Abstract

An analytic model is developed for the mean and clutter infrared radiance emitted from the ocean surface near the horizon and in the presence of solar glint. The model is based on the identification of a characteristic facet dimension over which the ocean surface is essentially flat. Fluctuations in the facet orientation generated by the water wave motion are modeled by a parameterized wave height power spectral density that provides the two orthogonal wave slope variances. The mean and root-mean-square facet radiances are calculated with Gaussian probability-density functions for the wave slopes. One can determine the number of facets within the field of view of a single detector by estimating the exposed ocean area and dividing by the facet area. This estimation takes into account shadowing effects of the swell wave, the swell wavelength, and the transverse detector field of view. The number of exposed facets together with the central-limit theorem permits computation of the radiance clutter as a function of look-down angle below the horizon. Vertical radiance profiles, parameterized by the azimuthal offset from the solar position, are calculated over a sensor look-down angle range of ±50 mrad about the horizon. The results of this analysis are compared with infrared radiance measurements of the ocean surface near the horizon and in the presence of solar glint. Agreement between the measured and calculated values of the mean and clutter radiances is good.

© 1994 Optical Society of America

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    [CrossRef]
  2. D. J. Gambling, “Sunglitter on the surface of the ocean in the infrared spectral region,” Infrared Phys. 15, 149–155 (1975).
    [CrossRef]
  3. A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation: preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
    [CrossRef]
  4. I. Wilf, Y. Manor, “Simulation of sea surface images in the infrared,” Appl. Opt. 23, 3174–3180 (1984).
    [CrossRef] [PubMed]
  5. R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Ocean. 16, 1293–1316 (1986).
    [CrossRef]
  6. F. G. Wollenweber, “Infrared sea radiance modeling using lowtran 6,” in Optical Infrared, Millimeter Wave Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.926, 213–220 (1988).
    [CrossRef]
  7. A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
    [CrossRef]
  8. P. Davis, A. Daniell, M. Farber, S. Hemple, “Infrared ocean clutter at low grazing angles: data analysis results and 1-D simulation,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1992), pp. 307–325.
  9. B. B. Ball, SYNSEA code for generating synthetic IR imagery of sea backgrounds,” in Characterization, Propagation, and Simulation of Sources and Backgrounds II, D. Clement, W. R. Watkins, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1687, 289–299 (1992).
    [CrossRef]
  10. E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.
  11. F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).
  12. E. H. Takken, R. G. Priest, E. P. Shettle, J. C. Kershenstein, “IR horizon phenomenology: report on IRAMMP field test,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination, ERIM document 213400-78-X(I) (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1991).
  13. G. R. Fowler, Introduction to Modern Optics (Holt, Rinehart & Winston, New York, 1975), Chap. 6.
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  15. J. S. Hornstein, E. H. Takken, R. G. Priest, D. Baukman, “Models of refraction in the marine atmospheric surface layer,” NRL Tech. Rep. 93-9547 (Naval Research Laboratory, Washington, D.C., 1993).
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    [CrossRef]
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    [CrossRef] [PubMed]
  20. F. G. Wollenweber, “Impact of atmospheric layering on lowtran 6 radiance calculations,” Appl. Opt. 29, 5177–5181 (1990).
    [CrossRef] [PubMed]
  21. M. A. Donelan, W. H. Hui, “Mechanics of ocean surface waves,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 209–246.
    [CrossRef]
  22. M. A. Donelan, W. J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry,” J. Geophys. Res. 92(C5), 4971–5028 (1987).
    [CrossRef]
  23. M. A. Srokosz, “Wave statistics,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 285–332.
    [CrossRef]
  24. C. Cox, W. Munk, “Measurement of the roughness of the sea surface from photographs of the Sun's glitter,” J. Opt. Soc. Am. 44, 838–850 (1954).
    [CrossRef]
  25. J. Mandel, The Statistical Analysis of Experimental Data, (Dover, New York, 1964), Chap. 4.

