Abstract

A simple technique is described for calculating the maximum scintillation factor in a statistical model of optical beam propagation within the atmosphere. This enables laser safety analyses to be performed within a semideterministic framework.

© 1990 Optical Society of America

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References

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  1. W. J. Marshall, “Hazard Analysis of Gaussian Shaped Laser Beams,” J. Am. Indust. Hyg. Ass. 41, 547–551 (1980).
    [CrossRef]
  2. W. J. Marshall, P. W. Conner, “Field Laser Hazard Calculations,” Health Phys. 52, 27–37 (1987).
    [CrossRef] [PubMed]
  3. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).
  4. J. A. Hermann, “Statistical Model for Laser Safety Analysis,” DSTO Report No. MRL-R-983, Mat. Res. Labs., Melbourne (1986).
  5. J. A. Hermann, S. R. Kennett, “Atmospheric Turbulence Effects in Laser Safety,” Rad. Prot. in Aust. 4, 89–93 (1986).
  6. D. A. de Wolf, “Saturation or Irradiance Fluctuations due to Turbulent Atmosphere,” J. Opt. Soc. Am. 58, 461–466 (1968).
    [CrossRef]
  7. P. H. Deitz, “Probability Analysis of Ocular Damage due to Laser Radiation through the Atmosphere,” Appl. Opt. 8, 371–375 (1969).
    [CrossRef] [PubMed]
  8. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  9. V. I. Tatarski, “The Effects of the Turbulent Atmosphere in Wave Propagation,” Natl. Tech. Info. Serv., Springfield, VA (1971).
  10. J. W. Strohbehn, T. Wang, J. Speck, “On the Probability Distribution of Line-of-Sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
    [CrossRef]
  11. W. S. Smerdon, “A Probabilistic Approach to Laser Safety,” presented at Colloquium Effects Biologiques de Fixceaux Lasers et Normes de Protection, Paris, Nov. 1986.
  12. M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1972).
  13. P. H. Deitz, N. J. Wright, “Saturation of Scintillation Magnitude in Near-Earth Optical Propagation,” J. Opt, Soc. Am. 59, 527–535 (1969).
    [CrossRef]
  14. S. Clifford, G. Ochs, R. Lawrence, “Saturation of Optical Scintillations by Strong Turbulence,” J. Opt. Soc. Am. 64, 148–154 (1974).
    [CrossRef]
  15. W. F. Dabbert, “An Investigation of Atmospheric Effects on Propagation and the Impact on Eye Safety,” Stanford Res. Inst., Menlo Park, CA 94025, USA, Project Report 1341, Contract F41609-71-C-0029 NTIS AD 755405 (1972).
  16. W. F. Dabbert, W. B. Johnson, “Atmospheric Effects upon Laser Eye Safety—Part II,” Stanford Res. Inst., Menlo park CA 94025, USA, Project Report 7472 (1971).
  17. H. T. Yura, “Optical Beam Spread in a Turbulent Medium: Effect of the Outer Scale of Turbulence,” J. Opt. Soc. Am. 63, 107–109 (1973).
    [CrossRef]
  18. H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
    [CrossRef] [PubMed]
  19. W. E. K. Middleton, Vision Through the Atmosphere (U. Toronto Press, Toronto, 1952).
  20. R. J. Hill, J. H. Churnside, D. H. Sliney, “Measured Statistics of Laser Beam Scintillation in Strong Refractive Turbulence Relevant to Eye Safety,” Health Phys. 53, 639–647 (1987).
    [CrossRef] [PubMed]
  21. G. Parry, P. N. Pusey, “K Distributions in Atmospheric Propagation of Laser Light,” J. Opt, Soc. Am. 69, 796–805 (1979).
    [CrossRef]
  22. E. Jakeman, “On the Statistics of K-Distributed Noise,” J. Phys. A. 13, 31–38 (1980).
    [CrossRef]
  23. G. Parry, “Measurements of Atmospheric Turbulence Induced Intensity Fluctuations in a Laser Beam,” Opt. Acta 28, 715–728 (1981).
    [CrossRef]
  24. L. C. Andrews, R. L. Phillips, “Mathematical Genesis of the I-K Distribution for Random Optical Fields,” J. Opt. Soc. Am. A 3, 1912–1919 (1986).
    [CrossRef]

1987 (2)

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

R. J. Hill, J. H. Churnside, D. H. Sliney, “Measured Statistics of Laser Beam Scintillation in Strong Refractive Turbulence Relevant to Eye Safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

1986 (2)

