Abstract

Several plano–convex aluminum thin films, ∼30 nm thick in the center and ∼2 mm in diameter, were deposited on microscope cover slides to function as inverse-Gaussian transmittive filters. By placing one of these filters in front of the Gaussian He–Ne laser, we can modify the beam intensity profile in the downstream direction. To yield a uniform beam, the position of the filter must be aligned in the transverse plane for maximum intensity at the output of the filter. These filters are easy to fabricate and are inexpensive. Most important, they can help produce collimated phase-coherent uniform beams, which are useful in high-precision fringe-analysis techniques.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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1995

1994

1992

1991

1990

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

1989

N. C. Roberts, “Beam shaping by holographic filters,” Appl. Opt. 28, 31–32 (1989).
[CrossRef] [PubMed]

S. R. Jahan, M. A. Karim, “Refraction systems for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

1987

1985

1983

1982

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

W. B. Veldkamp, “Technique for generating focal-plane flattop laser-beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

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

W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. 21, 3209–3212 (1982).
[CrossRef] [PubMed]

1981

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 38, 381–386 (1981).
[CrossRef]

W. H. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
[CrossRef]

1980

1975

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

1974

1972

1965

Aagard, R. L.

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]

Arima, Y.

Basit, A.

Bélanger, P. A.

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]

Cantin, D.

Chen, D.

Cherri, A. K.

Colombeau, B.

Dai, K.

De Silvestri, S.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Dohnalik, T.

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.

Froehly, C.

Furtak, T. E.

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986), p. 295.

Han, C. Y.

Hanafi, A. M.

Hussain, F.

Ih, C. S.

Imai, Y.

Ishii, Y.

Jahan, S. R.

S. R. Jahan, M. A. Karim, “Refraction systems for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

Johnson, B. C.

Karim, M. A.

Kastner, C. J.

Kermene, V.

Klein, M. V.

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986), p. 295.

Lachance, R. L.

Lee, W. H.

W. H. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
[CrossRef]

Leger, J. R.

Leppelmeier, G. W.

Magni, V.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), p. 729.

Mowry, G.

J. R. Leger, D. Chen, G. Mowry, “Design and performance of diffractive optics for custom laser resonators,” Appl. Opt. 34, 2498–2509 (1995).
[CrossRef] [PubMed]

J. R. Leger, D. Chen, G. Mowry, Z. Wang, “Diffractive optic laser resonator,” Opt. Photon. News, 19–20 (December1994).

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]

Ohtsuka, Y.

Paré, C.

Pichè, M.

Rhodes, P. W.

Roberts, N. C.

Samberid, Z.

Sami Awwal, A. A.

Saviot, A.

Shafer, D.

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

Shealy, D. L.

Simmons, W. W.

Svelto, O.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Valentini, G.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Vampouille, M.

Veldkamp, W. B.

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

W. B. Veldkamp, “Technique for generating focal-plane flattop laser-beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. 21, 3209–3212 (1982).
[CrossRef] [PubMed]

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 38, 381–386 (1981).
[CrossRef]

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, Z.

J. R. Leger, D. Chen, G. Mowry, Z. Wang, “Diffractive optic laser resonator,” Opt. Photon. News, 19–20 (December1994).

J. R. Leger, D. Chen, Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG laser,” Opt. Lett. 19, 108–110 (1994).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), p. 118.

Zain, N. M.

Appl. Opt.

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

R. L. Aagard, “Methods for optimizing the beam shape in a focused coherent optical system,” Appl. Opt. 13, 1633–1638 (1974).
[CrossRef] [PubMed]

W. B. Veldkamp, “Laser beam profile shaping with interlaced binary diffraction gratings,” Appl. Opt. 21, 3209–3212 (1982).
[CrossRef] [PubMed]

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

M. A. Karim, A. K. Cherri, A. A. Sami Awwal, A. Basit, “Refracting system for annular laser beam transformation,” Appl. Opt. 26, 2446–2449 (1987).
[CrossRef] [PubMed]

Y. Ohtsuka, Y. Arima, Y. Imai, “Acoustooptic 2-D profile shaping of a Gaussian laser beam,” Appl. Opt. 24, 2813–2819 (1985).
[CrossRef] [PubMed]

N. C. Roberts, “Beam shaping by holographic filters,” Appl. Opt. 28, 31–32 (1989).
[CrossRef] [PubMed]

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

W. W. Simmons, G. W. Leppelmeier, B. C. Johnson, “Optical beam shaping devices using polarization effects,” Appl. Opt. 13, 1629–1632 (1974).
[CrossRef] [PubMed]

J. R. Leger, D. Chen, G. Mowry, “Design and performance of diffractive optics for custom laser resonators,” Appl. Opt. 34, 2498–2509 (1995).
[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]

IEEE J. Quantum Electron.

