Abstract

The aim of this paper is to develop a straightforward rigorous and flexible computational method to determine the coordinate points on an aspheric surface. The computational method chosen is based on the basic slope-point form of a straight-line equation [slope-point method (SPM)]. The practical instrumental example chosen to illustrate this method is a rotationally symmetric catadioptric collimator for a light-emitting diode (LED) source. This optical system has both a refractive and a totally internally reflective aspheric surface. It is a particularly illuminating example because it requires careful computational attention to the smooth transition between the refracting inner zones and the reflective outer zones of the aperture. The chosen SPM computational method deals satisfactorily with the transition points at the junction between the refractive and total internal reflecting (TIR) zones of the collimator. As part of this study, the effect of the position of the start point of the SPM surface evolution for the TIR zones of the collimator emerges as being particularly important, and the details of this are discussed. Finally, an extension of the basic SPM-based method is used to generalize the development of the catadioptric collimator surfaces to illustrate this general algorithm for aspheric surface design for an extended LED light source.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

2010

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

2009

2008

2005

S. Kudaev and P. Schreiber, “Automated optimization of non-imaging optics for luminaires,” Proc. SPIE 5962, 59620B (2005).
[CrossRef]

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Aslanov, E.

Bruegge, T.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Cen, S.

Chen, F.

Chen, J.-J.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20, 10984–10995 (2012).
[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]

Ding, Y.

Doskolovich, L. L.

Dow, T.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Garrard, K.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Gu, P.-f.

Hoffman, J.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Huang, K.-L.

Jin, S.

Kudaev, S.

S. Kudaev and P. Schreiber, “Automated optimization of non-imaging optics for luminaires,” Proc. SPIE 5962, 59620B (2005).
[CrossRef]

Lin, C.-T.

J.-J. Chen, T.-Y. Wang, K.-L. Huang, T.-S. Liu, M.-D. Tsai, and C.-T. Lin, “Freeform lens design for LED collimating illumination,” Opt. Express 20, 10984–10995 (2012).
[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]

Liu, S.

Liu, T.-S.

Liu, X.

Liu, Z.

Luo, X.

Moiseev, M. A.

Schreiber, P.

S. Kudaev and P. Schreiber, “Automated optimization of non-imaging optics for luminaires,” Proc. SPIE 5962, 59620B (2005).
[CrossRef]

Smith, W. J.

W. J. Smith, “Radiance and Lambert’s law,” in Modern Optical Engineering (McGraw-Hill, 2008), pp. 257–259.

Sohn, A.

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Sun, L.

Tsai, M.-D.

Wang, K.

Wang, T.-Y.

Zheng, Z.-r.

Appl. Opt.

Opt. Eng.

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

Proc. SPIE

S. Kudaev and P. Schreiber, “Automated optimization of non-imaging optics for luminaires,” Proc. SPIE 5962, 59620B (2005).
[CrossRef]

K. Garrard, T. Bruegge, J. Hoffman, T. Dow, and A. Sohn, “Design tools for freeform optics,” Proc. SPIE 5874, 58740A (2005).
[CrossRef]

Other

, “Geometrical product specifications (GPS)—filtration—Part 49: morphological profile filters: scale space techniques,” 2002.

W. J. Smith, “Radiance and Lambert’s law,” in Modern Optical Engineering (McGraw-Hill, 2008), pp. 257–259.

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Figures (22)

Fig. 1.
Fig. 1.

LED freeform collimator.

Fig. 2.
Fig. 2.

Reflection surface of freeform collimator.

Fig. 3.
Fig. 3.

Refraction at the refracting aspheric surface.

Fig. 4.
Fig. 4.

Scheme to determine the coordinates for the TIR surface of the reflective aspheric surface.

Fig. 5.
Fig. 5.

Transition point of the refractive and reflective surfaces.

Fig. 6.
Fig. 6.

Scheme to calculate the coordinates for the refracting section of the aspheric surface.

Fig. 7.
Fig. 7.

3D layout of the LED collimator.