L. C. Andrews, R. L. Phillips, “Mathematical Genesis of the I-K Distribution for Random Optical Fields,” J. Opt. Soc. Am. A 3, 1912–1919 (1986).
[CrossRef]

J. A. Hermann, S. R. Kennett, “Atmospheric Turbulence Effects in Laser Safety,” Rad. Prot. in Aust. 4, 89–93 (1986).

1981 (1)

G. Parry, “Measurements of Atmospheric Turbulence Induced Intensity Fluctuations in a Laser Beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

1980 (2)

E. Jakeman, “On the Statistics of K-Distributed Noise,” J. Phys. A. 13, 31–38 (1980).
[CrossRef]

W. J. Marshall, “Hazard Analysis of Gaussian Shaped Laser Beams,” J. Am. Indust. Hyg. Ass. 41, 547–551 (1980).
[CrossRef]

1979 (2)

H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
[CrossRef] [PubMed]

G. Parry, P. N. Pusey, “K Distributions in Atmospheric Propagation of Laser Light,” J. Opt, Soc. Am. 69, 796–805 (1979).
[CrossRef]

1975 (1)

J. W. Strohbehn, T. Wang, J. Speck, “On the Probability Distribution of Line-of-Sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

1974 (1)

1973 (1)

1969 (2)

P. H. Deitz, N. J. Wright, “Saturation of Scintillation Magnitude in Near-Earth Optical Propagation,” J. Opt, Soc. Am. 59, 527–535 (1969).
[CrossRef]

P. H. Deitz, “Probability Analysis of Ocular Damage due to Laser Radiation through the Atmosphere,” Appl. Opt. 8, 371–375 (1969).
[CrossRef] [PubMed]

1968 (1)

Andrews, L. C.

Breaux, H.

H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
[CrossRef] [PubMed]

Churnside, J. H.

R. J. Hill, J. H. Churnside, D. H. Sliney, “Measured Statistics of Laser Beam Scintillation in Strong Refractive Turbulence Relevant to Eye Safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

Clifford, S.

Conner, P. W.

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

Dabbert, W. F.

W. F. Dabbert, “An Investigation of Atmospheric Effects on Propagation and the Impact on Eye Safety,” Stanford Res. Inst., Menlo Park, CA 94025, USA, Project Report 1341, Contract F41609-71-C-0029 NTIS AD 755405 (1972).

W. F. Dabbert, W. B. Johnson, “Atmospheric Effects upon Laser Eye Safety—Part II,” Stanford Res. Inst., Menlo park CA 94025, USA, Project Report 7472 (1971).

de Wolf, D. A.

Deitz, P. H.

P. H. Deitz, “Probability Analysis of Ocular Damage due to Laser Radiation through the Atmosphere,” Appl. Opt. 8, 371–375 (1969).
[CrossRef] [PubMed]

P. H. Deitz, N. J. Wright, “Saturation of Scintillation Magnitude in Near-Earth Optical Propagation,” J. Opt, Soc. Am. 59, 527–535 (1969).
[CrossRef]

Evers, W.

H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
[CrossRef] [PubMed]

Hermann, J. A.

J. A. Hermann, S. R. Kennett, “Atmospheric Turbulence Effects in Laser Safety,” Rad. Prot. in Aust. 4, 89–93 (1986).

J. A. Hermann, “Statistical Model for Laser Safety Analysis,” DSTO Report No. MRL-R-983, Mat. Res. Labs., Melbourne (1986).

Hill, R. J.

R. J. Hill, J. H. Churnside, D. H. Sliney, “Measured Statistics of Laser Beam Scintillation in Strong Refractive Turbulence Relevant to Eye Safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

Jakeman, E.

E. Jakeman, “On the Statistics of K-Distributed Noise,” J. Phys. A. 13, 31–38 (1980).
[CrossRef]

Johnson, W. B.

W. F. Dabbert, W. B. Johnson, “Atmospheric Effects upon Laser Eye Safety—Part II,” Stanford Res. Inst., Menlo park CA 94025, USA, Project Report 7472 (1971).

Kennett, S. R.

J. A. Hermann, S. R. Kennett, “Atmospheric Turbulence Effects in Laser Safety,” Rad. Prot. in Aust. 4, 89–93 (1986).

Lawrence, R.

Marshall, W. J.

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

W. J. Marshall, “Hazard Analysis of Gaussian Shaped Laser Beams,” J. Am. Indust. Hyg. Ass. 41, 547–551 (1980).
[CrossRef]

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (U. Toronto Press, Toronto, 1952).

Ochs, G.

Parry, G.

