Abstract

A method for generating smooth freeform optical surfaces from B-spline is proposed. In this method, the unit tangent vectors of feature data points are employed as constraints. Based on design methods of freeform surface, both feature data points and unit tangent vectors are obtained, and control points and knot vectors of the freeform surface are computed by the interpolation theory. The freeform surfaces are constructed with the control points and knot vectors to ensure the desired normal at each feature data point. Freeform surfaces are constructed by this method and compared with the traditional method. The results show that beams are controlled well by this method with a maximum uniformity more than 99%, and better results can be obtained with fewer feature data points for this method.

© 2011 Optical Society of America

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References

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2011

2010

2009

2008

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16, 12958–12966 (2008).
[CrossRef] [PubMed]

M. G. Turner and K. J. Garcia, “Optimization using rational Bézier control points and weighting factors,” Proc. SPIE 7061, 70610H (2008).
[CrossRef]

2007

2006

2004

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

T. L. R. Davenport, T. A. Hougha, and W. J. Cassarlya, “Optimization for illumination systems: the next level of design,” Proc. SPIE 5456, 81–90 (2004).
[CrossRef]

J. Bortz, N. Shatz, and M. Keuper, “Optimal design of a nonimaging TIR doublet lens for an illumination system using an LED source,” Proc. SPIE 5529, 8–16 (2004).
[CrossRef]

2002

W. J. Cassarly and M. J. Hayford, “Illumination optimization: the revolution has begun,” Proc. SPIE 4832, 258–269 (2002).
[CrossRef]

T. R. Davenport, “3D NURBS representation of surfaces for illumination,” Proc. SPIE 4832, 293–301 (2002).
[CrossRef]

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

2000

1995

1994

1993

1984

W. Böhm, G. Farin, and J. Kahmann, “A survey of curve and surface methods in CAGD,” Comp. Aided Geom. Des. 1, 1–60(1984).
[CrossRef]

Alvarez, J. L.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

Benitez, P.

Benítez, P.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

Blen, J.

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

Böhm, W.

W. Böhm, G. Farin, and J. Kahmann, “A survey of curve and surface methods in CAGD,” Comp. Aided Geom. Des. 1, 1–60(1984).
[CrossRef]

Bortz, J.

J. Bortz, N. Shatz, and M. Keuper, “Optimal design of a nonimaging TIR doublet lens for an illumination system using an LED source,” Proc. SPIE 5529, 8–16 (2004).
[CrossRef]

Cassarly, W. J.

W. J. Cassarly and M. J. Hayford, “Illumination optimization: the revolution has begun,” Proc. SPIE 4832, 258–269 (2002).
[CrossRef]

Cassarlya, W. J.

T. L. R. Davenport, T. A. Hougha, and W. J. Cassarlya, “Optimization for illumination systems: the next level of design,” Proc. SPIE 5456, 81–90 (2004).
[CrossRef]

Chaves, J.

A. Cvetkovic, O. Dross, J. Chaves, P. Benitez, J. C. Miñano, and R. Mohedano, “Etendue-preserving mixing and projection optics for high-luminance LEDs, applied to automotive headlamps,” Opt. Express 14, 13014–13020 (2006).
[CrossRef] [PubMed]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

Chen, F.

Chitode, J. S.

J. S. Chitode, Numerical Methods (Technical Publications Pune, 2010).

Cvetkovic, A.

Davenport, T. L. R.

T. L. R. Davenport, T. A. Hougha, and W. J. Cassarlya, “Optimization for illumination systems: the next level of design,” Proc. SPIE 5456, 81–90 (2004).
[CrossRef]

Davenport, T. R.

T. R. Davenport, “3D NURBS representation of surfaces for illumination,” Proc. SPIE 4832, 293–301 (2002).
[CrossRef]

de Casteljau, P.

Y. Gardan and P. de Casteljau, Shape Mathematics and CAD (Kogan Page, 1986).

Ding, Y.

Dross, O.

A. Cvetkovic, O. Dross, J. Chaves, P. Benitez, J. C. Miñano, and R. Mohedano, “Etendue-preserving mixing and projection optics for high-luminance LEDs, applied to automotive headlamps,” Opt. Express 14, 13014–13020 (2006).
[CrossRef] [PubMed]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

Falicoff, W.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

Farin, G.