1990 (1)

1988 (1)

J. L. Walmsley, “On theoretical wind speed and temperature profiles over the sea with applications to data from Sable Island, Nova Scotia,” Atmos. Ocean 26, 203–233 (1988).
[CrossRef]

1987 (2)

R. G. Isaacs, W. C. Wang, R. D. Worsham, S. Goldberg, “Multiple scattering lowtran and fascode models,” Appl. Opt. 26, 1272–1282 (1987).
[CrossRef] [PubMed]

M. A. Donelan, W. J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry,” J. Geophys. Res. 92(C5), 4971–5028 (1987).
[CrossRef]

1986 (1)

R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Ocean. 16, 1293–1316 (1986).
[CrossRef]

1984 (1)

1981 (2)

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation: preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

K. L. Davidson, G. E. Schacher, C. W. Fairall, A. K. Goroch, “Verification of the bulk method for calculating overwater optical turbulence,” Appl. Opt. 20, 2919–2924 (1981).
[CrossRef] [PubMed]

1975 (1)

D. J. Gambling, “Sunglitter on the surface of the ocean in the infrared spectral region,” Infrared Phys. 15, 149–155 (1975).
[CrossRef]

1968 (1)

1954 (1)

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Anderson, G. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Ball, B. B.

B. B. Ball, SYNSEA code for generating synthetic IR imagery of sea backgrounds,” in Characterization, Propagation, and Simulation of Sources and Backgrounds II, D. Clement, W. R. Watkins, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1687, 289–299 (1992).
[CrossRef]

Baukman, D.

J. S. Hornstein, E. H. Takken, R. G. Priest, D. Baukman, “Models of refraction in the marine atmospheric surface layer,” NRL Tech. Rep. 93-9547 (Naval Research Laboratory, Washington, D.C., 1993).

Ben-Shalom, A.

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation: preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 3.

Caulfield, J. T.

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Clough, S. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Cooper, A. W.

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

Cox, C.

Crittenden, E. C.

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

Daniell, A.

P. Davis, A. Daniell, M. Farber, S. Hemple, “Infrared ocean clutter at low grazing angles: data analysis results and 1-D simulation,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1992), pp. 307–325.

Davidson, K. L.

Davis, P.

P. Davis, A. Daniell, M. Farber, S. Hemple, “Infrared ocean clutter at low grazing angles: data analysis results and 1-D simulation,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1992), pp. 307–325.

Donelan, M. A.

M. A. Donelan, W. J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry,” J. Geophys. Res. 92(C5), 4971–5028 (1987).
[CrossRef]

M. A. Donelan, W. H. Hui, “Mechanics of ocean surface waves,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 209–246.
[CrossRef]

Fairall, C. W.

Farber, M.

P. Davis, A. Daniell, M. Farber, S. Hemple, “Infrared ocean clutter at low grazing angles: data analysis results and 1-D simulation,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1992), pp. 307–325.

Fowler, G. R.

G. R. Fowler, Introduction to Modern Optics (Holt, Rinehart & Winston, New York, 1975), Chap. 6.

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Gambling, D. J.

D. J. Gambling, “Sunglitter on the surface of the ocean in the infrared spectral region,” Infrared Phys. 15, 149–155 (1975).
[CrossRef]

Goldberg, S.

Goroch, A. K.

Gregoris, D.

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

Hemple, S.

P. Davis, A. Daniell, M. Farber, S. Hemple, “Infrared ocean clutter at low grazing angles: data analysis results and 1-D simulation,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1992), pp. 307–325.

Hornstein, J. S.

J. S. Hornstein, E. H. Takken, R. G. Priest, D. Baukman, “Models of refraction in the marine atmospheric surface layer,” NRL Tech. Rep. 93-9547 (Naval Research Laboratory, Washington, D.C., 1993).

Hui, W. H.

M. A. Donelan, W. H. Hui, “Mechanics of ocean surface waves,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 209–246.
[CrossRef]

Isaacs, R. G.

Kershenstein, J. C.

E. H. Takken, R. G. Priest, E. P. Shettle, J. C. Kershenstein, “IR horizon phenomenology: report on IRAMMP field test,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination, ERIM document 213400-78-X(I) (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1991).

