Abstract

A feedback modification method based on variable separation mapping is proposed in the design of free-form optical system with uniform illuminance for LED source. In this method, the non-negligible size of LED source is taken into account, and a smooth optical system is established with single freeform surface regenerated by adding feedback to the lens design for a point light source. More rounds of feedback can improve the lens performance. As an example, a smooth free-form lens with rectangular illuminance distribution is designed, and the illuminance uniformity is improved from 18.75% to 81.08% after eight times feedback.

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  1. R. Winston, J. C. Miñano, and P. Benítez, eds., with contributions by N. Shatz and J. C. Bortz, eds., Nonimaging Optics (Elsevier, 2005), Chapter 7.
  2. J. S. Schruben, “Formulation a reflector-design problem for a lighting fixture,” J. Opt. Soc. Am. A 6, 1498–1501 (1972).
  3. H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
    [CrossRef]
  4. A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
    [CrossRef]
  5. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
    [CrossRef]
  6. L. Caffarelli, S. Kochengin, and V. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math. 226, 13–32 (1999).
  7. X.-J. Wang, “On design of a reflector antenna II,” Calculus Var. Partial Differ. Equ. 20(3), 329–341 (2004).
    [CrossRef]
  8. W. A. Parkyn, “The design of illumination lenses via extrinsic differential geometry,” Proc. SPIE 3482, 191–193 (1998).
  9. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007).
    [CrossRef] [PubMed]
  10. P. Benítez, 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, 1489–1502 (2004).
    [CrossRef]
  11. Y. Han, X. Zhang, Z. Feng, K. Qian, H. Li, Y. Luo, X. Li, G. Huang, and B. Zhu, “Variable-separation three dimensional freeform nonimaging optical system design based on target-to-source mapping and micro belt surface construction, ” Sciencepaper Online 1–9(2010). http://www.paper.edu.cn/en/paper.php?serial_number=201002-443
  12. L. Piegl and W. Tiller, The NURBS Book 2nd, ed (Springer-Verlag, Berlin, 1997).

2007

2005

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
[CrossRef]

2004

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

X.-J. Wang, “On design of a reflector antenna II,” Calculus Var. Partial Differ. Equ. 20(3), 329–341 (2004).
[CrossRef]

2003

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

2002

1999

L. Caffarelli, S. Kochengin, and V. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math. 226, 13–32 (1999).

1998

W. A. Parkyn, “The design of illumination lenses via extrinsic differential geometry,” Proc. SPIE 3482, 191–193 (1998).

1972

J. S. Schruben, “Formulation a reflector-design problem for a lighting fixture,” J. Opt. Soc. Am. A 6, 1498–1501 (1972).

Benítez, P.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Blen, J.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Caffarelli, L.

L. Caffarelli, S. Kochengin, and V. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math. 226, 13–32 (1999).

Chaves, J.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Dross, O.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Falicoff, W.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Hernández, M.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Kochengin, S.

L. Caffarelli, S. Kochengin, and V. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math. 226, 13–32 (1999).

Luo, Y.

Miñano, J. C.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Mohedano, R.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Muschaweck, J.

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

Muschaweck, J. A.

Oliker, V.

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
[CrossRef]

L. Caffarelli, S. Kochengin, and V. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math. 226, 13–32 (1999).

Parkyn, W. A.

W. A. Parkyn, “The design of illumination lenses via extrinsic differential geometry,” Proc. SPIE 3482, 191–193 (1998).

Qian, K. Y.

Ries, H.

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
[CrossRef]

Schruben, J. S.

J. S. Schruben, “Formulation a reflector-design problem for a lighting fixture,” J. Opt. Soc. Am. A 6, 1498–1501 (1972).

Timinger, A.

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

Wang, L.

Wang, X.-J.

X.-J. Wang, “On design of a reflector antenna II,” Calculus Var. Partial Differ. Equ. 20(3), 329–341 (2004).
[CrossRef]

Appl. Opt.

Calculus Var. Partial Differ. Equ.

X.-J. Wang, “On design of a reflector antenna II,” Calculus Var. Partial Differ. Equ. 20(3), 329–341 (2004).
[CrossRef]

Contemp. Math.

L. Caffarelli, S. Kochengin, and V. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math. 226, 13–32 (1999).

J. Opt. Soc. Am. A

J. S. Schruben, “Formulation a reflector-design problem for a lighting fixture,” J. Opt. Soc. Am. A 6, 1498–1501 (1972).

H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
[CrossRef]

Opt. Eng.