C. Paré, P. A. Bélanger, “Custom laser resonators using graded-phase mirrors,” IEEE J. Quantum Electron. 28, 355–362 (1992).
[CrossRef]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Opt. Commun.

W. H. Lee, “Method for converting a Gaussian laser beam into a uniform beam,” Opt. Commun. 36, 469–471 (1981).
[CrossRef]

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction gratings,” Opt. Commun. 38, 381–386 (1981).
[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.

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.

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

S. R. Jahan, M. A. Karim, “Refraction systems for Gaussian-to-uniform beam transformations,” Opt. Laser Technol. 21, 27–30 (1989).
[CrossRef]

Opt. Lett.

Opt. Photon. News

J. R. Leger, D. Chen, G. Mowry, Z. Wang, “Diffractive optic laser resonator,” Opt. Photon. News, 19–20 (December1994).

Rev. Sci. Instrum.

W. B. Veldkamp, “Technique for generating focal-plane flattop laser-beam profiles,” Rev. Sci. Instrum. 53, 294–297 (1982).
[CrossRef]

Other

M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986), p. 295.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), p. 729.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989), p. 118.

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Figures (12)

Fig. 1
Fig. 1

Thickness profile of the thin film; the radius of curvature of this thin film, F, has been greatly reduced to show the details.

Fig. 2
Fig. 2

Thin films with a wide flat plateau in the center, obtained for cases of large holes with a diameter D.

Fig. 3
Fig. 3

Plano–convex (or bell shaped) thin films, obtained for cases of small holes with a diameter D.

Fig. 4
Fig. 4

Schematic diagram of the mask (A), spacer (S), and substratum (C) combinations. D is the hole diameter on the mask, and H is the distance from the mask to the substratum. The thin film with effective radius R on the substratum is the filter to be used in our experiments.

Fig. 5
Fig. 5

Thickness profile (measured) of a thin-film filter. The thickness in the center is B 0 ≈ 30 nm, the effective radius R ≈ 1 mm, and the radius of curvature is F ≈ 16.5 m.

Fig. 6
Fig. 6

Intensity profile of the unfiltered (top curve) and filtered (bottom curve) Gaussian laser beam illumination.

Fig. 7
Fig. 7

Filtered beam-intensity profile as the power of the input laser beam was increased 6 times.

Fig. 8
Fig. 8

Heavy-sided beam obtained as a result of a misalignment.

Fig. 9
Fig. 9

Flatter Gaussian beam that can be obtained if the absorption in the central core is not large enough.

Fig. 10
Fig. 10

Inverse-Gaussian beam that can be obtained if the absorption in the central core is large.

Fig. 11
Fig. 11

Relative intensity profile of a Michelson interferogram with a Gaussian laser uniform beam illumination. The fringes are modulated by a Gaussian envelope.

Fig. 12
Fig. 12

Relative intensity profile of the same Michelson interferogram with uniform beam illumination. As can be seen, the figures are not modulated by an envelope function.

Equations (8)

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

B r = F - F 2 - R 2 1 / 2 - F - F 2 - r 2 1 / 2 , = B 0 - F [ 1 / 2 r / F 2 + 1 / 2 3 r / F 4 + , B 0 - r 2 / 2 F ,
T r = exp - α B r = exp - α B 0 exp α r 2 / 2 F ,     for   r R , T r = 1 ,     for   r   > R ,
I r = I 1 r × T r , = I 1 p × exp - 2 r / ω 1 2 × exp - α B 0 × exp α r 2 / 2 F , = I 1 p × exp - α B 0 × exp α r 2 / 2 F - 2 r 2 / ω 1 2 , = I 1 p × exp - α B 0 × exp α / 2 F - 2 / ω 1 2 r 2 .
α / 2 F - 2 / ω 1 2 0 ,
I r I 1 p × exp - α B 0 for   r R .
I r = I 2 p exp - α B 0 exp - r 2 2 / ω 2 2 - α / 2 F I 2 p exp - α B 0 exp - β r 2 .
1 / ω 3 2 - α / 2 F - γ < 0 ,
I r = I 3 p exp - α B 0 exp - r 2 1 / ω 3 2 - α / 2 F , = I 3 p exp - α B 0 exp γ r 2 .

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