Abstract

A numerical double-freeform-optical-surface design method is proposed for beam shaping applications. In this method, both the irradiance distribution and the wavefront of the output beam are taken into account. After numerically obtaining the input-output ray mapping based on Energy conservation using the variable separation method, the two freeform optical surfaces can be constructed simultaneously and point by point corresponding to the ray mapping based on Snell’s law and the constancy of the optical path length. The method is only applicable for separable irradiance distributions. However, such a restriction is fulfilled by many practical laser beam shaping examples. Moreover, the restriction can simplify the computation considerably. Therefore, the method may be quite useful in practice, although it is not applicable to more general cases. As an example, the method was applied to design a two-plano-freeform-lens system for transforming a collimated 20 mm Gaussian laser beam (beam waist: 5mm) into a uniform 10 × 40 mm2 rectangular one without changing the wavefront. Simulation results show that we can obtain a dual lens beam shaping system with the relative root mean square deviation of the irradiance ranging from 0.0652 to 0.326 and the power ratio concentrated on the desired region ranging from 97.5% to 88.3% as the output beam transfers from 0mm to 1000mm.

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References

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  1. Eugene Hecht, Optics, 4th Ed. (Addison-Wesley, 2002).
  2. W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE 3482, 389–396 (1998).
    [CrossRef]
  3. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
    [CrossRef] [PubMed]
  4. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207, 594207-12 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20(13), 14477–14485 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
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2012 (1)

2011 (1)

2010 (2)

2008 (1)

2007 (1)

2005 (2)

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207, 594207-12 (2005).
[CrossRef]

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE 5876, 587607, 587607-6 (2005).
[CrossRef]

2004 (1)

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

2002 (1)

1998 (1)

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

Bäuerle, A.

Benítez, P.

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

Blen, J.

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

Bräuer, A.

Bruneton, A.

Cassarly, W. J.

Chaves, J.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hern’andez, 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. Hern’andez, 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. Hern’andez, 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.

Gu, P. F.

Han, Y.

Hern’andez, M.

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

Li, H.

Liu, X.

Loosen, P.

Luo, Y.

Michaelis, D.

Miñano, J. C.

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

Mohedano, R.

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

Muschaweck, J.

Oliker, V.

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207, 594207-12 (2005).
[CrossRef]

Parkyn, W. A.

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

Qian, K. Y.

Ries, H.

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE 5876, 587607, 587607-6 (2005).
[CrossRef]

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
[CrossRef] [PubMed]

Rolland, J. P.

Schreiber, P.

Stollenwerk, J.

Wang, L.

Wester, R.

Zheng, Z. R.

Appl. Opt. (1)

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

Opt. Eng. (1)

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

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (3)

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207, 594207-12 (2005).
[CrossRef]

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

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE 5876, 587607, 587607-6 (2005).
[CrossRef]

Other (4)

L. Piegl and W. Tiller, The NURBS Book, 2nd, ed (Springer-Verlag, Berlin, 1997).

Y. Han, X. Zhang, Z. Feng, K. Qian, H. Li, Y. Luo, X. Li, G. Huang, and B. Zhu, “Variable-separation three dimensional freeform nonimaging optical system design based on target-to-source mapping and micro belt surface construction, ” Sciencepaper Online 1–9(2010). http://www.paper.edu.cn/en/paper.php?serial_number=201002-443 .

Eugene Hecht, Optics, 4th Ed. (Addison-Wesley, 2002).

W. B. Elmer, The optical design of reflectors, 2nd ed. (Wiley, New York, 1980).

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Figures (7)

Fig. 1
Fig. 1

Geometrical construction of the double freeform optical surfaces for achieving a specified input-output ray mapping

Fig. 2
Fig. 2

The flow diagram of the proposed design method

Fig. 3
Fig. 3

The prescribed irradiance distributions of the (a) input and (b) output beams.

Fig. 4
Fig. 4

The pseudo-color images of the (a) first and (b) second freeform surfaces.

Fig. 5
Fig. 5

Designed two-plano-freeform-lens beam shaping system (Not all the grids are displayed).

Fig. 6
Fig. 6

The simulated irradiance distributions (30 × 50 grids) on the receivers placed at (a) 0 mm, (b) 200mm, (c) 400mm, (d) 600mm, (e) 800mm and (e) 1000mm away from the emitted surface of the second lens.

Fig. 7
Fig. 7

RRMSD and Pr change with the receive positions.

Tables (1)

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Table 1 Design parameters

Equations (16)

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I in ( x s , y s )d x s d y s = I out ( x t , y t )d x t d y t
x s,1 x s,j I in,x ( x s )d x s y s,1 y s,n I in,y ( y s )d y s = x t,1 x t,j I out,x ( x t )d x t y t,1 y t,n I out,y ( y t )d y t
x s,1 x s,m I in,x ( x s )d x s y s,1 y s,i I in,y ( y s )d y s = x t,1 x t,m I out,x ( x t )d x t y t,1 y t,i I out,y ( y t )d y t
I n i,j = [ ( z s x ) x s,j , y s,i , ( z s y ) x s,j , y s,i ,1 ] / 1+ ( z s x ) x s,j , y s,i 2 + ( z s y ) x s,j , y s,i 2
Ou t i,j = [ ( z t x ) x t,j , y t,i , ( z t y ) x t,j , y t,i ,1 ] / 1+ ( z t x ) x t,j , y t,i 2 + ( z t y ) x t,j , y t,i 2
N 1,1 = ( n 0 R 1,1 n 1 I n 1,1 ) / n 0 2 + n 1 2 +2 n 0 n 1 ( R 1,1 I n 1,1 )
( P 2,1 P 1,1 ) N 1,1 =0
( P 2,1 S 2,1 ) / | P 2,1 S 2,1 | =I n 2,1
n 1 [ S 2,1 , P 2,1 ]+ n 0 [ P 2,1 , Q 2,1 ]+ n 2 [ Q 2,1 , T 2,1 ]= n 1 [ S 1,1 , P 1,1 ]+ n 0 [ P 1,1 , Q 1,1 ]+ n 2 [ Q 1,1 , T 1,1 ]
( T 2,1 Q 2,1 ) / | T 2,1 Q 2,1 | =Ou t 2,1
( P i,2 P i,1 ) N i,1 =0
( P i,2 S i,2 ) / | P i,2 S i,2 | =I n i,2
n 1 [ S i,2 , P i,2 ]+ n 0 [ P i,2 , Q i,2 ]+ n 2 [ Q i,2 , T i,2 ]= n 1 [ S i,1 , P i,1 ]+ n 0 [ P i,1 , Q i,1 ]+ n 2 [ Q i,1 , T i,1 ]
( T i,2 Q i,2 ) / | T i,2 Q i,2 | =Ou t i,2
RRMSD= i=1 30 j=1 50 ( I out ( x t ,j , y t ,i ) I simulate ( x t ,j , y t ,i ) ) 2 i=1 30 j=1 50 I out ( x t ,j , y t ,i ) 2
P r = 10×40m m 2 I simulate d x t d y t P = i=11 20 j=6 45 I simulate ( x t,j , y t,i )×1m m 2 P

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