Abstract

We propose a method for the design of an optical element generating the required irradiance distribution in a rectangular area with a large aspect ratio. Application fields include streetlights, the illumination of halls or corridors, and so forth. The design assumes that the optical element has a complex form and contains two refractive surfaces. The first one converts a spherical beam from the light source to a cylindrical beam. The second one transforms an incident cylindrical beam and generates the required irradiance distribution in the target plane. Two optical elements producing a uniform irradiance distribution from a Cree® XLamp® source in rectangular regions of 17 m × 4 m and 17 m × 2 m are designed. The light efficiency of the designed optical element is larger than 83%, whereas the irradiance nonuniformity is less than 9%.

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References

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  8. J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
    [CrossRef]
  14. B. A. Jacobson and R. D. Gendelbach, “Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source,” Proc. SPIE 4446, 130–138 (2001).
  15. B. Parkyn and D. Pelka, “Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808, 633808-7 (2006).
    [CrossRef]
  16. A. A. Belousov, L. L. Doskolovich, and S. I. Kharitonov, “A gradient method of designing optical elements for forming a specified irradiance on a curved surface,” J. Opt. Technol. 75(3), 161–165 (2008).
    [CrossRef]
  17. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
    [CrossRef] [PubMed]
  18. M. A. Moiseev and L. L. Doskolovich, “Design of refractive spline surface for generating required irradiance distribution with large angular dimension,” J. Mod. Opt. 57(7), 536–544 (2010).
    [CrossRef]
  19. L. L. Doskolovich and M. A. Moiseev, “Calculations for refracting optical elements for forming directional patterns in the form of a rectangle,” J. Opt. Technol. 76(7), 430–434 (2009).
    [CrossRef]
  20. P. R. Kanwal, Generalized Functions: Theory and Applications (Birkhäuser, 2004).
  21. C. De Boor, A Practical Guide to Splines (Springer, 2001).
  22. J. F. Bonnans, Numerical Optimization: Theoretical and Practical Aspects (Springer, 2006).

2010

M. A. Moiseev and L. L. Doskolovich, “Design of refractive spline surface for generating required irradiance distribution with large angular dimension,” J. Mod. Opt. 57(7), 536–544 (2010).
[CrossRef]

2009

2008

2007

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[CrossRef]

2006

B. Parkyn and D. Pelka, “Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808, 633808-7 (2006).
[CrossRef]

2005

2002

2001

B. A. Jacobson and R. D. Gendelbach, “Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source,” Proc. SPIE 4446, 130–138 (2001).

H. Ries and J. A. Muschaweck, “Tailoring freeform lenses for illumination,” Proc. SPIE 4442, 43–50 (2001).
[CrossRef]

2000

J. Bortz, N. Shatz, and D. Pitou, “Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target,” Proc. SPIE 4092, 130–138 (2000).
[CrossRef]

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

1998

G. Pengfei and W. Xu-Jia, “On a Monge–Ampere equation arising in geometric optics,” J. Differential Geom. 48, 205–223 (1998).

1978

Belousov, A. A.

Bernard, S.

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[CrossRef]

Bortz, J.

J. Bortz, N. Shatz, and D. Pitou, “Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target,” Proc. SPIE 4092, 130–138 (2000).
[CrossRef]

Ding, Y.

Doskolovich, L. L.

Elmer, W. B.

Gendelbach, R. D.

B. A. Jacobson and R. D. Gendelbach, “Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source,” Proc. SPIE 4446, 130–138 (2001).

Gu, P. F.

Hicks, R. A.

Honkanen, M.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Jacobson, B. A.

B. A. Jacobson and R. D. Gendelbach, “Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source,” Proc. SPIE 4446, 130–138 (2001).

Kazanskiy, N. L.

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[CrossRef]

Kettunen, V.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Kharitonov, S. I.

Kuittinen, M.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Laakkonen, P.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Lautanen, J.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Liu, X.

Moiseev, M. A.

M. A. Moiseev and L. L. Doskolovich, “Design of refractive spline surface for generating required irradiance distribution with large angular dimension,” J. Mod. Opt. 57(7), 536–544 (2010).
[CrossRef]

L. L. Doskolovich and M. A. Moiseev, “Calculations for refracting optical elements for forming directional patterns in the form of a rectangle,” J. Opt. Technol. 76(7), 430–434 (2009).
[CrossRef]

Muschaweck, J. A.

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

H. Ries and J. A. Muschaweck, “Tailoring freeform lenses for illumination,” Proc. SPIE 4442, 43–50 (2001).
[CrossRef]

Parkyn, B.

B. Parkyn and D. Pelka, “Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808, 633808-7 (2006).
[CrossRef]

Pelka, D.

B. Parkyn and D. Pelka, “Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808, 633808-7 (2006).
[CrossRef]

Pengfei, G.

G. Pengfei and W. Xu-Jia, “On a Monge–Ampere equation arising in geometric optics,” J. Differential Geom. 48, 205–223 (1998).

Pitou, D.

J. Bortz, N. Shatz, and D. Pitou, “Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target,” Proc. SPIE 4092, 130–138 (2000).
[CrossRef]

Ries, H.

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

H. Ries and J. A. Muschaweck, “Tailoring freeform lenses for illumination,” Proc. SPIE 4442, 43–50 (2001).
[CrossRef]

Shatz, N.

J. Bortz, N. Shatz, and D. Pitou, “Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target,” Proc. SPIE 4092, 130–138 (2000).
[CrossRef]

Turunen, J.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Xu-Jia, W.

G. Pengfei and W. Xu-Jia, “On a Monge–Ampere equation arising in geometric optics,” J. Differential Geom. 48, 205–223 (1998).

Zheng, Z. R.

