Abstract

A method for simulating sea surface images obtained by forward-looking infrared (FLIR) sensors in the 8–12-μm band, which can be readily implemented on a computer, has been developed. The model consists of a bottom-up process based on oceanographic models of sea waves and radiometric properties of sky and sea. The clutter which is generated by sea surface roughness and nonuniformity of sky radiation has been found to be a Gaussian homogeneous random process, under reasonable assumptions. The variance of this process as well as its spatial correlation has been investigated. The value of the method as a synthetic image generator and the application of the results to FLIR image processing are discussed.

© 1984 Optical Society of America

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References

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  1. J. Otazo, R. Parenti, “Digital Filters for the Detection of Resolved and Unresolved Targets Embedded in IR Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 178, 13 (1979).
  2. N. Ben-Yosef, B. Rahat, G. Feigin, “Simulation of IR Images of Natural Backgrounds,” Appl. Opt. 22, 190 (1983).
    [CrossRef] [PubMed]
  3. B. Kinsman, Wind Waves (Prentice-Hall, Englewood Cliffs, N.J., 1965).
  4. M. S. Longuet-Higgins, “The Statistical Analysis of a Random Moving Surface,” Philos. Trans. R. Soc. London Ser. A 249, 321 (1957).
    [CrossRef]
  5. M. S. Longuet-Higgins, “On the Statistical Distribution of the Heights of Sea Waves,” J. Mar. Res. 11, 245 (1952).
  6. G. Neumann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1966), pp. 336–346.
  7. C. Cox, W. Munk, “Statistics of the Sea Surface Derived from Sun Glitter,” J. Mar. Res. 16, 199 (1954).
  8. P. M. Saunders, “Infrared Radiance of Sea and Sky, 800–1200 cm−1,” J. Opt. Soc. Am. 58, 645 (1968).
    [CrossRef]
  9. P. M. Saunders, “Shadowing on the Ocean and the Existence of the Horizon,” J. Geophys. Res. 72, 4643 (1967).
    [CrossRef]
  10. L. J. Free, “Background Noise Measurements at the Sea Horizon,” J. Opt. Soc. Am. 49, 1007 (1958).
    [CrossRef]
  11. B. F. Andresen, “An Investigation of Correlation Properties of Fluctuations in Sea-Surface Infrared Radiation,” Internal Report E-165, Norwegian Defense Research Establishment (1964).
  12. W. Futterman, R. Benson, “Infra-Red Scene Generation and Analytical Statistical Modeling,” Proc. Soc. Photo-Opt. Instrum. Eng. 253, 107 (1980).
  13. J. J. Simpson, C. A. Paulson, “Small Scale Sea Surface Temperature Structure,” J. Phys. Ocean 10, 399 (1980).
    [CrossRef]
  14. D. Wilson, “A Method of Computing Ship Contrast Temperatures,” NTIS AD-A078794 (1979).
  15. R. D. Chapman, G. B. Irani, “Errors in Estimating Slope Spectra from Wave Images,” Appl. Opt. 20, 3645 (1981).
    [CrossRef] [PubMed]

1983 (1)

1981 (1)

1980 (2)

W. Futterman, R. Benson, “Infra-Red Scene Generation and Analytical Statistical Modeling,” Proc. Soc. Photo-Opt. Instrum. Eng. 253, 107 (1980).

J. J. Simpson, C. A. Paulson, “Small Scale Sea Surface Temperature Structure,” J. Phys. Ocean 10, 399 (1980).
[CrossRef]

1979 (2)

D. Wilson, “A Method of Computing Ship Contrast Temperatures,” NTIS AD-A078794 (1979).

J. Otazo, R. Parenti, “Digital Filters for the Detection of Resolved and Unresolved Targets Embedded in IR Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 178, 13 (1979).

1968 (1)

1967 (1)

P. M. Saunders, “Shadowing on the Ocean and the Existence of the Horizon,” J. Geophys. Res. 72, 4643 (1967).
[CrossRef]

1958 (1)

1957 (1)

M. S. Longuet-Higgins, “The Statistical Analysis of a Random Moving Surface,” Philos. Trans. R. Soc. London Ser. A 249, 321 (1957).
[CrossRef]

1954 (1)

C. Cox, W. Munk, “Statistics of the Sea Surface Derived from Sun Glitter,” J. Mar. Res. 16, 199 (1954).

1952 (1)

M. S. Longuet-Higgins, “On the Statistical Distribution of the Heights of Sea Waves,” J. Mar. Res. 11, 245 (1952).

Andresen, B. F.

