Abstract

Different geometric shapes of light pipes cause different irradiance distributions. We analytically explore the irradiance distributions of on-axis Lambertian pointlike sources in polygonal total-internal-reflection (TIR) straight light pipes. It is analytically shown that the irradiance of pentagonal light pipes concentrates on the center of the exit plane. Numerical verifications are also provided, and experimental explorations with different shapes of acrylic light pipes are carried out for comparison. We also analyze the influence of light-pipe length on distribution uniformity and deduce the smallest uniform-mixing length/circumradius ratios for polygonal light pipes.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. K. Li, "Illumination engine for a projection display using a tapered light pipe," U.S. patent 6,739,726 (May 25, 2004).
  2. N. Takahashi and S. Umemoto, "Liquid crystal display apparatus having light pipe with reflective polarizer," U.S. patent 6,778,235 (August 17, 2004).
  3. E. Nestler, "Light pipe for an optical mouse," U.S. patent 4,716,287 (December 29, 1987).
  4. S. Staley and S. W. Stout, "Eject button for disk drive with light pipe," U.S. patent 6,717,769 (April 6, 2004).
  5. J. Lee and J. E. Greivenkamp, "Modeling of automotive interior illumination systems," Opt. Eng. (Bellingham) 43, 1537-1544 (2004).
    [CrossRef]
  6. J. F. V. Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. (Bellingham) 43, 1503-1510 (2004).
    [CrossRef]
  7. A. Gupta, J. Lee, and R. J. Koshel, "Design of efficient light pipes for illumination by an analytical approach," Appl. Opt. 40, 3640-3648 (2001).
    [CrossRef]
  8. Y.-K. Cheng and J.-L. Chern, "Irradiance formations in hollow straight light pipes with square and circular shapes," J. Opt. Soc. Am. A 23, 427-434 (2006).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43, 50-51.
  10. More information on MATLAB can be found at http://www.mathworks.com.
  11. R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000), p. 297.
  12. More information on TracePro can be found at http://www.lambdares.com.
  13. More information on PW-09 LED can be found at http://www.lumileds.com/.

2006 (1)

2004 (2)

J. Lee and J. E. Greivenkamp, "Modeling of automotive interior illumination systems," Opt. Eng. (Bellingham) 43, 1537-1544 (2004).
[CrossRef]

J. F. V. Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. (Bellingham) 43, 1503-1510 (2004).
[CrossRef]

2001 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43, 50-51.

Cheng, Y.-K.

Chern, J.-L.

Derlofske, J. F. V.

J. F. V. Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. (Bellingham) 43, 1503-1510 (2004).
[CrossRef]

Fischer, R. E.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000), p. 297.

Greivenkamp, J. E.

J. Lee and J. E. Greivenkamp, "Modeling of automotive interior illumination systems," Opt. Eng. (Bellingham) 43, 1537-1544 (2004).
[CrossRef]

Gupta, A.

Hough, T. A.

J. F. V. Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. (Bellingham) 43, 1503-1510 (2004).
[CrossRef]

Koshel, R. J.

Lee, J.

J. Lee and J. E. Greivenkamp, "Modeling of automotive interior illumination systems," Opt. Eng. (Bellingham) 43, 1537-1544 (2004).
[CrossRef]

A. Gupta, J. Lee, and R. J. Koshel, "Design of efficient light pipes for illumination by an analytical approach," Appl. Opt. 40, 3640-3648 (2001).
[CrossRef]

Li, K. K.

K. K. Li, "Illumination engine for a projection display using a tapered light pipe," U.S. patent 6,739,726 (May 25, 2004).

Nestler, E.

E. Nestler, "Light pipe for an optical mouse," U.S. patent 4,716,287 (December 29, 1987).

Staley, S.

S. Staley and S. W. Stout, "Eject button for disk drive with light pipe," U.S. patent 6,717,769 (April 6, 2004).

Stout, S. W.

S. Staley and S. W. Stout, "Eject button for disk drive with light pipe," U.S. patent 6,717,769 (April 6, 2004).

Tadic-Galeb, B.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000), p. 297.

Takahashi, N.

N. Takahashi and S. Umemoto, "Liquid crystal display apparatus having light pipe with reflective polarizer," U.S. patent 6,778,235 (August 17, 2004).

Umemoto, S.