W. Böhm, G. Farin, and J. Kahmann, “A survey of curve and surface methods in CAGD,” Comp. Aided Geom. Des. 1, 1–60(1984).
[CrossRef]

Feng, Z. X.

Gao, H. F.

W. Z. Zhang, Q. X. Liu, H. F. Gao, and F. H. Yu, “Free-form reflector optimization for general lighting,” Opt. Eng. 49, 063003 (2010).
[CrossRef]

Garcia, K. J.

M. G. Turner and K. J. Garcia, “Optimization using rational Bézier control points and weighting factors,” Proc. SPIE 7061, 70610H (2008).
[CrossRef]

Gardan, Y.

Y. Gardan and P. de Casteljau, Shape Mathematics and CAD (Kogan Page, 1986).

Gordon, J. M.

Gu, P. F.

Han, Y. J.

Hao, X.

Hayford, M. J.

W. J. Cassarly and M. J. Hayford, “Illumination optimization: the revolution has begun,” Proc. SPIE 4832, 258–269 (2002).
[CrossRef]

Hernández, M.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

Hougha, T. A.

T. L. R. Davenport, T. A. Hougha, and W. J. Cassarlya, “Optimization for illumination systems: the next level of design,” Proc. SPIE 5456, 81–90 (2004).
[CrossRef]

Kahmann, J.

W. Böhm, G. Farin, and J. Kahmann, “A survey of curve and surface methods in CAGD,” Comp. Aided Geom. Des. 1, 1–60(1984).
[CrossRef]

Keuper, M.

J. Bortz, N. Shatz, and M. Keuper, “Optimal design of a nonimaging TIR doublet lens for an illumination system using an LED source,” Proc. SPIE 5529, 8–16 (2004).
[CrossRef]

Li, H. F.

Li, H. T.

Liu, Q. X.

W. Z. Zhang, Q. X. Liu, H. F. Gao, and F. H. Yu, “Free-form reflector optimization for general lighting,” Opt. Eng. 49, 063003 (2010).
[CrossRef]

Liu, S.

Liu, X.

Luo, X. B.

Luo, Y.

Miñano, J. C.

A. Cvetkovic, O. Dross, J. Chaves, P. Benitez, J. C. Miñano, and R. Mohedano, “Etendue-preserving mixing and projection optics for high-luminance LEDs, applied to automotive headlamps,” Opt. Express 14, 13014–13020 (2006).
[CrossRef] [PubMed]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

Mohedano, R.

A. Cvetkovic, O. Dross, J. Chaves, P. Benitez, J. C. Miñano, and R. Mohedano, “Etendue-preserving mixing and projection optics for high-luminance LEDs, applied to automotive headlamps,” Opt. Express 14, 13014–13020 (2006).
[CrossRef] [PubMed]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

Muñoz, F.

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

Muschaweck, J.

Oliker, V.

Ong, P. T.

Paikyn, B.

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

Piegl, L.

L. Piegl and W. Tiller, The Nurbs Books, 2nd ed. (Springer-Verlag, 1997).
[CrossRef]

Qin, Z.

Rabl, A.

Ries, H.

Ries, H. R.

Schwarte, R.

Shatz, N.

J. Bortz, N. Shatz, and M. Keuper, “Optimal design of a nonimaging TIR doublet lens for an illumination system using an LED source,” Proc. SPIE 5529, 8–16 (2004).
[CrossRef]

Tai, W.

Tiller, W.

L. Piegl and W. Tiller, The Nurbs Books, 2nd ed. (Springer-Verlag, 1997).
[CrossRef]

Turner, M. G.

M. G. Turner and K. J. Garcia, “Optimization using rational Bézier control points and weighting factors,” Proc. SPIE 7061, 70610H (2008).
[CrossRef]

Wang, K.

Winston, R.

Wu, D.

Wu, R. M.

Yu, F. H.

W. Z. Zhang, Q. X. Liu, H. F. Gao, and F. H. Yu, “Free-form reflector optimization for general lighting,” Opt. Eng. 49, 063003 (2010).
[CrossRef]

Zhang, W. Z.

