Abstract

It is known that scattering by particulates within natural waters is the main cause of the blur in underwater images. Underwater images can be better restored or enhanced with knowledge of the point spread function (PSF) of the water. This will extend the performance range as well as the information retrieval from underwater electro-optical systems, which is critical in many civilian and military applications, including target and especially mine detection, search and rescue, and diver visibility. A better understanding of the physical process involved also helps to predict system performance and simulate it accurately on demand. The presented effort first reviews several PSF models, including the introduction of a semi-analytical PSF given optical properties of the medium, including scattering albedo, mean scattering angles and the optical range. The models under comparison include the empirical model of Duntley, a modified PSF model by Dolin et al, as well as the numerical integration of analytical forms from Wells, as a benchmark of theoretical results. For experimental results, in addition to that of Duntley, we validate the above models with measured point spread functions by applying field measured scattering properties with Monte Carlo simulations. Results from these comparisons suggest it is sufficient but necessary to have the three parameters listed above to model PSFs. The simplified approach introduced also provides adequate accuracy and flexibility for imaging applications, as shown by examples of restored underwater images.

© 2008 Optical Society of America

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References

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  1. G. D. Gilbert and R. C. Honey, "Optical turbulence in the sea," 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, "Light scattering on oceanic turbulence," Appl. Opt. 43, 5662-5668 (2004).
    [CrossRef] [PubMed]
  3. C. D. Mobley, Light and Water: radiative transfer in natural waters (Academic Press, New York, 1994).
  4. D. Gray, "Order-of-Scattering Point Spread and Modulation Transfer Functions for Natural Waters," to be submitted to OE (2008).
  5. I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
    [CrossRef]
  6. W. Hou, D. Gray, A. Weidemann, G. R. Fournier, and J. L. Forand, "Automated underwater image restoration and retrieval of related optical properties," in IEEE International Geoscience and Remote Sensing Symposium, IGARSS (2007), pp. 1889-1892.
  7. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N.J., 2002).
  8. L. E. Mertens, and J. F. S. Replogle, "Use of point spread and beam spread functions for analysis of imaging systems in water," J. Opt. Soc. Am. 67, 1105-1117 (1977).
    [CrossRef]
  9. J. Zhang, Q. Zhang, and G. He, "Blind deconvolution: multiplicative iterative algorithm," Opt. Lett. 33, 25-27 (2008).
    [CrossRef]
  10. S. Q. Duntley, "Underwater lighting by submerged lasers and incandescent sources," (Scripts Instituition of Oceanography, University of California, San Diego, 1971).
  11. K. Voss, "Simple empirical model of the oceanic point spread function," Appl. Opt. 30, 2647-2651 (1991).
    [CrossRef] [PubMed]
  12. L. S. Dolin, G. D. Gilbert, I. Levin, and A. Luchinin, Theory of imaging through wavy sea surface (Russian Academy of Sciences, Inst of Applied Physics, Nizhniy Novgorod, 2006).
  13. W. Hou, D. Gray, A. Weidemann, and R. A. Arnone, "A PRACTICAL POINT SPREAD MODEL FOR OCEAN WATERS," in IV International Conf. Current Problems in Optics of Natural Waters (N. Novgorod, Russia, 2007), pp. 86-90.
  14. A. Gordon, "Practical approaches to underwater multiple-scattering problems," in Ocean Optics (SPIE, 1975), pp. 85-93.
  15. W. H. Wells, "Theory of small angle scattering," in AGARD Lec. Series No. 61(NATO, 1973).
  16. W. Hou, Z. Lee, and A. Weidemann, "Why does the Secchi disk disappear? An imaging perspective," Opt. Express 15, 2791-2802 (2007).
    [CrossRef] [PubMed]
  17. W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).
  18. J. Jaffe, "Monte Carlo modeling of underwater image formation: validity of the linear and small-angle approximations," Appl. Opt. 34, 5421-5421 (1995).
    [CrossRef]

2008 (1)

2007 (2)

W. Hou, Z. Lee, and A. Weidemann, "Why does the Secchi disk disappear? An imaging perspective," Opt. Express 15, 2791-2802 (2007).
[CrossRef] [PubMed]

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).

2004 (1)

1997 (1)

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
[CrossRef]

1995 (1)

J. Jaffe, "Monte Carlo modeling of underwater image formation: validity of the linear and small-angle approximations," Appl. Opt. 34, 5421-5421 (1995).
[CrossRef]

1991 (1)

1977 (1)

Bogucki, D. J.

Domaradzki, J. A.

Ecke, R. E.

Fournier, G. R.

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).

Gray, D.

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).

He, G.

Hou, W.

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).

W. Hou, Z. Lee, and A. Weidemann, "Why does the Secchi disk disappear? An imaging perspective," Opt. Express 15, 2791-2802 (2007).
[CrossRef] [PubMed]

Jaffe, J.

J. Jaffe, "Monte Carlo modeling of underwater image formation: validity of the linear and small-angle approximations," Appl. Opt. 34, 5421-5421 (1995).
[CrossRef]

Katsev, I. L.

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
[CrossRef]

Lee, Z.

Mertens, L. E.

Polonsky, I. N.

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
[CrossRef]

Prikhach, A. S.

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
[CrossRef]

Replogle, J. F. S.

Truman, C. R.

Voss, K.

Weidemann, A.

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).

W. Hou, Z. Lee, and A. Weidemann, "Why does the Secchi disk disappear? An imaging perspective," Opt. Express 15, 2791-2802 (2007).
[CrossRef] [PubMed]

Zege, E. P.

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
[CrossRef]

Zhang, J.