Appl. Opt.

J. Differential Geom.

G. Pengfei and W. Xu-Jia, “On a Monge–Ampere equation arising in geometric optics,” J. Differential Geom. 48, 205–223 (1998).

J. Mod. Opt.

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[CrossRef]

M. A. Moiseev and L. L. Doskolovich, “Design of refractive spline surface for generating required irradiance distribution with large angular dimension,” J. Mod. Opt. 57(7), 536–544 (2010).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Technol.

Opt. Commun.

J. Lautanen, M. Honkanen, V. Kettunen, M. Kuittinen, P. Laakkonen, and J. Turunen, “Wide-angle far-field line generation with diffractive optics,” Opt. Commun. 176(4-6), 273–280 (2000).
[CrossRef]

Opt. Express

Proc. SPIE

B. A. Jacobson and R. D. Gendelbach, “Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source,” Proc. SPIE 4446, 130–138 (2001).

B. Parkyn and D. Pelka, “Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808, 633808-7 (2006).
[CrossRef]

J. Bortz, N. Shatz, and D. Pitou, “Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target,” Proc. SPIE 4092, 130–138 (2000).
[CrossRef]

H. Ries and J. A. Muschaweck, “Tailoring freeform lenses for illumination,” Proc. SPIE 4442, 43–50 (2001).
[CrossRef]

Other

I. Knowles and Y. Satio, “Radially symmetric solutions of a Monge–Ampere equation arising in the reflector mapping problem,” in Proceedings of the UAB International Conference on Differential Equations and Mathematical Physics, Lecture Notes in Math (Springer-Verlag, 1987), pp. 973–1000.

V. Oliker and A. Treibergs, Geometry and Nonlinear Partial Differential Equations (AMS Bookstore, 1992).

W. B. Elmer, The Optical Design of Reflectors (Wiley, 1980).

O. Kusch, Computer-aided Optical Design of Illumination and Irradiating Devices (ASLAN Publishing House, 1993).

P. R. Kanwal, Generalized Functions: Theory and Applications (Birkhäuser, 2004).

C. De Boor, A Practical Guide to Splines (Springer, 2001).

J. F. Bonnans, Numerical Optimization: Theoretical and Practical Aspects (Springer, 2006).

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Figures (8)

Fig. 1
Fig. 1

Design of the optical element.

Fig. 2
Fig. 2

Collimating profile.

Fig. 3
Fig. 3

Optical element producing the uniform irradiance distribution in a 17 × 4 m rectangle area (overall dimensions are given in millimeters).

Fig. 4
Fig. 4

Irradiance distribution in the target plane produced by the optical element in Fig. 3. (a) The grayscale distribution. (b) The irradiance profiles–solid line: v = 0 ; dashed line, u = 0 .

Fig. 5
Fig. 5

Optical element with a single refractive surface producing the uniform irradiance distribution in a 17 × 4 m rectangle area (overall dimensions are given in millimeters).

Fig. 6
Fig. 6

Irradiance distribution in the target plane produced by the optical element in Fig. 5. (a) The grayscale distribution. (b) The irradiance profiles–solid line, v = 0 ; dashed line, u = 0 .

Fig. 7
Fig. 7

Optical element producing the uniform irradiance distribution in a shifted 17 × 2 m rectangle area (overall dimensions are given in millimeters).

Fig. 8
Fig. 8

Irradiance distribution in the target plane produced by the optical element in Fig. 7. (a) The grayscale distribution. (b) The irradiance profiles–solid line. v = 0 ; dashed line, u = 0 .

Equations (12)

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r ( φ , y ; p ) = ( r ( φ , y ; p ) sin φ ;     y ;     r ( φ , y ; p ) cos φ )
f ( p ) = E ( u , v ; p ) E 0 ( u , v ) min ,
T ( φ , y ; p ) E ( φ , y ) R d φ d y = E ( u ( φ , y ; p ) ) d u d v , E ( u ( φ , y ; p ) ) = T ( φ , y ; p ) E ( φ , y ) R | J ( u ( φ , y ; p ) ) | ,
a 0 ( φ ) = { sin φ , 0 , cos φ } ,
a 1 ( φ , y ; p ) = n 1 n 2 a 0 ( φ ) + ( 1 [ n 1 n 2 a 0 , n ] 2 n 1 n 2 ( a 0 , n ) ) n ( φ , y ; p ) .
u ( φ , y ; p ) = r ( φ , y ; p ) sin φ + a 1 x ( φ , y ; p ) l ( φ , y ; p ) , v ( φ , y ; p ) = y + a 1 y ( φ , y ; p ) l ( φ , y ; p ) ,
f ( x , y ) | J ( u ( x , y ) ) | | x = x ˜ y = y ˜ = + + f ( x , y ) δ ( u ˜ u ( x , y ) , v ˜ v ( x , y ) ) d x d y ,
E ( u , v ; p ) = R y max y max π / 2 π / 2 T ( φ , y ; p ) E ( φ , y ) δ ( u u ( φ , y ; p ) ) d φ d y .
δ σ ( u , v ) = 1 2 π σ 2 exp ( u 2 + v 2 2 σ 2 ) .
E ( u , v ; p ) = y max y max π / 2 π / 2 R T ( φ , y ; p ) E ( φ , y ) δ σ ( u u ( φ , y ; p ) ) d φ d y .
f p i = 1 f ( p ) u , v ( E ( u , v ; p ) E 0 ( u , v ) ) E ( u , v ; p ) p i d u d v ,
E ( u , v ; p ) p i = y max y max π / 2 π / 2 R E ( φ , y ) p i ( T ( φ , y ; p ) δ σ ( u u ( φ , y ; p ) ) ) d φ d y .

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