Abstract

Lens array arrangements are commonly used for the homogenization of highly coherent laser beams. These fly’s eye condenser configurations can be used to shape almost arbitrary input intensity distributions into a top hat. Due to the periodic structure of regular arrays the output intensity distribution is modulated by equidistant sharp intensity peaks which are disturbing the homogeneity. As a new approach we apply chirped microlens arrays to the beam shaping system. These are non-regular arrays consisting of individually shaped lenses defined by a parametric description which can be derived completely from analytical functions. The advantages of the new concept and design rules are presented.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. M. Dickey and S. C. Holswade, "Laser beam shaping: Theory and Techniques," (Marcel Deller, New York, 2000).
  2. C. Kopp, L. Ravel, and P. Meyrueis, "Efficient beam shaper homogenizer design combining diffractive optical elements, microlens array, and random phase plate," J. Opt. Soc. Am. A: Pure Appl. Opt. 1, 398-403 (1999).
    [CrossRef]
  3. H. Aagedal, M. Schmid, S. Egner, J. Muller-Quade, T. Beth, and F. Wyrowski, "Analytical beam shaping with application to laser-diode arrays," J. Opt. Soc. Am. A 14, 1549-1553 (1997).
    [CrossRef]
  4. A. Buttner and U. D. Zeitner, "Wave optical analysis of light-emitting diode beam shaping using microlens arrays," Opt. Eng. 41, 2393-2401 (2002).
    [CrossRef]
  5. N. Streibel, U. Nolscher, J. Jahns, and S. J. Walker, "Array generation with lenslet arrays," Appl. Opt. 30, 2739- 2742 (1991).
    [CrossRef]
  6. J. Duparre, F. Wippermann, P. Dannberg, and A. Reimann, "Chirped arrays of refractive ellipsoidal microlenses for aberration correction under oblique incidence," Opt. Express 13, 10539-10551 (2005).
    [CrossRef] [PubMed]
  7. F. Wippermann, J. Duparre, P. Schreiber, and P. Dannberg "Design and fabrication of a chirped array of refractive ellipsoidal micro-lenses for an apposition eye camera objective,"Proc. SPIE 5962, 723-733 (2005).
  8. D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
    [CrossRef]
  9. P. Dannberg, G. Mann, L. Wagner, and A. Brauer, "Polymer UV-molding for micro-optical systems and O/Eintegration," Proc. SPIE 4179, 137-145 (2000).
    [CrossRef]
  10. E. Hecht, Optics, 2nd Edition, (Addison-Wesley Publishing Co., Reading, Mass, USA, 1987)
  11. U.-D. Zeitner and E.-B. Kley, "Advanced lithography for micro-optics," Proc. SPIE 6290, 629009-1 - 629009-8 (2006).

2005 (2)

J. Duparre, F. Wippermann, P. Dannberg, and A. Reimann, "Chirped arrays of refractive ellipsoidal microlenses for aberration correction under oblique incidence," Opt. Express 13, 10539-10551 (2005).
[CrossRef] [PubMed]

F. Wippermann, J. Duparre, P. Schreiber, and P. Dannberg "Design and fabrication of a chirped array of refractive ellipsoidal micro-lenses for an apposition eye camera objective,"Proc. SPIE 5962, 723-733 (2005).

2002 (1)

A. Buttner and U. D. Zeitner, "Wave optical analysis of light-emitting diode beam shaping using microlens arrays," Opt. Eng. 41, 2393-2401 (2002).
[CrossRef]

2000 (1)

P. Dannberg, G. Mann, L. Wagner, and A. Brauer, "Polymer UV-molding for micro-optical systems and O/Eintegration," Proc. SPIE 4179, 137-145 (2000).
[CrossRef]

1999 (1)

C. Kopp, L. Ravel, and P. Meyrueis, "Efficient beam shaper homogenizer design combining diffractive optical elements, microlens array, and random phase plate," J. Opt. Soc. Am. A: Pure Appl. Opt. 1, 398-403 (1999).
[CrossRef]

1997 (1)

1991 (1)

1990 (1)

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
[CrossRef]

Aagedal, H.

Daly, D.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
[CrossRef]

Dannberg, P.

P. Dannberg, G. Mann, L. Wagner, and A. Brauer, "Polymer UV-molding for micro-optical systems and O/Eintegration," Proc. SPIE 4179, 137-145 (2000).
[CrossRef]

Davies, N.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
[CrossRef]

Egner, S.

Hutley, M. C.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
[CrossRef]

Kopp, C.

