Abstract

Glare and visual discomfort are important factors that should be taken into account in illumination design. Conventional freeform lenses offer perfect control over the outgoing intensity distribution, thereby allowing optical radiation patterns with sharp cut-offs in order to optimize the unified glare rating index. However, these freeform lenses do not offer control over the near-field luminance distribution. Observing the emitted light distribution from a high-brightness LED through a freeform lens gives a high peak luminance that can result in glare. To reduce this peak luminance, freeform lenses should be used in conjunction with light diffusing structures. However, this diminishes the control over the outgoing intensity distribution what is the main benefit of a freeform lens. Another approach to reduce the observed peak luminance, is by spreading the emitted light over multiple optical channels via freeform lens arrays. This paper proposes a novel method to design luminance spreading freeform lens arrays that offer perfect control over the resulting intensity pattern. The method is based on a non-invertible mapping of a 2D parameter space. This results in a source-target mapping in which multiple ingoing ray directions are mapped onto every position of the target distribution. The case of continuous and discontinuous mappings are both discussed in this paper. Finally, the example of a discontinuous freeform lens array with $7\times 7$ individual lenses is designed and experimentally demonstrated.

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

Full Article  |  PDF Article
OSA Recommended Articles
Freeform lens design for light-emitting diode uniform illumination by using a method of source–target luminous intensity mapping

Jin-Jia Chen, Ze-Yu Huang, Te-Shu Liu, Ming-Da Tsai, and Kuang-Lung Huang
Appl. Opt. 54(28) E146-E152 (2015)

Freeform lens design for a point source and far-field target

L. B. Romijn, J. H. M. ten Thije Boonkkamp, and W. L. IJzerman
J. Opt. Soc. Am. A 36(11) 1926-1939 (2019)

References

  • View by:
  • |
  • |
  • |

  1. L. Geerdinck, J. V. Gheluwe, and M. Vissenberg, “Discomfort glare perception of non-uniform light sources in an office setting,” J. Environ. Psychol. 39, 5–13 (2014).
    [Crossref]
  2. G. H. Scheir, P. Hanselaer, and W. R. Ryckaert, “Defining the actual luminous surface in the unified glare rating,” Leukos 13(4), 201–210 (2017).
    [Crossref]
  3. W. Kim, H. Han, and J. T. Kim, “The position index of a glare source at the borderline between comfort and discomfort (bcd) in the whole visual field,” Build. Environ. 44(5), 1017–1023 (2009).
    [Crossref]
  4. 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(7), 1700310 (2018).
    [Crossref]
  5. Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).
    [Crossref]
  6. Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55(16), 4301–4306 (2016).
    [Crossref]
  7. A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20(13), 14477–14485 (2012).
    [Crossref]
  8. C. Bösel and H. Gross, “Ray mapping approach for the efficient design of continuous freeform surfaces,” Opt. Express 24(13), 14271–14282 (2016).
    [Crossref]
  9. K. Desnijder, P. Hanselaer, and Y. Meuret, “Flexible design method for freeform lenses with an arbitrary lens contour,” Opt. Lett. 42(24), 5238–5241 (2017).
    [Crossref]
  10. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18(5), 5295–5304 (2010).
    [Crossref]
  11. D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36(6), 918–920 (2011).
    [Crossref]
  12. V. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds., (Springer Berlin Heidelberg, 2003), pp. 193–224.
  13. R. Wu, Y. Zhang, M. M. Sulman, Z. Zheng, P. Benítez, and J. C. Minano, “Initial design with l2 monge-kantorovich theory for the monge-ampère equation method in freeform surface illumination design,” Opt. Express 22(13), 16161–16177 (2014).
    [Crossref]
  14. 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-ampère equation,” Opt. Lett. 38(2), 229–231 (2013).
    [Crossref]
  15. K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
    [Crossref]
  16. E. Aslanov, L. L. Doskolovich, and M. A. Moiseev, “Thin led collimator with free-form lens array for illumination applications,” Appl. Opt. 51(30), 7200–7205 (2012).
    [Crossref]
  17. X.-H. Lee, I. Moreno, and C.-C. Sun, “High-performance led street lighting using microlens arrays,” Opt. Express 21(9), 10612–10621 (2013).
    [Crossref]
  18. K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
    [Crossref]
  19. A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21(9), 10563–10571 (2013).
    [Crossref]
  20. K. Desnijder, P. Hanselaer, and Y. Meuret, “Ray mapping method for off-axis and non-paraxial freeform illumination lens design,” Opt. Lett. 44(4), 771–774 (2019).
    [Crossref]
  21. A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “Limitations of the ray mapping approach in freeform optics design,” Opt. Lett. 38(11), 1945–1947 (2013).
    [Crossref]
  22. C. Prins, “Inverse methods for illumination optics,” Ph.D. thesis, Department of Applied Physics - Technische Universiteit Eindhoven (2014).

