Abstract

The supporting quadric method (SQM) is a versatile method for the design of a wide class of freeform optical elements. In the present work, a novel SQM-based approach for the computation of total internal reflection (TIR) optical elements generating arbitrary narrow-angle light distributions is proposed. High performance of the presented method is confirmed by two designed optical elements: the first one forms an illuminance distribution in a square region with angular size of 17°, and the second one generates a bat-shaped uniformly illuminated area with an angular size of 43.6° x 22.6°. The lighting efficiencies in both cases exceed 90%, and the relative root-mean-square deviations of the generated light distributions from the required ones are less than 6%.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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2017 (2)

2016 (2)

2015 (4)

2014 (3)

2013 (2)

2012 (4)

2011 (2)

2010 (4)

2009 (1)

2003 (1)

S. A. Kochengin and V. I. Oliker, “Computational algorithms for constructing reflectors,” Comput. Vis. Sci. 6(1), 15–21 (2003).
[Crossref]

Aslanov, E.

Benítez, P.

Borisova, K. V.

Bräuer, A.

Byzov, E. V.

Cassarly, W. J.

Cen, S.

Chang, J. Y.

Chen, C.

Chen, F.

Chen, J. J.

Doskolovich, L. L.

Feng, Z.

Fournier, F. R.

Grabovickic, D.

Han, Y.

Hongtao, L.

Huang, K. L.

Jin, S.

Kazanskiy, N. L.

Keys, R. G.

R. G. Keys, “Cubic convolution interpolation for digital image processing,” Proceedings of IEEE Transactions on Acoustics, Speech, and Signal Processing, 1153–1160 (1981).
[Crossref]

Kochengin, S. A.

S. A. Kochengin and V. I. Oliker, “Computational algorithms for constructing reflectors,” Comput. Vis. Sci. 6(1), 15–21 (2003).
[Crossref]

Kravchenko, S. V.

Li, H.

Liang, R.

Lin, C. T.

Liu, P.

Liu, S.

Liu, T. S.

Liu, X.

Luo, Y.

Ma, D.

Mao, X.

Michaelis, D.

Miñano, J. C.

Moiseev, M. A.

Oliker, V.

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method(SQM),” Opt. Express 25(4), A58–A72 (2017).
[Crossref] [PubMed]

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Oliker, V. I.

S. A. Kochengin and V. I. Oliker, “Computational algorithms for constructing reflectors,” Comput. Vis. Sci. 6(1), 15–21 (2003).
[Crossref]

Pan, J. W.

Rolland, J. P.

Rubinstein, J.

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Schreiber, P.

Shichao, C.

Sun, L.

Sun, W. S.

Tsai, C. Y.

Tsai, M. D.

Tu, S. H.

Wang, C. M.

Wang, K.

Wang, T. Y.

Wolansky, G.

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Wu, D.

Wu, R.

Xu, L.

Yanjun, H.

Yi, L.

Zhang, X.

Zhang, Y.

Zhao, S.

Zheng, Z.

Adv. Appl. Math. (1)

V. Oliker, J. Rubinstein, and G. Wolansky, “Supporting quadric method in optical design of freeform lenses for illumination control of a collimated light,” Adv. Appl. Math. 62, 160–183 (2015).
[Crossref]

Appl. Opt. (4)

Comput. Vis. Sci. (1)

S. A. Kochengin and V. I. Oliker, “Computational algorithms for constructing reflectors,” Comput. Vis. Sci. 6(1), 15–21 (2003).
[Crossref]

J. Mod. Opt. (1)

M. A. Moiseev and L. L. Doskolovich, “Design of refractive spline surface for generating required irradiance distribution with large angular dimension,” J. Mod. Opt. 57(7), 536–544 (2010).
[Crossref]

J. Opt. Soc. Am. A (4)

Opt. Express (11)

S. V. Kravchenko, E. V. Byzov, M. A. Moiseev, and L. L. Doskolovich, “Development of multiple-surface optical elements for road lighting,” Opt. Express 25(4), A23–A35 (2017).
[Crossref] [PubMed]

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method(SQM),” Opt. Express 25(4), A58–A72 (2017).
[Crossref] [PubMed]

X. Mao, H. Li, Y. Han, and Y. Luo, “Two-step design method for highly compact three-dimensional freeform optical system for LED surface light source,” Opt. Express 22(S6Suppl 6), A1491–A1506 (2014).
[Crossref] [PubMed]

X. Mao, H. Li, Y. Han, and Y. Luo, “Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape,” Opt. Express 23(4), 4313–4328 (2015).
[Crossref] [PubMed]

M. A. Moiseev, E. V. Byzov, S. V. Kravchenko, and L. L. Doskolovich, “Design of LED refractive optics with predetermined balance of ray deflection angles between inner and outer surfaces,” Opt. Express 23(19), A1140–A1148 (2015).
[Crossref] [PubMed]

