Abstract

A new source-target mapping for the design of mirrors generating prescribed 2D intensity distributions is proposed. The surface of the mirror implementing the obtained mapping is expressed in an analytical form. Presented simulation results demonstrate high performance of the proposed method. In the case of generation of rectangular and elliptical intensity distributions with angular dimensions from 80° x 20° to 40° x 20°, relative standard error does not exceed 8.5%. The method can be extended to the calculation of refractive optical elements.

© 2016 Optical Society of America

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References

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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]
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    [Crossref]
  20. http://www.lambdares.com

2016 (1)

2015 (2)

2014 (2)

2013 (3)

2012 (1)

2011 (1)

2010 (2)

2008 (1)

2007 (1)

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[Crossref]

2005 (1)

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

1996 (1)

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).
[Crossref]

1978 (1)

Benítez, P.

Bernard, S.

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[Crossref]

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

Bezus, E. A.

Borisova, K. V.

Bräuer, A.

Cassarly, W. J.

Cooke, F.

Ding, Y.

Dmitriev, A. Y.

Doskolovich, L. L.

L. L. Doskolovich, K. V. Borisova, M. A. Moiseev, and N. L. Kazanskiy, “Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method,” Appl. Opt. 55(4), 687–695 (2016).
[Crossref] [PubMed]

L. L. Doskolovich, A. Y. Dmitriev, M. A. Moiseev, and N. L. Kazanskiy, “Analytical design of refractive optical elements generating one-parameter intensity distributions,” J. Opt. Soc. Am. A 31(11), 2538–2544 (2014).
[Crossref] [PubMed]

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).
[Crossref] [PubMed]

M. A. Moiseev and L. L. Doskolovich, “Design of TIR optics generating the prescribed irradiance distribution in the circle region,” J. Opt. Soc. Am. A 29(9), 1758–1763 (2012).
[Crossref] [PubMed]

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[Crossref]

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).
[Crossref]

Elmer, W.

Feng, Z.

Fournier, F. R.

Gu, P. F.

Han, Y.

Hongtao, L.

Kazanskiy, N. L.

L. L. Doskolovich, K. V. Borisova, M. A. Moiseev, and N. L. Kazanskiy, “Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method,” Appl. Opt. 55(4), 687–695 (2016).
[Crossref] [PubMed]

L. L. Doskolovich, A. Y. Dmitriev, M. A. Moiseev, and N. L. Kazanskiy, “Analytical design of refractive optical elements generating one-parameter intensity distributions,” J. Opt. Soc. Am. A 31(11), 2538–2544 (2014).
[Crossref] [PubMed]

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[Crossref]

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

Kazansky, N. L.

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).
[Crossref]

Kharitonov, S. I.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).
[Crossref]

Li, H.

Liang, R.

Liu, P.

Liu, X.

Luo, Y.

Ma, D.

Mao, X.

Michaelis, D.

Miñano, J. C.

Moiseev, M. A.

Perlo, P.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

Rolland, J. P.

Schreiber, P.

Shichao, C.

Soifer, V. A.

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).
[Crossref]

Wu, R.

Xu, L.

Yanjun, H.

Yi, L.

Zhang, Y.

Zheng, Z.

Zheng, Z. R.

Appl. Opt. (4)

J. Mod. Opt. (3)

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).
[Crossref]

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, “Designing reflectors to generate a line-shaped directivity diagram,” J. Mod. Opt. 52(11), 1529–1536 (2005).
[Crossref]

L. L. Doskolovich, N. L. Kazanskiy, and S. Bernard, “Designing a mirror to form a line-shaped directivity diagram,” J. Mod. Opt. 54(4), 589–597 (2007).
[Crossref]

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

Opt. Express (5)

Opt. Lett. (3)

Other (3)

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, 2003).

