Abstract

We propose an approach to deal with the problem of freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this approach, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge–Ampére equation. The theory and numerical method are given for solving this boundary problem. Experimental results show the feasibility of this approach in tackling this freeform design problem.

© 2013 Optical Society of America

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References

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T. Glimm and V. I. Oliker, J. Math. Sci. 117, 4096 (2003).
[CrossRef]

2002

1998

1996

1994

1993

1992

Bräuer, A.

Cassarly, W. J.

Chen, F.

Ding, Y.

Feng, Z. X.

Fournier, F. R.

Glimm, T.

T. Glimm and V. I. Oliker, J. Math. Sci. 117, 4096 (2003).
[CrossRef]

González, J. C.

Gordon, J. M.

Gu, P. F.

Han, Y. J.

Jenkins, D.

Li, H. T.

Liu, S.

Liu, X.

Liu, Z. Y.

Luo, X. B

Luo, Y.

Michaelis, D.

Miñano, J. C.

Muschaweck, J.

Oliker, V. I.

T. Glimm and V. I. Oliker, J. Math. Sci. 117, 4096 (2003).
[CrossRef]

Qian, K. Y.

Rabl, A.

Ries, H.

Ries, H. R.

Rolland, J. P.

Schreiber, P.

Wang, K.

Wang, L.

Winston, R.

Zheng, Z. R.

Supplementary Material (1)

» Media 1: MOV (8786 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Geometrical design layout of the lens.

Fig. 2.
Fig. 2.

(a) Model of the freeform lens and (b) obtained illumination pattern on the target plane.

Fig. 3.
Fig. 3.

Irradiance distribution along the line y=50mm. The black dotted curve represents the result obtained from the experimental test. The red solid curve and the blue dashed curve represent the simulation results obtained from the small source and a 1mm×1mm Lambertian emitter, respectively.

Fig. 4.
Fig. 4.

Difference of radial length between all the data points and the data point with φ=π/4 and θ=0 on the freeform surface.

Fig. 5.
Fig. 5.

(a) Fabricated freeform lens, (b) experimental setup, and (c) illumination pattern recorded at the back of the panel.

Fig. 6.
Fig. 6.

3D irradiance distribution.

Fig. 7.
Fig. 7.

LED and the freeform lens are moved together to change the lighting distance (Media 1).

Tables (1)

Tables Icon

Table 1. Design Parameters for the Freeform Lensa

Equations (7)

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

N=(Pφ×Pθ)/|Pφ×Pθ|,
x=Px+(zPz)niIx+P0NxniIz+P0Nz,y=Py+(zPz)niIy+P0NyniIz+P0Nz,
dxdy=|J(T)|dθdφ
RE(x,y)dxdy=ΩI(θ,φ)dω,
E(x,y)|J(T)|=I(θ,φ)sinφ.
A1(ρθθρφφρθφ2)+A2ρφφ+A3ρθθ+A4ρθφ+A5=0,
{x=x(θ,φ,ρ,ρθ,ρφ)y=y(θ,φ,ρ,ρθ,ρφ):ΩR,

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