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Mandel, J.

J. Mandel, The Statistical Analysis of Experimental Data, (Dover, New York, 1964), Chap. 4.

Manor, Y.

Mermelstein, M. D.

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

Milne, F. A.

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

Mobley, C. D.

R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Ocean. 16, 1293–1316 (1986).
[CrossRef]

Moss, E.

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

Munk, W.

Otterman, J.

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation: preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Paulus, R. A.

R. A. Paulus, “Specification for evaporation duct height calculations,” NOSC Technical Document 1596 (Naval Ocean Systems Command, San Diego, Calif., 1989).

Pierson, W. J.

M. A. Donelan, W. J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry,” J. Geophys. Res. 92(C5), 4971–5028 (1987).
[CrossRef]

Preisendorfer, R. W.

R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Ocean. 16, 1293–1316 (1986).
[CrossRef]

Priest, R. G.

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

E. H. Takken, R. G. Priest, E. P. Shettle, J. C. Kershenstein, “IR horizon phenomenology: report on IRAMMP field test,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination, ERIM document 213400-78-X(I) (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1991).

J. S. Hornstein, E. H. Takken, R. G. Priest, D. Baukman, “Models of refraction in the marine atmospheric surface layer,” NRL Tech. Rep. 93-9547 (Naval Research Laboratory, Washington, D.C., 1993).

Saunders, P. M.

Schacher, G. E.

Schechner, P.

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation: preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

E. H. Takken, R. G. Priest, E. P. Shettle, J. C. Kershenstein, “IR horizon phenomenology: report on IRAMMP field test,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination, ERIM document 213400-78-X(I) (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1991).

Srokosz, M. A.

M. A. Srokosz, “Wave statistics,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 285–332.
[CrossRef]

Stone, E. J.

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

Takken, E. H.

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

E. H. Takken, R. G. Priest, E. P. Shettle, J. C. Kershenstein, “IR horizon phenomenology: report on IRAMMP field test,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination, ERIM document 213400-78-X(I) (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1991).

J. S. Hornstein, E. H. Takken, R. G. Priest, D. Baukman, “Models of refraction in the marine atmospheric surface layer,” NRL Tech. Rep. 93-9547 (Naval Research Laboratory, Washington, D.C., 1993).

Walker, P. L.

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

Walmsley, J. L.

J. L. Walmsley, “On theoretical wind speed and temperature profiles over the sea with applications to data from Sable Island, Nova Scotia,” Atmos. Ocean 26, 203–233 (1988).
[CrossRef]

Wang, W. C.

Wilf, I.

Wollenweber, F. G.

F. G. Wollenweber, “Impact of atmospheric layering on lowtran 6 radiance calculations,” Appl. Opt. 29, 5177–5181 (1990).
[CrossRef] [PubMed]

F. G. Wollenweber, “Infrared sea radiance modeling using lowtran 6,” in Optical Infrared, Millimeter Wave Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.926, 213–220 (1988).
[CrossRef]

Worsham, R. D.

York, R.

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

Appl. Opt. (4)

Atmos. Ocean (1)

J. L. Walmsley, “On theoretical wind speed and temperature profiles over the sea with applications to data from Sable Island, Nova Scotia,” Atmos. Ocean 26, 203–233 (1988).
[CrossRef]

Geophys. Res. Lett. (1)

A. Ben-Shalom, J. Otterman, P. Schechner, “Measured infrared radiances near sea horizon and their interpretation: preliminary results,” Geophys. Res. Lett. 8, 772–774 (1981).
[CrossRef]

Infrared Phys. (1)

D. J. Gambling, “Sunglitter on the surface of the ocean in the infrared spectral region,” Infrared Phys. 15, 149–155 (1975).
[CrossRef]

J. Geophys. Res. (1)

M. A. Donelan, W. J. Pierson, “Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry,” J. Geophys. Res. 92(C5), 4971–5028 (1987).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Ocean. (1)

R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Ocean. 16, 1293–1316 (1986).
[CrossRef]

Other (14)

