Abstract

A Monte Carlo model has been used to compute a set of point-spread functions (PSF's) and modulation transfer functions (MTF's) that determine underwater-image quality in a range of different environments. The results have been used to analyze the range of application under which a linear-approximation theory holds. Conclusions of the study are that the linear-approximation theory seems to hold quite well over a broad range of applications. The ramifications of the Wells small-angle-scattering theory that predicts the PSF from a knowledge of the volume-scattering function (VSF) are also considered.

Discrepancies are noted between a predicted and a computationally obtained MTF; these discrepancies increase with range. Therefore, the results of the simulations indicate that the small-angle-scattering theory is more valid at a limited number of attenuation lengths. The results of the simulations indicate that the theory is valid to approximately three attenuation lengths.

© 1995 Optical Society of America

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References

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1994 (1)

1991 (1)

1990 (2)

J. S. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Ocean Eng. 15, 101–111 (1990).
[CrossRef]

J. Arvo, D. Kirk, “Particle transport and image synthesis,” Comput. Graphics 24, 63–66 (1990).
[CrossRef]

1989 (2)

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

J. T. O. Kirk, “The upwelling light stream in natural water,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

1987 (1)

1985 (1)

1980 (1)

A. V. Oppenheim, G. Frisk, D. R. Marinez, “Computation of the Hankel transform using projections,” J. Acoust. Soc. Am. 68, 523–529 (1980).
[CrossRef]

1977 (1)

1973 (1)

W. H. Wells, “Theory of small-angle scattering,” AGARD Lect. Ser. 61, 1–19 (1973).

1972 (1)

1969 (1)

Adams, C. N.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Arnush, D.

Arvo, J.

J. Arvo, D. Kirk, “Particle transport and image synthesis,” Comput. Graphics 24, 63–66 (1990).
[CrossRef]

Bryant, S. B.

C. J. Funk, S. B. Bryant, P. J. Heckman, Handbook of Underwater Imaging System Design (Ocean Technology Department, Naval Undersea Center, San Diego, Calif., 1972).

Crawford, D. R.

Cummings, J. D.

B. Swartz, J. D. Cummings, “Laser range-gated underwater imaging including polarization discrimination,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1537, 42–56 (1991).

Frisk, G.

A. V. Oppenheim, G. Frisk, D. R. Marinez, “Computation of the Hankel transform using projections,” J. Acoust. Soc. Am. 68, 523–529 (1980).
[CrossRef]

Funk, C. J.

C. J. Funk, S. B. Bryant, P. J. Heckman, Handbook of Underwater Imaging System Design (Ocean Technology Department, Naval Undersea Center, San Diego, Calif., 1972).

Garvis, D.

T. J. Kulp, D. Garvis, R. Kennedy, T. Salmon, “Results of the second tank trial of the LLNL/NAVSEA underwater laser imaging system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 398–413 (1990).

Gordon, H. R.

Gordon, R. H.

Heckman, P. J.

C. J. Funk, S. B. Bryant, P. J. Heckman, Handbook of Underwater Imaging System Design (Ocean Technology Department, Naval Undersea Center, San Diego, Calif., 1972).

Hindman, C. L.

Jaffe, J. S.

J. S. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Ocean Eng. 15, 101–111 (1990).
[CrossRef]

Jerlov, N. G.

N. G. Jerlov, Marine Optics, Vol. 14 of Elvesier Oceanography Series (Elvesier, New York, 1976).
[CrossRef]

Kattawar, G. W.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Kennedy, R.

T. J. Kulp, D. Garvis, R. Kennedy, T. Salmon, “Results of the second tank trial of the LLNL/NAVSEA underwater laser imaging system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 398–413 (1990).

Kirk, D.

J. Arvo, D. Kirk, “Particle transport and image synthesis,” Comput. Graphics 24, 63–66 (1990).
[CrossRef]

Kirk, J. T. O.

J. T. O. Kirk, “The upwelling light stream in natural water,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

J. T. O. Kirk, “Monte Carlo procedure for simulating the penetration of light into natural waters,” CSIRO Paper 36 (Commonwealth Scientific and Industrial Research Organization, Division of Plant and Industrial Technology, Canberra, Australia, 1981), pp. 1–16.

