Abstract

We present the method for computation of highly effective total internal reflection (TIR) optics for LED-based illumination systems. The computation problem is reduced to the integration of several explicit independent first-order differential equations. Two designs of TIR optics are considered and compared: with flat and with aspherical upper surface. The dependence of nonuniformity of generated irradiance distribution on the size of the light source is studied for both designs numerically. It is shown that point source approximation is acceptable in cases when the size of the light source is 5 (or more) times less than the distance to the inner surface of the optical element.

© 2012 Optical Society of America

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References

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  1. P. Guan and X.-J. Wang, “On a Monge-Ampere equation arising in geometric optics,” J. Diff. Geom. 48, 205–223 (1998).
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    [CrossRef]
  4. D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
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    [CrossRef]
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2012

2011

2010

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik 121, 1761–1765 (2010).
[CrossRef]

D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
[CrossRef]

2009

1998

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

1978

Alvarez, A.

D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
[CrossRef]

Benitez, P.

Bernabeu, E.

D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
[CrossRef]

Cen, S.

Chen, F.

Cheung, B.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik 121, 1761–1765 (2010).
[CrossRef]

Elmer, W. B.

Gadegaard, J.

Gonzalez-Montez, M.

D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
[CrossRef]

Grabovickic, D.

Guan, P.

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

Jiang, J.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik 121, 1761–1765 (2010).
[CrossRef]

Jin, Sh.

Kari, Th.

Lee, W. B.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik 121, 1761–1765 (2010).
[CrossRef]

Liu, Sh.

Minano, J. C.

Pedersen, K.

Pedersen, Th. G.

Sondergaard, Th.

Sun, L.

To, S.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik 121, 1761–1765 (2010).
[CrossRef]

Vazquez-Molini, D.

D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
[CrossRef]

Wang, K.

Wang, X.-J.

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

Wu, D.

Zhao, Sh.

Appl. Opt.

J. Diff. Geom.

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

J. Opt. Soc. Am. A

Opt. Eng.

D. Vazquez-Molini, M. Gonzalez-Montez, A. Alvarez, and E. Bernabeu, “High-efficiency light-emitting diode collimator,” Opt. Eng. 49, 123001 (2010).
[CrossRef]

Opt. Express

Optik

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik 121, 1761–1765 (2010).
[CrossRef]

Other

“TracePro Suite of Optical and Illumination Design Software,” http://lambdares.com/software_products/tracepro/ .

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Figures (10)

Fig. 1.
Fig. 1.

TIR optics with flat upper surface.

Fig. 2.
Fig. 2.

Profile of TIR optics with flat upper surface.

Fig. 3.
Fig. 3.

(a) Refraction on the upper surface. (b) Refraction on the inner lateral surface.

Fig. 4.
Fig. 4.

Profile of TIR optics with aspherical upper surface.

Fig. 5.
Fig. 5.

Computed profile of optical element with flat upper surfacegenerating uniform irradiance distribution in circle area.

Fig. 6.
Fig. 6.

Irradiance distribution generated by the optical element in Fig. 5. (a) Half-tone irradiance distribution; (b) Profile of generated irradiance distribution.

Fig. 7.
Fig. 7.

Computed profile of optical element with inner collimating profile and aspherical upper surface generating uniform irradiance distribution in circle area.

Fig. 8.
Fig. 8.

Irradiance distribution generated by the optical element in Fig. 7. (a) Half-tone irradiance distribution. (b) Profile of generated irradiance distribution.

Fig. 9.
Fig. 9.

Dependence of RRMSE of generated irradiance distribution on the relative radius of the light source. Radius is measured in distances from the light source to the inner surface along the Oz axis. The solid line shows the dependence for optical element in Fig. 5, dashed line for the optical element in Fig. 7.

Fig. 10.
Fig. 10.

Refraction of ray on the r(φ) surface.

Equations (24)

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dra(β0)dβ0=ra(β0)sin(β0βa(β0))n1/n2cos(β0βa(β0)),
n1l2+rb2(γ)2lrb(γ)cosγ+n2(Rrb(γ))=Ψ0,
drc(γ)dγ=rc(γ)cotπ/2γβc(γ)2,
π/2+γβc(γ)2>αTIR,
2πI0(β0)sinβ0dβ0=2πE(ρ)ρdρ,
dρ2dβ0=2I0(β0)sinβ0E(ρ).
βa(β0)=βc(β0)=arcsin(n1n2sinarctanρ(β0)f).
β0(γ)=arccosrb(γ)sinγl2+rb2(γ)2lrb(γ)cosγ.
ρa(β0)=Rsinβ0sinβ0max,ρc(γ)=R1sin2β0(γ)1sin2β0max.
dzdρ=z(β0)ρ(β0)=n2n1sinβ0+sinβout(β0)n2n1cosβ0cosβout(β0),
dzdρ=sinβout(ρ)n2/n1cosβout(ρ).
E0(ρ)2πρdρ=E(r)2πrdr,
dr2dρ=2E0(ρ)ρE(r),
βout(ρ)=arctanr(ρ)ρfz(ρ).
r=rcotθ.
n1sin(π2θ)=n2sinα,
n1cosθ=n2cos(θ+φβ).
n1cosθ=n2[cosθcos(φβ)sinθsin(φβ)].
n1cotθ=n2[cotθcos(φβ)sin(φβ)],
cotθ=sin(φβ)n1/n2cos(φβ).
drdφ=rsin(φβ(φ))n1/n2cos(φβ(φ)).
ρ(φ)=r(φ)sinφ,z(φ)=r(φ)cosφ.
dzdρ=z(φ)ρ(φ)=r(φ)sinφ+r(φ)cosφr(φ)cosφr(φ)sinφ.
dzdρ=z(φ)ρ(φ)=n1n2sinφ+sinβ(φ)n1n2cosφcosβ(φ).

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