Abstract

We propose a novel design methodology to tackle the multi-surface catadioptric freeform lens design for off-axis road illumination applications based on an ideal source. The lens configuration contains an analytic refractive entrance surface, an analytic total internal reflective (TIR) surface and two freeform exit surfaces. A curl-free energy equipartition is established between the source and target plane and applied to implement the composite ray mapping mechanism. Furthermore, the analytic TIR surface and refractive entrance surface are optimized for the minimal Fresnel losses and surface error based on Genetic algorithm (GA). The results show a significant improvement on illuminance uniformity and ultra-high transfer efficiency compared to the design employed our proposed method in [Zhu et al., Opt. Express 26, A54–A65 (2018)].

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. 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]
  2. A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).
    [Crossref] [PubMed]
  3. A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).
    [Crossref] [PubMed]
  4. K. Desnijder, P. Hanselaer, and Y. Meuret, “Ray mapping method for off-axis and non-paraxial freeform illumination lens design,” Opt. Lett. 44, 771–774 (2019).
    [Crossref] [PubMed]
  5. D. Ma, Z. Feng, and R. Liang, “Tailoring freeform illumination optics in a double-pole coordinate system,” Appl. Opt. 54, 2395–2399 (2015).
    [Crossref] [PubMed]
  6. V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method (sqm),” Opt. Express 25, A58–A72 (2017).
    [Crossref]
  7. V. Oliker, “Freeform optical systems with prescribed irradiance properties in near-field,” in International Optical Design Conference 2006, vol. 6342 (International Society for Optics and Photonics, 2006), p. 634211.
    [Crossref]
  8. D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
    [Crossref] [PubMed]
  9. R. Wu, L. Xu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Freeform illumination design: a nonlinear boundary problem for the elliptic monge–ampére equation,” Opt. Lett. 38, 229–231 (2013).
    [Crossref] [PubMed]
  10. R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser & Photonics Rev. 12, 1700310 (2018).
    [Crossref]
  11. P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
    [Crossref]
  12. M. A. Moiseev, S. V. Kravchenko, and L. L. Doskolovich, “Design of efficient led optics with two free-form surfaces,” Opt. Express 22, A1926–A1935 (2014).
    [Crossref]
  13. M. A. Moiseev, E. V. Byzov, S. V. Kravchenko, and L. L. Doskolovich, “Design of led refractive optics with predetermined balance of ray deflection angles between inner and outer surfaces,” Opt. Express 23, A1140–A1148 (2015).
    [Crossref] [PubMed]
  14. S. V. Kravchenko, E. V. Byzov, M. A. Moiseev, and L. L. Doskolovich, “Development of multiple-surface optical elements for road lighting,” Opt. Express 25, A23–A35 (2017).
    [Crossref] [PubMed]
  15. M. A. Moiseev, L. L. Doskolovich, and N. L. Kazanskiy, “Design of high-efficient freeform led lens for illumination of elongated rectangular regions,” Opt. Express 19, A225–A233 (2011).
    [Crossref] [PubMed]
  16. R. Wu, S. Chang, Z. Zheng, L. Zhao, and X. Liu, “Formulating the design of two freeform lens surfaces for point-like light sources,” Opt. Lett. 43, 1619–1622 (2018).
    [Crossref] [PubMed]
  17. Z. Zhu, D. Ma, Q. Hu, Y. Tang, and R. Liang, “Catadioptric freeform optical system design for led off-axis road illumination applications,” Opt. Express 26, A54–A65 (2018).
    [Crossref] [PubMed]
  18. D. Ma, Z. Feng, and R. Liang, “Freeform illumination lens design using composite ray mapping,” Appl. Opt. 54, 498–503 (2015).
    [Crossref]
  19. C. Bösel and H. Gross, “Ray mapping approach for the efficient design of continuous freeform surfaces,” Opt. Express 24, 14271–14282 (2016).
    [Crossref] [PubMed]
  20. Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21, 14728–14735 (2013).
    [Crossref] [PubMed]
  21. Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21, 28693–28701 (2013).
    [Crossref]
  22. Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).
    [Crossref] [PubMed]
  23. R. Wu, Y. Zhang, M. M. Sulman, Z. Zheng, P. Benítez, and J. C. Miñano, “Initial design with l 2 monge-kantorovich theory for the monge–ampère equation method in freeform surface illumination design,” Opt. Express,  2216161–16177 (2014).
    [Crossref] [PubMed]
  24. B. D. Froese and A. M. Oberman, “Convergent filtered schemes for the monge–ampère partial differential equation,” SIAM J. on Numer. Analysis 51, 423–444 (2013).
    [Crossref]
  25. S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
    [Crossref]
  26. M. M. Sulman, J. Williams, and R. D. Russell, “An efficient approach for the numerical solution of the monge–ampère equation,” Appl. Numer. Math. 61, 298–307 (2011).
    [Crossref]
  27. C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
    [Crossref]
  28. J. Herrmann, “Least-squares wave front errors of minimum norm,” JOSA 70, 28–35 (1980).
    [Crossref]

