Abstract

We present the concept of principal sections of a lightpipe to analyze the propagation of light through the lightpipe by total internal reflection. Only the principal sections determine the acceptance angle and thus help in the identification of regions where the leakage occurs first. Use of principal sections for analysis leads to a significant reduction in the design effort. We present an analysis of several commonly used lightpipe configurations, e.g., straight and single circular bend, and different cross sections, e.g., elliptical and rectangular. This analysis leads to the maximization of throughput and transfer efficiency. The uniformity characteristics of elementary configurations and scaling factors for a lightpipe with a single circular bend are also discussed.

© 2001 Optical Society of America

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References

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  1. Y. Oki, “Novel backlight with high luminance and low power consumption by prism-on-lightpipe technology,” SID Dig. 29, 157–160 (1998).
    [CrossRef]
  2. H. J. Cornelissen, M. J. J. Donna, H. Greiner, “Frontlights for reflective LCDs based on lightguides with micro-grooves,” SID Dig. 30, 912–915 (1999).
    [CrossRef]
  3. D. Decker, “CELIS–a concept for high-quality car interior lighting with light-guide technology,” SAE Tech. Paper 960488 (Society of Automotive Engineers, Warrendale, Pa., 1996).
  4. J. Spigulis, D. Pfafords, “Clinical potential of side-glowing optical fibers,” in Speciality Fiber Optics for Biomedical and Industrial Applications, A. Katzir, J. A. Harrington, eds., Proc. SPIE2977, 84–88 (1997).
    [CrossRef]
  5. H. van den Bergh, “On the evoution of some endoscopic light delivery systems for photodynamic therapy,” Endoscopy 30, 392–407 (1998).
    [CrossRef] [PubMed]
  6. M. Poppendieck, D. Brown, “Control of light output from plastic optical fiber with optical elements,” SAE Tech. Paper 960491 (Society of Automotive Engineers, Warrendale, Pa., 1996).
  7. D. J. Lamb, J. F. V. Derlofske, L. W. Hillman, “The use of aspheric surfaces in waveguide illumination systems for automotive displays,” SAE Tech. Paper 980874 (Society of Automotive Engineers, Warrendale, Pa., 1998).
  8. R. Edmonds, J. Reppel, P. Jardine, “Extractors and emitters for light distribution from hollow light guides,” Light. Res. Technol. 29, 23–32 (1997).
    [CrossRef]
  9. J. M. Teijido, H. P. Herzig, C. Fuhrer, P. J. Evard, “Design methods for illumination lightpipes,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 34–44 (1998).
    [CrossRef]
  10. T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).
  11. I. M. Bassett, G. W. Forbes, “A new class of non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
    [CrossRef]
  12. G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
    [CrossRef]
  13. J. V. Derlofske, “Nonrotationally symmetric mirrors provide even light,” Laser Focus World (July1999), pp. S23–S25.
  14. J. Schweyen, D. Jenkins, “Smart lightpipe designs,” Photonics Spectra (January1997), pp. 101–103.
  15. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980).
  16. Breault Research Organization, Inc., Advanced System Analysis Program (Tucson, Ariz., 1995).
  17. B. J. Cassarly, “Design of efficient illumination systems,” short course presented at the annual meeting of the Society of Photo-Optical Instrumentation Engineers, Denver, Colorado, 18–23 July 1999.

1999

H. J. Cornelissen, M. J. J. Donna, H. Greiner, “Frontlights for reflective LCDs based on lightguides with micro-grooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

J. V. Derlofske, “Nonrotationally symmetric mirrors provide even light,” Laser Focus World (July1999), pp. S23–S25.

1998

Y. Oki, “Novel backlight with high luminance and low power consumption by prism-on-lightpipe technology,” SID Dig. 29, 157–160 (1998).
[CrossRef]

H. van den Bergh, “On the evoution of some endoscopic light delivery systems for photodynamic therapy,” Endoscopy 30, 392–407 (1998).
[CrossRef] [PubMed]

1997

R. Edmonds, J. Reppel, P. Jardine, “Extractors and emitters for light distribution from hollow light guides,” Light. Res. Technol. 29, 23–32 (1997).
[CrossRef]

J. Schweyen, D. Jenkins, “Smart lightpipe designs,” Photonics Spectra (January1997), pp. 101–103.

1982

I. M. Bassett, G. W. Forbes, “A new class of non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

Allen, G. R.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Bassett, I. M.