F. G. Wollenweber, “Infrared sea radiance modeling using lowtran 6,” in Optical Infrared, Millimeter Wave Propagation Engineering, N. S. Kopeika, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.926, 213–220 (1988).
[CrossRef]

A. W. Cooper, E. C. Crittenden, F. A. Milne, P. L. Walker, E. Moss, D. Gregoris, “Mid and far infrared measurements of sun glint from the sea surface,” in Optics of the Air–Sea Interface: Theory and Measurement. L. Ester, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1749, 176–185 (1992).
[CrossRef]

P. Davis, A. Daniell, M. Farber, S. Hemple, “Infrared ocean clutter at low grazing angles: data analysis results and 1-D simulation,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1992), pp. 307–325.

B. B. Ball, SYNSEA code for generating synthetic IR imagery of sea backgrounds,” in Characterization, Propagation, and Simulation of Sources and Backgrounds II, D. Clement, W. R. Watkins, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1687, 289–299 (1992).
[CrossRef]

E. H. Takken, J. T. Caulfield, E. J. Stone, E. P. Shettle, R. G. Priest, M. D. Mermelstein, R. York, “Analysis of ocean horizon image measurements in the MWIR,” in Proceedings of the 1993 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1993), pp. 17–36.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User's Guide to lowtran 7,” AFGL-TR-88-0177 (Air Force Geophysics Laboratory, Bedford, Mass., 1988).

E. H. Takken, R. G. Priest, E. P. Shettle, J. C. Kershenstein, “IR horizon phenomenology: report on IRAMMP field test,” in Proceedings of the 1991 Meeting of the Infrared Information Symposia Specialty Group on Targets, Backgrounds and Discrimination, ERIM document 213400-78-X(I) (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1991).

G. R. Fowler, Introduction to Modern Optics (Holt, Rinehart & Winston, New York, 1975), Chap. 6.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 3.

J. S. Hornstein, E. H. Takken, R. G. Priest, D. Baukman, “Models of refraction in the marine atmospheric surface layer,” NRL Tech. Rep. 93-9547 (Naval Research Laboratory, Washington, D.C., 1993).

R. A. Paulus, “Specification for evaporation duct height calculations,” NOSC Technical Document 1596 (Naval Ocean Systems Command, San Diego, Calif., 1989).

M. A. Srokosz, “Wave statistics,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 285–332.
[CrossRef]

M. A. Donelan, W. H. Hui, “Mechanics of ocean surface waves,” in Surface Waves and Fluxes, G. L. Geernaert, W. J. Plant, eds. (Kluwer Academic, Boston, Mass., 1990), Vol. 1, pp. 209–246.
[CrossRef]

J. Mandel, The Statistical Analysis of Experimental Data, (Dover, New York, 1964), Chap. 4.

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of the ocean–horizon viewing geometry showing the Earth with a mean radius Re, the swell wave of amplitude Asw, and the sensor height h. The look-down angle to the horizon is ∊0, and deviations of the sensor angular orientation are given by ∊′.

Fig. 2
Fig. 2

Schematic diagram of the facet model for the ocean radiance. Six radiation sources are depicted in the diagram: (i) the Sun having an angular width Δψs and radiance Ls, (ii) the thermal atmospheric radiance Latm, (iii) sunlight scattered by aerosols in the path between the Sun and the ocean surface Lsc, (iv) thermal emission from the ocean Lth, (v) thermal emission from the air column between the ocean surface and the sensor Lp,th, and (vi) sunlight scattered by aerosols suspended in the air column between the sensor and the ocean surface. The ocean facet has a characteristic dimension ξc. Other notations are discussed in the text.

Fig. 3
Fig. 3

Plot of the midwave atmospheric transmission from the sensor to the ocean surface as a function of range. The data points are transmission values determined by use of lowtran 7, and the solid curve is the fitting function given by Eq. (16).

Fig. 4
Fig. 4

Plot of the scattered sunlight and the thermal emission associated with the air column between the sensor and the ocean surface as a function of transmission. The data points are obtained from lowtran 7, and the solid curves are fitting functions given by Eqs. (14) and (15) for the thermal path radiance and scattered path radiance, respectively.

