Abstract

It is commonly known that underwater imaging is hindered by both absorption and scattering by particles of various origins. However, evidence also indicates that the turbulence in natural underwater environments can cause severe image-quality degradation. A model is presented to include the effects of both particle and turbulence on underwater optical imaging through optical transfer functions to help quantify the limiting factors under different circumstances. The model utilizes Kolmogorov-type index of refraction power spectra found in the ocean, along with field examples, to demonstrate that optical turbulence can limit imaging resolution by affecting high spatial frequencies. The effects of the path radiance are also discussed.

© 2009 Optical Society of America

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References

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  1. G. D. Gilbert and R. C. Honey, in Underwater Photo-Optical Instrumentation Applications (SPIE, 1972), pp. 49-55.
  2. D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, Appl. Opt. 43, 5662 (2004).
    [CrossRef] [PubMed]
  3. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, 1967).
  4. M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC Press, 1996).
  5. J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).
  6. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  7. A. S. Fields, Rep. 3577, Naval Ship Research and Development Center, 1972.
  8. G. K. Batchelor, J. Fluid Mech. 5, 113 (1959).
    [CrossRef]
  9. J. A. DomaradzkiLight Scattering Induced by Turbulence Flow: a Numerical Study (U. Southern California, 1997), p. 65.
  10. J. D. Nash and J. N. Moum, J. Atmos. Ocean. Technol. 16, 263 (1999).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  12. W. Hou, Z. Lee, and A. Weidemann, Opt. Express 15, 2791 (2007).
    [CrossRef] [PubMed]
  13. N. Kopeika, Opt. Eng. 26, 1146 (1987).
  14. W. Hou, D. Gray, A. Weidemann, and R. Arnone, Opt. Express 16, 9958 (2008).
    [CrossRef] [PubMed]
  15. W. Hou and A. Weidemann, Proc. SPIE 7317, 731701 (2009).
  16. S. Q. Duntley, in Optical Aspects of Oceanography, N.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974).

2009 (1)

W. Hou and A. Weidemann, Proc. SPIE 7317, 731701 (2009).

2008 (1)

2007 (1)

2004 (1)

1999 (1)

J. D. Nash and J. N. Moum, J. Atmos. Ocean. Technol. 16, 263 (1999).
[CrossRef]

1987 (1)

N. Kopeika, Opt. Eng. 26, 1146 (1987).

1966 (1)

1959 (1)

G. K. Batchelor, J. Fluid Mech. 5, 113 (1959).
[CrossRef]

Arnone, R.

Batchelor, G. K.

G. K. Batchelor, J. Fluid Mech. 5, 113 (1959).
[CrossRef]

Bogucki, D. J.

Domaradzki, J. A.

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, Appl. Opt. 43, 5662 (2004).
[CrossRef] [PubMed]

J. A. DomaradzkiLight Scattering Induced by Turbulence Flow: a Numerical Study (U. Southern California, 1997), p. 65.

Duntley, S. Q.

S. Q. Duntley, in Optical Aspects of Oceanography, N.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974).

Ecke, R. E.

Fields, A. S.

A. S. Fields, Rep. 3577, Naval Ship Research and Development Center, 1972.

Fried, D. L.

Gilbert, G. D.

G. D. Gilbert and R. C. Honey, in Underwater Photo-Optical Instrumentation Applications (SPIE, 1972), pp. 49-55.

Goodman, J. W.

J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Gray, D.

Honey, R. C.

G. D. Gilbert and R. C. Honey, in Underwater Photo-Optical Instrumentation Applications (SPIE, 1972), pp. 49-55.

Hou, W.

Kopeika, N.

N. Kopeika, Opt. Eng. 26, 1146 (1987).

Lee, Z.

Moum, J. N.

J. D. Nash and J. N. Moum, J. Atmos. Ocean. Technol. 16, 263 (1999).
[CrossRef]

Nash, J. D.