Kulp, T. J.

T. J. Kulp, D. Garvis, R. Kennedy, T. Salmon, “Results of the second tank trial of the LLNL/NAVSEA underwater laser imaging system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 398–413 (1990).

Lewis, E. E.

E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport (Wiley, New York, 1984).

Marinez, D. R.

A. V. Oppenheim, G. Frisk, D. R. Marinez, “Computation of the Hankel transform using projections,” J. Acoust. Soc. Am. 68, 523–529 (1980).
[CrossRef]

McGlamery, B. J.

B. J. McGlamery, “A computer model for underwater camera systems,” in Ocean Optics VI, S. Q. Duntley, ed., Proc. Soc. Photo-Opt. Instrum. Eng.208, 221–231 (1979).

McLean, J. W.

Mertens, L. E.

Miller, W. F.

E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport (Wiley, New York, 1984).

Oppenheim, A. V.

A. V. Oppenheim, G. Frisk, D. R. Marinez, “Computation of the Hankel transform using projections,” J. Acoust. Soc. Am. 68, 523–529 (1980).
[CrossRef]

Petzold, T. J.

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, La Jolla, Calif., 1972), pp. 72–78.

Replogle, F. S.

Salmon, T.

T. J. Kulp, D. Garvis, R. Kennedy, T. Salmon, “Results of the second tank trial of the LLNL/NAVSEA underwater laser imaging system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 398–413 (1990).

Swartz, B.

B. Swartz, J. D. Cummings, “Laser range-gated underwater imaging including polarization discrimination,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1537, 42–56 (1991).

Tyler, J.

J. Tyler, “Optical properties of water,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 15.1–15.38.

Voss, K. J.

J. W. McLean, K. J. Voss, “Point-spread function in ocean water: comparison between theory and experiment,” Appl. Opt. 30, 2027–2030 (1991).
[CrossRef] [PubMed]

K. J. Voss, “Variation of the point-spread function in the Sargasso Sea,” in Underwater Image, Photography, and Visibility, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1537, 97–103 (1991).

Wells, W. H.

AGARD Lect. Ser. (1)

W. H. Wells, “Theory of small-angle scattering,” AGARD Lect. Ser. 61, 1–19 (1973).

Appl. Opt. (4)

Comput. Graphics (1)

J. Arvo, D. Kirk, “Particle transport and image synthesis,” Comput. Graphics 24, 63–66 (1990).
[CrossRef]

IEEE J. Ocean Eng. (1)

J. S. Jaffe, “Computer modeling and the design of optimal underwater imaging systems,” IEEE J. Ocean Eng. 15, 101–111 (1990).
[CrossRef]

J. Acoust. Soc. Am. (1)

A. V. Oppenheim, G. Frisk, D. R. Marinez, “Computation of the Hankel transform using projections,” J. Acoust. Soc. Am. 68, 523–529 (1980).
[CrossRef]

J. Opt. Soc. Am. (3)

Limnol. Oceanogr. (2)

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

J. T. O. Kirk, “The upwelling light stream in natural water,” Limnol. Oceanogr. 34, 1410–1425 (1989).
[CrossRef]

Other (10)

J. Tyler, “Optical properties of water,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 15.1–15.38.

J. T. O. Kirk, “Monte Carlo procedure for simulating the penetration of light into natural waters,” CSIRO Paper 36 (Commonwealth Scientific and Industrial Research Organization, Division of Plant and Industrial Technology, Canberra, Australia, 1981), pp. 1–16.

K. J. Voss, “Variation of the point-spread function in the Sargasso Sea,” in Underwater Image, Photography, and Visibility, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1537, 97–103 (1991).

B. Swartz, J. D. Cummings, “Laser range-gated underwater imaging including polarization discrimination,” in Underwater Imaging, Photography, and Visibility, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1537, 42–56 (1991).

T. J. Kulp, D. Garvis, R. Kennedy, T. Salmon, “Results of the second tank trial of the LLNL/NAVSEA underwater laser imaging system,” in Ocean Optics X, R. W. Spinrad, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1302, 398–413 (1990).

B. J. McGlamery, “A computer model for underwater camera systems,” in Ocean Optics VI, S. Q. Duntley, ed., Proc. Soc. Photo-Opt. Instrum. Eng.208, 221–231 (1979).