2019 (1)

2018 (3)

2017 (2)

2016 (2)

2015 (4)

2014 (2)

2013 (5)

2012 (1)

2011 (3)

2008 (1)

2004 (2)

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
[Crossref]

1980 (1)

J. Herrmann, “Least-squares wave front errors of minimum norm,” JOSA 70, 28–35 (1980).
[Crossref]

Angenent, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
[Crossref]

Arroyo, R. M.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Bäuerle, A.

Beltman, R.

C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
[Crossref]

Benítez, P.

Blen, J.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Bösel, C.

Bräuer, A.

Bruneton, A.

Byzov, E. V.

Chang, S.

Chaves, J.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Desnijder, K.

Ding, Y.

Doskolovich, L. L.

Dross, O.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Duerr, F.

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser & Photonics Rev. 12, 1700310 (2018).
[Crossref]

Falicoff, W.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Feng, Z.

Froese, B. D.

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).
[Crossref] [PubMed]

B. D. Froese and A. M. Oberman, “Convergent filtered schemes for the monge–ampère partial differential equation,” SIAM J. on Numer. Analysis 51, 423–444 (2013).
[Crossref]

Gimenez-Benitez, P.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Gong, M.

Gross, H.

Gu, P.-f.

Haker, S.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
[Crossref]

Hanselaer, P.

Hernández, M.

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Herrmann, J.

J. Herrmann, “Least-squares wave front errors of minimum norm,” JOSA 70, 28–35 (1980).
[Crossref]

Hu, Q.

Huang, L.

IJzerman, W.

C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
[Crossref]

Jin, G.

Kazanskiy, N. L.

Kravchenko, S. V.

Li, H.

Liang, R.

Liu, P.

Liu, X.

Loosen, P.

Ma, D.

Meuret, Y.

Michaelis, D.

Miñano, J. C.

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser & Photonics Rev. 12, 1700310 (2018).
[Crossref]

R. Wu, Y. Zhang, M. M. Sulman, Z. Zheng, P. Benítez, and J. C. Miñano, “Initial design with l 2 monge-kantorovich theory for the monge–ampère equation method in freeform surface illumination design,” Opt. Express,  2216161–16177 (2014).
[Crossref] [PubMed]

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Moiseev, M. A.

Oberman, A. M.

B. D. Froese and A. M. Oberman, “Convergent filtered schemes for the monge–ampère partial differential equation,” SIAM J. on Numer. Analysis 51, 423–444 (2013).
[Crossref]

Oliker, V.

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method (sqm),” Opt. Express 25, A58–A72 (2017).
[Crossref]

V. Oliker, “Freeform optical systems with prescribed irradiance properties in near-field,” in International Optical Design Conference 2006, vol. 6342 (International Society for Optics and Photonics, 2006), p. 634211.
[Crossref]

Prins, C.

C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
[Crossref]

Russell, R. D.

M. M. Sulman, J. Williams, and R. D. Russell, “An efficient approach for the numerical solution of the monge–ampère equation,” Appl. Numer. Math. 61, 298–307 (2011).
[Crossref]

Schreiber, P.

