Abstract

The surface of the wind-ruffled sea contains capillary wave facets whose curvature is much larger than the wavelength of visible and infrared light. As a result, visible sea radiance consists of the sum of all the mirrorlike reflections of the sky and sun from each facet. In the infrared, additional radiance arises from blackbody emission by the facet and along the atmospheric path to the point of observation. Numerical calculations of mean sea radiance based on this model agree to within 1 °C with infrared data obtained in the long-wave band and in the short- and mid-wave bands outside the sun-glint corridor. If sun glint can be neglected, the spectral radiance of the ocean horizon is approximately given by the Planck function at the temperature of the ocean and lower atmosphere.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. E. Bell, L. Eisner, J. Young, R. A. Oetjen, “Spectral radiance of sky and terrain at wavelengths between 1 and 20 microns. II. Sky measurements,” J. Opt. Soc. Am. 50, 1313–1320 (1960).
    [CrossRef]
  2. M. S. Longuet-Higgins, “Reflection and refraction at a random moving surface. I. Pattern and paths of specular points,” J. Opt. Soc. Am. 50, 838–844 (1960).
    [CrossRef]
  3. M. S. Longuet-Higgins, “Reflection and refraction at a random moving surface. II. Number of specular points in a Gaussian surface,” J. Opt. Soc. Am. 50, 845–856 (1960).
    [CrossRef]
  4. S. Q. Duntley, “Measurements of the distribution of water wave-slopes,” J. Opt. Soc. Am. 44, 574–575 (1954).
    [CrossRef]
  5. C. Cox, W. H. 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]
  6. C. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–487 (1956).
  7. R. W. Preisendorfer, C. D. Mobley, “Albedos and glitter patterns of a wind-roughened sea surface,” J. Phys. Oceanogr. 16, 1293–1316 (1986).
    [CrossRef]
  8. R. E. Walker, Marine Light Field Statistics (Wiley, New York1994), Chap. 7, pp. 297–343.
  9. Ref. 8, p. 11.
  10. M. D. Mermelstein, E. P. Shettle, E. H. Takken, R. G. Priest, “Infrared radiance and solar glint at the ocean–sky horizon,” Appl. Opt. 33, 6022–6034 (1994).
    [CrossRef] [PubMed]
  11. In this paper the word “path” refers only to the optical path between the footprint and the receiver.
  12. Strictly speaking, the name “thermal” is misleading because the nonglint radiance does include scattered sunlight. However, scattered sunlight (which falls off with wave number) is not very evident in our data, so the term is descriptive for our purposes. The reader should nevertheless be aware that it might not be as appropriate a term in the short-wave infrared band.
  13. C. R. Zeisse, “Radiance of the ocean horizon,” J. Opt. Soc. Am. A 12, 2022–2030 (1995).
    [CrossRef]
  14. C. R. Zeisse, “Radiance of the ocean horizon,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1994).
  15. With the receiver position fixed, selection of an ocean slope defines a unique sky position for a specular reflection.
  16. G. N. Plass, G. W. Kattawar, J. A. Guinn, “Radiative transfer in the earth’s atmosphere and ocean: influence of ocean waves,” Appl. Opt. 14, 1924–1936 (1975).
    [CrossRef] [PubMed]
  17. A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1988), pp. 1–38.
  18. 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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.
  19. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 622.
  20. C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).
  21. M. Minnaert, Light & Colour in the Open Air (Dover, New York, 1954), p. 319.
  22. C. R. Zeisse, “Relative spectral responsivity of two AGEMA infrared scanning cameras,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1995).
  23. R. D. Hudson, Infrared System Engineering (Wiley, New York, 1969), pp. 287 ff.
  24. This law will not apply at spectral resolutions less than the width of a typical molecular line (0.01 to 0.1 cm-1) because the low-resolution outcome will be a sum over many high-resolution exponentials. The sum of two or more exponentials is no longer an exponential.
  25. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 505 ff.
  26. These data for the index, available between 52.63 cm-1 and 25000 cm-1, set the spectral range of SeaRad.
  27. G. M. Hale, M. R. Querry, “Optical constants of water in the 200 nm to 200 µm wavelength region,” Appl. Opt. 3, 555–563 (1973).
    [CrossRef]
  28. M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
    [CrossRef]
  29. C. R. Zeisse, “SeaRad, a sea radiance prediction code,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1995). Copies of the source and executable code are available on the Internet. The Internet address is http://sunspot.nosc.mil/543/software.html .
  30. AGEMA Infrared Systems, 550 County Avenue, Secaucus, N.J. 07094.
  31. H. G. Hughes, “Infrared ship and background signatures in a coastal environment,” (Science and Technology Corporation, Hampton, Va., 1995).
  32. H. G. Hughes, “Dependence of mid and far infrared sea radiances on viewing altitude,” (Science and Technology Corporation, Hampton, Va., 1994).
  33. R. E. Turner, A. K. Goroch, “Solar-reflected radiation from the sea surface,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1996) pp. 93–102.
  34. P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
    [CrossRef]
  35. D. E. Freund, R. I. Joseph, D. J. Donohue, K. T. Constantikes, “Numerical computations of rough sea surface emissivity using the interaction probability density,” J. Opt. Soc. Am. A 14, 1836–1849 (1997).
    [CrossRef]