Zhang, Q.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

L. E. Mertens, and J. F. S. Replogle, "Use of point spread and beam spread functions for analysis of imaging systems in water," J. Opt. Soc. Am. 67, 1105-1117 (1977).
[CrossRef]

I. L. Katsev, E. P. Zege, A. S. Prikhach, and I. N. Polonsky, "Efficient technique to determine backscattered light power for various atmospheric and oceanic sounding and imaging systems," J. Opt. Soc. Am. 14, 1338-1346 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

W. Hou, A. Weidemann, D. Gray, and G. R. Fournier, "Imagery-derived modulation transfer function and its applications for underwater imaging," Proc. SPIE 6696, 6696221-6696228 (2007).

Other (10)

S. Q. Duntley, "Underwater lighting by submerged lasers and incandescent sources," (Scripts Instituition of Oceanography, University of California, San Diego, 1971).

G. D. Gilbert and R. C. Honey, "Optical turbulence in the sea," in Underwater photo-optical instrumentation applications (SPIE, 1972), pp. 49-55.

W. Hou, D. Gray, A. Weidemann, G. R. Fournier, and J. L. Forand, "Automated underwater image restoration and retrieval of related optical properties," in IEEE International Geoscience and Remote Sensing Symposium, IGARSS (2007), pp. 1889-1892.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, N.J., 2002).

C. D. Mobley, Light and Water: radiative transfer in natural waters (Academic Press, New York, 1994).

D. Gray, "Order-of-Scattering Point Spread and Modulation Transfer Functions for Natural Waters," to be submitted to OE (2008).

L. S. Dolin, G. D. Gilbert, I. Levin, and A. Luchinin, Theory of imaging through wavy sea surface (Russian Academy of Sciences, Inst of Applied Physics, Nizhniy Novgorod, 2006).

W. Hou, D. Gray, A. Weidemann, and R. A. Arnone, "A PRACTICAL POINT SPREAD MODEL FOR OCEAN WATERS," in IV International Conf. Current Problems in Optics of Natural Waters (N. Novgorod, Russia, 2007), pp. 86-90.

A. Gordon, "Practical approaches to underwater multiple-scattering problems," in Ocean Optics (SPIE, 1975), pp. 85-93.

W. H. Wells, "Theory of small angle scattering," in AGARD Lec. Series No. 61(NATO, 1973).

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Figures (3)

Fig. 1.
Fig. 1.

Comparison of PSFs from different methods from a-f: “Current” (current study), “Duntley” and “Dolin” (empirical relationship in text), and “MVSM” (Monte Carlo simulated PSF based on measured volume scattering function during NATO experiment) and Wells numerical integrated PSF. Normalized to 100 mrad. See text for details.

Fig. 2.
Fig. 2.

An example of PSF comparison under different θ0 values. Notice that the variation of θ0 does not affect Duntley or MVSM and all rest parameters of other models are the same as in Fig.1. Normalized to 100 mrad.

Fig. 3.
Fig. 3.

A diver captured image and restorations with different PSFs. Image (top left, 3a) was taken during August 21, 2002 diving at Mississippi Bight with total attenuation c=1.5m-1 at 5ft distance. 3b (top right) shows the restored image using the correct PSF model. 3c (bottom left) shows the image restored assuming a longer distance. 3d (bottom right) shows the result of a blind deconvolution with a Gaussian PSF.

Tables (1)

Tables Icon

Table 1. Optical parameters used to compare different PSF models as shown in Figs. 1–2.

Equations (17)

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g ( x , y ) = f ( x , y ) h ( x , y ) + n ( x , y ) ,
H ( θ ) P = 10 A C θ B 2 π sin θ ,
E ( θ , r ) = P 0 ( q r ) 2 G ( θ q , τ b ) exp ( a ef r ) ,
G ( θ q , τ b ) = δ ( θ q ) π θ q exp ( τ b ) + 0.525 τ b θ q exp ( 2.6 θ q 0 . 7 τ b ) + β 2 2 2 π [ 2 ( 1 + τ b ) exp ( τ b ) ]
× exp [ β 1 ( β 2 θ q ) 1 3 ( β 2 θ q ) 2 + β 3 ] ,
β 1 = 6.857 1.5737 τ b + 0.143 τ b 2 6.027 · 10 3 · τ b 3 + 1.069 · 10 4 · τ b 4 1 0.1869 τ b + 1.97 · 10 2 · τ b 2 1.317 · 10 3 · τ b 3 + 4.31 · 10 5 · τ b 4 ,
β 2 = 0.469 7.41 · 10 2 τ b + 2.78 · 10 3 τ b 2 + 9.6 · 10 5 · τ b 3 1 9.16 · 10 2 τ b 6.07 · 10 3 · τ b 2 + 8.33 · 10 4 · τ b 3 ,
β 3 = 6.27 0.723 τ b + 5.82 · 10 2 · τ b 2 1 0.072 τ b + 6.3 · 10 3 · τ b 2 + 9.4 · 10 4 · τ b 3 ,
θ q = q θ , τ b = br = ω τ ,
2 π 0 G ( θ q , τ b ) θ q d θ q = 1 , 0 δ ( θ q ) θ q d θ q = 1 ·
q = [ 1 cos θ 1 2 b ~ b ] 1 2 4 [ 1 cos θ 1 2 b ~ b ] 1 2 , b ~ b = b b b .
PSF ( θ ) = B 1 θ m ,
PSF ( θ , r ) = d Φ d ω ,
Φ ( θ , r ) = exp [ ( c 0 1 0 θ t β d ω dt ) r ] ,
PSF ( θ ) = e τ r 0 1 β ( θ t ) dt t 2 ·
β ( θ ) = b θ 0 2 π ( θ 0 2 + θ 2 ) 3 2 ,
PSF ( θ ) = K ( θ 0 ) bre τ 2 π θ m = K ( θ 0 ) ω 0 τ e τ 2 π θ m ,

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