Abstract

The polarization state of infrared emission from water at large viewing angles is explained mathematically by a polarization-dependent emissivity. To provide polarized emissivity values for a wind-roughened water surface in a convenient format, this electronic paper provides interactive tables and plots of polarized water emissivity for the spectral range of 3–15 µm. The rough surface is modeled as a collection of specular facets with slopes given by a Gaussian distribution. The interactive electronic format provides a tutorial on emission polarization and it allows readers to copy the desired numbers and paste them into their electronic applications without the difficulty of transcribing numbers from printed tables.

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References

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  1. J. A. Shaw, "Degree of linear polarization in spectral radiances from water-viewing infrared radiometers," Appl. Opt. 38, 3157-3165 (1999).
    [CrossRef]
  2. F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, "Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing," in Polarization and Remote Sensing III, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE 4133, 270-282 (2000).
  3. W. G. Egan, Photometry and Polarization in Remote Sensing (Elsevier, New York, 1985), pp. 337-354.
  4. R. D. Tooley, "Man-made target detection using infrared polarization," in Polarization considerations for optical systems II, R.A. Chipman, ed., Proc. SPIE 1166, 52-58 (1989).
  5. A. W. Cooper, W. J. Lentz, and P. L. Walker, "Infrared polarization ship images and contrast in the MAPTIP experiment," in Image Propagation Through the Atmosphere, L. R. Bissonnette and C. Dainty, eds., Proc. SPIE 2828, 85-96 (1996).
  6. J. A. Shaw, "The impact of polarization on infrared sea-surface temperature remote sensing," Proc. IGARSS98 (IEEE), 496-498 (1998).
  7. T. S. Pagano, H. H. Aumann, K. Overoye, G. W. Gigioli, Jr.,"Scan-angle-dependent radiometric modulation due to polarization for the Atmospheric Infrared Sounder," in Earth Observing Systems V, W. L. Barnes, ed., Proc. SPIE 4135, 108-116 (2000).
  8. K. Masuda, T. Takashima, and Y. Takayama, "Emissivity of pure and sea waters for the model sea surface in the infrared window regions," Remote Sensing of Environment 24, 313-329 (1988).
    [CrossRef]
  9. X. Wu and W. L. Smith, "Emissivity of rough sea surface for 8-13 �m: modeling and verification," Appl. Opt. 36, 2609-2619 (1997).
    [CrossRef] [PubMed]
  10. C. R. Zeisse, C. P. McGrath, and K. M. Littfin, "Infrared radiance of the wind-ruffled sea," J. Opt. Soc. Am. A 16, 1439-1452 (1999).
    [CrossRef]
  11. C. Cox and 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]
  12. J. A. Shaw and J. H. Churnside, "Scanning-laser glint measurements of sea-surface slope statistics," Appl. Opt. 36, 4202-4213 (1997).
    [CrossRef] [PubMed]
  13. G. M. Hale and M. R. Querry, "Optical constants of water in the 200-nm to 200-�m wavelength region," Appl. Opt. 12, 555-563 (1973).
    [CrossRef] [PubMed]
  14. P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the along track scanning radiometer," J. Atmos. Ocean. Technol. 13, 126-141 (1996).
    [CrossRef]

Other (14)

J. A. Shaw, "Degree of linear polarization in spectral radiances from water-viewing infrared radiometers," Appl. Opt. 38, 3157-3165 (1999).
[CrossRef]

F. J. Iannarilli, J. A. Shaw, S. H. Jones, and H. E. Scott, "Snapshot LWIR hyperspectral polarimetric imager for ocean surface sensing," in Polarization and Remote Sensing III, D. H. Goldstein, D. B. Chenault, W. G. Egan, and M. J. Duggin, eds., Proc. SPIE 4133, 270-282 (2000).

W. G. Egan, Photometry and Polarization in Remote Sensing (Elsevier, New York, 1985), pp. 337-354.

R. D. Tooley, "Man-made target detection using infrared polarization," in Polarization considerations for optical systems II, R.A. Chipman, ed., Proc. SPIE 1166, 52-58 (1989).