1997 (1)

1995 (1)

1994 (1)

1986 (1)

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

1977 (1)

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

1975 (1)

1973 (1)

G. M. Hale, M. R. Querry, “Optical constants of water in the 200 nm to 200 µm wavelength region,” Appl. Opt. 3, 555–563 (1973).
[CrossRef]

1967 (1)

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

1960 (3)

1956 (1)

C. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–487 (1956).

1955 (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

1954 (2)

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

Bell, E. E.

Berk, A.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1988), pp. 1–38.

Bernstein, L. S.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1988), pp. 1–38.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 622.

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

Constantikes, K. T.

Cox, C.

C. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–487 (1956).

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

C. Cox, W. H. 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]

Donohue, D. J.

Duntley, S. Q.

Earls, L. M.

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

Eisner, L.

Freund, D. E.

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

Goroch, A. K.

R. E. Turner, A. K. Goroch, “Solar-reflected radiation from the sea surface,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1996) pp. 93–102.

Guinn, J. A.

Hale, G. M.

G. M. Hale, M. R. Querry, “Optical constants of water in the 200 nm to 200 µm wavelength region,” Appl. Opt. 3, 555–563 (1973).
[CrossRef]

Holland, W. E.

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

Hudson, R. D.

R. D. Hudson, Infrared System Engineering (Wiley, New York, 1969), pp. 287 ff.

Hughes, H. G.

H. G. Hughes, “Infrared ship and background signatures in a coastal environment,” (Science and Technology Corporation, Hampton, Va., 1995).

H. G. Hughes, “Dependence of mid and far infrared sea radiances on viewing altitude,” (Science and Technology Corporation, Hampton, Va., 1994).

Joseph, R. I.

Kattawar, G. W.

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

Longuet-Higgins, M. S.

Mermelstein, M. D.

Minnaert, M.

M. Minnaert, Light & Colour in the Open Air (Dover, New York, 1954), p. 319.

Mobley, C. D.

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

Munk, W.

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

Munk, W. H.

C. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–487 (1956).

C. Cox, W. H. 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]

Oetjen, R. A.

Plass, G. N.

Preisendorfer, R. W.

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

Priest, R. G.

Querry, M. D.

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

Querry, M. R.

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

G. M. Hale, M. R. Querry, “Optical constants of water in the 200 nm to 200 µm wavelength region,” Appl. Opt. 3, 555–563 (1973).
[CrossRef]

Robertson, D. C.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1988), pp. 1–38.

Saunders, P. M.

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

Shettle, E. P.

M. D. Mermelstein, E. P. Shettle, E. H. Takken, R. G. Priest, “Infrared radiance and solar glint at the ocean–sky horizon,” Appl. Opt. 33, 6022–6034 (1994).
[CrossRef] [PubMed]

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 505 ff.

Takken, E. H.

Turner, R. E.

R. E. Turner, A. K. Goroch, “Solar-reflected radiation from the sea surface,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1996) pp. 93–102.

Walker, R. E.