W. Z. Zhang, Q. X. Liu, H. F. Gao, and F. H. Yu, “Free-form reflector optimization for general lighting,” Opt. Eng. 49, 063003 (2010).
[CrossRef]

Zheng, Z. R.

Appl. Opt.

Comp. Aided Geom. Des.

W. Böhm, G. Farin, and J. Kahmann, “A survey of curve and surface methods in CAGD,” Comp. Aided Geom. Des. 1, 1–60(1984).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

W. Z. Zhang, Q. X. Liu, H. F. Gao, and F. H. Yu, “Free-form reflector optimization for general lighting,” Opt. Eng. 49, 063003 (2010).
[CrossRef]

F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Paikyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530(2004).
[CrossRef]

Opt. Express

Proc. SPIE

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. L. Alvarez, and W. Falicoff, “SMS design method in 3D geometry: examples and applications,” Proc. SPIE 5185, 18–29 (2004).
[CrossRef]

O. Dross, R. Mohedano, P. Benítez, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS design methods and real world applications,” Proc. SPIE 5529, 35–47(2004).
[CrossRef]

W. J. Cassarly and M. J. Hayford, “Illumination optimization: the revolution has begun,” Proc. SPIE 4832, 258–269 (2002).
[CrossRef]

T. L. R. Davenport, T. A. Hougha, and W. J. Cassarlya, “Optimization for illumination systems: the next level of design,” Proc. SPIE 5456, 81–90 (2004).
[CrossRef]

T. R. Davenport, “3D NURBS representation of surfaces for illumination,” Proc. SPIE 4832, 293–301 (2002).
[CrossRef]

J. Bortz, N. Shatz, and M. Keuper, “Optimal design of a nonimaging TIR doublet lens for an illumination system using an LED source,” Proc. SPIE 5529, 8–16 (2004).
[CrossRef]

M. G. Turner and K. J. Garcia, “Optimization using rational Bézier control points and weighting factors,” Proc. SPIE 7061, 70610H (2008).
[CrossRef]

Other

L. Piegl and W. Tiller, The Nurbs Books, 2nd ed. (Springer-Verlag, 1997).
[CrossRef]

R. Winston, Nonimaging Optics, 2nd ed. (SPIE, 2005).

Y. Gardan and P. de Casteljau, Shape Mathematics and CAD (Kogan Page, 1986).

J. S. Chitode, Numerical Methods (Technical Publications Pune, 2010).

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Figures (14)

Fig. 1
Fig. 1

A net of data points and unit tangent vectors in u and v directions at each data point for local bicubic surface interpolation.

Fig. 2
Fig. 2

Computed control points of a set of data points with u = const ( v = const ).

Fig. 3
Fig. 3

A bicubic Bézier patch with 16 control points.

Fig. 4
Fig. 4

(a) Geometric relationship of the freeform surface and the rays. (b) Annular uniform illumination on the target plane.

Fig. 5
Fig. 5

Irradiance distribution and surface differences when N = 7 . Irradiance distribution on the target plane for (a) the traditional method and (b) the new construction method. (c) Profiles of the freeform surfaces constructed from the two construction methods. The red solid line represents the new method, and the blue dashed line represents the traditional method. (d) Radial distance difference Δ ρ versus φ when N = 7 .

Fig. 6
Fig. 6

Irradiance curves for the two methods. The red solid line represents the new method, and the blue dashed line represents the traditional method. (a)  N = 7 and (b)  N = 47 .

Fig. 7
Fig. 7

The relations between the surface differences and the number of data points from N = 7 to N = 47 . Usually, there are obvious differences between the freeform surfaces constructed from the new method and the traditional method. Both the unit normals at the same data point on two surfaces cannot coincide, angles are formed between each two normals, and radial distance ρ of two sample points with the same angel φ is also different. (a) Average angular difference versus number of data points and (b) average Δ ρ versus number of data points.

Fig. 8
Fig. 8

Irradiance distribution for N = 17 obtained from (a) the traditional method and (b) the new method.

Fig. 9
Fig. 9

The relations between the surface differences and the number of data points from N = 7 to N = 47 . (a) Average angular difference versus number of data points and (b) average sag difference versus number of data points.

Fig. 10
Fig. 10

Schematic representation of the freeform lens.

Fig. 11
Fig. 11

The desired dipole pattern on the target plane.