A. W. Cooper, W. J. Lentz, and P. L. Walker, "Infrared polarization ship images and contrast in the MAPTIP experiment," in Image Propagation Through the Atmosphere, L. R. Bissonnette and C. Dainty, eds., Proc. SPIE 2828, 85-96 (1996).

J. A. Shaw, "The impact of polarization on infrared sea-surface temperature remote sensing," Proc. IGARSS98 (IEEE), 496-498 (1998).

T. S. Pagano, H. H. Aumann, K. Overoye, G. W. Gigioli, Jr.,"Scan-angle-dependent radiometric modulation due to polarization for the Atmospheric Infrared Sounder," in Earth Observing Systems V, W. L. Barnes, ed., Proc. SPIE 4135, 108-116 (2000).

K. Masuda, T. Takashima, and Y. Takayama, "Emissivity of pure and sea waters for the model sea surface in the infrared window regions," Remote Sensing of Environment 24, 313-329 (1988).
[CrossRef]

X. Wu and W. L. Smith, "Emissivity of rough sea surface for 8-13 �m: modeling and verification," Appl. Opt. 36, 2609-2619 (1997).
[CrossRef] [PubMed]

C. R. Zeisse, C. P. McGrath, and K. M. Littfin, "Infrared radiance of the wind-ruffled sea," J. Opt. Soc. Am. A 16, 1439-1452 (1999).
[CrossRef]

C. Cox and 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]

J. A. Shaw and J. H. Churnside, "Scanning-laser glint measurements of sea-surface slope statistics," Appl. Opt. 36, 4202-4213 (1997).
[CrossRef] [PubMed]

G. M. Hale and M. R. Querry, "Optical constants of water in the 200-nm to 200-�m wavelength region," Appl. Opt. 12, 555-563 (1973).
[CrossRef] [PubMed]

P. D. Watts, M. R. Allen, and T. J. Nightingale, "Wind speed effects on sea surface emission and reflection for the along track scanning radiometer," J. Atmos. Ocean. Technol. 13, 126-141 (1996).
[CrossRef]

Supplementary Material (2)

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Figures (3)

Fig. 1.
Fig. 1.

An example of how infrared emission from water becomes increasingly p-polarized as the viewing angle increases. The left-hand graph shows the polarized emissivity components and the right-hand graph shows the resulting degree of emission polarization. This example is for zero wind speed and 70° viewing angle. Click the figure to activate an interactive version. [Media 1]

Table 1.
Table 1.

Click the table to obtain polarized emissivity values for the chosen wind speed and viewing angle. [Media 2]

Fig. 2.
Fig. 2.

Degree of polarization versus viewing angle for reflection from water (top) and emission from water (bottom) at two thermal infrared wavelengths. Note that the significantly large imaginary component of the refractive index at 12 µm results in peak reflection polarization less than 100%.

Equations (11)

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

ε s , p ( λ , θ ) = 1 R s , p ( λ , θ ) ,
R s ( λ , θ ) = cos ( θ ) n ( λ ) cos ( θ r ) cos ( θ ) + n ( λ ) cos ( θ r ) 2
R p ( λ , θ ) = n ( λ ) cos ( θ ) cos ( θ r ) n ( λ ) cos ( θ ) + cos ( θ r ) 2 .
θ r ( λ , θ ) = sin 1 [ sin ( θ ) n ( λ ) ] .
p ( θ n ) = 1 2 π σ 2 exp ( tan 2 ( θ n ) 2 σ 2 )
2 σ 2 = 0.003 + 0.00512 w ( ± 0.004 ) .
cos ( χ ) = μ e μ n + ( 1 μ e ) 1 2 ( 1 μ n ) 1 2 cos ( ϕ ) .
ε - s , p ( λ , μ e ) = ε - s , p ( λ , μ e ) μ e ,
ε - s , p ( λ , μ e ) = 2 μ e 0 1 0 π ε s , p ( λ , χ ) cos ( χ ) p ( θ n ) μ n 4 d ϕ d μ n
( μ e ) = 2 μ e 0 1 0 π cos ( χ ) p ( θ n ) μ n 4 d ϕ d μ n , cos ( χ ) > 0 .
D = ε s ε p ε s + ε p ,

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