R. E. Walker, Marine Light Field Statistics (Wiley, New York1994), Chap. 7, pp. 297–343.

Waring, R. C.

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 622.

Young, J.

Zeisse, C. R.

C. R. Zeisse, “Radiance of the ocean horizon,” J. Opt. Soc. Am. A 12, 2022–2030 (1995).
[CrossRef]

C. R. Zeisse, “Relative spectral responsivity of two AGEMA infrared scanning cameras,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1995).

C. R. Zeisse, “SeaRad, a sea radiance prediction code,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1995). Copies of the source and executable code are available on the Internet. The Internet address is http://sunspot.nosc.mil/543/software.html .

C. R. Zeisse, “Radiance of the ocean horizon,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1994).

Appl. Opt. (3)

J. Geophys. Res. (2)

M. R. Querry, W. E. Holland, R. C. Waring, L. M. Earls, M. D. Querry, “Relative reflectance and complex refractive index in the infrared for saline environmental waters,” J. Geophys. Res. 82, 1425–1433 (1977).
[CrossRef]

P. M. Saunders, “Shadowing on the ocean and the existence of the horizon,” J. Geophys. Res. 72, 4643–4649 (1967).
[CrossRef]

J. Mar. Res. (1)

C. Cox, W. Munk, “Some problems in optical oceanography,” J. Mar. Res. 14, 63–78 (1955).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (2)

J. Phys. Oceanogr. (1)

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

Scripps Inst. Oceanogr. Bull. (1)

C. Cox, W. H. Munk, “Slopes of the sea surface deduced from photographs of sun glitter,” Scripps Inst. Oceanogr. Bull. 6, 401–487 (1956).

Other (20)

R. E. Walker, Marine Light Field Statistics (Wiley, New York1994), Chap. 7, pp. 297–343.

Ref. 8, p. 11.

In this paper the word “path” refers only to the optical path between the footprint and the receiver.

Strictly speaking, the name “thermal” is misleading because the nonglint radiance does include scattered sunlight. However, scattered sunlight (which falls off with wave number) is not very evident in our data, so the term is descriptive for our purposes. The reader should nevertheless be aware that it might not be as appropriate a term in the short-wave infrared band.

M. Minnaert, Light & Colour in the Open Air (Dover, New York, 1954), p. 319.

C. R. Zeisse, “Relative spectral responsivity of two AGEMA infrared scanning cameras,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1995).

R. D. Hudson, Infrared System Engineering (Wiley, New York, 1969), pp. 287 ff.

This law will not apply at spectral resolutions less than the width of a typical molecular line (0.01 to 0.1 cm-1) because the low-resolution outcome will be a sum over many high-resolution exponentials. The sum of two or more exponentials is no longer an exponential.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 505 ff.

These data for the index, available between 52.63 cm-1 and 25000 cm-1, set the spectral range of SeaRad.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1988), pp. 1–38.

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, “Users guide to lowtran 7,” (Air Force Geophysics Laboratory, Hanscom Air Force Base, 1989), pp. 1–137.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 622.

C. R. Zeisse, “Radiance of the ocean horizon,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1994).

With the receiver position fixed, selection of an ocean slope defines a unique sky position for a specular reflection.

C. R. Zeisse, “SeaRad, a sea radiance prediction code,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1995). Copies of the source and executable code are available on the Internet. The Internet address is http://sunspot.nosc.mil/543/software.html .

AGEMA Infrared Systems, 550 County Avenue, Secaucus, N.J. 07094.

H. G. Hughes, “Infrared ship and background signatures in a coastal environment,” (Science and Technology Corporation, Hampton, Va., 1995).

H. G. Hughes, “Dependence of mid and far infrared sea radiances on viewing altitude,” (Science and Technology Corporation, Hampton, Va., 1994).

R. E. Turner, A. K. Goroch, “Solar-reflected radiation from the sea surface,” (Naval Command, Control and Ocean Surveillance Center, San Diego, Calif., 1996) pp. 93–102.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (24)

Fig. 1
Fig. 1

Four contributions to sea radiance: (upper) path radiance, (second) reflected sky radiance, (third) reflected solar radiance, and (lower) thermal blackbody radiance. The wavy line represents the footprint of a single pixel in an ocean image. Specular reflection of the sky and sun occurs at individual capillary wave facets inside the footprint. Because these facets are not explicitly shown, the second and third parts of this figure appear to involve unequal angles of incidence and reflection; they actually do not.

