), which accounts for the increase in LCE.

Fig. 6
Fig. 6

LED is 1mm*1mm in size. The lens is restricted to 10 mm in height.Target plane is a rectangular zone of 30*10m on the road [9].

Fig. 7
Fig. 7

The freeform lens models with LEDs before and after fitting. (a)Before fitting, there are 22*4 truncation surfaces. (b)After fitting the number reduces to 7*4.

Fig. 8
Fig. 8

Variation of uniformity during feedback iterations and after fitting. (a) Initial. (b) After1 feedback iteration. (c) After 2 feedback iterations. (d) After fitting process.

Fig. 9
Fig. 9

Variation of uniformity and efficiency during feedback iterations and after fitting

Fig. 10
Fig. 10

Illuminance distribution after adding another round of feedback iteration and fitting. It is shown that the uniformity could reach 85%.

Equations (6)

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φ(i,j)= π 2 m=1 i1 E stripe (m) E stripe
E= φ φ+dφ θ θ+dθ I 0 cos 2 θsinφdθdφ
E φ,0~θ E φ,0~ θ end = 0.5*sin( 2θ )+θ 0.5*sin( 2* θ end )+ θ end  
E prescribed =f( E prescribed_pre , E simu , E initial )
E prescribed = E prescribed_pre +( E initial E simu )0.5
E prescribed =  E prescribed_pre ( E simu E initial E simu E source )0.5 

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