Abstract

We propose a compact optical system made up of a thin collimator and a free-form lens array to provide the uniform illumination of various-shape regions. Analytical formulas to design the lens array are derived. The simulation results for the designed optical elements demonstrate the high-level illumination uniformity of various regions in the form of a rectangle, a cross, a flag-shaped region, a line segment, and a set of line segments.

© 2012 Optical Society of America

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References

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  1. P. Guan and X.-J. Wang, “On a Monge-Ampère equation arising in geometric optics,” J. Diff. Geom. 48, 205–223 (1998).
  2. V. I. Oliker and P. Waltman, “Radially symmetric solutions of Monge-Ampère equation arising in the reflector mapping problem,” in Differential Equations and Mathematical Physics, I. Knowles, ed., Vol. 1285 of Lecture Notes in Math (Springer, 1987), pp. 361–374.
  3. H. Ries and J. Muschaweck, “Tailoring freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590–595 (2002).
    [CrossRef]
  4. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18, 5295–5304 (2010).
    [CrossRef]
  5. D. Michaelis, P. Schreiber, and A. Bäuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett. 36, 918–920 (2011).
    [CrossRef]
  6. L. L. Doskolovich and M. A. Moiseev, “Design of refractive spline surface for generating required irradiance distribution with large angular dimension,” J. Mod. Opt. 57, 536–544(2010).
    [CrossRef]
  7. L. L. Doskolovich, N. L. Kazanskiy, and M. A. Moiseev, “Design of high-efficient freeform LED lens for illumination of elongated rectangular regions,” Opt. Express 19, A225–A233 (2011).
    [CrossRef]
  8. K. Wang, F. Chen, and Z. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express 18, 413–425 (2010).
    [CrossRef]
  9. R. Wu, H. Li, Z. Zheng, and X. Liu, “Freeform lens arrays for off-axis illumination in an optical lithography system,” Appl. Opt. 50, 725–732 (2011).
    [CrossRef]
  10. D. Grabovičkić, P. Benítez, and J. C. Miñano, “TIR RXI collimator,” Opt. Express 20, A51–A61 (2012).
    [CrossRef]
  11. F. Muñoz, P. Benítez, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. 43, 1522–1530 (2004).
    [CrossRef]
  12. J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001 (2010).
    [CrossRef]
  13. E. Aslanov, N. Petrov, A. Borodulin, and G. Tananaev, “Ultra-slim collimator with an inverse design,” Proc. SPIE 8170, 81700U (2011).
    [CrossRef]
  14. E. Aslanov and L. Doskolovich, “Slim collimator for light emitting diodes,” J. Comput. Opt. 36, 96–101 (2012).
  15. L. Sun, S. Jin, and S. Cen, “Free-form microlens for illumination applications,” Appl. Opt. 48, 5520–5527 (2009).
    [CrossRef]
  16. http://www.zemax.com .
  17. B. Grunbaum and G. C. Shephard, Tilings and Patterns(W. H. Freeman and Co., 1987).
  18. L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
    [CrossRef]
  19. R. Courant and F. John, Introduction to Calculus and Analysis (Springer-Verlag, 1989), Vol. 2.

2012

E. Aslanov and L. Doskolovich, “Slim collimator for light emitting diodes,” J. Comput. Opt. 36, 96–101 (2012).

D. Grabovičkić, P. Benítez, and J. C. Miñano, “TIR RXI collimator,” Opt. Express 20, A51–A61 (2012).
[CrossRef]

2011

2010

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

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001 (2010).
[CrossRef]

K. Wang, F. Chen, and Z. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express 18, 413–425 (2010).
[CrossRef]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18, 5295–5304 (2010).
[CrossRef]

2009

2004

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

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

2002

1998

P. Guan and X.-J. Wang, “On a Monge-Ampère equation arising in geometric optics,” J. Diff. Geom. 48, 205–223 (1998).

Aslanov, E.

E. Aslanov and L. Doskolovich, “Slim collimator for light emitting diodes,” J. Comput. Opt. 36, 96–101 (2012).

E. Aslanov, N. Petrov, A. Borodulin, and G. Tananaev, “Ultra-slim collimator with an inverse design,” Proc. SPIE 8170, 81700U (2011).
[CrossRef]

Bäuer, A.

Benítez, P.

D. Grabovičkić, P. Benítez, and J. C. Miñano, “TIR RXI collimator,” Opt. Express 20, A51–A61 (2012).
[CrossRef]

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

Borodulin, A.

E. Aslanov, N. Petrov, A. Borodulin, and G. Tananaev, “Ultra-slim collimator with an inverse design,” Proc. SPIE 8170, 81700U (2011).
[CrossRef]

Cassarly, W. J.

Cen, S.

Chen, F.

Chen, J.-J.

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001 (2010).
[CrossRef]

Courant, R.

R. Courant and F. John, Introduction to Calculus and Analysis (Springer-Verlag, 1989), Vol. 2.

Doskolovich, L.

E. Aslanov and L. Doskolovich, “Slim collimator for light emitting diodes,” J. Comput. Opt. 36, 96–101 (2012).

Doskolovich, L. L.

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

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

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

Dross, O.

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

Fournier, F. R.

Grabovickic, D.

Grunbaum, B.

B. Grunbaum and G. C. Shephard, Tilings and Patterns(W. H. Freeman and Co., 1987).

Guan, P.

P. Guan and X.-J. Wang, “On a Monge-Ampère equation arising in geometric optics,” J. Diff. Geom. 48, 205–223 (1998).

Jin, S.

John, F.

R. Courant and F. John, Introduction to Calculus and Analysis (Springer-Verlag, 1989), Vol. 2.

Kazanskiy, N. L.

