Abstract

In this article a performance bound is derived for feasible image resolution among a class of imaging systems that can be referred to as synchronous laser line scan systems. Most often, these systems use a narrow beam projected source (typically a laser) in conjunction with a very small field of view receiver that is synchronously scanned. Here, a bound on the maximum system resolution is derived when both source and receiver are “delta function like”. The bound demonstrates that the best achievable overall system point spread function is the square of the one way point spread function for the medium.

©2005 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, 2nd edition, (McGraw Hill, Massachusetts, 1996).
  2. T. Wilson, T., and C. Sheppard, Theory and Practice of Scanning Optical Microscopy, (Associated Press, London, U.K, 1984).
  3. J. S. Jaffe, “Computer Modeling and the Design of Optimal Underwater Imaging Systems,” IEEE J. of Ocean Engineering 15, 101–111 (1990).
    [Crossref]
  4. J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
    [Crossref]
  5. E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium, (Springer Verlag, Berlin, Germany, 1991)
    [Crossref]
  6. K. S. Schifrin, “Physical Optics of Ocean Water,” (American Institute of Physics, New York, 1988)
  7. C. D. Mobley, “Light and Water. Radiative Transfer in Natural Waters,” (Academic Press, New York, 1994).
  8. B. J. McGlamery , “A Computer Model for Underwater Camera Systems,” in Ocean Optics VI, S. Q. Duntley, Ed., SPIE28, (1979).
  9. J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation: Validity of the Linear and Small-angle Approximations,” Applied Optics. 34, 5413–5421, (1995).
    [Crossref] [PubMed]
  10. R. W. Preisendorfer, “Hydrologic Optics, Vol II: Foundations,” Honolulu, HI: U. S. Dept of Commerce, (1976).
  11. K. J. Voss, “Simple Empirical Model of the Oceanic Point Spread Function,” Applied Optics 30, 2647–2651, (1991).
    [Crossref] [PubMed]
  12. W. H. Wells, “Loss of resolution in water as a result of Multiple Small-Angle Scattering,” J. Opt. Soc. Amer. 59, 686–691, (1969).
    [Crossref]
  13. J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation - Validity of the linear and small angle approximations,” Applied Optics 34, 5413–5421, (1995)
    [Crossref] [PubMed]
  14. K. D. Moore, J. S. Jaffe, and B. L Ochoa, ‘Development of a new underwater bathymetric laser imaging system: L-bath,” Journal of Atmospheric & Oceanic Technology 17, 1106–1117, (2000).
    [Crossref]
  15. K. D. Moore and J. S. Jaffe, “Time-evolution of high-resolution topographic measurements of the sea floor using a 3-D laser line scan mapping system,” IEEE Journal of Oceanic Engineering 27, 525–545, (2002).
    [Crossref]

2002 (2)

J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
[Crossref]

K. D. Moore and J. S. Jaffe, “Time-evolution of high-resolution topographic measurements of the sea floor using a 3-D laser line scan mapping system,” IEEE Journal of Oceanic Engineering 27, 525–545, (2002).
[Crossref]

2000 (1)

K. D. Moore, J. S. Jaffe, and B. L Ochoa, ‘Development of a new underwater bathymetric laser imaging system: L-bath,” Journal of Atmospheric & Oceanic Technology 17, 1106–1117, (2000).
[Crossref]

1995 (2)

J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation - Validity of the linear and small angle approximations,” Applied Optics 34, 5413–5421, (1995)
[Crossref] [PubMed]

J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation: Validity of the Linear and Small-angle Approximations,” Applied Optics. 34, 5413–5421, (1995).
[Crossref] [PubMed]

1991 (1)

K. J. Voss, “Simple Empirical Model of the Oceanic Point Spread Function,” Applied Optics 30, 2647–2651, (1991).
[Crossref] [PubMed]

1990 (1)

J. S. Jaffe, “Computer Modeling and the Design of Optimal Underwater Imaging Systems,” IEEE J. of Ocean Engineering 15, 101–111 (1990).
[Crossref]

1969 (1)

W. H. Wells, “Loss of resolution in water as a result of Multiple Small-Angle Scattering,” J. Opt. Soc. Amer. 59, 686–691, (1969).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd edition, (McGraw Hill, Massachusetts, 1996).