B. F. Andresen, “An Investigation of Correlation Properties of Fluctuations in Sea-Surface Infrared Radiation,” Internal Report E-165, Norwegian Defense Research Establishment (1964).

Benson, R.

W. Futterman, R. Benson, “Infra-Red Scene Generation and Analytical Statistical Modeling,” Proc. Soc. Photo-Opt. Instrum. Eng. 253, 107 (1980).

Ben-Yosef, N.

Chapman, R. D.

Cox, C.

C. Cox, W. Munk, “Statistics of the Sea Surface Derived from Sun Glitter,” J. Mar. Res. 16, 199 (1954).

Feigin, G.

Free, L. J.

Futterman, W.

W. Futterman, R. Benson, “Infra-Red Scene Generation and Analytical Statistical Modeling,” Proc. Soc. Photo-Opt. Instrum. Eng. 253, 107 (1980).

Irani, G. B.

Kinsman, B.

B. Kinsman, Wind Waves (Prentice-Hall, Englewood Cliffs, N.J., 1965).

Longuet-Higgins, M. S.

M. S. Longuet-Higgins, “The Statistical Analysis of a Random Moving Surface,” Philos. Trans. R. Soc. London Ser. A 249, 321 (1957).
[CrossRef]

M. S. Longuet-Higgins, “On the Statistical Distribution of the Heights of Sea Waves,” J. Mar. Res. 11, 245 (1952).

Munk, W.

C. Cox, W. Munk, “Statistics of the Sea Surface Derived from Sun Glitter,” J. Mar. Res. 16, 199 (1954).

Neumann, G.

G. Neumann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1966), pp. 336–346.

Otazo, J.

J. Otazo, R. Parenti, “Digital Filters for the Detection of Resolved and Unresolved Targets Embedded in IR Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 178, 13 (1979).

Parenti, R.

J. Otazo, R. Parenti, “Digital Filters for the Detection of Resolved and Unresolved Targets Embedded in IR Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 178, 13 (1979).

Paulson, C. A.

J. J. Simpson, C. A. Paulson, “Small Scale Sea Surface Temperature Structure,” J. Phys. Ocean 10, 399 (1980).
[CrossRef]

Pierson, W. J.

G. Neumann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1966), pp. 336–346.

Rahat, B.

Saunders, P. M.

P. M. Saunders, “Infrared Radiance of Sea and Sky, 800–1200 cm−1,” J. Opt. Soc. Am. 58, 645 (1968).
[CrossRef]

P. M. Saunders, “Shadowing on the Ocean and the Existence of the Horizon,” J. Geophys. Res. 72, 4643 (1967).
[CrossRef]

Simpson, J. J.

J. J. Simpson, C. A. Paulson, “Small Scale Sea Surface Temperature Structure,” J. Phys. Ocean 10, 399 (1980).
[CrossRef]

Wilson, D.

D. Wilson, “A Method of Computing Ship Contrast Temperatures,” NTIS AD-A078794 (1979).

Appl. Opt. (2)

J. Geophys. Res. (1)

P. M. Saunders, “Shadowing on the Ocean and the Existence of the Horizon,” J. Geophys. Res. 72, 4643 (1967).
[CrossRef]

J. Mar. Res. (2)

M. S. Longuet-Higgins, “On the Statistical Distribution of the Heights of Sea Waves,” J. Mar. Res. 11, 245 (1952).

C. Cox, W. Munk, “Statistics of the Sea Surface Derived from Sun Glitter,” J. Mar. Res. 16, 199 (1954).

J. Opt. Soc. Am. (2)

J. Phys. Ocean (1)

J. J. Simpson, C. A. Paulson, “Small Scale Sea Surface Temperature Structure,” J. Phys. Ocean 10, 399 (1980).
[CrossRef]

NTIS AD-A078794 (1)

D. Wilson, “A Method of Computing Ship Contrast Temperatures,” NTIS AD-A078794 (1979).

Philos. Trans. R. Soc. London Ser. A (1)

M. S. Longuet-Higgins, “The Statistical Analysis of a Random Moving Surface,” Philos. Trans. R. Soc. London Ser. A 249, 321 (1957).
[CrossRef]

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

J. Otazo, R. Parenti, “Digital Filters for the Detection of Resolved and Unresolved Targets Embedded in IR Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 178, 13 (1979).

