Abstract

The hazardous range of laser beams and their reflections from surfaces must be known when one uses lasers outdoors in areas where individuals could be exposed above the applicable exposure limits. In this paper, we describe formulas that can be used to calculate these hazardous ranges, and a few experimental data are presented that indicate the validity of the formulas and the underlying assumptions. The hazardous range depends on the laser parameters, the exposure limit, the atmospheric attenuation, the distance between the laser and reflector, the dimensions of the reflector, the angle of incidence on the reflector, and the surface parameters such as the reflection coefficient and flatness of the surface. The hazardous range of some commonly used lasers by the U.S. Army extends from 5 to 25 km for unaided viewing.

© 1986 Optical Society of America

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References

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  1. ANSI, Z 136.1-1980, American National Standard for the Safe Use of Lasers, American National Standard Institute, New York.
  2. W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser Beams,” AIHA J. 41, 547 (1980).
    [CrossRef]
  3. W. J. Marshall, P. Conner, “Field Laser Hazards Calculation Program for the Hewlett Packard model 15C Calculator,” Submitted to Health Phys. J. In press, 1986.
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).
  5. D. H. Sliney, M. C. Wolbarsht, Safety with Lasers and other Optical Sources (Plenum, New York, 1980).
  6. W. P. Van De Merwe, P. W. Conner, D. H. Sliney, “Optical Hazard Evaluation of Laser Energy Transmitted through Pinholes in Eye Protective Filters,” Appl. Opt. 24, 3615 (1985).
    [CrossRef] [PubMed]

1985 (1)

1980 (1)

W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser Beams,” AIHA J. 41, 547 (1980).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Conner, P.

W. J. Marshall, P. Conner, “Field Laser Hazards Calculation Program for the Hewlett Packard model 15C Calculator,” Submitted to Health Phys. J. In press, 1986.

Conner, P. W.

Marshall, W. J.

W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser Beams,” AIHA J. 41, 547 (1980).
[CrossRef]

W. J. Marshall, P. Conner, “Field Laser Hazards Calculation Program for the Hewlett Packard model 15C Calculator,” Submitted to Health Phys. J. In press, 1986.

Sliney, D. H.

Van De Merwe, W. P.

Wolbarsht, M. C.

D. H. Sliney, M. C. Wolbarsht, Safety with Lasers and other Optical Sources (Plenum, New York, 1980).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

AIHA J. (1)

W. J. Marshall, “Hazard Analysis on Gaussian Shaped Laser Beams,” AIHA J. 41, 547 (1980).
[CrossRef]

Appl. Opt. (1)

Other (4)

ANSI, Z 136.1-1980, American National Standard for the Safe Use of Lasers, American National Standard Institute, New York.

W. J. Marshall, P. Conner, “Field Laser Hazards Calculation Program for the Hewlett Packard model 15C Calculator,” Submitted to Health Phys. J. In press, 1986.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

D. H. Sliney, M. C. Wolbarsht, Safety with Lasers and other Optical Sources (Plenum, New York, 1980).

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Figures (7)

Fig. 1
Fig. 1

Overlapping area of the laser beam and rectangular target.

Fig. 2
Fig. 2

Hazardous range for the direct beam and reflections from a 30- × 15-cm glass surface for laser unpolarized (a), horizontally polarized (b), and vertically polarized (c). Laser parameters are: a = 2.5 cm; ϕ = 0.15 mrad; Q = 65 mJ; λ = 1064 nm; EL = 5 × 10−6 J/cm2; μ = 1 × 10−6 cm−1.

Fig. 3
Fig. 3

Hazardous range for a reflected laser beam from a 5- × 5-cm glass target. Laser parameters in (a) are the same as in Fig. 2 and in (b) λ = 530 nm and EL = 5 × 10−7 J/cm2 with other parameters the same.

Fig. 4
Fig. 4

Hazardous range for the direct beam and reflections from a 5- × 5-cm glass target viewed through 7 × 50 binoculars. The laser parameters are the same as in Fig. 2.

Fig. 5
Fig. 5

Diffraction patterns from a He–Ne laser reflected from a gold-plated mirror: (a) Fraunhofer pattern at 50 m from a 0.5-cm aperture; (b) Fresnel pattern at 100 m from a 1.0-cm aperture; (c) Fresnel pattern at 100 m from a 4.5-cm aperture.

Fig. 6
Fig. 6

Reflection pattern from a glass window. Photograph taken at 100 m from the glass with a distance of 50 m between the He–Ne laser and the glass. The incident beam diameter on the glass was ∼5.5 cm.

Fig. 7
Fig. 7

Reflection pattern from a Plexiglas plate. Photograph taken at ∼20 m with 50 m between laser and Plexiglas.

Equations (19)

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ϕ = ( D L a ) / r ,
H = Q 0 π 4 D L 2 ,
Q d = Q 0 [ 1 exp ( d 2 / D L 2 ) ]
H d = Q 0 π 4 d 2 [ 1 exp ( d 2 / D L 2 ) ] .
NOH D = 1 ϕ [ d 2 ln ( 1 π d 2 EL 4 Q 0 ) a ] .
H d = Q 0 exp ( μ r ) π 4 d 2 [ 1 exp ( d 2 / D L 2 ) ] ,
NOHD = 1 2 μ ( 16 + 24 μ NOH D + 1.16 μ 2 ( NOH D ) 2 4 μ NOH D ) .
H i = Q 0 exp ( μ r ) π 4 D L 2 .
H ( R ) = Q reflected exp ( μ R ) beam area at R .
ϕ 1 = a 1 a / ϕ + r + λ x cos θ + ϕ s ,
ϕ 2 = a 2 a / ϕ + r + λ y + ϕ s ,
Q R = Q 0 exp ( μ r ) π 4 D L 2 ρ { 1 2 D 2 ( θ 1 θ 2 ) + 1 2 ( a 1 D 2 a 1 2 + a 2 D 2 a 2 2 ) } ,
ρ s = p tan 2 ( θ θ ) tan 2 ( θ + θ ) + p sin 2 ( θ θ ) sin 2 ( θ + θ ) ,
ρ d = 2 ρ s 2 [ p tan 4 ( θ θ ) tan 4 ( θ + θ ) + p sin 4 ( θ θ ) sin 4 ( θ + θ ) ] + [ p tan 6 ( θ θ ) tan 6 ( θ + θ ) + p sin 6 ( θ θ ) sin 6 ( θ + θ ) ] .
H ( R ) = Q 0 exp ( μ r ) π 4 D L 2 ρ a 1 a 2 exp ( μ r ) ( a 1 + R ϕ 1 ) ( a 2 + R ϕ 2 ) .
NOH D r = 1 4 ( a 1 ϕ 1 + a 2 ϕ 2 ) 2 + Q 0 exp ( μ r ) ρ a 1 a 2 π 4 D L 2 EL ϕ 1 ϕ 2 a 1 a 2 ϕ 1 ϕ 2 1 2 ( a 1 ϕ 1 + a 2 ϕ 2 ) .
T ( D 0 D e ) 2 ,
EL T ( D e D 0 ) 2 .
OD = log EL H ( R ) ,

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