I. M. Bassett, G. W. Forbes, “A new class of non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980).

Brown, D.

M. Poppendieck, D. Brown, “Control of light output from plastic optical fiber with optical elements,” SAE Tech. Paper 960491 (Society of Automotive Engineers, Warrendale, Pa., 1996).

Buelow, R. F.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Cassarly, B. J.

B. J. Cassarly, “Design of efficient illumination systems,” short course presented at the annual meeting of the Society of Photo-Optical Instrumentation Engineers, Denver, Colorado, 18–23 July 1999.

Cassarly, W. J.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Cornelissen, H. J.

H. J. Cornelissen, M. J. J. Donna, H. Greiner, “Frontlights for reflective LCDs based on lightguides with micro-grooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Davenport, T. L.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Decker, D.

D. Decker, “CELIS–a concept for high-quality car interior lighting with light-guide technology,” SAE Tech. Paper 960488 (Society of Automotive Engineers, Warrendale, Pa., 1996).

Derlofske, J. F. V.

D. J. Lamb, J. F. V. Derlofske, L. W. Hillman, “The use of aspheric surfaces in waveguide illumination systems for automotive displays,” SAE Tech. Paper 980874 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Derlofske, J. V.

J. V. Derlofske, “Nonrotationally symmetric mirrors provide even light,” Laser Focus World (July1999), pp. S23–S25.

Donna, M. J. J.

H. J. Cornelissen, M. J. J. Donna, H. Greiner, “Frontlights for reflective LCDs based on lightguides with micro-grooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Edmonds, R.

R. Edmonds, J. Reppel, P. Jardine, “Extractors and emitters for light distribution from hollow light guides,” Light. Res. Technol. 29, 23–32 (1997).
[CrossRef]

Evard, P. J.

J. M. Teijido, H. P. Herzig, C. Fuhrer, P. J. Evard, “Design methods for illumination lightpipes,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 34–44 (1998).
[CrossRef]

Forbes, G. W.

I. M. Bassett, G. W. Forbes, “A new class of non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

Fuhrer, C.

J. M. Teijido, H. P. Herzig, C. Fuhrer, P. J. Evard, “Design methods for illumination lightpipes,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 34–44 (1998).
[CrossRef]

Greiner, H.

H. J. Cornelissen, M. J. J. Donna, H. Greiner, “Frontlights for reflective LCDs based on lightguides with micro-grooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Hansler, R. L.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Herzig, H. P.

J. M. Teijido, H. P. Herzig, C. Fuhrer, P. J. Evard, “Design methods for illumination lightpipes,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 34–44 (1998).
[CrossRef]

Hillman, L. W.

D. J. Lamb, J. F. V. Derlofske, L. W. Hillman, “The use of aspheric surfaces in waveguide illumination systems for automotive displays,” SAE Tech. Paper 980874 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Jardine, P.

R. Edmonds, J. Reppel, P. Jardine, “Extractors and emitters for light distribution from hollow light guides,” Light. Res. Technol. 29, 23–32 (1997).
[CrossRef]

Jenkins, D.

J. Schweyen, D. Jenkins, “Smart lightpipe designs,” Photonics Spectra (January1997), pp. 101–103.

Lamb, D. J.

D. J. Lamb, J. F. V. Derlofske, L. W. Hillman, “The use of aspheric surfaces in waveguide illumination systems for automotive displays,” SAE Tech. Paper 980874 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Oki, Y.

Y. Oki, “Novel backlight with high luminance and low power consumption by prism-on-lightpipe technology,” SID Dig. 29, 157–160 (1998).
[CrossRef]

Pfafords, D.

J. Spigulis, D. Pfafords, “Clinical potential of side-glowing optical fibers,” in Speciality Fiber Optics for Biomedical and Industrial Applications, A. Katzir, J. A. Harrington, eds., Proc. SPIE2977, 84–88 (1997).
[CrossRef]

Poppendieck, M.

M. Poppendieck, D. Brown, “Control of light output from plastic optical fiber with optical elements,” SAE Tech. Paper 960491 (Society of Automotive Engineers, Warrendale, Pa., 1996).

Reppel, J.

R. Edmonds, J. Reppel, P. Jardine, “Extractors and emitters for light distribution from hollow light guides,” Light. Res. Technol. 29, 23–32 (1997).
[CrossRef]

Schweyen, J.