Fig. 2
Fig. 2

Geometry of facet reflection. The facet normal Un has been left out for clarity. Azimuths are considered positive when measured counterclockwise, looking toward the nadir.

Fig. 3
Fig. 3

Occurrence probability density versus capillary wave slope for a wind speed of 10 m s-1. The coordinate system of Fig. 2 has been inserted at the top of this figure to demonstrate the connection between coordinates and slopes.

Fig. 4
Fig. 4

Interaction probability density versus capillary wave slope for a wind speed of 10 m s-1 and a ray pointing toward (80°, 270°). The ray direction at the point of reflection is indicated by the coordinate system at the top of the figure.

Fig. 5
Fig. 5

Spectral atmospheric transmission for a slant path to space at zenith angles of 0° (upper curve), looking straight up, and 80° (shaded areas), looking 10° above the horizon. The dashed lines labeled by the circle (at 700 cm-1) and the triangle (at 950 cm-1) mark regions of strong and weak absorption, respectively.

Fig. 6
Fig. 6

Spectral sky radiance at 700 cm-1 (right), a region of strong absorption and at 950 cm-1 (left), a region of weak absorption. The spectral radiance of a 288-K blackbody at wave numbers of 700 cm-1 (circle) and 950 cm-1 (triangle) is shown by dashed lines in this figure and solid symbols in the next.

Fig. 7
Fig. 7

Spectral radiance of blackbodies near room temperature (shaded area) and near the temperature of the sun (right, divided by 104).

Fig. 8
Fig. 8

Fresnel spectral reflectance and emittance at 2500 cm-1.

Fig. 9
Fig. 9

Spectral transmission of an atmospheric path with a length of 1 km (solid curves) and 10 km (shaded areas). Each path originates at the ocean surface and terminates at a receiver whose altitude is 10 m.

Fig. 10
Fig. 10

Spectral radiance of an atmospheric path with a length of 1 km (dashed curve) and 10 km (solid curve). Each path originates at the ocean surface and terminates at a receiver whose altitude is 10 m. The spectral radiance of a 288-K blackbody is shown by the shading.

Fig. 11
Fig. 11

Relative spectral responsivity of AGEMA model 900 LW and 900 SW scanning cameras.

Fig. 12
Fig. 12

Airborne view of ship near Point Loma, California, looking away from the sun’s azimuth from an altitude of 51 m on 13 September 1994. Upper, long-wave image; lower, mid- and short-wave image. The vertical lines labeled LI01 mark the location from which data have been taken. The color palette at the right, given in degrees Celsius, is the same for each image.

Fig. 13
Fig. 13

Computed spectral radiance in the long-wave band for 13 September 1994. The altitude is 51 m, the observation angle is 91°, and the computed range to the sea is 2.9 km. The thick solid curve labeled THERMAL is the sum of individual contributions from the path (thin curve with circles), sky (thin curve with triangles), and sea (thin curve). No solar radiance was observed in this direction on this day. The shading shows the spectral radiance of a 293-K blackbody.

Fig. 14
Fig. 14

Computed spectral radiance in the mid- and short-wave bands for 13 September 1994. The observation geometry and curve meanings are the same as in Fig. 13.

Fig. 15
Fig. 15

Vertical radiance profile in the long-wave band for 13 September 1994. The circles show the data; the curves show the calculation. Each square is the integral of the corresponding curve in Fig. 13.

Fig. 16
Fig. 16

Vertical radiance profile in the mid- and short-wave bands for 13 September 1994. The circles show the data; the curves show the calculation. Each square is the integral of the corresponding curve in Fig. 14.

Fig. 17
Fig. 17

Long-wave comparison of the numerical calculation (solid curve) with the 13 September 1994 data (circles).

Fig. 18
Fig. 18

Mid- and short-wave comparison of the numerical calculation (solid curve) with the 13 September 1994 data (circles).

