Abstract

A system of two aspheric lenses is described, which efficiently converts a collimated Gaussian beam to a flattop beam. Departing from earlier designs, both aspheric surfaces were convex, simplifying their fabrication; the output beam was designed with a continuous roll-off, allowing control of the far-field diffraction pattern; and diffraction from the entrance and exit apertures was held to a negligible level. The design principles are discussed in detail, and the performance of the as-built optics is compared quantitatively with the theoretical design. Approximately 78% of the incident power is enclosed in a region with 5% rms power variation. The 8-mm-diameter beam propagates approximately 0.5 m without significant change in the intensity profile; when the beam is expanded to 32 mm in diameter, this range increases to several meters.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  2. C. S. Ih, “Absorption lens for producing uniform laser beams,” Appl. Opt. 11, 694–695 (1972).
    [CrossRef]
  3. S. P. Chang, J.-M. Kuo, Y.-P. Lee, C.-M. Lu, K.-J. Ling, “Transformation of Gaussian to coherent uniform beams by inverse-Gaussian transmittive filters,” Appl. Opt. 37, 747–752 (1998).
    [CrossRef]
  4. Y. Belvaux, S. P. S. Virdi, “A method for obtaining a uniform non-Gaussian laser illumination,” Opt. Commun. 15, 193–195 (1975).
    [CrossRef]
  5. M. A. Karim, A. M. Hanafi, F. Hussain, S. Mustafa, Z. Samerid, N. M. Zain, “Realization of a uniform circular source using a two-dimensional binary filter,” Opt. Lett. 10, 470–471 (1985).
    [CrossRef] [PubMed]
  6. B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400–1403 (1965).
    [CrossRef]
  7. J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent3,476,463 (4November1969).
  8. P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
    [CrossRef] [PubMed]
  9. W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
    [CrossRef]
  10. D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
    [CrossRef]
  11. J. J. Kasinski, R. L. Burnham, “Near-diffraction-limited laser beam shaping with diamond-turned aspheric optics,” Opt. Lett. 22, 1062–1064 (1997).
    [CrossRef] [PubMed]
  12. C. Wang, D. L. Shealy, “Design of gradient-index lens systems for laser beam reshaping,” Appl. Opt. 32, 4763–4769 (1993).
    [CrossRef] [PubMed]
  13. P. H. Malyak, “Two-mirror unobscured optical system for reshaping the irradiance distribution of a laser beam,” Appl. Opt. 31, 4377–4383 (1992).
    [CrossRef] [PubMed]
  14. K. Nemoto, T. Fujii, N. Goto, H. Takino, T. Kobayashi, N. Shibata, K. Yamamura, Y. Mori, “Laser beam intensity profile transformation with a fabricated mirror,” Appl. Opt. 36, 551–557 (1997).
    [CrossRef] [PubMed]
  15. M. Quintanilla, A. M. de Frutos, “Holographic filter that transforms a Gaussian into a uniform beam,” Appl. Opt. 20, 879–880 (1981).
    [CrossRef] [PubMed]
  16. C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
    [CrossRef] [PubMed]
  17. C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
    [CrossRef]
  18. W. B. Veldcamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982).
    [CrossRef]
  19. J. E. Mayer, M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977).
  20. C. Palma, V. Bagini, “Propagation of super-Gaussian beams,” Opt. Commun. 111, 6–10 (1994).
    [CrossRef]
  21. J. P. Campbell, L. G. DeShazer, “Near fields of truncated-Gaussian apertures,” J. Opt. Soc. Am. 59, 1427–1429 (1969).
    [CrossRef]
  22. D. Golini, W. I. Kordonski, P. Dumas, S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 80–91 (1999).
    [CrossRef]

1998 (1)

1997 (2)

1994 (1)

C. Palma, V. Bagini, “Propagation of super-Gaussian beams,” Opt. Commun. 111, 6–10 (1994).
[CrossRef]

1993 (1)

1992 (1)

1991 (1)

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

1985 (1)

1983 (1)

1982 (2)

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
[CrossRef]

W. B. Veldcamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982).
[CrossRef]

1981 (1)

1980 (1)

1975 (1)

Y. Belvaux, S. P. S. Virdi, “A method for obtaining a uniform non-Gaussian laser illumination,” Opt. Commun. 15, 193–195 (1975).
[CrossRef]

1972 (1)

1969 (1)

1966 (1)

1965 (1)

Aleksoff, C. C.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Bagini, V.

C. Palma, V. Bagini, “Propagation of super-Gaussian beams,” Opt. Commun. 111, 6–10 (1994).
[CrossRef]

Belvaux, Y.