Fig. 12
Fig. 12

Irradiance distribution on the target plane when N = 30 for (a)  the traditional method and (b)  the new method.

Fig. 13
Fig. 13

Irradiance curves for the two methods. The solid line represents irradiance distribution along the line x = 0 mm , and the dashed line represents irradiance distribution along the line y = 35 mm . (a) and (c) represent the new method. (b) and (d) represent the traditional method.

Fig. 14
Fig. 14

The relations between the surface differences and the number of data points. Obvious differences between the freeform surfaces constructed from the new method and the traditional method usually exist. Both the unit normals at the same data point on two surfaces cannot coincide, angles are formed between each two normals, and coordinates z of two sample points with the same coordinates x and y are also different. For each specified number of data points, the average angular difference and the average Δ z are calculated at all data points and sample points. (a) Average angular difference versus number of data points and (b) average Δ z versus number of data points.

Tables (5)

Tables Icon

Table 1 Design Parameters for Annular Illumination

Tables Icon

Table 2 Comparison of Irradiance Uniformities for the Two Construction Methods

Tables Icon

Table 3 Comparison of Irradiance Uniformities for the Two Construction Methods

Tables Icon

Table 4 Design Parameters for Dipole Uniform Illumination (mm) a

Tables Icon

Table 5 Comparison of Irradiance Uniformities for the Two Construction Methods

Equations (14)

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S ( u , v ) = i = 0 n j = 0 m N i , p ( u ) N j , q ( v ) P i , j , 0 u 1 , 0 v 1 ,
P 0 , 1 k 0 , l = Q k 0 , l + a T k 0 , l v P 0 , 2 k 0 , l = Q k 0 , l + 1 a T k 0 , l + 1 v ,
D k , l u = s l T k , l u D k , l v = r k T k , l v .
{ d k , l v u = ( 1 α k ) D k , l v D k 1 , l v Δ u ¯ k + α k D k + 1 , l v D k , l v Δ u ¯ k + 1 d k , l u v = ( 1 β l ) D k , l u D k , l 1 u Δ v ¯ l + β k D k , l + 1 u D k , l u Δ v ¯ l + 1 ,
D k , l u v = ( α k d k , l u v + β l d k , l v u ) / ( α k + β l ) .
{ P 1 , 1 k , l = γ D k , l u v + P 0 , 1 k , l + P 1 , 0 k , l P 0 , 0 k , l P 2 , 1 k , l = γ D k + 1 , l u v + P 3 , 1 k , l P 3 , 0 k , l + P 2 , 0 k , l P 1 , 2 k , l = γ D k , l + 1 u v + P 1 , 3 k , l P 0 , 3 k , l + P 0 , 2 k , l P 2 , 2 k , l = γ D k + 1 , l + 1 u v + P 2 , 3 k , l + P 3 , 2 k , l P 3 , 2 k , l ,
{ U = { 0 , 0 , 0 , 0 , u ¯ 1 , u ¯ 1 , u ¯ 2 , u ¯ 2 , , u ¯ n 1 , u ¯ n 1 , 1 , 1 , 1 , 1 } V = { 0 , 0 , 0 , 0 , v ¯ 1 , v ¯ 1 , v ¯ 2 , v ¯ 2 , , v ¯ n 1 , v ¯ n 1 , 1 , 1 , 1 , 1 } .
| C ( 0 ) | = | C ( 1 / 2 ) | = | C ( 1 ) | = a ,
A a 2 + B a + C = 0 ,
U = { 0 , 0 , 0 , 0 , u ¯ 1 u ¯ n , u ¯ 1 u ¯ n , u ¯ 2 u ¯ n , u ¯ 2 u ¯ n , , u ¯ n 1 u ¯ n , u ¯ n 1 u ¯ n , 1 , 1 , 1 , 1 } ,
ρ φ = f ( ρ , φ ) ,
T = P φ / | P φ | = ( ρ φ × I + ρ × I φ ) / | ( ρ φ × I + ρ × I φ ) | ,
{ z x = n o O x / ( n o O z n I ) z y = n o O y / ( n o O z n I ) ,
T x = ( 1 1 + z x 2 , 0 , z x 1 + z x 2 ) , T y = ( 0 , 1 1 + z y 2 , z y 1 + z y 2 ) .

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