Fig. 8.
Fig. 8.

Bare LED illuminance with a detector at 5 m away in 3 m (L) × 2.8 m (W).

Fig. 9.
Fig. 9.

Collimated illuminance of the LED collimator with its TIR surface starting at 1 mm radius at the source plane, with the detector as in Fig. 8.

Fig. 10.
Fig. 10.

Collimated illuminance of the LED collimator with its TIR surface starting at 10 mm radius at the source plane, with the detector as in Fig. 8.

Fig. 11.
Fig. 11.

Collimated illuminance of the LED collimator with its TIR surface starting at 20 mm radius at the source plane, with the detector as in Fig. 8.

Fig. 12.
Fig. 12.

Collimated illuminance of the LED collimator with its TIR surface starting at 50 mm radius at the source plane, with the detector as in Fig. 8.

Fig. 13.
Fig. 13.

Collimated illuminance of the LED collimator with its TIR surface starting at 100 mm radius at the source plane, with the detector as in Fig. 8.

Fig. 14.
Fig. 14.

Scheme of extended LED light source. Each coordinate is the origin of its corresponding integrated sample collimator.

Fig. 15.
Fig. 15.

Illuminance of LED in 5.76 mm square with single catadioptric collimator (assuming its flux is 900 lm).

Fig. 16.
Fig. 16.

Auto CAD drawing of the single catadioptric collimator of LED in 5.76 mm square.

Fig. 17.
Fig. 17.

Scheme of extended LED (1.2mm×1.2mm).

Fig. 18.
Fig. 18.

Auto CAD drawing of the quasi-freeform catadioptric collimator of LED in 1.44 mm square.

Fig. 19.
Fig. 19.

Illuminance of LED in 1.44 mm square, with a quasi-freeform catadioptric collimator set as Fig. 17 (assuming each individual flux of the LED is 100 lm).

Fig. 20.
Fig. 20.

Illuminance of LED in 23.06 mm square with single catadioptric collimator (assuming its flux is 900 lm).

Fig. 21.
Fig. 21.

Scheme of extended LED (2.4mm×2.4mm).

Fig. 22.
Fig. 22.

Illuminance of LED in 5.76 mm square, with quasi-freeform catadioptric collimator set as in Fig. 21 (assuming each individual flux of the LED is 100 lm).

Tables (2)

Tables Icon

Table 1. Collimator Surface Type Classified by Incident Angle

Tables Icon

Table 2. Lighting Performance of LED with Freeform Collimator Varying by Start Point Position

Equations (36)

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

θ1i+θ2=π2,
β=i+(π2θ1).
θ1+θ2=2θ=i+π2.
θ=i2+π4.
β=i+(π2θ1)=i+[π2(i2+π4)]=i2+π4.
θc=sin111.493542.0337415°.
i+x1=π2,
x1=θ4θ3,
i+x1=iθ3+θ4=π2
θ4=θ3+π2i.
n1sinθ3=n2sinθ4,
n1sinθ3=n2sinθ4=sin(θ3+π2i).
θ3=tan1(cos(i)n1sin(i)).
β+x2=π2.
x2=iθ3.
β+iθ3=π2
β=π2i+θ3.
β=π2i+tan1(cos(i)n1sin(i)),
mr1xy=0,
mrt1xy=10mrt1,
xr1=10mr1mrt1mr1,
yr1=mr1·xr1.
βr1=ir12+π2.
mr2xy=0,
mrt2xy=mrt2xr1yr1,
xr2=mrt2xr1yr1mrt2mr2,
yr2=mr2·xr2.
it=tan1(cos(it)n1sin(it)).
mrr1xy=0,
mrrt1y=mrrt1·xrr0yrr0,
xrr1=mrrt1xrr0yrr0mrrt1mrr1,
xrr1=mrrt1xrr0yrr0mrrt1mrr1,
mrr2xy=0,
mrrt2xy=mrrt2xrr1yrr1,
xrr2=mrrt2xrr1yrr1mrrt2mrr2,
yrr2=mrr2·xrr2.

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