Y. Belvaux, S. P. S. Virdi, “A method for obtaining a uniform non-Gaussian laser illumination,” Opt. Commun. 15, 193–195 (1975).
[CrossRef]

Burnham, R. L.

Campbell, J. P.

Chang, S. P.

de Frutos, A. M.

DeShazer, L. G.

Dumas, P.

D. Golini, W. I. Kordonski, P. Dumas, S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 80–91 (1999).
[CrossRef]

Ellis, K. K.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Frieden, B. R.

Fujii, T.

Golini, D.

D. Golini, W. I. Kordonski, P. Dumas, S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 80–91 (1999).
[CrossRef]

Goto, N.

Han, C.-Y.

Hanafi, A. M.

Hogan, S.

D. Golini, W. I. Kordonski, P. Dumas, S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 80–91 (1999).
[CrossRef]

Hussain, F.

Ih, C. S.

Ishii, Y.

Jiang, W.

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

Karim, M. A.

Kasinski, J. J.

Kastner, C. J.

Kobayashi, T.

Kogelnik, H.

Kordonski, W. I.

D. Golini, W. I. Kordonski, P. Dumas, S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 80–91 (1999).
[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. patent3,476,463 (4November1969).

Kuo, J.-M.

Lee, Y.-P.

Li, T.

Ling, K.-J.

Lu, C.-M.

Malyak, P. H.

Martin, J. C.

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

Mayer, J. E.

J. E. Mayer, M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977).

Mayer, M. G.

J. E. Mayer, M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977).

Mori, Y.

Murata, K.

Mustafa, S.

Neagle, B. D.

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Nemoto, K.

Palma, C.

C. Palma, V. Bagini, “Propagation of super-Gaussian beams,” Opt. Commun. 111, 6–10 (1994).
[CrossRef]

Quintanilla, M.

Rhodes, P. W.

Samerid, Z.

Shafer, D.

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
[CrossRef]

Shealy, D. L.

C. Wang, D. L. Shealy, “Design of gradient-index lens systems for laser beam reshaping,” Appl. Opt. 32, 4763–4769 (1993).
[CrossRef] [PubMed]

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
[CrossRef] [PubMed]

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

Shibata, N.

Takino, H.

Veldcamp, W. B.

Virdi, S. P. S.

Y. Belvaux, S. P. S. Virdi, “A method for obtaining a uniform non-Gaussian laser illumination,” Opt. Commun. 15, 193–195 (1975).
[CrossRef]

Wang, C.

Yamamura, K.

Zain, N. M.

Appl. Opt. (11)

H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
[CrossRef] [PubMed]

C. S. Ih, “Absorption lens for producing uniform laser beams,” Appl. Opt. 11, 694–695 (1972).
[CrossRef]

S. P. Chang, J.-M. Kuo, Y.-P. Lee, C.-M. Lu, K.-J. Ling, “Transformation of Gaussian to coherent uniform beams by inverse-Gaussian transmittive filters,” Appl. Opt. 37, 747–752 (1998).
[CrossRef]

B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400–1403 (1965).
[CrossRef]

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545–3553 (1980).
[CrossRef] [PubMed]

C. Wang, D. L. Shealy, “Design of gradient-index lens systems for laser beam reshaping,” Appl. Opt. 32, 4763–4769 (1993).
[CrossRef] [PubMed]

P. H. Malyak, “Two-mirror unobscured optical system for reshaping the irradiance distribution of a laser beam,” Appl. Opt. 31, 4377–4383 (1992).
[CrossRef] [PubMed]

K. Nemoto, T. Fujii, N. Goto, H. Takino, T. Kobayashi, N. Shibata, K. Yamamura, Y. Mori, “Laser beam intensity profile transformation with a fabricated mirror,” Appl. Opt. 36, 551–557 (1997).
[CrossRef] [PubMed]

M. Quintanilla, A. M. de Frutos, “Holographic filter that transforms a Gaussian into a uniform beam,” Appl. Opt. 20, 879–880 (1981).
[CrossRef] [PubMed]

C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beams with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
[CrossRef] [PubMed]

W. B. Veldcamp, C. J. Kastner, “Beam profile shaping for laser radars that use detector arrays,” Appl. Opt. 21, 345–356 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

C. Palma, V. Bagini, “Propagation of super-Gaussian beams,” Opt. Commun. 111, 6–10 (1994).
[CrossRef]

Y. Belvaux, S. P. S. Virdi, “A method for obtaining a uniform non-Gaussian laser illumination,” Opt. Commun. 15, 193–195 (1975).
[CrossRef]

Opt. Eng. (1)

C. C. Aleksoff, K. K. Ellis, B. D. Neagle, “Holographic conversion of a Gaussian beam to a near-field uniform beam,” Opt. Eng. 30, 537–543 (1991).
[CrossRef]

Opt. Laser Technol. (1)

D. Shafer, “Gaussian to flat-top intensity distributing lens,” Opt. Laser Technol. 14, 159–160 (1982).
[CrossRef]

Opt. Lett. (2)

Other (4)

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
[CrossRef]

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. patent3,476,463 (4November1969).

