Abstract

Many laser applications require specific irradiance distributions to ensure optimal performance. In addition, some applications can benefit from time-varying distributions. In this work, we present the analytic design of a zoom XY-beam expander based on movable freeform optics that allows to simultaneously vary the magnification in x- and y-direction, respectively. This concept is not new: the new is to design and optimally exploit freeform lenses to achieve such an optical functionality. In comparison with zoom beam expanders that use combinations of rotated cylindrical lenses, a freeform system can be more compact, yet achieving excellent overall optical performance throughout the full zoom range.

© 2015 Optical Society of America

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References

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  15. A. Mikš and P. Novák, “Paraxial properties of three-element zoom systems for laser beam expanders,” Opt. Express 22, 21535–21540 (2014).
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2014 (2)

2013 (2)

2012 (6)

D. L. Shealy and J. A. Hoffnagle, “Review: design and analysis of plano-aspheric laser beam shapers,” Proc. SPIE 8490, 849003 (2012).
[Crossref]

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photon. Rev. 6, 607–621 (2012).
[Crossref]

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

G. Nadorff, F. DeWitt, and S. Lindau, “Variable xy-UV beam expander for high-power laser beam shaping,” Proc. SPIE 8490, 84900I (2012).
[Crossref]

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles,” Opt. Express 20, 5576–5585 (2012).
[Crossref] [PubMed]

F. Duerr, P. Benítez, J. C. Miñano, Y. Meuret, and H. Thienpont, “Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces,” Opt. Express 20, 10839–10846 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

2009 (1)

S. Woods, “Understanding materials processing lasers,” Laser Tech. J. 6, 23–26 (2009).
[Crossref]

2005 (1)

1997 (1)

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photon. Rev. 6, 607–621 (2012).
[Crossref]

Becker, M. F.

Benítez, P.

Beyer, E.

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

Bonss, S.

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

Bulte, H.

DeWitt, F.

G. Nadorff, F. DeWitt, and S. Lindau, “Variable xy-UV beam expander for high-power laser beam shaping,” Proc. SPIE 8490, 84900I (2012).
[Crossref]

Duerr, F.

Duocastella, M.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photon. Rev. 6, 607–621 (2012).
[Crossref]

El-Agmy, R.

Feng, Z.

Fujii, T.

Gong, M.

Goto, N.

Greenaway, A.

Hannweber, J.

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

Heinzen, D. J.

Hoffnagle, J. A.

D. L. Shealy and J. A. Hoffnagle, “Review: design and analysis of plano-aspheric laser beam shapers,” Proc. SPIE 8490, 849003 (2012).
[Crossref]

Huang, L.

Jin, G.

Kanai, Y.-k.

Karsunke, U.

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

Kohn, R. N.

Kuehn, S.

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

Liang, J.

Lindau, S.

G. Nadorff, F. DeWitt, and S. Lindau, “Variable xy-UV beam expander for high-power laser beam shaping,” Proc. SPIE 8490, 84900I (2012).
[Crossref]

Meuret, Y.

Mikš, A.

Miñano, J. C.

Nadorff, G.

G. Nadorff, F. DeWitt, and S. Lindau, “Variable xy-UV beam expander for high-power laser beam shaping,” Proc. SPIE 8490, 84900I (2012).
[Crossref]

Nayuki, T.

Nemoto, K.

Novák, P.

Reid, D.

Seifert, M.

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

Shealy, D. L.

D. L. Shealy and J. A. Hoffnagle, “Review: design and analysis of plano-aspheric laser beam shapers,” Proc. SPIE 8490, 849003 (2012).
[Crossref]

Smilie, P. J.

Suleski, T. J.

Thienpont, H.

Woods, S.

