Abstract

The point spread function (PSF) is an important property for predicting beam propagation and imaging system performance. Measurements of the PSF in three different locations (Pacific Ocean, Tongue of the Ocean, and Sargasso Sea) are presented. These measurements are used to validate extensive laboratory measurements [ S. Q. Duntley, “ Underwater Lighting by Submerged Lasers and Incandescent Sources,” SIO Ref. 71-1, Scripps Institution of Oceanography, U. California, San Diego ( 1971)]. In all three locations a simple exponential expression describes the angular variation of the PSF in the 4–100-mrad range. The exponent in this relationship has a simple location specific dependence on attenuation length and the ratio of the absorption to beam attenuation coefficient. These relationships can be used to predict the PSF for an arbitrary path length.

© 1991 Optical Society of America

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References

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  1. B. L. McGlamery, “Computer Analysis and Simulation of Underwater Camera System Performance,” SIO Ref. 75-2, Scripps Institution of Oceanography, U. California, San Diego (1975).
  2. 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]
  3. W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser.61 (NATO, 1973).
  4. T. J. Petzold, “Volume Scattering Functions for Selected Ocean Waters,” SIO Ref. 72-78, Scripps Institution of Oceanography, U. California, San Diego (1972).
  5. S. Q. Duntley, “Underwater Lighting by Submerged Lasers and Incandescent Sources,” SIO Ref. 71–1, Scripps Institution of Oceanography, U. California, San Diego (1971).
  6. 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).
  7. K. J. Voss, A. L. Chapin, “Measurement of the Point Spread Function in the Ocean,” Appl. Opt. 29, 3638–3642 (1990).
    [CrossRef] [PubMed]
  8. A. Morel, R. C. Smith, “Terminology and Units in Optical Oceanography,” Mar. Geod. 5, 335–349 (1982).
    [CrossRef]
  9. K. J. Voss, “Variability of the Point Spread Function in the Water Column,” Proc. Soc. Photo-Opt. Instrum. Eng. 1302, 355–362 (1990).
  10. J. Smart, Applied Physics Laboratory, Johns Hopkins U., Laurel, Md. 20707 (unpublished data, 1990).
  11. K. J. Voss, “Use of the Radiance Distribution to Measure the Optical Absorption Coefficient in the Ocean,” Limnol. Oceanogr. 34, 1614–1622 (1989).
    [CrossRef]

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).

1989 (1)

K. J. Voss, “Use of the Radiance Distribution to Measure the Optical Absorption Coefficient in the Ocean,” Limnol. Oceanogr. 34, 1614–1622 (1989).
[CrossRef]

1982 (1)

A. Morel, R. C. Smith, “Terminology and Units in Optical Oceanography,” Mar. Geod. 5, 335–349 (1982).
[CrossRef]

1979 (1)

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).

1977 (1)

Chapin, A. L.

Duntley, S. Q.

S. Q. Duntley, “Underwater Lighting by Submerged Lasers and Incandescent Sources,” SIO Ref. 71–1, Scripps Institution of Oceanography, U. California, San Diego (1971).

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).

McGlamery, B. L.

B. L. McGlamery, “Computer Analysis and Simulation of Underwater Camera System Performance,” SIO Ref. 75-2, Scripps Institution of Oceanography, U. California, San Diego (1975).

Mertens, L. E.

Morel, A.

A. Morel, R. C. Smith, “Terminology and Units in Optical Oceanography,” Mar. Geod. 5, 335–349 (1982).
[CrossRef]

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.

Smart, J.

J. Smart, Applied Physics Laboratory, Johns Hopkins U., Laurel, Md. 20707 (unpublished data, 1990).

Smith, R. C.

A. Morel, R. C. Smith, “Terminology and Units in Optical Oceanography,” Mar. Geod. 5, 335–349 (1982).
[CrossRef]

Voss, K. J.

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

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, “Use of the Radiance Distribution to Measure the Optical Absorption Coefficient in the Ocean,” Limnol. Oceanogr. 34, 1614–1622 (1989).
[CrossRef]

Wells, W. H.

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser.61 (NATO, 1973).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Limnol. Oceanogr. (1)

K. J. Voss, “Use of the Radiance Distribution to Measure the Optical Absorption Coefficient in the Ocean,” Limnol. Oceanogr. 34, 1614–1622 (1989).
[CrossRef]

Mar. Geod. (1)

A. Morel, R. C. Smith, “Terminology and Units in Optical Oceanography,” Mar. Geod. 5, 335–349 (1982).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

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

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).

Other (5)

B. L. McGlamery, “Computer Analysis and Simulation of Underwater Camera System Performance,” SIO Ref. 75-2, Scripps Institution of Oceanography, U. California, San Diego (1975).

J. Smart, Applied Physics Laboratory, Johns Hopkins U., Laurel, Md. 20707 (unpublished data, 1990).

W. H. Wells, “Theory of Small Angle Scattering,” in Optics of the Sea, AGARD Lect. Ser.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).

S. Q. Duntley, “Underwater Lighting by Submerged Lasers and Incandescent Sources,” SIO Ref. 71–1, Scripps Institution of Oceanography, U. California, San Diego (1971).

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Figures (9)

Fig. 1
Fig. 1

Illustration of PSF (a) and BSF (b) definitions. These illustrations show the geometry of the measurement along with the similarity of the two measurements.

Fig. 2
Fig. 2

Beam attenuation coefficient profiles from each location at ~500 nm. These profiles illustrate the differences in water column structure at these station locations, particularly the structure evident in the Pacific Ocean station.

Fig. 3
Fig. 3

PSF vs angle, showing the variability of the PSF with depth in an inhomogeneous water column, specifically the Pacific Ocean station. These data sets were taken at the same location within a period of 4 min. The variation is due to the structured water properties in this location; τ was 4.6, 3.1, and 2.4 for the 30-, 40-, and 50-m depths, respectively. The range was kept constant.

Fig. 4
Fig. 4

BSF calculated from the empirical formula. This formula was derived from a series of laboratory measurements.5 Parameters chosen were cr = 4, a/c = 0.1.

Fig. 5
Fig. 5

The m vs τ calculated with the empirical formula.

Fig. 6
Fig. 6

The m vs τ derived from the coastal Pacific Ocean data set.

Fig. 7
Fig. 7

The m vs τ derived from the Sargasso Sea data set.

Fig. 8
Fig. 8

The m vs τ derived from the TOTO data set.

Fig. 9
Fig. 9

The B vs a/c for calculated values. Also illustrated are the B terms for the field measurements.

Tables (1)

Tables Icon

Table I Regressions for the Field Measurements of the Slope of the PSF(m) vs Attenuation Length(τ)

Equations (4)

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BSF ( θ ) = E ( θ ) P = 10 ( A - C ) θ B 2 π r 2 sin θ ,
PSF ( θ ) = B 1 θ - m ,
τ = z 1 z 2 c ( z ) d z / cos ψ ,
c r = τ - log ( A / 2.158 ) / B .

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