Abstract

A novel approach to incorporate surface information into the ray mapping method is proposed. This method calculates irradiance at the physical optical surface and target plane instead of the usually flat or hemispherical dummy surface, resulting in a mapping relationship which reflects the true geometry of the system. The robustness of the method is demonstrated in an extreme example (60° off axis) where the uniformity is as high as 82%.

© 2017 Optical Society of America

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References

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2016 (1)

2015 (3)

2013 (2)

2012 (1)

2010 (1)

2008 (1)

2007 (1)

2006 (1)

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808 (2006).
[Crossref]

2002 (1)

1998 (1)

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
[Crossref]

Bäuerle, A.

Bruneton, A.

Cassarly, W. J.

Chen, J.-J.

Ding, Y.

Feng, Z.

Fournier, F. R.

Froese, B. D.

Gu, P. F.

Han, Y.

Huang, K.-L.

Huang, Z.-Y.

Li, H.

Liang, R.

Liu, P.

Liu, T.-S.

Liu, X.

Loosen, P.

Luo, Y.

Ma, D.

Mao, X.

Muschaweck, J.

Parkyn, B.

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808 (2006).
[Crossref]

Parkyn, W. A.

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
[Crossref]

Pelka, D.

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808 (2006).
[Crossref]

Qian, K.

Ries, H.

Rolland, J. P.

Stollenwerk, J.

Tsai, M.-D.

Wang, L.

Wester, R.

Wu, R.

Xu, L.

Zhang, Y.

Zheng, Z.

Zheng, Z. R.

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Opt. Express (4)

Opt. Lett. (2)

Proc. SPIE (2)

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
[Crossref]

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE 6338, 633808 (2006).
[Crossref]

Other (1)

R. Winston, J. C. Minano, P. Benitez, N. Shatz and J. C. Bortz, Nonimaging Optics (Elsevier Academic Press, 2005).

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Figures (12)

Fig. 1
Fig. 1

Rays from the source hit the real surface in drastically different locations than a sample plane near the input can predict. The resulting mapping from the sampled plane poorly reflects the final spatial location of those rays.

Fig. 2
Fig. 2

Irradiance distributions for an off-axis design: (a) sampled on a hemispherical dummy surface and (b) sampled on the final surface.

Fig. 3
Fig. 3

Z component of the curl in the vector field between the physical surface and the target plane for (a) the on axis case and (b) 60° off axis. Notice the curl in the off axis case has increased by more than an order of magnitude.

Fig. 4
Fig. 4

Vector definitions and surface locations used to calculate the output vectors and the irradiance distribution on the surface. Although r i,j is a unit vector, it has been extended to the surface point for greater clarity on its direction.

Fig. 5
Fig. 5

(a) A typical mapping relationship between a square sample of a Lambertian source and a uniform square target plane, shown here as the deformation of a unit grid. (b) The new mapping relationship calculated between the energy distribution on the actual surface and the target plane for an off-axis case, shown as the deformation of a unit grid.

Fig. 6
Fig. 6

Test geometry for the 60° off-axis case shown in LightTools Simulation software. The surface was placed 10mm above the source and pointed directly away from the target plane. The angular offset was measured as the angle between the surface normal at the center of the target plane and the source.

Fig. 7
Fig. 7

Irradiance patterns on the target surface for (a) traditional method and (b) the proposed method for the on-axis case. The corresponding uniformities within the 200mmx200mm target are 95% and 98% respectively. The Irradiance uniformity was calculated as 100%(1-RMSdeviation/mean) on the entire 101x101 grid with a 3 pixel smoothing kernel to reduce statistical error from the raytracing.

Fig. 8
Fig. 8

Performance measured in terms of the uniformity within the target region as a function of angular offset for both the traditional method and the proposed method.

Fig. 9
Fig. 9

Irradiance patterns at 60° off axis for (a) the traditional method (b) the proposed method. The corresponding uniformities within the 200mmx200mm target are 56% and 82% respectively. The Irradiance uniformity was calculated as 100%(1-RMSdeviation/mean) on the entire 101x101 grid with a 3 pixel smoothing kernel to reduce statistical error from the raytracing.

Fig. 10
Fig. 10

Residual Z component of the curl in the vector field between the physical surface and the target plane using the proposed method.

Fig. 11
Fig. 11

Ray Diagram comparing the design for point source and extended sources. When designing with point sources, each surface point has only one ray to redirect. This is not the case for an extended source, where a single surface point redirects rays from each point on the source.

Fig. 12
Fig. 12

Irradiance pattern produced when a 1mmx1mm LED is used instead of a point source with the proposed method at 60° off axis. The uniformity is slightly worse at 80%, largely due to the drop off regions at the edges of the pattern.

Equations (6)

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(×N)×N=0
O i,j = T i,j - P i,j T i,j - P i,j .
N i,j = O i,j - n lens r i,j O i,j - n lens r i,j ,
E= LA r 2 cos θ 1 cos θ 2 .
cos θ 1 = r i,j N Surfac e i,j , cos θ 2 = r i,j N Source .
E i,j = LA r i,j 2 ( r i,j N Source )( r i,j N Surfac e i,j )