Abstract

A new instrument to measure the point spread function (PSF) in the ocean has provided the opportunity for direct comparison between theoretical predictions and experimental measurement. Theoretical predictions are derived from small angle scattering theory using a simple algebraic fit to the single scattering phase function. The resulting predictions for the PSF are found to match the experimental measurements over a wide range of angles and optical depths.

© 1991 Optical Society of America

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References

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  1. K. J. Voss, A. L. Chapin, “Measurement of the Point Spread Function in the Ocean,” Appl. opt. 29, 3638–3642 (1990).
    [CrossRef] [PubMed]
  2. K. J. Voss, “Variability of the Point Spread Function in the Water Column,” Proc. Soc. Photo-Opt. Instrum. Eng. 1302, 355–362 (1990).
  3. T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” SIO Ref. 72–78, Scripps Institution of Oceanography, U. California, San Diego (1972).
  4. J. W. McLean, D. R. Crawford, C. L. Hindman, “Limits of Small Angle Scattering Theory,” Appl. Opt. 26, 2053–2054 (1987).
    [CrossRef] [PubMed]
  5. H. Hodara, “Experimental Results of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).
  6. L. E. Mertens, 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]
  7. R. C. Honey, “Beam Spread and Point Spread Functions and Their Measurement in the Ocean,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 242–248 (1979).
  8. D. Arnush, “Underwater Light Beam Propagation in the Small Angle Scattering Approximation,” J. Opt. Soc. Am. 62, 1109–1111 (1972).
    [CrossRef]
  9. W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).
  10. W. Wilson, “Spreading of Light Beams in Ocean Water,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 64–72 (1979).
  11. W. H. Wells, “Medium and System Transform Functions,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

1990 (2)

K. J. Voss, A. L. Chapin, “Measurement of the Point Spread Function in the Ocean,” Appl. opt. 29, 3638–3642 (1990).
[CrossRef] [PubMed]

K. J. Voss, “Variability of the Point Spread Function in the Water Column,” Proc. Soc. Photo-Opt. Instrum. Eng. 1302, 355–362 (1990).

1987 (1)

1979 (2)

R. C. Honey, “Beam Spread and Point Spread Functions and Their Measurement in the Ocean,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 242–248 (1979).

W. Wilson, “Spreading of Light Beams in Ocean Water,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 64–72 (1979).

1977 (1)

1972 (1)

Arnush, D.

Chapin, A. L.

Crawford, D. R.

Hindman, C. L.

Hodara, H.

H. Hodara, “Experimental Results of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

Honey, R. C.

R. C. Honey, “Beam Spread and Point Spread Functions and Their Measurement in the Ocean,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 242–248 (1979).

McLean, J. W.

Mertens, L. E.

Petzold, T. J.

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” SIO Ref. 72–78, Scripps Institution of Oceanography, U. California, San Diego (1972).

Replogle, F. S.

Voss, K. J.

K. J. Voss, A. L. Chapin, “Measurement of the Point Spread Function in the Ocean,” Appl. opt. 29, 3638–3642 (1990).
[CrossRef] [PubMed]

K. J. Voss, “Variability of the Point Spread Function in the Water Column,” Proc. Soc. Photo-Opt. Instrum. Eng. 1302, 355–362 (1990).

Wells, W. H.

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

W. H. Wells, “Medium and System Transform Functions,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

Wilson, W.

W. Wilson, “Spreading of Light Beams in Ocean Water,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 64–72 (1979).

Appl. opt. (1)

J. Opt. Soc. Am. (2)

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

R. C. Honey, “Beam Spread and Point Spread Functions and Their Measurement in the Ocean,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 242–248 (1979).

K. J. Voss, “Variability of the Point Spread Function in the Water Column,” Proc. Soc. Photo-Opt. Instrum. Eng. 1302, 355–362 (1990).

W. Wilson, “Spreading of Light Beams in Ocean Water,” Proc. Soc. Photo-Opt. Instrum. Eng. 208, 64–72 (1979).

Other (4)

W. H. Wells, “Medium and System Transform Functions,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” SIO Ref. 72–78, Scripps Institution of Oceanography, U. California, San Diego (1972).

H. Hodara, “Experimental Results of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser., No. 61 (NATO, 1973).

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Figures (3)

Fig. 1
Fig. 1

Single scattering distribution functions for various water types (from Petzold3).

Fig. 2
Fig. 2

Comparison of TOTO measurements of the scattering phase function with Wells’s algebraic fit. For deep TOTO waters, Wells’s model agrees with the median scattering angle if θ0 = 0.06 rad. Data are from Petzold.3

Fig. 3
Fig. 3

Comparison of the PSF predicted by small angle scattering theory and TOTO measurements. The predicted PSF has been corrected for the finite sensor resolution: (a) bR = 1.1 (11 m); (b) bR = 2.0 (20 m); (c) bR = 3.9 (39 m); (d) bR = 5.7 (57 m); and (e) bR = 7.6 (76 m).

Equations (8)

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F ( ψ , R ) = 2 π J 0 ( 2 π θ ψ ) f ( θ , R ) θ d θ , F ( θ , R ) = 2 π J 0 ( 2 π θ ψ ) F ( ψ , R ) ψ d ψ ,
F ( ψ , R ) = exp [ - 0 R c ( r ) d r + 0 R ( ψ r R , r ) d r ] ,
Σ ( ψ , r ) = b · S ( ψ ) ,
S ( ψ ) = 2 π J 0 ( 2 π θ ψ ) s ( θ ) θ d θ .
F ( ψ , R ) = exp [ - c R + b 0 R S ( ψ r R ) d r ] .
s ( θ ) = θ 0 2 π ( θ 0 2 + θ 2 ) 3 / 2 ,
S ( ψ ) = exp ( - 2 π θ 0 ψ ) ,
F ( ψ , R ) = exp { - c R + b R [ 1 - exp ( - 2 π θ 0 ψ ) 2 π θ 0 ψ ] } ,

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