D. Grabovičkić, P. Benítez, and J. C. Miñano, “TIR RXI collimator,” Opt. Express 20(S1), A51–A61 (2012).
[Crossref] [PubMed]

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(10), 10984–10995 (2012).
[Crossref] [PubMed]

L. Hongtao, C. Shichao, H. Yanjun, and L. Yi, “A fast feedback method to design easy-molding freeform optical system with uniform illuminance and high light control efficiency,” Opt. Express 21(1), 1258–1269 (2013).
[Crossref] [PubMed]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation usingsource-target maps,” Opt. Express 18(5), 5295–5304 (2010).
[Crossref] [PubMed]

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010).
[Crossref] [PubMed]

J. W. Pan, S. H. Tu, W. S. Sun, C. M. Wang, and J. Y. Chang, “Integration of Non-Lambertian LED and Reflective Optical Element as Efficient Street Lamp,” Opt. Express 18(S2Suppl 2), A221–A230 (2010).
[Crossref] [PubMed]

Opt. Lett. (3)

Other (4)

V. I. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, F. Tomi, eds. (Springer, 2003).

M. Born and E. Wolf, Principles of optics (Cambridge University, 2003).

R. G. Keys, “Cubic convolution interpolation for digital image processing,” Proceedings of IEEE Transactions on Acoustics, Speech, and Signal Processing, 1153–1160 (1981).
[Crossref]

S. Baumer, Handbook of Plastic Optics (Wiley-VCH, 2010).

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Figures (11)

Fig. 1
Fig. 1 Geometry of the optical element.
Fig. 2
Fig. 2 Geometry of the problem of designing the segment of surface (a)
Fig. 3
Fig. 3 Geometry of the problem of designing the segment of surface (c).
Fig. 4
Fig. 4 Optical surfaces of the optical element generating a uniformly illuminated square: (a) inner free-form refractive surface; (b) inner lateral refractive surface; (с) lateral free-form TIR surface; (d) full optical element with colored surfaces.
Fig. 5
Fig. 5 Grayscale illuminance distribution generated by a segmented TIR surface of optical element for focusing into a set of points in a square domain.
Fig. 6
Fig. 6 Simulated illuminance distribution generated by the optical element in Fig. 4: (a) grayscale illuminance distribution; (b) illuminance cross sections along the coordinate axes.
Fig. 7
Fig. 7 Optical elements with axisymmetrical TIR surface and different output surfaces: a) lens array; b) single free-form surface.
Fig. 8
Fig. 8 Simulated illuminance distributions generated by the optical elements in Fig. 7 with the outer lens array (a) and the outer free-form surface (b).
Fig. 9
Fig. 9 Grayscale illuminance distribution generated by a segmented TIR surface of optical element for focusing into a set of points in a bat-shaped domain
Fig. 10
Fig. 10 Optical surfaces of the optical element generating a uniformly bat-shaped region: (a) inner free-form refractive surface; (b) inner lateral refractive surface; (с) lateral free-form TIR surface; (d) full optical element with colored surfaces.
Fig. 11
Fig. 11 Simulated illuminance distribution generated by the optical element in Fig. 10(d).

Tables (1)

Tables Icon

Table 1 Dimensions and optical performance of the computed optical elements.

Equations (14)

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

W i = Δ Ω i I( q ) dΩ, q i = 1 W i Δ Ω i qI( q ) dΩ,
p i = 1 n [ N×( N× q i ) ]N 1 1 n 2 ( N× q i )( N× q i ) ,
( x, p i )=C,
r a,i ( s 0 )+n h i ( s 0 )= Ψ a, i ,
x( h )= r a,i ( s 0 ) s 0 + p i h.
r a,i ( s 0 )= C a, i 1n( s 0 , p i ) ,
r a,i ( φ,ψ; C a, i )= s 0 ( φ,ψ ) r a,i ( φ,ψ )= s 0 ( φ,ψ ) C a, i 1n( s 0 ( φ,ψ ), p i ) ,
r a ( φ,ψ )= min 1iN r a,i ( φ,ψ; C a, i )
r c,i ( φ,ψ )= r b ( φ,ψ )+ l i ( φ,ψ ) s 1 ( φ,ψ ),
r b ( φ,ψ )+n l i ( φ,ψ )+n h i ( φ,ψ )= Ψ c,i ,
x( h )= r b ( φ,ψ )+ l i ( φ,ψ ) s 1 ( φ,ψ )+ p i h.
l i ( φ,ψ; C c,i )= C c,i r b ( φ,ψ )( 1n( p i , s 0 ( φ,ψ ) ) ) n( 1( p i , s 1 ( φ,ψ ) ) ) ,
r c ( φ,ψ )= min 1iN [ r b ( φ,ψ )+ l i ( φ,ψ; C c,i ) s 1 ( φ,ψ ) ].
I( q )=E( x,y ) x 2 + y 2 + H 2 q z ,

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