Ivanov, A. P.

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium, (Springer Verlag, Berlin, Germany, 1991)
[Crossref]

Jaffe, J. S.

J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
[Crossref]

K. D. Moore and J. S. Jaffe, “Time-evolution of high-resolution topographic measurements of the sea floor using a 3-D laser line scan mapping system,” IEEE Journal of Oceanic Engineering 27, 525–545, (2002).
[Crossref]

K. D. Moore, J. S. Jaffe, and B. L Ochoa, ‘Development of a new underwater bathymetric laser imaging system: L-bath,” Journal of Atmospheric & Oceanic Technology 17, 1106–1117, (2000).
[Crossref]

J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation - Validity of the linear and small angle approximations,” Applied Optics 34, 5413–5421, (1995)
[Crossref] [PubMed]

J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation: Validity of the Linear and Small-angle Approximations,” Applied Optics. 34, 5413–5421, (1995).
[Crossref] [PubMed]

J. S. Jaffe, “Computer Modeling and the Design of Optimal Underwater Imaging Systems,” IEEE J. of Ocean Engineering 15, 101–111 (1990).
[Crossref]

Katsev, I. L.

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium, (Springer Verlag, Berlin, Germany, 1991)
[Crossref]

McClean, J.

J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
[Crossref]

McGlamery, B. J.

B. J. McGlamery , “A Computer Model for Underwater Camera Systems,” in Ocean Optics VI, S. Q. Duntley, Ed., SPIE28, (1979).

Mobley, C. D.

C. D. Mobley, “Light and Water. Radiative Transfer in Natural Waters,” (Academic Press, New York, 1994).

Moore, K. D.

J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
[Crossref]

K. D. Moore and J. S. Jaffe, “Time-evolution of high-resolution topographic measurements of the sea floor using a 3-D laser line scan mapping system,” IEEE Journal of Oceanic Engineering 27, 525–545, (2002).
[Crossref]

K. D. Moore, J. S. Jaffe, and B. L Ochoa, ‘Development of a new underwater bathymetric laser imaging system: L-bath,” Journal of Atmospheric & Oceanic Technology 17, 1106–1117, (2000).
[Crossref]

Ochoa, B. L

K. D. Moore, J. S. Jaffe, and B. L Ochoa, ‘Development of a new underwater bathymetric laser imaging system: L-bath,” Journal of Atmospheric & Oceanic Technology 17, 1106–1117, (2000).
[Crossref]

Preisendorfer, R. W.

R. W. Preisendorfer, “Hydrologic Optics, Vol II: Foundations,” Honolulu, HI: U. S. Dept of Commerce, (1976).

Schifrin, K. S.

K. S. Schifrin, “Physical Optics of Ocean Water,” (American Institute of Physics, New York, 1988)

Sheppard, C.

T. Wilson, T., and C. Sheppard, Theory and Practice of Scanning Optical Microscopy, (Associated Press, London, U.K, 1984).

Strand, M. P.

J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
[Crossref]

T.,

T. Wilson, T., and C. Sheppard, Theory and Practice of Scanning Optical Microscopy, (Associated Press, London, U.K, 1984).

Voss, K. J.

K. J. Voss, “Simple Empirical Model of the Oceanic Point Spread Function,” Applied Optics 30, 2647–2651, (1991).
[Crossref] [PubMed]

Wells, W. H.

W. H. Wells, “Loss of resolution in water as a result of Multiple Small-Angle Scattering,” J. Opt. Soc. Amer. 59, 686–691, (1969).
[Crossref]

Wilson, T.

T. Wilson, T., and C. Sheppard, Theory and Practice of Scanning Optical Microscopy, (Associated Press, London, U.K, 1984).

Zege, E. P.