C. Kopp, L. Ravel, and P. Meyrueis, "Efficient beam shaper homogenizer design combining diffractive optical elements, microlens array, and random phase plate," J. Opt. Soc. Am. A: Pure Appl. Opt. 1, 398-403 (1999).
[CrossRef]

Mann, G.

P. Dannberg, G. Mann, L. Wagner, and A. Brauer, "Polymer UV-molding for micro-optical systems and O/Eintegration," Proc. SPIE 4179, 137-145 (2000).
[CrossRef]

Meyrueis, P.

C. Kopp, L. Ravel, and P. Meyrueis, "Efficient beam shaper homogenizer design combining diffractive optical elements, microlens array, and random phase plate," J. Opt. Soc. Am. A: Pure Appl. Opt. 1, 398-403 (1999).
[CrossRef]

Ravel, L.

C. Kopp, L. Ravel, and P. Meyrueis, "Efficient beam shaper homogenizer design combining diffractive optical elements, microlens array, and random phase plate," J. Opt. Soc. Am. A: Pure Appl. Opt. 1, 398-403 (1999).
[CrossRef]

Schmid, M.

Stevens, R. F.

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
[CrossRef]

Streibel, N.

Wagner, L.

P. Dannberg, G. Mann, L. Wagner, and A. Brauer, "Polymer UV-molding for micro-optical systems and O/Eintegration," Proc. SPIE 4179, 137-145 (2000).
[CrossRef]

Wippermann, F.

F. Wippermann, J. Duparre, P. Schreiber, and P. Dannberg "Design and fabrication of a chirped array of refractive ellipsoidal micro-lenses for an apposition eye camera objective,"Proc. SPIE 5962, 723-733 (2005).

Appl. Opt. (1)

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

J. Opt. Soc. Am. A: Pure Appl. Opt. (1)

C. Kopp, L. Ravel, and P. Meyrueis, "Efficient beam shaper homogenizer design combining diffractive optical elements, microlens array, and random phase plate," J. Opt. Soc. Am. A: Pure Appl. Opt. 1, 398-403 (1999).
[CrossRef]

Meas. Sci. Technol. (1)

D. Daly, R. F. Stevens, M. C. Hutley, and N. Davies, "The manufacture of microlenses by melting photo resist," Meas. Sci. Technol. 1, 4729-4735 (1990).
[CrossRef]

Opt. Eng. (1)

A. Buttner and U. D. Zeitner, "Wave optical analysis of light-emitting diode beam shaping using microlens arrays," Opt. Eng. 41, 2393-2401 (2002).
[CrossRef]

Opt. Express (1)

Proc. of SPIE (1)

F. Wippermann, J. Duparre, P. Schreiber, and P. Dannberg "Design and fabrication of a chirped array of refractive ellipsoidal micro-lenses for an apposition eye camera objective,"Proc. SPIE 5962, 723-733 (2005).

Proc. SPIE (1)

P. Dannberg, G. Mann, L. Wagner, and A. Brauer, "Polymer UV-molding for micro-optical systems and O/Eintegration," Proc. SPIE 4179, 137-145 (2000).
[CrossRef]

Other (3)

E. Hecht, Optics, 2nd Edition, (Addison-Wesley Publishing Co., Reading, Mass, USA, 1987)

U.-D. Zeitner and E.-B. Kley, "Advanced lithography for micro-optics," Proc. SPIE 6290, 629009-1 - 629009-8 (2006).

F. M. Dickey and S. C. Holswade, "Laser beam shaping: Theory and Techniques," (Marcel Deller, New York, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1.

Comparison of fly’s eye condenser types. Top: Schematic drawing of setup; Bottom: far field intensity distribution of single channel and lens array.

Fig. 2.
Fig. 2.

Geometry of a tandem cMLA with two plane surfaces in a wedge configuration. 2a 0 - width of lens 0, 2ai - width of lens i, f 0 - focal length of lens 0, fi - focal length of lens i, α - wedge angle, δ - deflection angle.

Fig. 3.
Fig. 3.

Far field intensity distribution in arbitrary units in the focal plane of the Fourier lens as a function of the aperture clipping in the focal plane of the first microlens. wnorm - ratio of aperture width to diffraction limited spot diameter in the focal plane of the first microlens, y′′ - coordinate in focal plane of the Fourier lens.

Fig. 4.
Fig. 4.

Staircase model of a tandem cMLA with constant NA for all channels as approximation of a wedge configuration.

Fig. 5.
Fig. 5.

Schematic drawing illustrating the of quality factor for regular MLA. (a) Periodic rectangular pulse string. (b) Periodic sinc-pulse string. p - period, b - width.