Fig. 19
Fig. 19

Airborne view of ship near Point Loma, California, looking along the sun’s azimuth from an altitude of 31 m on 8 February 1995. Upper, long-wave image; lower, mid- and short-wave image. The vertical lines labeled LI01 mark the location from which data have been taken. The color palette at the right, given in degrees Celsius, is different for each image. Note, for example, that although the ship is white in the upper image and dark blue in the lower image, it has the same temperature (∼16 °C) in each.

Fig. 20
Fig. 20

Computed spectral radiance in the long-wave band for 8 February 1995. The altitude is 31 m, the observation angle is 91° looking along the azimuth of the sun, and the computed range to the sea is 1.8 km. The thick solid curve labeled THERMAL is the total of the individual contributions from the path, sky, and sea. Computed solar radiance is not shown, as it was negligible for this band, day, and direction. The shading shows the spectral radiance of a 288-K blackbody.

Fig. 21
Fig. 21

Computed spectral radiance in the mid- and short-wave bands for 8 February 1995. The observation geometry is the same as in Fig. 20. The curves labeled SUN show two different calculations: The solid curve is for a solar zenith angle of 53.3° (the actual value), and the dashed curve is for a solar zenith angle of 59.3° (required for best fit to the data).

Fig. 22
Fig. 22

Vertical radiance profile in the long-wave band for 8 February 1995. The circles show the data; the solid curves show the calculation. Each square is the integral of the corresponding curve in Fig. 20.

Fig. 23
Fig. 23

Vertical radiance profile in the mid- and short-wave bands for 8 February 1995. The circles show the data. The solid curve labeled SUN shows the solar calculation for the actual solar zenith angle, and the dashed curve labeled SUN shows the solar calculation for the solar zenith angle that gives the best fit to the data. The curves labeled TOTAL are the sum of the thermal and solar contributions for these two cases. Each square is the integral of the corresponding curve in Fig. 21.

Fig. 24
Fig. 24

Comparison of the numerical calculation (curves) with the 8 February 1995 data (circles). The long-wave comparison is shown to the left. The mid- and short-wave comparison is shown to the right. On the right, the solid curve refers to the calculation with the actual solar zenith angle, 53.3°, and the dashed curve refers to the calculation with the solar zenith angle, 59.3°, that is required for the best fit to the data.

Tables (1)

Tables Icon

Table 1 Meteorological and Geographical Data Pertaining to Airborne Infrared Images

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

=1-ρ.
N=Npath+(Nsky+Nsun+Nsea)τpath.
Ntherm=Npath+(Nsky+Nsea)τpath.
Nf=Npathf+(Nsky+Nsun+Nsea)τpathf.
Us+Ur=2 cos ωUn,
Npath(θr, ϕr)+{ρ(ω)Ns(θs, ϕs)+ρ(ω)No(θs, ϕs)
+(ω)Nbb(Tsea)}τpath(θr, ϕr),
Nsky=ρNsr,
Nsun=ρNor,
Nsea=Nbbr.
grωπ/2Ur=const.gcos ωcos θnp(ζx, ζy, W)dζxdζyωπ/2Ur=const.cos ωcos θnp(ζx, ζy, W)dζxdζy.
P=p(ζx, ζy, W)dζxdζy
p(ζx, ζy, W)12πσuσcexp-12ζx2σu2+ζy2σc2,
σu2=0.000+3.16×10-3W,
σc2=0.003+1.92×10-3W.
Q=q(θ, ϕ, ζx, ζy, W)dζxdζy
q(θ, ϕ, ζx, ζy, W)=cos ωcos θnp(ζx, ζy, W)ωπ/2U=const.cos ωcos θnp(ζx, ζy, W)dζxdζy,
0N(ν)f(ν)dν0Nbb(ν, T)f(ν)dν,
NthermalpathNbb(T¯)+[ρ(ω)Nbb(T¯)+(ω)Nbb(T¯)]τpathr.
path=αpath1-τpath,
Nthermal(1-τpath)Nbb(T¯)+[ρ(ω)Nbb(T¯)+{1-ρ(ω)}Nbb(T¯)]τpathr=Nbb(T¯).

Metrics