http://www.lambdares.com

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Freeform Reflector Design Using Integrable Maps,” in International Optical Design Conference and Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2010), paper IWB4.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Geometry of a typical illuminated domain.
Fig. 2
Fig. 2 Mirror for generating one-parameter intensity distribution (a) and its central profile (b).
Fig. 3
Fig. 3 Theoretical ray mapping for a mirror generating uniform rectangular intensity distribution with angular dimensions of 60 o × 20 o : one half of the mirror surface and the light source emission solid angle Ω (a), one half of the illuminated domain D (b). The light source is depicted with a small black sphere in Fig. (a). The mapping is indicated by color: the “stripes” in area Ω (and the corresponding “stripes” on the mirror surface) in Fig. (a) are mapped to the corresponding rectangles in Fig. (b). One particular pair of “stripes” in the area Ω and on the mirror surface as well as the corresponding rectangle in the illuminated domain are marked with red and connected by black arrows.
Fig. 4
Fig. 4 (a)–(d) Mirrors generating uniform intensity distributions in rectangular domains with the following angular dimensions: 80 o × 20 o (a), 60 o × 20 o (b), 40 o × 20 o (c), 20 o × 20 o (d). Mirror dimensions along the coordinate axes: 12.90 x 4.94 x 3.42 mm (a), 9.42 x 4.92 x 2.77 mm (b), 7.41 x 4.91 x 2.39 mm (c), 6.12 x 4.89 x 2.15 mm (d). (e)–(h) Intensity distributions generated by the mirrors in Figs. (a)–(d) in the case of a compact light source with the diameter of 0.06 mm (depicted with black spheres in Figs. (a)–(d)). The distance from the source to the mirror vertex equals to 1 mm for all examples.
Fig. 5
Fig. 5 (а) Mirror calculated using the conventional source-target mapping (see Fig. 1(b) in [13]) generating uniform intensity distribution in a rectangular domain with the angular dimensions of 20 o × 20 o . Mirror dimensions along the coordinate axes: 6.77 x 6.77 x 2.33 mm. (b) Intensity distribution generated by the mirror in the case of a compact light source with the diameter of 0.06 mm (depicted with a black sphere). The distance from the source to the mirror vertex equals to 1 mm.
Fig. 6
Fig. 6 (a), (b) Mirrors generating uniform intensity distributions in an elliptical domain with angular dimensions of 60 o × 20 o (a) and in a domain in the form of a half ellipse with angular dimensions of 60 o × 10 o (b). Mirror dimensions along the coordinate axes: 9.51 x 4.92 x 2.77 mm (a) and 9.51 x 5.85 x 2.80 mm (b). (c), (d) Intensity distributions generated by the mirrors in Figs. (a), (b) in the case of a compact light source with the diameter of 0.06 mm (depicted with black spheres in Figs. (a), (b)). The distance from the source to the mirror vertex equals to 1 mm for both examples.

Equations (20)

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p( β )=(sinβ,0,cosβ),β[ β d , β d ]
S( u,σ )=e( u,σ )l( u,σ;β )=e( u,σ ) 2f( σ ) / [ 1( e( u,σ ),p( β( σ ) ) ) ] ,
e( u,σ )=( sinα( σ )sinτ( σ )cosu+cosα( σ )cosτ( σ ) sinusinα( σ ) sinα( σ )cosτ( σ )cosu+cosα( σ )sinτ( σ ) )
r( σ )= r 0 exp( 0 σ tan( [ ξβ( ξ ) ] /2 )dξ ),
f( σ )=r( σ ) cos 2 ( [ σβ ] /2 ).
dβ( σ ) dσ = cos( [ σβ ] /2 )[ F 1 ( σ,g( σ,β ) )+ F 2 ( σ,g( σ,β ) ) ] 2I( β )cos( [ σβ ] /2 )[ F 1 ( σ,g( σ,β ) ) F 2 ( σ,g( σ,β ) ) ] ,
F 1 ( σ,g( σ,β ) )= 0 g( σ,β ) I 0 ( u,σ )cosudu , F 2 ( σ,g( σ,β ) )= 0 g( σ,β ) I 0 ( u,σ )du ,
g( σ,β )=arccos( cos α 0 +sin( [ σβ ] /2 )sin( [ σ+β ] /2 ) cos( [ σβ ] /2 )cos( [ σ+β ] /2 ) ).
p(β,γ)=( sinβcosγ,sinγ,cosβcosγ ), ( β,γ )D.
I( β )= γ 1 ( β ) γ 2 ( β ) I( β,γ )cosγdγ , β[ β d , β d ].
d Ω c =| e( u,σ ) / u × e( u,σ ) / σ |dudσ=( cosu dτ / dσ dα / dσ )dudσ.
I( β )dβ=dσ I 0 (u,σ)| e( u,σ ) / u × e( u,σ ) / σ | du.
I( β,γ )cosγdβdγ= I 0 ( u,σ )sinα( σ )( cosu dτ / dσ dα / dσ )dudσ.
γ( σ,u )=arcsin( I( β ){ F 1 ( σ,u ) dτ / dσ F 2 ( σ,u ) dα / dσ } I( β,γ ){ F 1 ( σ,g(σ) ) dτ / dσ F 2 ( σ,g(σ) ) dα / dσ } ).
S(σ,u;β,γ)=e(σ,u)l(σ,u;β,γ)=e(σ,u) 2f( β,γ ) / [ 1( e( σ,u ),p( β,γ ) ) ] ,
l( σ,u;β,γ ) / β =0, l( σ,u;β,γ ) / γ =0.
ln( f ) β = ( e, p / β ) 1( e,p ) , ln( f ) γ = ( e, p / γ ) 1( e,p ) .
G( σ,u ) σ = ( e, p / β ) 1( e,p ) dβ dσ ( e, p / γ ) 1( e,p ) γ σ , G( σ,u ) u = ( e, p / γ ) 1( e,p ) γ u .
G( σ,u )= 0 u ( e, p / γ ) 1( e,p ) γ u du +lnf( σ ).
S( σ,u )=e( σ,u ) 2f( σ ) 1( e( σ,u ),p( β( σ ),γ( σ,u ) ) ) exp( 0 u ( e, p / γ ) 1( e,p ) γ u du ),

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