Abstract

Illumination design used to redistribute the spatial energy distribution of light source is a key technique in lighting applications. However, there is still no effective illumination design method for extended sources, especially for extended non-Lambertian sources. What we present here is to our knowledge the first direct method for extended non-Lambertian sources in three-dimensional (3D) rotational geometry. In this method, both meridional rays and skew rays of the extended source are taken into account to tailor the lens profile in the meridional plane. A set of edge rays and interior rays emitted from the extended source which will take a given direction after the refraction of the aspherical lens are found by the Snell’s law, and the output intensity at this direction is then calculated to be the integral of the luminance function of the outgoing rays at this direction. This direct method is effective for both extended non-Lambertian sources and extended Lambertian sources in 3D rotational symmetry, and can directly find a solution to the prescribed design problem without cumbersome iterative illuminance compensation. Two examples are presented to demonstrate the effectiveness of the proposed method in terms of performance and capacity for tackling complex designs.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2015 (2)

2014 (1)

2013 (5)

2010 (3)

2008 (1)

2007 (1)

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE 6670, 66700A (2007).
[Crossref]

2004 (1)

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

2002 (1)

1995 (1)

P. T. Ong, J. M. Gordon, A. Rabl, and W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 134, 1726–1737 (1995).

1994 (1)

1993 (1)

Bäuerle, A.

Benítez, P.

Berens, M.

Blen, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Bortz, J.

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE 6670, 66700A (2007).
[Crossref]

Bruneton, A.

Cai, W.

P. T. Ong, J. M. Gordon, A. Rabl, and W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 134, 1726–1737 (1995).

Cassarly, W. J.

W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE 7652, 76522L (2010).
[Crossref]

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]

Chaves, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Ding, Y.

Dross, O.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Falicoff, W.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Feng, Z.

Fournier, F. R.

Gong, M.

Gordon, J. M.

P. T. Ong, J. M. Gordon, A. Rabl, and W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 134, 1726–1737 (1995).

A. Rabl and J. M. Gordon, “Reflector design for illumination with extended sources: the basic solutions,” Appl. Opt. 33(25), 6012–6021 (1994).
[Crossref] [PubMed]

Gu, P. F.

Han, Y.

Hernández, M.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Hua, H.

Huang, L.

Jin, G.

Li, H.

Liu, P.

Liu, X.

Loosen, P.

Luo, Y.

Meuret, Y.

Miñano, J. C.

Mohedano, R.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Müller, G.

Muschaweck, J.

Ong, P. T.

P. T. Ong, J. M. Gordon, A. Rabl, and W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 134, 1726–1737 (1995).

Qin, Y.

Rabl, A.

P. T. Ong, J. M. Gordon, A. Rabl, and W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 134, 1726–1737 (1995).

A. Rabl and J. M. Gordon, “Reflector design for illumination with extended sources: the basic solutions,” Appl. Opt. 33(25), 6012–6021 (1994).
[Crossref] [PubMed]

Ries, H.

Rolland, J. P.

Shatz, N.

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE 6670, 66700A (2007).
[Crossref]

Stollenwerk, J.

Völl, A.

Wang, K.

Wester, R.

Winston, R.

Wu, R.

Xu, L.

Zhang, Y.

Zheng, Z.

Zheng, Z. R.

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

P. T. Ong, J. M. Gordon, A. Rabl, and W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 134, 1726–1737 (1995).

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004).
[Crossref]

Opt. Express (8)

R. Wu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “A mathematical model of the single freeform surface design for collimated beam shaping,” Opt. Express 21(18), 20974–20989 (2013).
[Crossref] [PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).
[Crossref] [PubMed]

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).
[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]

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21(9), 10563–10571 (2013).
[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]

R. Wester, G. Müller, A. Völl, M. Berens, J. Stollenwerk, and P. Loosen, “Designing optical free-form surfaces for extended sources,” Opt. Express 22(S2Suppl 2), A552–A560 (2014).
[Crossref] [PubMed]

K. Wang, Y. Han, H. Li, and Y. Luo, “Overlapping-based optical freeform surface construction for extended lighting source,” Opt. Express 21(17), 19750–19761 (2013).
[Crossref] [PubMed]

Opt. Lett. (3)

Proc. SPIE (2)

J. Bortz and N. Shatz, “Iterative generalized functional method of nonimaging optical design,” Proc. SPIE 6670, 66700A (2007).
[Crossref]

W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE 7652, 76522L (2010).
[Crossref]

Other (3)

M. Hernandez, “Development of nonimaging optical concentrators,” PhD dissertation 04–030, UPM, 2003.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

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 and F. Tomi, eds. (Springer, 2000), pp. 193–224.