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium, (Springer Verlag, Berlin, Germany, 1991)
[Crossref]

Applied Optics (2)

K. J. Voss, “Simple Empirical Model of the Oceanic Point Spread Function,” Applied Optics 30, 2647–2651, (1991).
[Crossref] [PubMed]

J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation - Validity of the linear and small angle approximations,” Applied Optics 34, 5413–5421, (1995)
[Crossref] [PubMed]

Applied Optics. (1)

J. S. Jaffe, “Monte Carlo Modeling of Underwater Image Formation: Validity of the Linear and Small-angle Approximations,” Applied Optics. 34, 5413–5421, (1995).
[Crossref] [PubMed]

IEEE J. of Ocean Engineering (1)

J. S. Jaffe, “Computer Modeling and the Design of Optimal Underwater Imaging Systems,” IEEE J. of Ocean Engineering 15, 101–111 (1990).
[Crossref]

IEEE Journal of Oceanic Engineering (1)

K. D. Moore and J. S. Jaffe, “Time-evolution of high-resolution topographic measurements of the sea floor using a 3-D laser line scan mapping system,” IEEE Journal of Oceanic Engineering 27, 525–545, (2002).
[Crossref]

J. Opt. Soc. Amer. (1)

W. H. Wells, “Loss of resolution in water as a result of Multiple Small-Angle Scattering,” J. Opt. Soc. Amer. 59, 686–691, (1969).
[Crossref]

Journal of Atmospheric & Oceanic Technology (1)

K. D. Moore, J. S. Jaffe, and B. L Ochoa, ‘Development of a new underwater bathymetric laser imaging system: L-bath,” Journal of Atmospheric & Oceanic Technology 17, 1106–1117, (2000).
[Crossref]

Oceanography (1)

J. S. Jaffe, J. McClean, M. P. Strand, and K. D. Moore, “Underwater Optical Imaging: Status and Prospects,” Oceanography 14, 64–75 (2002).
[Crossref]

Other (7)

E. P. Zege, A. P. Ivanov, and I. L. Katsev, Image Transfer through a Scattering Medium, (Springer Verlag, Berlin, Germany, 1991)
[Crossref]

K. S. Schifrin, “Physical Optics of Ocean Water,” (American Institute of Physics, New York, 1988)

C. D. Mobley, “Light and Water. Radiative Transfer in Natural Waters,” (Academic Press, New York, 1994).

B. J. McGlamery , “A Computer Model for Underwater Camera Systems,” in Ocean Optics VI, S. Q. Duntley, Ed., SPIE28, (1979).

R. W. Preisendorfer, “Hydrologic Optics, Vol II: Foundations,” Honolulu, HI: U. S. Dept of Commerce, (1976).

J. W. Goodman, Introduction to Fourier Optics, 2nd edition, (McGraw Hill, Massachusetts, 1996).

T. Wilson, T., and C. Sheppard, Theory and Practice of Scanning Optical Microscopy, (Associated Press, London, U.K, 1984).

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Figures (4)

Fig. 1.
Fig. 1. (a) An example of a laser line scan system deployed on an underwater vehicle. (b) A simplified schematic diagram of the four-receiver LLS sensor which has been used for either fluorescence or color imaging. The diagram shows the optics associated with propagating a single color laser into the water and then receiving it on a set of 4 channels, each with its own PMT. (Reprinted courtesy of [4]).
Fig. 2.
Fig. 2. A diagram to illustrate the geometry of the approach taken. Starting on the left, the figure shows the projection of the source onto the plane (x0,y0) resulting in the light field I(x0,y0)=wT. This irradiance is then propagated to the right to just before plane (x1,y1) to obtain I-(x1,y1) by convolving this with the point spread function (psf) of the medium. The light is then attenuated by the screen T(x1,y1) via multiplication to yield light distribution I+(x1,y1). Propagation to the plane (x2,y2) occurs via convolution with the psf to yield light distribution I(x2,y2). This light field is then integrated over the region shown as wR (the small circle inside the ellipse) to yield a single value for the image. An image can be formed by translating the attenuating screen by (x’,y’): T(x1- x’,y1-x’) in order to obtain I(x’,y’).
Fig. 3.
Fig. 3. (a) A 3-dimensional model of the scanning laser system used for the simulations. (b) A schematic diagram illustrating the basic components of the system in (a).
Fig. 4.
Fig. 4. A comparison of the absolute values of the Fourier Transforms for the conventional imaging system (red) versus the scanning system (blue) for the four data sets. The total attenuation values for the environmental conditions are shown in Table 1.