G. Parry, “Measurements of Atmospheric Turbulence Induced Intensity Fluctuations in a Laser Beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

G. Parry, P. N. Pusey, “K Distributions in Atmospheric Propagation of Laser Light,” J. Opt, Soc. Am. 69, 796–805 (1979).
[CrossRef]

Phillips, R. L.

Pusey, P. N.

G. Parry, P. N. Pusey, “K Distributions in Atmospheric Propagation of Laser Light,” J. Opt, Soc. Am. 69, 796–805 (1979).
[CrossRef]

Sepucha, R.

H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
[CrossRef] [PubMed]

Severo, N. C.

M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1972).

Sliney, D.

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

Sliney, D. H.

R. J. Hill, J. H. Churnside, D. H. Sliney, “Measured Statistics of Laser Beam Scintillation in Strong Refractive Turbulence Relevant to Eye Safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

Smerdon, W. S.

W. S. Smerdon, “A Probabilistic Approach to Laser Safety,” presented at Colloquium Effects Biologiques de Fixceaux Lasers et Normes de Protection, Paris, Nov. 1986.

Speck, J.

J. W. Strohbehn, T. Wang, J. Speck, “On the Probability Distribution of Line-of-Sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Strohbehn, J. W.

J. W. Strohbehn, T. Wang, J. Speck, “On the Probability Distribution of Line-of-Sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

V. I. Tatarski, “The Effects of the Turbulent Atmosphere in Wave Propagation,” Natl. Tech. Info. Serv., Springfield, VA (1971).

Wang, T.

J. W. Strohbehn, T. Wang, J. Speck, “On the Probability Distribution of Line-of-Sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Whitney, C.

H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
[CrossRef] [PubMed]

Wolbarsht, M.

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

Wright, N. J.

P. H. Deitz, N. J. Wright, “Saturation of Scintillation Magnitude in Near-Earth Optical Propagation,” J. Opt, Soc. Am. 59, 527–535 (1969).
[CrossRef]

Yura, H. T.

Zelen, M.

M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1972).

Appl. Opt (1)

H. Breaux, W. Evers, R. Sepucha, C. Whitney, “Algebraic Model for CW Thermal-Blooming Effects,” Appl. Opt, 18, 2638–2644 (1979).
[CrossRef] [PubMed]

Appl. Opt. (1)

Health Phys. (2)

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

R. J. Hill, J. H. Churnside, D. H. Sliney, “Measured Statistics of Laser Beam Scintillation in Strong Refractive Turbulence Relevant to Eye Safety,” Health Phys. 53, 639–647 (1987).
[CrossRef] [PubMed]

J. Am. Indust. Hyg. Ass. (1)

W. J. Marshall, “Hazard Analysis of Gaussian Shaped Laser Beams,” J. Am. Indust. Hyg. Ass. 41, 547–551 (1980).
[CrossRef]

J. Opt, Soc. Am. (2)

P. H. Deitz, N. J. Wright, “Saturation of Scintillation Magnitude in Near-Earth Optical Propagation,” J. Opt, Soc. Am. 59, 527–535 (1969).
[CrossRef]

G. Parry, P. N. Pusey, “K Distributions in Atmospheric Propagation of Laser Light,” J. Opt, Soc. Am. 69, 796–805 (1979).
[CrossRef]

J. Opt. Soc. Am. (3)

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

J. Phys. A. (1)

E. Jakeman, “On the Statistics of K-Distributed Noise,” J. Phys. A. 13, 31–38 (1980).
[CrossRef]

Opt. Acta (1)

G. Parry, “Measurements of Atmospheric Turbulence Induced Intensity Fluctuations in a Laser Beam,” Opt. Acta 28, 715–728 (1981).
[CrossRef]

Rad. Prot. in Aust. (1)

J. A. Hermann, S. R. Kennett, “Atmospheric Turbulence Effects in Laser Safety,” Rad. Prot. in Aust. 4, 89–93 (1986).

Radio Sci. (1)

J. W. Strohbehn, T. Wang, J. Speck, “On the Probability Distribution of Line-of-Sight Fluctuations of Optical Signals,” Radio Sci. 10, 59–70 (1975).
[CrossRef]

Other (9)

W. S. Smerdon, “A Probabilistic Approach to Laser Safety,” presented at Colloquium Effects Biologiques de Fixceaux Lasers et Normes de Protection, Paris, Nov. 1986.

M. Zelen, N. C. Severo, “Probability Functions,” in Handbook of Mathematical Functions, M. Abramowitz, I. Stegun, Eds. (Dover, New York, 1972).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

V. I. Tatarski, “The Effects of the Turbulent Atmosphere in Wave Propagation,” Natl. Tech. Info. Serv., Springfield, VA (1971).