P. Benítez, 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, 1489–1502 (2004).
[CrossRef]

Proc. SPIE

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
[CrossRef]

W. A. Parkyn, “The design of illumination lenses via extrinsic differential geometry,” Proc. SPIE 3482, 191–193 (1998).

Other

R. Winston, J. C. Miñano, and P. Benítez, eds., with contributions by N. Shatz and J. C. Bortz, eds., Nonimaging Optics (Elsevier, 2005), Chapter 7.

Y. Han, X. Zhang, Z. Feng, K. Qian, H. Li, Y. Luo, X. Li, G. Huang, and B. Zhu, “Variable-separation three dimensional freeform nonimaging optical system design based on target-to-source mapping and micro belt surface construction, ” Sciencepaper Online 1–9(2010). http://www.paper.edu.cn/en/paper.php?serial_number=201002-443

L. Piegl and W. Tiller, The NURBS Book 2nd, ed (Springer-Verlag, Berlin, 1997).

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Figures (8)

Fig. 1
Fig. 1

(a). The direction of the rays can be controlled precise in the design with point light source. (b).Deviation caused by real size LED with single optical surface.

Fig. 2
Fig. 2

Slicing of the target plane and source angle region with energy conservation and variable separated Method. Each pair of corresponding cells contain same amount of energy. (a). Topological mapping from the source to target plane. (b).Topological mapping from target plane to the source.

Fig. 3
Fig. 3

Freeform surface construction: The curve C(j+1) is generated from the previous curve C(j), which specifies a smooth freeform surface, wherein j=1,2,3,…

Fig. 4
Fig. 4

A flow diagram of free-form lens design with LED.

Fig. 5
Fig. 5

Sketch of the setting: Length units are arbitrary; the drawing is not to scale.

Fig. 6
Fig. 6

The curve of the illuminance uniformity changed with the times of feedback.

Fig. 7
Fig. 7

Simulation results based on the Monte Carlo method of rectangular illuminance distribution before feedback and after eight feedbacks. (a). the first simulation result;(b). the ninth simulation result.

Fig. 8
Fig. 8

The freeform lens models with LEDs before and after eight times feedback. (a). the initial lens model; (b). the final lens model after eight times feedback; (c). the cross-sectional profiles on the yz plane of the initial and final lens; (d). the cross-sectional profiles on the xz plane of the initial and final lens.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

Ω I ( u , v ) | J ( u , v ) | d u d v = D E ( x , y ) | J ( x , y ) | d x d y
x = f 1 ( u )
y | x = f 1 ( u ) = h ( v | u )
u = f 2 ( x )
v | u = f 2 ( x ) = g ( y | x )
Out = ( T ( x 0 , y 0 , z 0 ) P ( r 0 , u 0 , v 0 ) ) / | T ( x 0 , y 0 , z 0 ) P ( r 0 , u 0 , v 0 ) |
N = ( Out n In ) / | ( Out n In ) |
( P ( r , u , v ) P ( r 0 , u 0 , v 0 ) ) N = 0
E i + 1 ( x , y ) = η i ( x , y ) E 0 ( x , y ) = η i ( E ' i ( x , y ) , E ' i 1 ( x , y ) , ... , E ' 1 ( x , y ), E 0 ( x , y )) E 0 ( x , y ) = η i ( E i ( x , y ) , E ' i ( x , y ) ) E 0 ( x , y )
η i ( x , y ) = E 0 ( x , y ) E ' i ( x , y ) E 0 ( x , y ) E ' i 1 ( x , y ) E 0 ( x , y ) E ' 1 ( x , y ) = 1 E ' i ( x , y ) [ E 0 ( x , y ) E ' i 1 ( x , y ) E 0 ( x , y ) E ' i 2 ( x , y ) E 0 ( x , y ) E ' 1 ( x , y ) E 0 ( x , y ) ] = E i ( x , y ) E ' i ( x , y )
η i ( x , y ) = β i ( x , y ) β i 1 ( x , y ) β 1 ( x , y )
β i ( x , y ) = { r 1 , i f E 0 ( x , y ) E ' i ( x , y ) r 1 E 0 ( x , y ) E ' i ( x , y ) , i f r 1 < E 0 ( x , y ) E ' i ( x , y ) r 2 r 2 , i f E 0 ( x , y ) E ' i ( x , y ) > r 2
η i ( l , m ) = β i ( l , m ) β i 1 ( l , m ) β 1 ( l , m )
β i ( l , m ) = { 0.5 , i f E 0 ( l , m ) E ' i ( l , m ) 0.5 E 0 ( l , m ) E ' i ( l , m ) , i f 0.5 < E 0 ( l , m ) E ' i ( l , m ) 2 2 , i f E 0 ( l , m ) E ' i ( l , m ) > 2
U n i f o r m i t y = E ' i min E ' i a v e r a g e

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