J. E. Mayer, M. G. Mayer, Statistical Mechanics (Wiley, New York, 1977).

D. Golini, W. I. Kordonski, P. Dumas, S. Hogan, “Magnetorheological finishing (MRF) in commercial precision optics manufacturing,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 80–91 (1999).
[CrossRef]

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 (14)

Fig. 1
Fig. 1

Ray paths in a conventional, refractive beam reshaping system.

Fig. 2
Fig. 2

Fermi–Dirac function for β = 5, 10, and 15 compared with a Gaussian (dashed curve) with the same width at half-maximum.

Fig. 3
Fig. 3

Super-Gaussian function for p = 2, 4, 8, and 12.

Fig. 4
Fig. 4

Relationship between efficiency and peak-to-peak uniformity for various beam profiles. Solid curves are for Fermi–Dirac functions with, from bottom to top, β = 5, 10, and 15; dashed curves are for super-Gaussian functions with, from bottom to top, p = 2 (Gaussian), 4, 8, and 16.

Fig. 5
Fig. 5

Effect of diffraction on Fermi–Dirac beams with R 0 = 3.25 mm after propagating 1 m.

Fig. 6
Fig. 6

Schematic representation of a Keplerian beam reshaping system, showing the path of a typical ray.

Fig. 7
Fig. 7

Sag curves for the fabricated beam reshaping optics. The solid curves show the aspheric surfaces from Eqs. (18) and the dashed curves are for spherical surfaces that were used as a starting point for the final, numerically controlled polishing step. The maximum deviation from sphericity is 13 µm for lens 1 and 8 µm for lens 2. Note that the length scales are different for radius and sag.

Fig. 8
Fig. 8

Optimal lens separation versus wavelength. The points are calculated with a numerical lens design program, which was also used to verify that the output beam was diffraction limited. The solid curve is the result of Eq. (22).

Fig. 9
Fig. 9

Image of the beam directly after the Gauss-to-flattop optics. The size of the field is 8.16-mm square.

Fig. 10
Fig. 10

Intensity values along the x axis directly before and directly after the Gauss-to-flattop optics.

Fig. 11
Fig. 11

Measured dependence of the relative rms variation of the output intensity on efficiency (filled circles) compared with the theoretical curves for ideal Gaussian and Fermi–Dirac (β = 16.25) profiles.

Fig. 12
Fig. 12

Evolution of the beam with propagation distance D from the second aspheric surface to the CCD sensor: (a) D = 25 mm; (b) D = 225 mm; (c) D = 425 mm; (d) D = 625 mm; (e) D = 1025 mm; (f) D = 1425 mm.

Fig. 13
Fig. 13

Slices through the center of the beam showing intensity versus radial distance for the images of Fig. 12. The solid curves are measured intensities and the dashed curves represent the design profile, normalized to the experimental data as described in the text.

Fig. 14
Fig. 14

Images (top row) and the corresponding intensity slices (bottom row) of the flattop beam 4.2 m after a beam expander with magnification M: (a) M = 1; (b) M = 2; (c) M = 3; (d) M = 4.

Equations (23)

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

2π 0 frrdr=2π 0 grrdr=1.
fGr=2/πw02exp-2r2/w02,
Uppa=gmina/gmaxa.
Vppa=1-Uppa.
ηa=2π 0a grrdr.
Īa=2a20a grrdr,
σ2a=2a20agr-Ī2rdr.
Vrmsa=σa/Īa,
Urmsa=1-Vrmsa,
gFDr=g01+expr-R0W-1.
gFDr=g01+expβrR0-1-1,
g0-1=πR021+exp-β-1+13 π2β-2+Oβ-4,
gSGr=g0 exp-2r/R0p,
g0=p22/p2πR02Γ2/p.
ux, D  0a ρUρJ0kρx/Dexpikρ2/2Ddρ.
R=hr,
0r fxxdx=0R gxxdx,
zr=0rn2-1+n-1dhx-x2-1/2dx,
ZR=0Rn2-1+n-1dh-1x-x2-1/2dx.
0r f1xxdx=0R g1xxdx,
g1R=gRf1r/fr.
g1R=gRw0/w12 exp-2r2w1-2-w0-2.
dλ=d0n0-1nλ-1.

Metrics