Fig. 5
Fig. 5

Plot of the thermal atmospheric radiance as a function of the m* parameter. The data points are obtained from lowtran 7, and the solid curve is the fitting function given by Eq. (20). The fitting parameters are indicated in the diagram.

Fig. 6
Fig. 6

Plot of the scattered solar radiance as a function of look-ray zenith angle about the solar position. The data points are determined by use of lowtran 7, and the solid curve is a fit to the Lorentzian function given by Eq. (23). The fitting parameters are indicated in the diagram.

Fig. 7
Fig. 7

Plot of the cutoff capillary wave vector kc, as a function of u10 wind speed for water temperatures of 0 and 30 °C.

Fig. 8
Fig. 8

Plot of the significant wave height H1/3 as a function of u10 wind speed. The data points correspond to numerical integrations of the wave height PSD, and the solid curve corresponds to a fit to a quadratic function of wind speed.

Fig. 9
Fig. 9

Plot of the wave slope spatial correlation function as a function of spatial displacement for wind speeds of 2.5 and 20 m/s and a water temperature of 30 deg.

Fig. 10
Fig. 10

Plots of the wave slope temporal correlation function as a function of time lag for wind speeds of 2.5 and 20 m/s and a water temperature of 30 deg.

Fig. 11
Fig. 11

Root-mean-square wave slope as a function of u10 wind speed. The upper two traces correspond to integrals of the Donelan–Pierson22 wave slope PSD. The lower two traces represent the results reported by Cox and Munk.24

Fig. 12
Fig. 12

Plot of the solar glint roll-off at the sea surface as a function of the solar azimuth from the look direction. The data points correspond to numerical integrations of the solar glint contribution given by Eqs. (38) and (24). The solid curve is a fit to the Gaussian roll-off function given by the small wave slope approximation of Eqs. (39), (40), and (41).

Fig. 13
Fig. 13

Schematic diagram of a swell wave with amplitude Asw and wavelength λsw corresponding to wind speed u10. The extent of the exposed wave ia given by x0 and corrosponda to a local look-down angle ∊.

Fig. 14
Fig. 14

Plot of the midwave radiance as a function of look angle about the horizon for a solar elevation of 36 deg with (a) 1-deg, (b) 3-deg, (c) 7-deg, and (d) 15-deg azimuthal offsets from the look direction. The solid traces are the measured radiances, and the filled circles are the calculated radiances. The sky is on the right-hand side of the plot, and the near ocean is to the left. The peak at 30 mrad in (c) corresponds to a cloud.

Tables (2)

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Table 1 Parameters Utilized in the Analysis

Tables Icon

Table 2 lowtran Input Parameters

Equations (71)