J. Schweyen, D. Jenkins, “Smart lightpipe designs,” Photonics Spectra (January1997), pp. 101–103.

Spigulis, J.

J. Spigulis, D. Pfafords, “Clinical potential of side-glowing optical fibers,” in Speciality Fiber Optics for Biomedical and Industrial Applications, A. Katzir, J. A. Harrington, eds., Proc. SPIE2977, 84–88 (1997).
[CrossRef]

Stenger, T. E.

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Teijido, J. M.

J. M. Teijido, H. P. Herzig, C. Fuhrer, P. J. Evard, “Design methods for illumination lightpipes,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 34–44 (1998).
[CrossRef]

van den Bergh, H.

H. van den Bergh, “On the evoution of some endoscopic light delivery systems for photodynamic therapy,” Endoscopy 30, 392–407 (1998).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980).

Endoscopy

H. van den Bergh, “On the evoution of some endoscopic light delivery systems for photodynamic therapy,” Endoscopy 30, 392–407 (1998).
[CrossRef] [PubMed]

Laser Focus World

J. V. Derlofske, “Nonrotationally symmetric mirrors provide even light,” Laser Focus World (July1999), pp. S23–S25.

Light. Res. Technol.

R. Edmonds, J. Reppel, P. Jardine, “Extractors and emitters for light distribution from hollow light guides,” Light. Res. Technol. 29, 23–32 (1997).
[CrossRef]

Opt. Acta

I. M. Bassett, G. W. Forbes, “A new class of non-imaging transformers,” Opt. Acta 29, 1271–1282 (1982).
[CrossRef]

G. W. Forbes, I. M. Bassett, “An axially symmetric variable-angle nonimaging transformer,” Opt. Acta 29, 1283–1297 (1982).
[CrossRef]

Photonics Spectra

J. Schweyen, D. Jenkins, “Smart lightpipe designs,” Photonics Spectra (January1997), pp. 101–103.

SID Dig.

Y. Oki, “Novel backlight with high luminance and low power consumption by prism-on-lightpipe technology,” SID Dig. 29, 157–160 (1998).
[CrossRef]

H. J. Cornelissen, M. J. J. Donna, H. Greiner, “Frontlights for reflective LCDs based on lightguides with micro-grooves,” SID Dig. 30, 912–915 (1999).
[CrossRef]

Other

D. Decker, “CELIS–a concept for high-quality car interior lighting with light-guide technology,” SAE Tech. Paper 960488 (Society of Automotive Engineers, Warrendale, Pa., 1996).

J. Spigulis, D. Pfafords, “Clinical potential of side-glowing optical fibers,” in Speciality Fiber Optics for Biomedical and Industrial Applications, A. Katzir, J. A. Harrington, eds., Proc. SPIE2977, 84–88 (1997).
[CrossRef]

J. M. Teijido, H. P. Herzig, C. Fuhrer, P. J. Evard, “Design methods for illumination lightpipes,” in Illumination and Source Engineering, A. V. Arecchi, ed., Proc. SPIE3428, 34–44 (1998).
[CrossRef]

T. L. Davenport, R. L. Hansler, T. E. Stenger, W. J. Cassarly, G. R. Allen, R. F. Buelow, “Changes in angular and spatial distribution introduced into fiber optic headlamp by the fiber optic cables,” SAE Tech. Paper 960490 (Society of Automotive Engineers, Warrendale, Pa., 1998).

M. Poppendieck, D. Brown, “Control of light output from plastic optical fiber with optical elements,” SAE Tech. Paper 960491 (Society of Automotive Engineers, Warrendale, Pa., 1996).

D. J. Lamb, J. F. V. Derlofske, L. W. Hillman, “The use of aspheric surfaces in waveguide illumination systems for automotive displays,” SAE Tech. Paper 980874 (Society of Automotive Engineers, Warrendale, Pa., 1998).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980).

Breault Research Organization, Inc., Advanced System Analysis Program (Tucson, Ariz., 1995).

B. J. Cassarly, “Design of efficient illumination systems,” short course presented at the annual meeting of the Society of Photo-Optical Instrumentation Engineers, Denver, Colorado, 18–23 July 1999.

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Figures (12)

Fig. 1
Fig. 1

Principal sections of a lightpipe are shown by the plane sections for (a) a rectangular cross section, (b) a circular cross section (only one of the infinite principal sections is shown), (c) an elliptical cross section, and (d) a lightpipe with a 90° bend.