Stollenwerk, J.

Sulman, M. M.

Tang, Y.

Tannenbaum, A.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
[Crossref]

ten Thije Boonkkamp, J.

C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
[Crossref]

Tukker, T. W.

C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
[Crossref]

Wester, R.

Williams, J.

M. M. Sulman, J. Williams, and R. D. Russell, “An efficient approach for the numerical solution of the monge–ampère equation,” Appl. Numer. Math. 61, 298–307 (2011).
[Crossref]

Wu, R.

Xu, L.

Zhang, Y.

Zhao, L.

Zheng, Z.

Zheng, Z.-r.

Zhu, L.

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
[Crossref]

Zhu, Z.

Appl. Numer. Math. (1)

M. M. Sulman, J. Williams, and R. D. Russell, “An efficient approach for the numerical solution of the monge–ampère equation,” Appl. Numer. Math. 61, 298–307 (2011).
[Crossref]

Appl. Opt. (3)

Int. J. computer vision (1)

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. computer vision 60, 225–240 (2004).
[Crossref]

JOSA (1)

J. Herrmann, “Least-squares wave front errors of minimum norm,” JOSA 70, 28–35 (1980).
[Crossref]

Laser & Photonics Rev. (1)

R. Wu, Z. Feng, Z. Zheng, R. Liang, P. Benítez, J. C. Miñano, and F. Duerr, “Design of freeform illumination optics,” Laser & Photonics Rev. 12, 1700310 (2018).
[Crossref]

Opt. Eng. (1)

P. Gimenez-Benitez, J. C. Miñano, J. Blen, R. M. Arroyo, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1503 (2004).
[Crossref]

Opt. Express (13)

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. A. Moiseev, E. V. Byzov, S. V. Kravchenko, and L. L. Doskolovich, “Design of led refractive optics with predetermined balance of ray deflection angles between inner and outer surfaces,” Opt. Express 23, A1140–A1148 (2015).
[Crossref] [PubMed]

M. A. Moiseev, L. L. Doskolovich, and N. L. Kazanskiy, “Design of high-efficient freeform led lens for illumination of elongated rectangular regions,” Opt. Express 19, A225–A233 (2011).
[Crossref] [PubMed]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).
[Crossref] [PubMed]

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).
[Crossref] [PubMed]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21, 14728–14735 (2013).
[Crossref] [PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21, 28693–28701 (2013).
[Crossref]

R. Wu, Y. Zhang, M. M. Sulman, Z. Zheng, P. Benítez, and J. C. Miñano, “Initial design with l 2 monge-kantorovich theory for the monge–ampère equation method in freeform surface illumination design,” Opt. Express,  2216161–16177 (2014).
[Crossref] [PubMed]

M. A. Moiseev, S. V. Kravchenko, and L. L. Doskolovich, “Design of efficient led optics with two free-form surfaces,” Opt. Express 22, A1926–A1935 (2014).
[Crossref]

C. Bösel and H. Gross, “Ray mapping approach for the efficient design of continuous freeform surfaces,” Opt. Express 24, 14271–14282 (2016).
[Crossref] [PubMed]

S. V. Kravchenko, E. V. Byzov, M. A. Moiseev, and L. L. Doskolovich, “Development of multiple-surface optical elements for road lighting,” Opt. Express 25, A23–A35 (2017).
[Crossref] [PubMed]

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method (sqm),” Opt. Express 25, A58–A72 (2017).
[Crossref]

Z. Zhu, D. Ma, Q. Hu, Y. Tang, and R. Liang, “Catadioptric freeform optical system design for led off-axis road illumination applications,” Opt. Express 26, A54–A65 (2018).
[Crossref] [PubMed]

Opt. Lett. (4)

SIAM J. on Numer. Analysis (1)

B. D. Froese and A. M. Oberman, “Convergent filtered schemes for the monge–ampère partial differential equation,” SIAM J. on Numer. Analysis 51, 423–444 (2013).
[Crossref]