S. Woods, “Understanding materials processing lasers,” Laser Tech. J. 6, 23–26 (2009).
[Crossref]

Appl. Opt. (2)

Laser Photon. Rev. (1)

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photon. Rev. 6, 607–621 (2012).
[Crossref]

Laser Tech. J. (1)

S. Woods, “Understanding materials processing lasers,” Laser Tech. J. 6, 23–26 (2009).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Proc. SPIE (3)

S. Bonss, J. Hannweber, U. Karsunke, S. Kuehn, M. Seifert, and E. Beyer, “Laser heat treatment with latest system components,” Proc. SPIE 8239, 82390I (2012).
[Crossref]

G. Nadorff, F. DeWitt, and S. Lindau, “Variable xy-UV beam expander for high-power laser beam shaping,” Proc. SPIE 8490, 84900I (2012).
[Crossref]

D. L. Shealy and J. A. Hoffnagle, “Review: design and analysis of plano-aspheric laser beam shapers,” Proc. SPIE 8490, 849003 (2012).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (2088 KB)      A ray tracing animation video of the zoom XY-beam expander: showing both the continuous lens’ movements in cross sections and the variable changes of the aspect ratio of the intensity distribution at the detector.

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Figures (7)

Fig. 1
Fig. 1 The shown movements result in a variable magnification of a collimated laser beam. Such lens profiles can be used to build a rotationally or cylindrically symmetric system.
Fig. 2
Fig. 2 Introduction of all required initial values and functions to derive the conditional equations from Fermat’s principle. The XY-zoom beam expander design is described by two different lens configurations (a), (b) and (c), (d) along the x- and y-axis, respectively.
Fig. 3
Fig. 3 The shown low collimation errors confirm the high accuracy of the simultaneously calculated solutions for configuration 1 (left) and 2 (right).
Fig. 4
Fig. 4 Similarly, the shown low wave-front errors confirm the high accuracy of the simultaneously calculated solutions for configuration 1 (left) and 2 (right).
Fig. 5
Fig. 5 The surface contour plots of the calculated freeform surfaces show and confirm that all four surfaces share saddle points at the optical axis.
Fig. 6
Fig. 6 Optimized lens movements of the zoom (surfaces f(x,y) and g(x,y)) and focus lens (surface h(x,y)) for a continuous and well-defined zoom operation in x- and y-direction, respectively.
Fig. 7
Fig. 7 Single-frame excerpt from a ray tracing animation video showing both the continuous lens’ movements in cross sections and the variable changes of the aspect ratio of the intensity distribution at the detector ( Visualization 1).

Equations (11)

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d 1 = n 2 ( W 0 e ( x ) ) d 6 = n 2 ( W 0 e ( x ) )
d 2 = ( e ( x ) f ( s ) ) 2 + ( x s ) 2 d 7 = ( e ( x ) f ( u ) z 1 ) 2 + ( x u ) 2
d 3 = n 2 ( f ( s ) g ( t ) ) 2 + ( s t ) 2 d 8 = n 2 ( f ( u ) g ( v ) ) 2 + ( u v ) 2
d 4 = ( g ( t ) h ( m 1 ) ) 2 + ( t m 1 ) 2 d 9 = ( g ( v ) + z 1 h ( m 2 ) z 2 ) 2 + ( v m 2 ) 2
d 5 = n 2 ( h ( m 1 ) W 1 ) d 10 = n 2 ( h ( m 2 ) + z 2 W 1 )
D i = χ i ( d i + d i + 1 ) = 0 ( i = 1..4 ) , χ = { x , s , t , m 1 } .
D i 1 = χ i ( d i + d i + 1 ) = 0 ( i = 6..9 ) , χ = { x , u , v , m 2 } .
e ( x ) = i = 0 e i x i f ( x ) = i = 0 f i x i g ( x ) = i = 0 g i x i h ( x ) = i = 0 h i x i
s ( x ) = i = 0 s i x i t ( x ) = i = 0 t i x i u ( x ) = i = 0 u i x i v ( x ) = i = 0 v i x i
lim x 0 n x n D i = 0 ( i = 1..8 ) , { n 1 } .
I ( x , y ) = I 0 1 ( 1 + ( x / R F L ) q ) 1 + 2 / q 1 ( 1 + ( y / R F L ) q ) 1 + 2 / q

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