Abstract

Bending a light pipe and maintaining the required volume and size, while at the same time preserving source energy and minimizing bend losses, is the basic criterion for designing a light pipe. An important requirement is the design of a light pipe that is capable of being bent without loss of light and with no limitations on acceptance angle. It is shown that in theory such a light pipe does exist, in a form corresponding to the so-called golden rectangle. Numerical simulations with six different no-loss light pipes with multiple bends are provided as a demonstration.

© 2005 Optical Society of America

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References

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  1. K. K. Li, “Illumination engine for a projection display using a tapered light pipe,” U.S. patent 6,739,726 (May 25, 2005).
  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. J. Lee and J. E. Greivenkamp, Opt. Eng. (Bellingham) 43, 1537 (2004).
    [CrossRef]
  4. H. Delattre, “Motor vehicle headlight with light pipe,” U.S. patent 6,547,428 (April 15, 2003).
  5. A. Gupta, J. Lee, and R. J. Koshel, Appl. Opt. 40, 3640 (2001).
    [CrossRef]
  6. See http://www.lumileds.com/products/ for technical information.
  7. R. Williams, The Geometrical Foundation of Natural Structure: a Source Book of Design (Dover, 1979), p. 53.
  8. See http://lambdares.com for technical information.

2004 (1)

J. Lee and J. E. Greivenkamp, Opt. Eng. (Bellingham) 43, 1537 (2004).
[CrossRef]

2001 (1)

Delattre, H.

H. Delattre, “Motor vehicle headlight with light pipe,” U.S. patent 6,547,428 (April 15, 2003).

Greivenkamp, J. E.

J. Lee and J. E. Greivenkamp, Opt. Eng. (Bellingham) 43, 1537 (2004).
[CrossRef]

Gupta, A.

Koshel, R. J.

Lee, J.

J. Lee and J. E. Greivenkamp, Opt. Eng. (Bellingham) 43, 1537 (2004).
[CrossRef]

A. Gupta, J. Lee, and R. J. Koshel, Appl. Opt. 40, 3640 (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, 2005).

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).

Williams, R.

R. Williams, The Geometrical Foundation of Natural Structure: a Source Book of Design (Dover, 1979), p. 53.

Appl. Opt. (1)

Opt. Eng. (Bellingham) (1)

J. Lee and J. E. Greivenkamp, Opt. Eng. (Bellingham) 43, 1537 (2004).
[CrossRef]

Other (6)

H. Delattre, “Motor vehicle headlight with light pipe,” U.S. patent 6,547,428 (April 15, 2003).

K. K. Li, “Illumination engine for a projection display using a tapered light pipe,” U.S. patent 6,739,726 (May 25, 2005).

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

See http://www.lumileds.com/products/ for technical information.

R. Williams, The Geometrical Foundation of Natural Structure: a Source Book of Design (Dover, 1979), p. 53.

See http://lambdares.com for technical information.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of the light pipe. (b) Range of the distribution of critical rays in the light pipe.

Fig. 2
Fig. 2

(a), (b) Relationship between the golden rectangle and the equiangular spiral. (c) Schematic layout of the equiangular spiral.

Fig. 3
Fig. 3

(Online color) Proposed no-loss bent light pipe with multiple factors (a) m = 1 and (c) m = 2.5 . The corresponding simulations are shown in (b) and (d).

Fig. 4
Fig. 4

(Online color) Six no-loss bent light pipes: Two no-loss bent light pipes are connected (a) in opposite directions, (b) in the same direction, and (c) perpendicular to each other. (d), (e) Two no-loss bent light pipes that have one straight light pipe inserted are connected in opposite directions and in the same direction, respectively. (f) Three no-loss bent light pipes are connected in opposite directions.

Equations (3)

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cos ϕ = f ( θ ) { [ f ( θ ) ] 2 + [ f ( θ ) ] 2 } 1 2 , cot ϕ = ± f ( θ ) f ( θ ) ;
r ( θ ) = C exp ( θ cot ϕ ) .
C 0 exp ( θ c cor ϕ ) = W sec ( θ c ) ,

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