2019 (2)

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Ray mapping method for off-axis and non-paraxial freeform illumination lens design,” Opt. Lett. 44(4), 771–774 (2019).
[Crossref]

2018 (2)

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(7), 1700310 (2018).
[Crossref]

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

2017 (2)

K. Desnijder, P. Hanselaer, and Y. Meuret, “Flexible design method for freeform lenses with an arbitrary lens contour,” Opt. Lett. 42(24), 5238–5241 (2017).
[Crossref]

G. H. Scheir, P. Hanselaer, and W. R. Ryckaert, “Defining the actual luminous surface in the unified glare rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

2016 (2)

2014 (2)

2013 (5)

2012 (2)

2011 (1)

2010 (1)

2009 (1)

W. Kim, H. Han, and J. T. Kim, “The position index of a glare source at the borderline between comfort and discomfort (bcd) in the whole visual field,” Build. Environ. 44(5), 1017–1023 (2009).
[Crossref]

Aslanov, E.

Bäuerle, A.

Benítez, P.

Bösel, C.

Bräuer, A.

Bruneton, A.

Cassarly, W. J.

Deketelaere, W.

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

Desnijder, K.

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Ray mapping method for off-axis and non-paraxial freeform illumination lens design,” Opt. Lett. 44(4), 771–774 (2019).
[Crossref]

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Flexible design method for freeform lenses with an arbitrary lens contour,” Opt. Lett. 42(24), 5238–5241 (2017).
[Crossref]

Doskolovich, L. L.

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(7), 1700310 (2018).
[Crossref]

Feng, Z.

Fournier, F. R.

Froese, B. D.

Geerdinck, L.

L. Geerdinck, J. V. Gheluwe, and M. Vissenberg, “Discomfort glare perception of non-uniform light sources in an office setting,” J. Environ. Psychol. 39, 5–13 (2014).
[Crossref]

Gheluwe, J. V.

L. Geerdinck, J. V. Gheluwe, and M. Vissenberg, “Discomfort glare perception of non-uniform light sources in an office setting,” J. Environ. Psychol. 39, 5–13 (2014).
[Crossref]

Gong, M.

Gross, H.

Han, H.

W. Kim, H. Han, and J. T. Kim, “The position index of a glare source at the borderline between comfort and discomfort (bcd) in the whole visual field,” Build. Environ. 44(5), 1017–1023 (2009).
[Crossref]

Hanselaer, P.

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Ray mapping method for off-axis and non-paraxial freeform illumination lens design,” Opt. Lett. 44(4), 771–774 (2019).
[Crossref]

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

G. H. Scheir, P. Hanselaer, and W. R. Ryckaert, “Defining the actual luminous surface in the unified glare rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Flexible design method for freeform lenses with an arbitrary lens contour,” Opt. Lett. 42(24), 5238–5241 (2017).
[Crossref]

Huang, L.

Jin, G.

Kim, J. T.

W. Kim, H. Han, and J. T. Kim, “The position index of a glare source at the borderline between comfort and discomfort (bcd) in the whole visual field,” Build. Environ. 44(5), 1017–1023 (2009).
[Crossref]

Kim, W.

W. Kim, H. Han, and J. T. Kim, “The position index of a glare source at the borderline between comfort and discomfort (bcd) in the whole visual field,” Build. Environ. 44(5), 1017–1023 (2009).
[Crossref]

Lee, X.-H.

Li, H.

Liang, R.

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(7), 1700310 (2018).
[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55(16), 4301–4306 (2016).
[Crossref]

Liu, P.

Liu, X.

Loosen, P.

Meuret, Y.

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Ray mapping method for off-axis and non-paraxial freeform illumination lens design,” Opt. Lett. 44(4), 771–774 (2019).
[Crossref]

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

K. Desnijder, P. Hanselaer, and Y. Meuret, “Flexible design method for freeform lenses with an arbitrary lens contour,” Opt. Lett. 42(24), 5238–5241 (2017).
[Crossref]

Michaelis, D.

Minano, J. C.

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(7), 1700310 (2018).
[Crossref]

Moiseev, M. A.

Moreno, I.

Oliker, V.

V. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds., (Springer Berlin Heidelberg, 2003), pp. 193–224.

Prins, C.

C. Prins, “Inverse methods for illumination optics,” Ph.D. thesis, Department of Applied Physics - Technische Universiteit Eindhoven (2014).

Rolland, J. P.

Ryckaert, W.

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

Ryckaert, W. R.

G. H. Scheir, P. Hanselaer, and W. R. Ryckaert, “Defining the actual luminous surface in the unified glare rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

Scheir, G. H.

G. H. Scheir, P. Hanselaer, and W. R. Ryckaert, “Defining the actual luminous surface in the unified glare rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

Schreiber, P.

Stollenwerk, J.

Sulman, M. M.

Sun, C.-C.

Thienpont, H.

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

Vervaeke, M.

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

Vissenberg, M.