Fig. 2
Fig. 2

Geometry of a straight lightpipe. (a) The critical angle is denoted by θ c , and the resulting acceptance angle is denoted by θ a . (b) Cross section of the straight lightpipe displaying different sections.

Fig. 3
Fig. 3

Angle of incidence does not change for a nonleaky ray inside a uniformly curved circular section. ΔAOB is similar to ΔCOB. Hence ∠ BCO is equal to ∠ θ. Similarly, all other angles made by the ray on the outer surface are ∠ θ. On the inner surface they are ∠ (ϕ + θ).

Fig. 4
Fig. 4

Principal section of the lightpipe with a circular bend.

Fig. 5
Fig. 5

Principal section results: the acceptance angle θ a versus the bend ratio m for two different refractive-index materials.

Fig. 6
Fig. 6

Horizontal section: (a) line CBA shows a horizontal slice cut off from the center of the lightpipe. (b) The cross section along OZ′ in (a).

Fig. 7
Fig. 7

Horizontal section slice of a lightpipe with circular bend for (a) circular cross section and (b) square cross section.

Fig. 8
Fig. 8

Horizontal section results. Angles of incidence at the bend θ (in deg) are plotted against the angular extent of the bend v 0 (in deg) for three different values of the elliptic ratio e, two extreme values of refractive index (1.4 < n < 1.7), and two extreme values of the bend ratio (1 < m < n). The horizontal line represents the critical angle.

Fig. 9
Fig. 9

Lightpipes with varying bend radius r, but the same n = 1.45, and bend ratio m = 1.22 for (a) a circular cross section and (b) a rectangular cross section. When we vary the bend radius, it does not affect the bend leakage for a constant m, n, cross section, and input angle. When we change the cross section from circular to square, the lightpipes have half the leakage but the leakage pattern is unchanged.

Fig. 10
Fig. 10

Distribution of light at the output facet of a straight lightpipe. The top row shows the spatial distribution and the bottom row shows the angular distribution for (a) a circular cross-section lightpipe and (b) a square cross-section lightpipe. The lighter regions correspond to higher flux.

Fig. 11
Fig. 11

Distribution of light at the output of a bent lightpipe. The top row shows the spatial distribution and the bottom row shows the angular distribution for (a) a circular cross-section lightpipe and (b) a square cross-section lightpipe. The lighter regions correspond to higher flux.

Fig. 12
Fig. 12

Uniformity distribution does not change when the bend radius is increased for a constant bend ratio (1.22), refractive index (1.45), and input angle (51.34°). The top row shows the spatial uniformity distribution and the bottom row shows the angular uniformity distribution for (a) a bend radius of 0.25 and (b) a bend radius of 1.75. The lighter regions correspond to higher flux.

Equations (28)

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θc=sin-11/n,
θa=sin-1n2-1.
cos θ=cos θ1 cos θ2,
e=t0/t1.
m=r2/r1,
t0=r2-r1/2.
r12+r22-2r1r2 cos ϕ=r32,
r32+r22-2r3r2 cos θc=r12.
cos ϕ=m/n2±n2-1n2-m21/2/n2,
θa=sin-1n cossin-11/n+ϕ).
cos θ=cos θxy cos θyz, θxy=θ-v0,
θ=π/2-sin-1sin θa/n.
y2/t12+z2/t02=1.
BD¯=z0=x0-r sin v02+z0-r cos v021/2,
BD¯=rsec v0-1=rb,
tan θyz=-1dzdy|z0,y0=t12z0t02y0,
r=r1+r2/2=m+1r1/2.
tan θyz=bm+1em-11-bm+1/m-121/2.
ϕin=sin-1sin θa/n,
tan ϕin=y0+t1/x0.
y0=t11-z02/t021/2.
e2β tan2 ϕin tan2 v0-2e tan ϕin tan v0+βsec v0-12=0.
cos θ=cosπ/2-θcos v0,
θ=cos-1m+1sin θa/2mn.
θminimum=sin-11/n=θc.
cos θ=rˆ1·rˆ2/|rˆ1||rˆ2|.
cos θ=rˆ1·rˆ3/|rˆ1||rˆ3|rˆ3·rˆ2/|rˆ3||rˆ2|.
cos θ=cos θ1 cos θ2.

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