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0 = cos 1 ( R e + A SW R e + h ) .
= 0 + η ,
η ( ) = sin 1 [ z ( ) cos ( 0 + ) R e + h ] ,
z ( ) = ( R e + h ) sin ( 0 + ) { ( R e + h ) 2 sin 2 ( 0 + ) [ ( R e + h ) 2 ( R e + A SW ) 2 ] } 1 / 2 .
n ̂ n = m x ( 1 + m x 2 + m y 2 ) 1 / 2 x ̂ + m y ( 1 + m x 2 + m y 2 ) 1 / 2 y ̂ + 1 ( 1 + m x 2 + m y 2 ) 1 / 2 z ̂ ,
n ̂ i = 1 1 + 2 x ̂ + 1 + 2 z ̂ ,
n ̂ i n ̂ n = cos ( α ) ,
n ̂ r n ̂ i = cos ( 2 α ) ,
n ̂ r n = 0 ,
n r x = γ 2 ( m x m y 2 1 ) + γ 1 ( 1 m x ) 2 Δ ,
n r y = m y [ γ 1 ( 1 + 2 ) γ 2 ( + m x ) ] Δ ,
n r z = γ 1 ( 1 m x ) γ 2 [ m x ( m x 2 + m y 2 ) ] Δ ,
γ 1 = ( 1 + m x 2 + m y 2 ) 1 / 2 cos ( α ) ,
γ 2 = 1 + 2 cos ( 2 α ) ,
cos ( α ) = m x + 1 + 2 ( 1 + m x 2 + m y 2 ) 1 / 2 ,
cos ( 2 α ) = ( m x 2 m y 2 ) + 4 m x 2 1 + [ 1 ( m x 2 + m y 2 ) ] ( 1 + 2 ) ( 1 + m x 2 + m y 2 ) ,
Δ = 1 2 m x + m y 2 + 2 ( m x 2 + m y 2 ) .
θ ( m x , m y , ) = tan 1 [ ( n r x 2 + n r y 2 ) 1 / 2 n r z ] ,
ϕ ( m x , m y , ) = tan 1 ( n r y n r z ) ,
R ( m x , m y , ) = | r s ( m x , m y , ) | 2 + | r p ( m x , m y , ) | 2 2 ,
r s ( m x , m y , ) = cos ( α ) [ N 2 sin ( α ) 2 ] 1 / 2 cos ( α ) + [ N 2 sin ( α ) 2 ] 1 / 2 ,
r p ( m x , m y , ) = N 2 cos ( α ) + [ N 2 sin ( α ) 2 ] 1 / 2 N 2 cos ( α ) + [ N 2 sin ( α ) 2 ] 1 / 2 .
N = n + i κ ,
L ( m x , m y , , θ s , ϕ s ) = L p ( ) + τ ( ) L 0 ( m x , m y , ) + τ s ( θ s ) τ ( ) L s ( m x , m y , , θ s , ϕ s ) ,
L p ( ) = L p , th ( ) + L p , sc ( ) ,
L p , th ( ) = [ 1 τ ( ) ] B ( T a ) ,
B ( T ) = c 1 π λ 1 λ 2 d λ λ 5 [ 1 exp ( c 2 / λ T ) 1 ] ,
τ ( z ) = exp ( α z β )
L p , sc ( , θ s , ϕ s ) = [ 1 1.05 τ ( ) ] L sc ( , θ s , ϕ s ) .
L 0 ( m x , m y , ) = [ 1 R ( m x , m y , ) ] B ( T w ) + R ( m x , m y , ) L atm ( m x , m y , ) + R ( m x , m y , ) L sc ( m x , m y , ) .
L sky ( m x , ) = α β exp [ γ m * ( m x , ) ] ,
m * ( m x , ) = 1 0.035 + cos [ θ ( m x , 0 , ) ] .
L sc ( θ ) = ( A / 2 ) 2 ( θ θ s ) 2 + ( Γ / 2 ) 2 + ,
Δ θ rs ( m x , m y , , θ s , ϕ s ) = cos 1 [ n ̂ r ( m x , m y , ) n ̂ s ( θ s , ϕ s ) ] ,
L sc ( m x , m y , , θ s , ϕ s ) = ( A / 2 ) 2 [ Δ θ rs ( m x , m y , , θ s , ϕ s ) ] 2 + ( Γ / 2 ) 2 ] + .
L s ( m x , m y , , θ s , ϕ s ) = { R ( m x , m y , ) B ( T s ) Δ θ rs ( m x , m y , , θ s , ϕ s ) Δ Ψ s / 2 0 otherwise ,
z ( r , t ) = k A k exp { i [ k r ω ( k ) t + Ψ k ] } ,