L. Geerdinck, J. V. Gheluwe, and M. Vissenberg, “Discomfort glare perception of non-uniform light sources in an office setting,” J. Environ. Psychol. 39, 5–13 (2014).
[Crossref]

Wester, R.

Wu, R.

Xu, L.

Zhang, Y.

Zheng, Z.

Appl. Opt. (2)

Build. Environ. (1)

W. Kim, H. Han, and J. T. Kim, “The position index of a glare source at the borderline between comfort and discomfort (bcd) in the whole visual field,” Build. Environ. 44(5), 1017–1023 (2009).
[Crossref]

J. Environ. Psychol. (1)

L. Geerdinck, J. V. Gheluwe, and M. Vissenberg, “Discomfort glare perception of non-uniform light sources in an office setting,” J. Environ. Psychol. 39, 5–13 (2014).
[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(7), 1700310 (2018).
[Crossref]

Leukos (2)

G. H. Scheir, P. Hanselaer, and W. R. Ryckaert, “Defining the actual luminous surface in the unified glare rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

K. Desnijder, W. Deketelaere, W. Ryckaert, P. Hanselaer, and Y. Meuret, “Efficient design method of segmented lenses for lighting applications with prescribed intensity and low peak luminance,” Leukos 15(4), 281–292 (2019).
[Crossref]

Opt. Express (7)

Opt. Lett. (5)

Proc. SPIE (1)

K. Desnijder, W. Deketelaere, M. Vervaeke, H. Thienpont, P. Hanselaer, and Y. Meuret, “Design of a freeform, luminance spreading illumination lens with a continuous surface,” Proc. SPIE 10693, 13 (2018).
[Crossref]

Other (2)

V. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds., (Springer Berlin Heidelberg, 2003), pp. 193–224.

C. Prins, “Inverse methods for illumination optics,” Ph.D. thesis, Department of Applied Physics - Technische Universiteit Eindhoven (2014).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1. (a) A conventional freeform lens redirects every source ray towards a unique position in the target plane. (b) A freeform lens array redirects multiple source rays towards each position in the target plane. This effectively reduces the observed peak luminance from each point in the target plane while maintaining control over the target distribution.
Fig. 2.
Fig. 2. Schematic representation of the proposed algorithm to design freeform lens array with overlapping light intensity distributions.
Fig. 3.
Fig. 3. The tent map is the simplest, non-trivial example of a fold mapping.
Fig. 4.
Fig. 4. (a) The lens surface that is obtained by integrating the folded mapping $\psi \circ F \circ \phi ^{-1}$ in which $F$ is a continuous tent map. The lens surface contains a concave, a convex and two saddle shaped regions. (b) The simulated irradiance distribution at the target plane. (All simulations were performed in LightTools 8.6.0).
Fig. 5.
Fig. 5. Adaptation of the tent map into a discontinuous fold mapping.
Fig. 6.
Fig. 6. (a) The lens surface that is obtained by integrating the folded mapping $\psi \circ F \circ \phi ^{-1}$ in which $F$ is a discontinuous function. The lens surface consists of multiple convex lenses. (b) The simulated irradiance distribution at the target plane.
Fig. 7.
Fig. 7. (a) Continuous folding function for a freeform lens array with $7\times 7$ lenses in which the light towards each position comes out of $3\times 3$ lenses. (b) Discontinuous version of the same folding function.
Fig. 8.
Fig. 8. (a) The resulting discontinuous freeform lens array. (b) A fan of source rays is refracted by the freeform lens array into multiple overlapping fans of outgoing rays. (c) The simulated irradiance pattern that results from the lens array with a point source.
Fig. 9.
Fig. 9. (a) The source distribution divided into different source patches. (b) The discontinuous folding function $F_u$ in which three line segments are highlighted. (c) The target distribution divided into different target patches.
Fig. 10.
Fig. 10. (a) A rendered visualisation of a single freeform lens and a freeform lens array that are illuminated by a small light source. (b) The simulated irradiance pattern that results from a single freeform lens (left) and the freeform lens array (right) when illuminated by a lambertian disk source with diameter = $2$ mm.
Fig. 11.
Fig. 11. (a) Obtained irradiance distribution with the 3D printed prototype. (b) A picture of the illuminated freeform lens array by a small LED light source illustrates the spreading of the luminance towards the observer position, over 9 different lens segments.

Equations (5)

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

F ( u , v ) = ( F u ( u ) , F v ( v ) ) = ( u , v )
F u ( u ) = { u c , f o r u c 1 u 1 c , f o r u c
d u = d u 1 + d u 2 = | d F u d u | u 1 1 d u + | d F u d u | u 2 1 d u u [ 0 , 1 ]
d u = i = 1 n | d F u d u | u i 1 d u u [ 0 , 1 ]
{ u = F u ( u 1 ) = F u ( u 2 ) = F u ( u 3 ) v = F v ( v 1 ) = F v ( v 2 ) = F v ( v 3 )

Metrics