SIAM J. on Sci. Comput. (1)

C. Prins, R. Beltman, J. ten Thije Boonkkamp, W. IJzerman, and T. W. Tukker, “A least-squares method for optimal transport using the monge–ampère equation,” SIAM J. on Sci. Comput. 37, B937–B961 (2015).
[Crossref]

Other (1)

V. Oliker, “Freeform optical systems with prescribed irradiance properties in near-field,” in International Optical Design Conference 2006, vol. 6342 (International Society for Optics and Photonics, 2006), p. 634211.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 The conceptual design configuration of multi-surface catadioptric freeform lens.
Fig. 2
Fig. 2 (a)Cartesian coordinate system for source plane, (b) curl-free mapping between source and image plane.
Fig. 3
Fig. 3 Double surface freeform illumination system diagram.
Fig. 4
Fig. 4 Generating the freeform surface.
Fig. 5
Fig. 5 Design result of the catadioptric freeform lens.
Fig. 6
Fig. 6 (a) The irradiance distribution formed by the refractive part; (b) The irradiance distribution formed by the refractive part; (c) The irradiance distribution of the four surfaces design; (d) the irradiance distribution of the two surfaces design using the method proposed in [17].
Fig. 7
Fig. 7 The irradiance distribution on the road surface of several luminares aligned along the road.

Tables (1)

Tables Icon

Table 1 Parameters of the road illumination system

Equations (16)

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

d e t ( D 2 u ) = E s ( x 1 , x 2 ) E t ( u ( x 1 , x 2 ) ) , ( x 1 , x 2 ) X ,
u ( X ) = Y ,
N = O n I | O n I | ,
( × N ) I = 0 ,
( × N ) I = lim S 0 1 | S | C N d r ,
M F 1 = i , j [ N i , j + N i + 1 , j 2 ( W i + 1 , j W i , j ) + N i + 1 , j + N i + 1 , j + 1 2 ( W i + 1 , j + 1 W i + 1 , j ) + N i + 1 , j + 1 + N i , j + 1 2 ( W i , j + 1 W i + 1 , j + 1 ) + N i , j + 1 + N i , j 2 ( W i , j + 1 W i , j ) ] 2 .
T = 1 1 2 [ s i n 2 ( θ 1 θ 2 ) s i n 2 ( θ 1 + θ 2 ) + t a n 2 ( θ 1 θ 2 ) t a n 2 ( θ 1 + θ 2 ) ] ,
M F 2 = Y E t ( y 1 , y 2 ) d y 1 d y 2 X I ( θ , ϕ ) d θ d ϕ = i , j I 0 c o s θ i , j Ω i , j T 1 i , j T 2 i , j i , j I 0 c o s θ i , j Ω i , j ,
N ^ i , j = O ^ i , j n ρ ^ i , j | O ^ i , j n ρ ^ i , j | ,
( Q i + 1 , j Q i , j ) ( N ^ i + 1 , j + N ^ i , j ) = 0 ,
( Q i , j + 1 Q i , j ) ( N ^ i , j + 1 + N ^ i , j ) = 0 .
ρ ^ i + 1 , j ( N ^ i + 1 , j + N ^ i , j ) ρ i + 1 , j ρ ^ i , j ( N ^ i + 1 , j + N ^ i , j ) ρ i , j = ( r ^ i , j r i , j r ^ i + 1 , j r i + 1 , j ) ( N ^ i + 1 , j + N ^ i , j ) ,
ρ ^ i , j + 1 ( N ^ i , j + 1 + N ^ i , j ) ρ i , j + 1 ρ ^ i , j ( N ^ i , j + 1 + N ^ i , j ) ρ i , j = ( r ^ i , j r i , j r ^ i , j + 1 r i , j + 1 ) ( N ^ i , j + 1 + N ^ i , j ) .
HP = b ,
P = ( H T H ) 1 H T b .
R S D = 1 N p i = 1 N p [ E s ( i ) E 0 ( i ) E 0 ( i ) ] 2 ,