ω 2 ( k ) = g k ( 1 + α k 2 ) ,
S ( k , ω ) = 1 ( 2 π ) 3 A ξ d ξ + d τ z * ( r , t ) z ( r + ξ , t + τ ) r , t × exp [ i ( k ξ ω t ) ] ,
z * ( r , t ) z ( r + ξ , t + τ ) r , t = A k d k + d ω S ( k , ω ) exp [ i ( k ξ ω τ ) ] ,
S 0 ( k , ϕ ) = 2 0 d ω δ [ ω ω ( k ) ] S ( k , ω ) ,
z rms 2 = π + π d ϕ 0 k c d k k S 0 ( k , ϕ ) ,
k c ( u 10 , 0 ) = 297.6 + 191.5 u 10 820 u 10 2 + 0.113 u 10 3 ,
k c ( u 10 , 30 ) = 292.4 + 253.8 u 10 11.2 u 10 2 + 0.151 u 10 3 .
γ m ( ξ ) = z * ( r , t ) z ( r + ξ , t ) r | z ( r , t ) | 2 r
γ m ( ξ ) = π + π d ϕ 0 k c d k k 3 S 0 ( k , ϕ ) exp [ i k ξ cos ( ϕ ) ] π + π d ϕ 0 k c d k k 3 S 0 ( k , ϕ ) .
γ m ( t ) = z * ( r , t ) z * ( r , t + τ ) t | z ( r , t ) | 2 t ,
γ m ( τ ) = π + π d ϕ 0 k c d k k 3 S 0 ( k , ϕ ) exp [ i ω ( k ) τ ] π + π d ϕ 0 k c d k k 3 S 0 ( k , ϕ ) ,
p ( m x , m y ) = p x ( m x ) p y ( m y ) ,
p x ( m x ) = 1 2 π 1 σ x exp ( m x 2 / 2 σ x 2 ) ,
p y ( m y ) = 1 2 π 1 σ y exp ( m y 2 / 2 σ y 2 ) .
σ x 2 = σ x 2 cos 2 ( χ ) + σ y 2 sin 2 ( χ ) ,
σ y 2 = σ x 2 sin 2 ( χ ) + σ y 2 cos 2 ( χ ) ,
σ x 2 = π π d ϕ cos 2 ( ϕ ) 0 k c d k k 3 S 0 ( k , ϕ ) ,
σ y 2 = π π d ϕ sin 2 ( ϕ ) 0 k c d k k 3 S 0 ( k , ϕ )
σ x = 0.091 + 0.019 u 10 4.6 × 10 4 u 10 2 ,
σ y = 0.059 + 0.021 u 10 5.5 × 10 4 u 10 2 .
p x ( m x ) = 2 / π 1 + erf [ | | 2 σ x ] 1 σ x exp ( m x 2 / 2 σ x 2 )
L m ( ) = d m x + d m y L ( m x , m y , ) p ( m x , m y ) ,
L s ( m x , m y , , θ , ϕ s ) = { R ( m x , m y , ) B ( T s ) μ c x Δ ψ s 4 m x < μ c x + Δ ψ s 4 , μ c y Δ ψ s 4 μ c x m y < μ c y + Δ ψ s 4 μ c x . 0 otherwise
μ c x ( , θ s ) = tan ( π 4 θ s 2 ) 2 ,
μ c y ( , θ s , ϕ s ) = ϕ s 2 μ c x ( , θ s ) .
L ms ( , θ s , ϕ s ) = A s ( , θ s , ϕ s ) exp ( ϕ s 2 / 2 ϕ s , rms 2 )
A s ( , θ s , ϕ s ) = τ s ( θ s ) B ( T s ) R ( μ c x , μ c y , ) ( Δ ψ s ) 2 16 σ x σ y μ c x ( , θ s ) exp [ ( μ c x / 2 σ x 2 ) ] ,
ϕ s , rms ( , θ s ) = 2 μ c x ( , θ s ) σ y .
L rms 2 ( ) = + d m y d m x p ( m x , m y ) × [ L 2 ( m x , m y , ) L m 2 ( ) ] .
σ 2 ( , θ s , ϕ s ) = ( 16 σ x σ y μ c x ( Δ ψ ) 2 ) exp [ 1 2 ( μ c x 2 σ x 2 + ϕ s 2 ϕ s , rms 2 ) ] ,
cos ( k sw x ) ( λ sw x ) / A sw = 1 ,
N ( ) = M ϕ d z R ( ) x 0 ( ) k sw Δ s ( ) 2 π ξ c 2 ,
Δ L c ( ) = L rms ( ) N ( ) .
s ( 0 , θ s , 0 ) = L m s ( 0 , θ s , 0 ) B ( T w ) ,

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