J. D. Nash and J. N. Moum, J. Atmos. Ocean. Technol. 16, 263 (1999).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC Press, 1996).

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, 1967).

Truman, C. R.

Weidemann, A.

Welsh, B. M.

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC Press, 1996).

Appl. Opt. (1)

J. Atmos. Ocean. Technol. (1)

J. D. Nash and J. N. Moum, J. Atmos. Ocean. Technol. 16, 263 (1999).
[CrossRef]

J. Fluid Mech. (1)

G. K. Batchelor, J. Fluid Mech. 5, 113 (1959).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

N. Kopeika, Opt. Eng. 26, 1146 (1987).

Opt. Express (2)

Proc. SPIE (1)

W. Hou and A. Weidemann, Proc. SPIE 7317, 731701 (2009).

Other (8)

S. Q. Duntley, in Optical Aspects of Oceanography, N.G.Jerlov and E.S.Nielsen, eds. (Academic, 1974).

G. D. Gilbert and R. C. Honey, in Underwater Photo-Optical Instrumentation Applications (SPIE, 1972), pp. 49-55.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

A. S. Fields, Rep. 3577, Naval Ship Research and Development Center, 1972.

J. A. DomaradzkiLight Scattering Induced by Turbulence Flow: a Numerical Study (U. Southern California, 1997), p. 65.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, 1967).

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC Press, 1996).

J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).

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Figures (2)

Fig. 1
Fig. 1

A sinusoid (single frequency) is used to illustrate effects of the path radiance on the modulation transfer. The left side shows the case of the initial wave form (solid) with an amplitude of 1 (varies between 0 and 2) and the wave form after the transmission (dashed) with an amplitude of x from the mean, where x also equals the modulation (see text); the normalized path radiance ( D ) is shown to elevate the previous wave form by 1/(D+1) for all spatial frequencies.

Fig. 2
Fig. 2

Comparison of relative contributions under different conditions: (T), the OTF contribution from the turbulence; (P), the particle scattering contribution; (A), all combined contributions. Figure legends under corresponding labels indicate attenuation coefficients, imaging ranges, and seeing parameters respectively (in m 1 , m and m). The single-scattering albedo of all curves is assumed a constant (0.8). The last three curves in the legend are contributions from the particle, the turbulence, and combined (from top to bottom) under the same optical conditions. No path radiance was included (D=0).

Equations (9)

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Φ n K ( κ , r ) = K 3 κ 11 3 ,
OTF LE ( f ) = exp [ 3.44 ( λ ¯ d i f r 0 ) 5 3 ] ,
r 0 = 0.185 [ 4 π 2 k 2 0 r d z C n 2 ( z ) ] 3 5 ,
r 0 = 0.185 [ 4 π 2 k 2 C w 2 ] 3 5 , r 3 5 = 0.185 [ 0.132 π 2 k 2 K 3 ] 3 5 ,
r 3 5 = R 0 r 3 5 ,
OTF tur ( ψ , r ) = exp [ 3.44 ( λ ¯ R 0 ) 5 3 ψ 5 3 r ] = exp ( S n ψ 5 3 r ) ,
M orig = I max I min I max + I min = 1 + x ( 1 x ) 1 + x + 1 x = x .
M = I max I min I max + I min = 1 + x + D ( 1 x + D ) 1 + x + D + 1 x + D = M orig ( 1 1 + D ) = M orig MTF path .
OTF ( ψ , r ) total = OTF ( ψ , r ) path OTF ( ψ , r ) par OTF ( ψ , r ) tur = ( 1 1 + D ) exp [ c r + b r ( 1 e 2 π θ 0 ψ 2 π θ 0 ψ ) ] exp ( S n ψ 5 3 r ) = ( 1 1 + D ) exp { [ c b ( 1 e 2 π θ 0 ψ 2 π θ 0 ψ ) + S n ψ 5 3 ] r } ,

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