Abstract

We challenge a recent paper in this journal suggesting that the well-established formula governing the transmittance of radiance across a refracting interface needs revision [Optics Express, 25(22) 27086 (2017)]. We provide a simple example of radiative transfer across an interface showing that the accepted formula is correct.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983).
    [Crossref]
  2. R. W. Preisendorfer, Hydrologic Optics V. 1: Introduction (Natl. Tech. Inform. Serv.PB-259 793/8ST, 1976).
  3. R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in).Optical aspects of Oceanography, N. G. Jerlov and E. Steemann Nielsen, eds. (Academic, 1974).
  4. C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic1994).
  5. P. J. Dev and P. Shanmugam, “New theoretical formulation for the determination of radiance transmittance at the water-air interface,” Opt. Express,  25(22) 27086 (2017).
    [Crossref] [PubMed]

2017 (1)

Austin, R. W.

R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in).Optical aspects of Oceanography, N. G. Jerlov and E. Steemann Nielsen, eds. (Academic, 1974).

Dev, P. J.

Gordon, H. R.

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983).
[Crossref]

Mobley, C. D.

C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic1994).

Morel, A. Y.

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983).
[Crossref]

Preisendorfer, R. W.

R. W. Preisendorfer, Hydrologic Optics V. 1: Introduction (Natl. Tech. Inform. Serv.PB-259 793/8ST, 1976).

Shanmugam, P.

Opt. Express (1)

Other (4)

H. R. Gordon and A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, 1983).
[Crossref]

R. W. Preisendorfer, Hydrologic Optics V. 1: Introduction (Natl. Tech. Inform. Serv.PB-259 793/8ST, 1976).

R. W. Austin, “The remote sensing of spectral radiance from below the ocean surface,” in).Optical aspects of Oceanography, N. G. Jerlov and E. Steemann Nielsen, eds. (Academic, 1974).

C. D. Mobley, Light and Water; Radiative Transfer in Natural Waters (Academic1994).

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Equations (7)

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L u + ( θ a , ϕ a ) = L u ( θ w , ϕ w ) n w 2 t f ( θ w , ϕ w )
L u = L u 0 + L u 1 + L u 2 = L u 0 1 r ¯ R = E d + t f + R π ( 1 r ¯ R )
L u + ( θ a , ϕ a ) = t f ( θ w , ϕ w ) n w 2 L u ( θ w , ϕ w ) = E d + t f + R π ( 1 r ¯ R ) t f ( θ w , θ a ) n w 2 .
E u + = Ω d L u + ( θ a , ϕ a ) cos θ a d Ω a = E d + t f + R π ( 1 r ¯ R ) Ω d t f ( θ w , θ a ) n w 2 cos θ a d Ω a .
Ω d t f ( θ w , θ a ) n w 2 cos θ a d Ω a = Ω d [ 1 r f ( θ w , θ a ) ] cos θ w d Ω w ,
E u + = E d + t f + ( 1 r ¯ ) R ( 1 r ¯ R )
E u + ( Total ) = E d + t f + ( 1 r ¯ ) R ( 1 r ¯ R ) + E d + ( 1 t f + ) .

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