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

J. A. Hermann, “Statistical Model for Laser Safety Analysis,” DSTO Report No. MRL-R-983, Mat. Res. Labs., Melbourne (1986).

W. E. K. Middleton, Vision Through the Atmosphere (U. Toronto Press, Toronto, 1952).

W. F. Dabbert, “An Investigation of Atmospheric Effects on Propagation and the Impact on Eye Safety,” Stanford Res. Inst., Menlo Park, CA 94025, USA, Project Report 1341, Contract F41609-71-C-0029 NTIS AD 755405 (1972).

W. F. Dabbert, W. B. Johnson, “Atmospheric Effects upon Laser Eye Safety—Part II,” Stanford Res. Inst., Menlo park CA 94025, USA, Project Report 7472 (1971).

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Figures (4)

Fig. 1
Fig. 1

Graphs of σs vs σT for the Nd.YAG laser wavelength λ = 1.064 μm (broken line), and of F(σs) against σT (full lines) for different values of Q: (a) 0.50, (b) 0.10, (c) 0.02, (d) 0.01, and (e) 0.001.

Fig. 2
Fig. 2

Graph of Q as a function of Fm for the wavelength λ = 1.062 μm.

Fig. 3
Fig. 3

Graph of Fm vs σm(λ) for (a) Q = 0.01, (b) Q = 0.001. The broken line represents the wavelength λ = 1.064 μm.

Fig. 4
Fig. 4

Graphs of the computed scintillation factor and hazard range vs C n 2 for different values of Q. The input parameters used are: V = 23.5 km (standard clear day), E = 0.1 J, T = 10−4 J,φ = 1.414 × 10−4 rad, λ = 1.064 × 10−6 m, w0 = 0.01 m, wc = we = wp = 3.5 × 10 m, z = 2 m, m = 1.0.

Tables (1)

Tables Icon

Table I Input Parameters

Equations (29)

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D = ( k 1 k 2 E / T ) 1 / 2 w c / φ ,
I ( r , D ) = P π r D 2 · exp ( - α λ D ) · exp ( - r 2 / r D 2 ) ,
T = k 2 E exp ( - α λ D ) [ 1 - exp ( - m 2 w 2 / r D 2 ) ]
w = min ( w e , w p , w r )
σ T 2 = 2.24 k 7 / 6 D 11 / 6 0 1 C n 2 ( u ) u 5 / 6 ( 1 - u ) 5 / 6 d u ,
F ( σ s ) = exp [ σ s ( b - ½ σ s ) ] ,
Q ( b ) = 1 - ( 2 π ) - 1 / 2 - b exp ( - 1 2 t 2 ) d t .
b = x - c 0 + c 1 x + c 2 x 2 1 + d 1 x + d 2 x 2 + d 3 x 3 + ,
σ s ( σ T ) = σ T { 1 + ρ σ T μ } - 1 ,
σ m ( λ ) = ( ρ μ ) - β ( 1 - β ) 1 - β ;             β = μ - 1 .
F m = exp { σ m ( b - ½ σ m ) } .
Q det = H ( D - D 0.5 )
r D = ( r D 2 + D 2 θ s t 2 ) 1 / 2
θ s t = { 0.427 θ l t κ 3 θ l t ( 1 - 1.8 κ - 1 / 3 ) κ > 3 ,
r 0 = 2.10 [ 1.455 k 2 D 0 1 C n 2 ( u ) ( 1 - u ) 5 / 3 d u ] - 3 / 5 .
θ l t = 0.604 κ .
α 0.55 = 3.912 / V ,
σ I 2 = I 2 - I 2 I 2
σ ln I 2 = ( ln I ) 2 - ln I 2 ln I 2 .
p ( x ) = ( 2 π ) - 1 / 2 σ ln I - 1 x - 1 exp { - ( ln x + ½ σ ln I ) 2 / 2 σ ln I 2 } .
x n = 0 x n p ( x ) d x = exp { 1 2 n ( n - 1 ) σ ln I 2 } .
σ ln I 2 = ln ( 1 + σ I 2 ) .
σ ln I 2 = 2.44 ln ( 1 + σ I 2 ) .
σ T = 1.11 k 7 / 12 D 11 / 12 C n .
P = 0 x t h p ( x ) d x
x t h = I t h / I .
P ( b ) = 1 - Q ( b ) = ( 2 π ) - 1 / 2 - b exp ( - 1 2 u 2 ) d u
b = ½ σ s + σ s - 1 ln ( x t h )
x t h = exp { σ s ( b - ½ σ s ) } .

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