Abstract

It was previously demonstrated in [Opt. Lett. 38, 229 (2013)] that the problem of freeform surface illumination design can be converted into a nonlinear boundary problem for the elliptic Monge–Ampére equation based on the ideal source assumption. But how the Monge–Ampére equation method is affected by the characteristics of the light source and target was not discussed there. This Letter systematically analyzes the influence of discontinuity, nonconvexity, and connectivity of light source and target on the Monge–Ampére equation method and presents some intrinsic features of this design method. These features are applied in practical examples in freeform optics design.

© 2014 Optical Society of America

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References

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2013 (3)

2012 (1)

2010 (1)

2009 (1)

2007 (1)

2004 (1)

J. Bortz, N. Shatz, and M. Keuper, Proc. SPIE 5529, 8 (2004).
[CrossRef]

2002 (1)

Bortz, J.

J. Bortz, N. Shatz, and M. Keuper, Proc. SPIE 5529, 8 (2004).
[CrossRef]

Cassarly, W. J.

Chen, J. J.

Fournier, F. R.

Hao, X.

Huang, K. L.

Keuper, M.

J. Bortz, N. Shatz, and M. Keuper, Proc. SPIE 5529, 8 (2004).
[CrossRef]

Li, H. F.

Li, K.

Lin, C. T.

Liu, P.

Liu, T. S.

Liu, X.

Muschaweck, J.

Oliker, V.

Ries, H.

Rolland, J. P.

Shatz, N.

J. Bortz, N. Shatz, and M. Keuper, Proc. SPIE 5529, 8 (2004).
[CrossRef]

Tsai, M. D.

Wang, T. Y.

Wu, R. M.

Xu, L.

Zhang, Y. Q.

Zheng, Z. R.

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Figures (10)

Fig. 1.
Fig. 1.

Illustration of the collimated beam shaping.

Fig. 2.
Fig. 2.

In the initial design, the incident beam with a uniform intensity distribution can be reshaped by the freeform lens to produce a uniform rectangular pattern.

Fig. 3.
Fig. 3.

Intensity distribution of the light source along the line y=0mm, and the obtained illumination pattern. (a) I(x,y) is an analytic function and (b) I(x,y) is a discontinuous function.

Fig. 4.
Fig. 4.

(a) S11 is a nonconvex set, and S1 is a regular domain after fill operation and (b) S11 is mutiply connected, and S1 is simply connected after fill operation.

Fig. 5.
Fig. 5.

(a) Incident rays of the source and (b) the intercept points of the incident rays on the target plane.

Fig. 6.
Fig. 6.

(a) Incident rays of the source and (b) the intercept points of the incident rays on the target plane.

Fig. 7.
Fig. 7.

(a) E(tx,ty) is a discontinuous function and (b) S2 is a nonconvex set.

Fig. 8.
Fig. 8.

(a) Cross section of the light source, (b) a multiply connected domain S2, and (c) two separate nonconvex domains S22 and S23.

Fig. 9.
Fig. 9.

(a) Discretization operation and bulge at the vertex and (b) a smooth surface with a circular aperture can be obtained by the fill operation.

Fig. 10.
Fig. 10.

Rays coming from a Lambertian point source are redirected by the TIR freeform lens to produce a uniform elliptical pattern. (a) The procedure of designing the TIR freeform lens, (b) the pattern produced by the TIR collimator in the near field, and (c) the pattern produced by the TIR freeform lens on the illumination plane.

Equations (6)

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{E(tx(x,y),ty(x,y))|J(T)|=I(x,y)BC:{tx=tx(x,y,z,zx,zy)ty=ty(x,y,z,zx,zy):S1S2,
EΦ(zxx,zyy,zxy,zx,zy,z,)I=0,
Ei,jf(zi1,j1,zi1,j,zi1,j+1,zi,j1,zi,j,zi,j+1,zi+1,j1,zi+1,j,zi+1,j+1)Ii,j=0.
F(Xk)+F(Xk)(Xk+1Xk)=0,
Ei,j(0,fi1,j1,0,fi1,j,0,fi1,j+1,0,fi,j1,0,fi,j,0,fi,j+1,0,fi+1,j1,0,fi+1,j,0,fi+1,j+1,0,)×(Xk+1Xk)=Fi,j(Xk),
AΔX=B,

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