Fig. 6.
Fig. 6.

Quality factor q is a function of the number of illuminated lenses for a regular array. crosses - numerical simulation, line - analytical function according to Eq. 26 with k=0.66.

Fig. 7.
Fig. 7.

Calculated far field intensity distribution of fly’s eye condensers using 50 lenses with NA 0.05 and a minimum focal length of 2.63mm with a wedge angle of 0° (regular MLA) and 7°. Unequal peak heights in the far field of the regular arrangement are due to graphics sampling effects.

Fig. 8.
Fig. 8.

Quality factor q as a function of the wedge angle α and the number of illuminated lenses N. Minimum focal length f 0=2.0mm, NA=0.03 for all microlenses.

Fig. 9.
Fig. 9.

Calculated far field distribution as a function of the wedge angle α. Minimum focal length f 0=2.63mm, NA=0.05 for all microlenses, λ=0.55μm, index of refraction n=1.52. Number of illuminated lenses: (a) 2, (b) 4, (c) 6, (d) 10, (e) 20, (f) 30, (g) 40, (h) 50.

Fig. 10.
Fig. 10.

Calculated far field distribution as a function of the wedge angle α. Minimum focal length f 0=2.0mm, NA=0.05 for all microlenses, number of illuminated lenses N=50. (a) index of refraction n=1.0 (air), (b) detail of Fig. 9(h) showing the shift of the hot spot and increasing homogeneity of surrounding areas with increasing wedge angle.

Fig. 11.
Fig. 11.

Details of the edge of the calculated far field distribution for different wedge angles α. Minimum focal length f 0=2.63mm, NA=0.05, 50 illuminated lenses. In case of a regular MLA (0° wedge angle) equidistantly located peaks result. If the wedge angle is smaller than the critical angle of 5.5° the hot spot caused by the zeroth orders of the lenses is within the distribution derogating the homogeneity. For a wedge angle larger than the critical angle a non-periodic speckle pattern with smaller peak distances results leading to an improved homogeneity. A further increase of the wedge angle influences the speckle pattern but does not significantly improve the homogeneity.

Fig. 12.
Fig. 12.

Calculated far field distribution as a function of the wedge angle α. Minimum focal length f 0=2.63mm, number of illuminated lenses N=50, λ=0.5μmm, index of refraction n=1.52. NA: (a) 0.01, (b) 0.03, (c) 0.05, (d) 0.07, (e) 0.10. Diagrams have different magnification in x-direction for better comparability.

Fig. 13.
Fig. 13.

Calculated far field distribution as a function of the wedge angle α. NA=0.05, number of illuminated lenses N=50,λ=0.55μm, index of refraction n=1.52, minimum focal length f 0: (a) 1.32mm, (b) 2.63mm, (c) 6.58mm, (d) 9.87mm.

Equations (28)

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

u ( y ) F { comb ( y p ) T ( y ) rect ( y p N ) } ,
u ( y ) p 2 N comb ( py ) F { T ( y ) } sin c ( pN y ) .
η = f i 2 a i ,
μ = a i f i = 1 2 η .
f 1 = f 0 + ( a 0 + a 1 ) tan α n ,
a 1 = f 0 + a 0 tan α n 2 η tan α n .
f i = f 0 + ( a 0 + 2 n = 1 i 1 a n + a i ) tan α n ,
a i = f 0 + ( f 0 2 η + 2 n = 1 i 1 a n ) tan α n 2 η tan α n .
u ( y ) F f { rect ( y 2 a ) } ,
u ( y ) 2 a sin c ( 2 av ) .
v = sin ϕ λ = y .
u ( y ) sin c ( 2 a y ) .
u ( y ) sin c ( y ηλ ) .
u ( y ) sin c ( y ηλ ) rect ( y 2 a ) .
u ( y ) rect ( v λη ) sin c ( 2 av ) .
u ( y ) rect ( y 2 ) sin c ( y 2 a λF ) .
u ( y ) sin c ( y ηλ ) rect ( y n = 0 N 1 2 a n )
i = 0 N 1 { δ ( y n i 1 a 0 + 2 a n + a i ) rect ( y 2 a i ) exp [ i 2 π λ ( n 1 ) n ( f i f 0 ) ] } .
q = σ m ,
σ = 1 M 1 i M ( x i m ) 2 ,
m = 1 M i M x i .
σ = v d 1 + d 2 ,
m = v d ,
q a = d 1 .
p = 2 a ,
b = F λ 2 a N .
q = k N 1 .
α c = arcsin ( μ n 1 ) .

Metrics