Abstract

We propose a refractive two-element system that converts the Gaussian irradiance of an incident laser beam into a nominally flat-top output spot at a given distance with the capability to vary the spot diameter. The elements are high-order freeform surfaces that, when laterally translated, form a variable composite beam shaper. The general approach for determining the required freeform surfaces is discussed, and example design results are presented.

© 2011 Optical Society of America

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References

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  1. B. R. Frieden, Appl. Opt. 4, 1400 (1965).
    [CrossRef]
  2. J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent 3,476,463 (November 4, 1969).
  3. P. W. Rhodes and D. L. Shealy, Appl. Opt. 19, 3545 (1980).
    [CrossRef] [PubMed]
  4. W. Jiang, D. L. Shealy, and J. C. Martin, Proc. SPIE 2000, 64(1993).
    [CrossRef]
  5. J. A. Hoffnagle and C. M. Jefferson, Opt. Eng. 42, 3090(2003).
    [CrossRef]
  6. S. Zhang, G. Neil, and M. Shinn, Opt. Express 11, 1942(2003).
    [CrossRef] [PubMed]
  7. A. Laskin, G. Williams, and A. Demidovich, Proc. SPIE 7579, 75790N (2010).
    [CrossRef]
  8. L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (February 21, 1967).
  9. I. A. Palusinski, J. M. Sasian, and J. E. Greivenkamp, Appl. Opt. 38, 86 (1999).
    [CrossRef]
  10. VirtualLab User’s Manual (v. 5.0.0) (LightTrans GmbH, 2011).

2010

A. Laskin, G. Williams, and A. Demidovich, Proc. SPIE 7579, 75790N (2010).
[CrossRef]

2003

J. A. Hoffnagle and C. M. Jefferson, Opt. Eng. 42, 3090(2003).
[CrossRef]

S. Zhang, G. Neil, and M. Shinn, Opt. Express 11, 1942(2003).
[CrossRef] [PubMed]

1999

1993

W. Jiang, D. L. Shealy, and J. C. Martin, Proc. SPIE 2000, 64(1993).
[CrossRef]

1980

1965

Alvarez, L. W.

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (February 21, 1967).

Demidovich, A.

A. Laskin, G. Williams, and A. Demidovich, Proc. SPIE 7579, 75790N (2010).
[CrossRef]

Frieden, B. R.

Greivenkamp, J. E.

Hoffnagle, J. A.

J. A. Hoffnagle and C. M. Jefferson, Opt. Eng. 42, 3090(2003).
[CrossRef]

Jefferson, C. M.

J. A. Hoffnagle and C. M. Jefferson, Opt. Eng. 42, 3090(2003).
[CrossRef]

Jiang, W.

W. Jiang, D. L. Shealy, and J. C. Martin, Proc. SPIE 2000, 64(1993).
[CrossRef]

Kreuzer, J. L.

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent 3,476,463 (November 4, 1969).

Laskin, A.

A. Laskin, G. Williams, and A. Demidovich, Proc. SPIE 7579, 75790N (2010).
[CrossRef]

Martin, J. C.

W. Jiang, D. L. Shealy, and J. C. Martin, Proc. SPIE 2000, 64(1993).
[CrossRef]

Neil, G.

Palusinski, I. A.

Rhodes, P. W.

Sasian, J. M.

Shealy, D. L.

W. Jiang, D. L. Shealy, and J. C. Martin, Proc. SPIE 2000, 64(1993).
[CrossRef]

P. W. Rhodes and D. L. Shealy, Appl. Opt. 19, 3545 (1980).
[CrossRef] [PubMed]

Shinn, M.

Williams, G.

A. Laskin, G. Williams, and A. Demidovich, Proc. SPIE 7579, 75790N (2010).
[CrossRef]

Zhang, S.

Appl. Opt.

Opt. Eng.

J. A. Hoffnagle and C. M. Jefferson, Opt. Eng. 42, 3090(2003).
[CrossRef]

Opt. Express

Proc. SPIE

A. Laskin, G. Williams, and A. Demidovich, Proc. SPIE 7579, 75790N (2010).
[CrossRef]

W. Jiang, D. L. Shealy, and J. C. Martin, Proc. SPIE 2000, 64(1993).
[CrossRef]

Other

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent 3,476,463 (November 4, 1969).

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent 3,305,294 (February 21, 1967).

VirtualLab User’s Manual (v. 5.0.0) (LightTrans GmbH, 2011).

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Figures (3)

Fig. 1
Fig. 1

Beam shaper geometry. The Gaussian input, I g , is redistributed to a flat-top output I f through the two laterally shifted freeform elements.

Fig. 2
Fig. 2

Freeform surface z ( x , y ) for the given design. The b 2 k coefficients, which correspond to terms that are odd in x, dominate the overall curvature.

Fig. 3
Fig. 3

Simulated outputs showing spot and irradiance profiles for (a)  d = 0.15 mm . (b)  d = 0.0 mm , and (c)  d = 0.45 mm . The output scale is based on a normalized Gaussian input scale.

Tables (2)

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Table 1 Freeform Surface Coefficients for Example Design

Tables Icon

Table 2 Predicted and Modeled Spot Diameters Spanning the Nominal Output Diameter Range

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

z ( r ) = k = 1 n a 2 k r 2 k ,
t ( x , y ) = k = 1 n 1 2 a 2 k ( x 2 + y 2 ) k + k = 1 n b 2 k ( x 2 + y 2 ) k d x + c 0 x + t 0 = z ( x , y ) + t 0 ,
T ( x , y ) = z [ ( x + d ) , y ] + z [ ( x d ) , y ] + 2 t 0 = k = 1 n [ ( a 2 k + 2 b 2 k d ) ( x 2 + y 2 ) k ] + ε ( x , y , d ) + T 0 .
b 2 k = Δ a 2 k 2 Δ d ,

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