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

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

Kharitonov, S. I.

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

Li, H.

Lin, C.-T.

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001 (2010).
[CrossRef]

Liu, X.

Liu, Z.

Michaelis, D.

Miñano, J. C.

D. Grabovičkić, P. Benítez, and J. C. Miñano, “TIR RXI collimator,” Opt. Express 20, A51–A61 (2012).
[CrossRef]

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

Moiseev, M. A.

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

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

Muñoz, F.

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

Muschaweck, J.

Oliker, V. I.

V. I. Oliker and P. Waltman, “Radially symmetric solutions of Monge-Ampère equation arising in the reflector mapping problem,” in Differential Equations and Mathematical Physics, I. Knowles, ed., Vol. 1285 of Lecture Notes in Math (Springer, 1987), pp. 361–374.

Parkyn, B.

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

Perlo, P.

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

Petrov, N.

E. Aslanov, N. Petrov, A. Borodulin, and G. Tananaev, “Ultra-slim collimator with an inverse design,” Proc. SPIE 8170, 81700U (2011).
[CrossRef]

Ries, H.

Rolland, J. P.

Schreiber, P.

Shephard, G. C.

B. Grunbaum and G. C. Shephard, Tilings and Patterns(W. H. Freeman and Co., 1987).

Soifer, V. A.

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

Sun, L.

Tananaev, G.

E. Aslanov, N. Petrov, A. Borodulin, and G. Tananaev, “Ultra-slim collimator with an inverse design,” Proc. SPIE 8170, 81700U (2011).
[CrossRef]

Waltman, P.

V. I. Oliker and P. Waltman, “Radially symmetric solutions of Monge-Ampère equation arising in the reflector mapping problem,” in Differential Equations and Mathematical Physics, I. Knowles, ed., Vol. 1285 of Lecture Notes in Math (Springer, 1987), pp. 361–374.

Wang, K.

Wang, X.-J.

P. Guan and X.-J. Wang, “On a Monge-Ampère equation arising in geometric optics,” J. Diff. Geom. 48, 205–223 (1998).

Wu, R.

Zheng, Z.

Appl. Opt.

J. Comput. Opt.

E. Aslanov and L. Doskolovich, “Slim collimator for light emitting diodes,” J. Comput. Opt. 36, 96–101 (2012).

J. Diff. Geom.

P. Guan and X.-J. Wang, “On a Monge-Ampère equation arising in geometric optics,” J. Diff. Geom. 48, 205–223 (1998).

J. Mod. Opt.

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

L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, and P. Perlo, “A DOE to form a line-shaped directivity diagram,” J. Mod. Opt. 51, 1999–2005 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

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

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

E. Aslanov, N. Petrov, A. Borodulin, and G. Tananaev, “Ultra-slim collimator with an inverse design,” Proc. SPIE 8170, 81700U (2011).
[CrossRef]

Other

V. I. Oliker and P. Waltman, “Radially symmetric solutions of Monge-Ampère equation arising in the reflector mapping problem,” in Differential Equations and Mathematical Physics, I. Knowles, ed., Vol. 1285 of Lecture Notes in Math (Springer, 1987), pp. 361–374.

http://www.zemax.com .

B. Grunbaum and G. C. Shephard, Tilings and Patterns(W. H. Freeman and Co., 1987).

R. Courant and F. John, Introduction to Calculus and Analysis (Springer-Verlag, 1989), Vol. 2.

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Figures (7)

Fig. 1.
Fig. 1.

Cross section of the collimator combined with lens array.

Fig. 2.
Fig. 2.

Normalized intensity of the output beam from the collimator versus angle.

Fig. 3.
Fig. 3.

(a) Collimator output aperture (dashed line) represented as the tiling of the same-shape curvilinear cells GG. (b) Geometry of the problem of designing an optical element (corresponding to one cell) generating a curvilinear region G.

Fig. 4.
Fig. 4.

Lens surfaces to produce uniform irradiance distributions in the form of (a) a square, (b) a line, (c) a rectangle, and (d) a cross-shaped area in the plane z=500mm.

Fig. 5.
Fig. 5.

Free-form lens array to generate the uniform illumination of a square region.

Fig. 6.
Fig. 6.

Normalized irradiance distributions generated by the collimator and the arrays of optical elements [with constituents in Figs. 4(a)4(d)] in the plane z=500mm.

Fig. 7.
Fig. 7.

(a) Lens array with four types of lenses to generate a cross-shaped pattern. (b) Normalized cross-shaped irradiance distribution in the plane z=500mm.

Equations (12)

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r(σ)=r0cos2(β02)/cos2(σβ02).
x(x)=x0+ax,
Ψ(x)=nz(x)=(px(x)+z(x)xpz(x),py(x)+z(x)ypz(x)),orz(x)=1npz(x)(px(x),py(x)).
p(x)=(x(x)x,f)(x(x)x)2+f2=(x0+(a1)x,f)(x0+(a1)x)2+f2.
z(x)=x0+(a1)xn(x0+(a1)x)2+f2f.
z(x)=1n(a1)((a1)x+x0)2+f2+fn2(a1)ln(n((a1)x+x0)2+f2f)+C,
x(x)=x0+Ax,
p(x)=(x0+(AI)x,f)(x0+(AI)x)2+f2,
z(x)=x0+(AI)xn(x0+(AI)x)2+f2f.
z(x)=1n(a1)((a1)x+x0)2+f2+fn2(a1)ln(n((a1)x+x0)2+f2f)+C.
z(x)=1(n1)f(x0+(AI)x).
z(x)=12(n1)f(2x0x+(AI)x2)+C.

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