W. Futterman, R. Benson, “Infra-Red Scene Generation and Analytical Statistical Modeling,” Proc. Soc. Photo-Opt. Instrum. Eng. 253, 107 (1980).

Other (3)

B. F. Andresen, “An Investigation of Correlation Properties of Fluctuations in Sea-Surface Infrared Radiation,” Internal Report E-165, Norwegian Defense Research Establishment (1964).

B. Kinsman, Wind Waves (Prentice-Hall, Englewood Cliffs, N.J., 1965).

G. Neumann, W. J. Pierson, Principles of Physical Oceanography (Prentice-Hall, Englewood Cliffs, N.J., 1966), pp. 336–346.

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Figures (6)

Fig. 1
Fig. 1

Geometry in spatial frequency plane (u,v) as used in generating the slope pictures. The four discrete components (±mΔk, ±nΔk) are indexed (m,n) in the computational procedure depicted in Fig. 2. These components are arranged in two pairs: ±(mΔk,nΔk), ±(mΔk,−nΔk). The wind vector is used as an axis for amplitude symmetry and phase antisymmetry (which ensures real slope values) for each pair. The amplitude values are determined by m, n, ψ, TET1, and TET2 in a manner depicted in Fig. 2.

Fig. 2
Fig. 2

Computational procedure for generating slope pictures where V = wind velocity (m/sec), ψ = azimuth offset angle between the LOS and wind direction (radian), K = wave number (m−1), and ΔK = spectral resolution (m−1).

Fig. 3
Fig. 3

Viewing geometry as seen in a plane perpendicular to the sea plane and containing the line of sight.

Fig. 4
Fig. 4

Computational procedure for generating the image from SX,SY slope arrays.

Fig. 5
Fig. 5

Standard deviation of sea clutter (σc) for ψ = 0 as a function of sensor depression angle (φ), for various wind velocities (V), as predicted by the model.

Fig. 6
Fig. 6

Standard deviation of sea clutter (σc) for V = 10 m/sec as a function of sensor depression angle (φ) for various azimuth offset angles (ψ), as predicted by the model. The dashed line represents an interpolation of Saunders’s8 results.

Tables (3)

Tables Icon

Table I Fixed Model Parameters Used in the Simulations

Tables Icon

Table II Spatial Correlation Coefficients Along Picture Horizontal Dimension as a Function of Wind Velocity (for a Zero Offset Angle)

Tables Icon

Table III Spatial Correlation Coefficients Along Picture Horizontal Dimension as a Function of Offset Angle (for a 10-m/sec Wind)

Equations (12)

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N t ( λ ) = τ ( λ ) ɛ ( λ ) N b b ( λ , T sea ) + τ ( λ ) ρ ( λ ) N sky ( λ ) + N A ( λ ) ,
N t ¯ = τ ¯ · ɛ ¯ · N b b ¯ ( T sea ) + τ ¯ · ρ ¯ · N s k y ¯ + N A ¯ ,
ρ ¯ + ɛ ¯ = 1.
ɛ ¯ ( ω ) = 0.98 [ 1 - ( 1 - cos ω ) 5 ] .
N sky ( μ ) = A - B exp [ - C ( Z - 1 ) ] ,
Z = ( 4.9 × 10 5 cos 2 μ + 1401 ) 1 / 2 - 700 cos μ .
tan S X = tan β cos α
tan S Y = tan β sin α .
cos ω = cos β sin φ - cos α cos φ sin β ,
cos μ = 2 cos β cos ω - sin φ .
N H = [ R Δ ] ϑ A Z / Δ X ] ,
N V = [ ( R Δ ϑ E L ) / ( Δ X sin φ ) ] ,

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