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Figures (13)

Fig. 1
Fig. 1 The illumination design for (a) a point light source and (b) an extended light source.
Fig. 2
Fig. 2 Illumination design for extended sources in 3D geometry. (a) In a translational design, the lens is created by translating the lens profile along the y-axis. The performance on each meridian plane is the same. (b) In a rotational design, the lens is created by applying the rotation to the lens profile. (c) In a freeform design, the lens has no rotational symmetry. H represents the distance between the optical surface to the light source, and d represents the size of the extended light source.
Fig. 3
Fig. 3 The luminance of an incident beam is conserved in a loss-less system.
Fig. 4
Fig. 4 (a) A set of the edge rays and interior rays of the extended source that take the same direction after the refraction of the optical surface, and (b) the domain Ω i formed by their outgoing rays in the xy-plane.
Fig. 5
Fig. 5 The flow chart of the proposed direct method.
Fig. 6
Fig. 6 (a) Calculate the initial curve and (b) calculate the rest of the profile.
Fig. 7
Fig. 7 Calculate a set of incident edge rays that take the same direction after refraction of the optical surface when (a) i<N/2 and (b) i≥N/2.
Fig. 8
Fig. 8 (a) The trajectories of points SRj in the xy-plane, (b) calculation of the interior intersection points, (c) a set of boundary intersection points and interior intersection points on the source, and (d) the domain Ω i formed by all the outgoing rays at the direction β = βi when i<N/2. (e) The trajectories of points SRj in the xy-plane, (f) calculation of the interior intersection points, (g) a set of boundary intersection points and interior intersection points on the source, and (h) the domain Ω i formed by all the outgoing rays at the direction β = βi when i≥N/2.
Fig. 9
Fig. 9 (a) A triangle formed by three neighboring intersection points on the domain Ω i , and (b) a quadrangle formed by four neighboring intersection points on the domain Ω i .
Fig. 10
Fig. 10 The rays from S2 between φ m<φφ max cannot be well controlled.
Fig. 11
Fig. 11 (a) The normalized luminance distribution of the light source at the direction φ = 0°. (b) The normalized luminance distribution of the outgoing rays at the direction β = 0° in the meridional plane. (c) The actual intensity and the prescribed intensity. (d) The lens model and the lens profile.
Fig. 12
Fig. 12 (a) The lens model and the lens profile. (b) The actual intensity and the prescribed intensity. (c) The intensity distribution of the non-Lambertian source and that of the Lambertian source. (d) The sag difference between the lens profile designed for the non-Lambertian source and that designed for the Lambertian source.
Fig. 13
Fig. 13 (a) The actual intensity and the prescribed intensity. (b) The sag difference between the lens profile generated by the feedback method and that generated by the direct method for the Lambertian source.

Tables (1)

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Table 1 Design parameters.

Equations (15)

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I ( β i ) = Ω i L i ( x , y ) cos β i d x d y
d Φ 1 = L ( r , φ ) d E
Φ 1 = 4 n 2 π 2 0 d 1 / 2 0 φ m a x r L ( r , φ ) sin φ cos φ d φ d r
Φ 1 = 2 π 0 β max I t ( β ) sin β d β
I ( 0 ) = i = N / 2 + 1 N π ( x i 2 x i 1 2 ) f 0 ( x i ) f 0 ( x i 1 ) 2
n Ο = Ι + T 1 N R
T 1 = n 2 1 + ( I N R ) 2 ( I N R )
X S = x cos θ j z O x O z , Y S = x sin θ j z O y O z
X S 2 + Y S 2 = ( d 1 / 2 ) 2
I j , 1 = 1 3 ( L j , 1 + L j , 2 + L j + 1 , 2 ) × ( A r e a ) j , 1 cos β i
I j , k = 1 4 ( L j , k + L j + 1 , k + L j , k + 1 + L j + 1 , k + 1 ) × ( A r e a ) j , k cos β i
I ( β i ) = 2 j = 1 N 1 1 k = 1 N 2 1 I j , k
L ( r , φ ) = 1 cos φ exp ( 2 r 2 ) , r [ 0 , d / 2 ] and φ [ 0 , φ max ]
I t ( β ) = { β + K 1 , 0 β β max / 2 β max 2 + K 1 , β max / 2 β β max
R M S = 1 N u m j 1 = 1 N u m ( I a j 1 I t j 1 I t j 1 ) 2

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