N. Takahashi and S. Umemoto, "Liquid crystal display apparatus having light pipe with reflective polarizer," U.S. patent 6,778,235 (August 17, 2004).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43, 50-51.

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (Bellingham) (2)

J. Lee and J. E. Greivenkamp, "Modeling of automotive interior illumination systems," Opt. Eng. (Bellingham) 43, 1537-1544 (2004).
[CrossRef]

J. F. V. Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. (Bellingham) 43, 1503-1510 (2004).
[CrossRef]

Other (9)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43, 50-51.

More information on MATLAB can be found at http://www.mathworks.com.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000), p. 297.

More information on TracePro can be found at http://www.lambdares.com.

More information on PW-09 LED can be found at http://www.lumileds.com/.

K. K. Li, "Illumination engine for a projection display using a tapered light pipe," U.S. patent 6,739,726 (May 25, 2004).

N. Takahashi and S. Umemoto, "Liquid crystal display apparatus having light pipe with reflective polarizer," U.S. patent 6,778,235 (August 17, 2004).

E. Nestler, "Light pipe for an optical mouse," U.S. patent 4,716,287 (December 29, 1987).

S. Staley and S. W. Stout, "Eject button for disk drive with light pipe," U.S. patent 6,717,769 (April 6, 2004).

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 (8)

Fig. 1
Fig. 1

Schematic diagram of a ray transported in a dielectric-filled straight light pipe.

Fig. 2
Fig. 2

(a) Schematic diagram of a ray propagated in a pentagonal light pipe, (b) ray path projection on the pentagonal light-pipe exit surface, (c) four conditions of the path projection method.

Fig. 3
Fig. 3

(a) Schematic diagram of a ray propagated in a folding square light pipe, (b) ray exit location range in a folding square light pipe, (c) four conditions of the mirror folding method.

Fig. 4
Fig. 4

Exit surface folding for different shapes of light pipes: (a) triangular, (b) pentagonal, (c) hexagonal.

Fig. 5
Fig. 5

(a) Schematic diagram of flux collection for a pentagonal light pipe; (b), (c) irradiance distribution of L 2 R = 5 light pipes for (b) pentagonal aperture and (c) different geometric shapes.

Fig. 6
Fig. 6

Simulation results of the irradiance distribution for different geometric shapes of light pipes: (a) circular, (b) triangular, (c) square, (d) pentagonal, (e) hexagonal. (f) Cross profiles of each light pipe.

Fig. 7
Fig. 7

Experimental results of the irradiance distribution for different geometric shapes of light pipes: (a) circular; (b) triangular, (c) square, (d) pentagonal, (e) hexagonal. (f) Cross profiles of each light pipe.

Fig. 8
Fig. 8

(a) Relative difference of analytical and experimental results for circular and pentagonal light pipes, (b) irradiance profiles for pentagonal light pipe with different L R ratio, (c) irradiance profiles for circular light pipe with different source size, (d) uniformity deviation versus light-pipe scale L R for a pentagonal light pipe.

Tables (3)

Tables Icon

Table 1 Ray Exit Location Deduction of Pentagonal Light Pipe (See Text)

Tables Icon

Table 2 Ray Exit Location Deduction of Square Light Pipe (See Text)

Tables Icon

Table 3 Lists of Smallest Uniform-Mixing L R Ratios (See Text)

Equations (9)

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

m = Int [ L tan θ e D ] ,
d ( θ e ) = i = 1 m + 1 d i ( θ e ) = i = 1 m + 1 L i tan θ e ,
w = R sin 45 ° , P = ( L tan θ e sin ϕ , L tan θ e cos ϕ ) ,
A = ( 0 , 0 ) , B = ( 0 , 2 w ) , C = ( 0 , 4 w ) ,
D = ( 0 , 6 w ) , E = ( 2 w , 2 w ) , F = ( 2 w , 4 w ) ,
G = ( 2 w , 6 w ) , H = ( 4 w , 4 w ) .
R = n i cos θ i n t cos θ t n i cos θ i + n t cos θ t 2 ,
E ( r ) = Total flux of one unit pixel Area of one unit pixel ( 1 R in ) ( 1 R out ) Φ ( θ e ) r Δ r Δ ϕ ,
δ = [ 1 n i = 1 n E i E ¯ ] E ¯ ,

Metrics