Tables (1)

Tables Icon

Table 1. The total attenuation coefficients measured for the experiments

Equations (20)

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I ( x , y ; d ) = I ( x , y ; 0 ) ( exp ( cd ) δ ( x , y ) + g ( x , y ; d ) ) ,
g ( x , y ; d ) = ( exp ( Gd ) exp ( cd ) ) 1 { exp ( Bdf ) } .
I ( x 1 , y 1 ) = psf ( x 0 , y 0 , x 1 , y 1 ; d ) w T ( x 0 , y 0 ) .
I + ( x 1 , y 1 ) = I ( x 1 , y 1 ) T ( x 1 , y 1 ) .
I ( x 2 , y 2 ) = psf ( x 1 , y 1 , x 2 , y 2 : d ) I + ( x 1 , y 1 )
I ( x , y ) = w R ( x 2 , y 2 ) I ( x 2 , y 2 ) d x 2 d y 2
I ( x , y ) = w R ( x 2 , y 2 ) psf ( x 1 , y 1 , x 2 , y 2 : d ) psf ( x 0 , y 0 , x 1 , y 1 : d ) w T ( x 0 , y 0 ) T ( x x 1 , y y 1 ) d x 2 d y 2 .
I ( x , y ) =
w R ( x 2 , y 2 ) w T ( x 0 , y 0 ) psf ( x 2 x 1 , y 2 y 1 : d ) psf ( x 1 x 0 , y 1 y 0 : d ) T ( x x 1 , y y 1 ) d x 0 d y 0 d x 1 d y 1 d x 2 d y 2 .
w R ( x 2 , y 2 ) psf ( x 2 x 1 , y 2 y 1 : d ) d x 2 d y 2 = w R ( x 2 , y 2 ) psf ( x 2 , y 2 , x 1 , y 1 : d ) .
w RP ( x 1 , y 1 : d ) = w R ( x 2 , y 2 ) psf ( x 2 , y 2 , x 1 , y 1 : d )
I ( x , y ) = w RP ( x 1 , y 1 : d ) w T ( x 0 , y 0 ) psf ( x 1 x 0 , y 1 y 0 : d ) T ( x x 1 , y y 1 ) d x 0 d y 0 d x 1 d y 1 .
w TP ( x 1 , y 1 :d)= w T ( x 0 , y 0 )psf( x 1 x 0 , y 1 y 0 :d)d x 0 d y 0 = w T ( x 0 , y 0 )psf( x 1 , y 1 , x 0 , y 0 :d)
I ( x , y ) = w RP ( x 1 , y 1 : d ) w TP ( x 1 , y 1 : d ) T ( x x 1 , y y 1 ) d x 1 d y 1 .
w RP , TR ( x 1 , y 1 : d ) = w RP ( x 1 , y 1 : d ) w TP ( x 1 , y 1 : d ) , so that
I ( x , y ) = w RP , TR ( x 1 , y 1 : d ) T ( x 1 , y 1 , x , y ) .
w RP , TR ( x 1 , y 1 : d ) = psf ( x 1 , y 1 : d ) psf ( x 1 , y 1 : d ) = ( psf ( x 1 , y 1 : d ) ) 2 ,
w RP , TR ( x 1 , y 1 : d ) = C psf ( x 1 , y 1 : d ) ( Case 2 )
w RP , TR ( x 1 , y 1 : d ) = C psf ( x 1 , y 1 : = d ) ( Case 3 )
w RP , TR ( x 1 , y 1 : d ) = C 2 .

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