N. G. Jerlov, Marine Optics, Vol. 14 of Elvesier Oceanography Series (Elvesier, New York, 1976).
[CrossRef]

T. J. Petzold, Volume Scattering Functions for Selected Ocean Waters (Scripps Institution of Oceanography, La Jolla, Calif., 1972), pp. 72–78.

C. J. Funk, S. B. Bryant, P. J. Heckman, Handbook of Underwater Imaging System Design (Ocean Technology Department, Naval Undersea Center, San Diego, Calif., 1972).

E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport (Wiley, New York, 1984).

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Figures (6)

Fig. 1
Fig. 1

Coordinate system for the Monte Carlo simulation.

Fig. 2
Fig. 2

PSF output after 107 photons at 6 attenuation lengths in bay water.

Fig. 3
Fig. 3

Logarithms of the values of the MTF's for (a) bay waters, (b) coastal waters, and (c) deep-ocean waters.

Fig. 4
Fig. 4

Values for the LN(R1, R2) functions (see text) for (a) bay waters, (b) coastal waters, and (c) deep-ocean waters

Fig. 5
Fig. 5

Comparison of the Q functions across water types at 6 attenuation lengths (solid curves) with the Wells theory (dashed curve).

Fig. 6
Fig. 6

A comparison of the PSF's for the four attenuation-length ranges and three water types: Simulations for (a) bay, (b) coastal, and (c) deep-ocean water are shown for 1, 3, 6, and 10 attenuation lengths. The results of the Monte Carlo simulations (solid curves) are shown along with the predictions of the Wells theory (dashed curves). The thickness of a curve indicates its attenuation length, with 1 attenuation length the thinnest and 10 attenuation lengths the thickest curves.

Tables (1)

Tables Icon

Table 1 Inherent Ocean Optical Parameters Used in the Simulations

Equations (18)

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MTF ( R 1 , ϕ ) = MTF ( R 2 , ϕ ) R 1 / R 2 ,
L O ( R , ξ ) = C ( ξ ) L u ( R , ξ ξ ) d Ω ,
L O ( R , ξ ) = 1 4 π L u i ( θ , ϕ , θ inc , ϕ inc ) sin θ d θ d ϕ = i = 0 N 1 L u i ( θ i , θ inc , ϕ inc ) ( cos θ i cos θ i + 1 ) 2 ,
p n ( θ i , θ inc , ϕ inc ) 2 π R 2 cos θ inc ( cos θ i cos θ i + 1 ) Δ Ω ( i ) inc ,
L O ( R , ξ ) = I = 0 N 1 p n ( θ i , θ inc , ϕ inc ) cos θ inc Δ Ω ( i ) inc 4 π R 2 .
L O ( θ inc ) = i = 1 N 1 p n ( θ i , Δ θ inc ) 8 π 2 R 2 cos ( θ inc ) ( cos θ ( i ) inc cos θ ( i + 1 ) inc ) ,
( ϕ ) = o π J 0 ( 2 π ϕ θ ) β ( θ ) θ d θ .
Q W ( ϕ ) = 0 1 Σ ( ϕ t ) d t ,
MTF W ( ϕ ) = exp [ Q W ( ϕ ) s t ] R .
s t = 2 π 0 θ max β ( θ ) sin ( θ ) d θ .
β ( θ ) = θ 0 2 π ( θ 0 3 + θ 3 ) 3 / 2 ,
Q W ( ϕ ) = 1 exp ( 2 π θ 0 ϕ ) 2 π θ 0 ϕ .
L N ( R 1 R 2 ) = ln [ MTF ( ϕ , R 1 ) ] ln [ MTF ( ϕ , R 2 ) ] .
L N ( R 1 R 2 ) = ln { exp [ Q ( ϕ ) s t ] R 1 } { exp [ Q ( ϕ ) s t ] R 2 } = R 1 R 2 .
MTF W ( ϕ ) = exp [ Q ( ϕ ) s t ] R exp ( s t R ) ,
PSF total = PSF unscat + PSF scat .
MTF total = MTF unscat + MTF scat .
MTF total = K + MTF scat .

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