Abstract

A simple method is presented for determining the nominal ocular hazard distance from non-Gaussian laser beams. The simplified method currently used for laser safety calculations when determining the laser beam diameter as a function of distance produces errors in the near field. The irradiance or radiant exposure of multimode and non-Gaussian laser beams in the near field may be calculated more precisely by the use of a simple proposed relationship with easily determined parameters.

© 1991 Optical Society of America

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References

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  1. W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser beams,” Am. Ind. Hyg. Assoc. J. 41, 547–551 (1980).
    [CrossRef] [PubMed]
  2. W. J. Marshall, P. W. Conner, “Field Laser Hazard Calculations,” Health Phys. 52(1), 27–37 (1987).
    [CrossRef] [PubMed]
  3. D. H. Sliney, W. J. Marshall, “Laser Safety Part IV: Measuring the Beam Diameter,” Electro-Opt. Syst. Des. 11, 31–36 (1979).
  4. D. H. Sliney, M. L. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980), Chap. 12.
  5. American National Standard for the Safe Use of Lasers, ANSI Z136.1 (1986).
  6. S. A. Self, “Focusing of Spherical Gaussian Beams,” Appl. Opt. 22, 658–661 (1983).
    [CrossRef] [PubMed]
  7. H. Kogelnik, T. Li, “Laser Beams and Resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  8. W. H. Carter, “Spot Size and Divergence for Hermite Gaussian Beams of Any Order,” Appl. Opt. 19, 1027–1029 (1980).
    [CrossRef] [PubMed]
  9. J. T. Luxon, D. E. Parker, J. Karkheck, “Waist Location and Rayleigh Range for Higher-Order Mode Laser Beams,” Appl. Opt. 23, 2088–2090 (1984).
    [CrossRef] [PubMed]
  10. Y. Suzaki, A. Tachibana, “Measurement of the Gaussian Laser Beam Divergence,” Appl. Opt. 16, 1481–1482 (1977).
    [CrossRef] [PubMed]
  11. P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 14.9.
  12. O. Svelto, Principles of Lasers, translated by D. C. Hanna (Plenum, New York, 1976), Chap. 7.
  13. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
    [CrossRef]

1987

W. J. Marshall, P. W. Conner, “Field Laser Hazard Calculations,” Health Phys. 52(1), 27–37 (1987).
[CrossRef] [PubMed]

1984

1983

1980

W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser beams,” Am. Ind. Hyg. Assoc. J. 41, 547–551 (1980).
[CrossRef] [PubMed]

W. H. Carter, “Spot Size and Divergence for Hermite Gaussian Beams of Any Order,” Appl. Opt. 19, 1027–1029 (1980).
[CrossRef] [PubMed]

1979

D. H. Sliney, W. J. Marshall, “Laser Safety Part IV: Measuring the Beam Diameter,” Electro-Opt. Syst. Des. 11, 31–36 (1979).

1977

1971

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

1966

Arnaud, J. A.

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

Carter, W. H.

Conner, P. W.

W. J. Marshall, P. W. Conner, “Field Laser Hazard Calculations,” Health Phys. 52(1), 27–37 (1987).
[CrossRef] [PubMed]

de la Claviere, B.

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

Eberly, J. H.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 14.9.

Franke, E. A.

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

Franke, J. M.

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

Hubbard, W. M.

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

Karkheck, J.

Kogelnik, H.

Li, T.

Luxon, J. T.

Mandeville, G. D.

J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, “Technique for Fast Measurement of Gaussian Laser Beam Parameters,” Appl. Opt. 10, 2275–2276 (1971).
[CrossRef]

Marshall, W. J.

W. J. Marshall, P. W. Conner, “Field Laser Hazard Calculations,” Health Phys. 52(1), 27–37 (1987).
[CrossRef] [PubMed]

W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser beams,” Am. Ind. Hyg. Assoc. J. 41, 547–551 (1980).
[CrossRef] [PubMed]

D. H. Sliney, W. J. Marshall, “Laser Safety Part IV: Measuring the Beam Diameter,” Electro-Opt. Syst. Des. 11, 31–36 (1979).

Milonni, P. W.

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 14.9.

Parker, D. E.

Self, S. A.

Sliney, D. H.

D. H. Sliney, W. J. Marshall, “Laser Safety Part IV: Measuring the Beam Diameter,” Electro-Opt. Syst. Des. 11, 31–36 (1979).

D. H. Sliney, M. L. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980), Chap. 12.

Suzaki, Y.

Svelto, O.

O. Svelto, Principles of Lasers, translated by D. C. Hanna (Plenum, New York, 1976), Chap. 7.

Tachibana, A.

Wolbarsht, M. L.

D. H. Sliney, M. L. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980), Chap. 12.

Am. Ind. Hyg. Assoc. J.

W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser beams,” Am. Ind. Hyg. Assoc. J. 41, 547–551 (1980).
[CrossRef] [PubMed]

Appl. Opt.

Electro-Opt. Syst. Des.

D. H. Sliney, W. J. Marshall, “Laser Safety Part IV: Measuring the Beam Diameter,” Electro-Opt. Syst. Des. 11, 31–36 (1979).

Health Phys.

W. J. Marshall, P. W. Conner, “Field Laser Hazard Calculations,” Health Phys. 52(1), 27–37 (1987).
[CrossRef] [PubMed]

Other

D. H. Sliney, M. L. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980), Chap. 12.

American National Standard for the Safe Use of Lasers, ANSI Z136.1 (1986).

P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), Chap. 14.9.

O. Svelto, Principles of Lasers, translated by D. C. Hanna (Plenum, New York, 1976), Chap. 7.

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Figures (2)

Fig. 1
Fig. 1

Measured beam diameters as a function of distance and theoretical curves near the beam waist of two units of a non-Gaussian laser range finder beam.

Fig. 2
Fig. 2

Corneal average radiant exposure vs range from laser Sn 07 for unaided viewing and optically aided viewing. The solid curves represent the proposed laser safety equation. The dashed curves represent the simplified equation currently used for laser safety. The lower solid horizontal line represents the exposure limit for the full power range finder and the upper horizontal line represents the adjusted exposure limit when the attenuating filter is installed on the laser.

Equations (11)

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W ( Z ) = W 0 [ 1 + ( Z / Z R ) 2 ] 1 / 2 ,
W FF = limit Z { W 0 [ 1 + ( Z / Z R ) 2 ] 1 / 2 } = W 0 Z / Z R .
θ FF = W FF / Z = W 0 / Z R .
W ( Z ) = ( W 0 2 + Z 2 θ FF 2 ) 1 / 2 .
θ FF = λ / ( π W 0 ) ;
Z R = π W 0 2 / λ .
θ FF = W f p / f ,
D L = { d 2 / ln [ 1 f ( d ) ] } 1 / 2 ,
D L = [ D W 2 + ( r r 0 ) 2 ϕ 2 ] 1 / 2 ,
D L = a + r ϕ ,
H d = ( 1 . 27 Q t ) / d f 2 [ 1 exp ( d 2 M 2 / D L 2 ) ] exp ( μ r ) ,

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