Abstract

A simple correction method to remove the spectral bandpass effects of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) on the derived normalized water-leaving radiances and ocean-near-surface chlorophyll concentration is developed and implemented in the SeaWiFS data-processing system. SeaWiFS has not only in-band response structures but also significant sensor out-of-band contributions. The effects of the SeaWiFS out-of-band contribution at the green bands is particularly significant for the derived normalized water-leaving radiances and therefore for the retrieved ocean-near-surface chlorophyll concentration. With the sensor spectral bandpass corrections, the low chlorophyll concentration is even lower in the clear ocean regions, whereas there are almost no changes for the oceans with a chlorophyll concentration of >0.2 mg/m3.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).
  2. D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
    [CrossRef]
  3. M. Wang, B. A. Franz, R. A. Barnes, Analyses of the SeaWiFS Spectral Bandpass Effects, SeaWiFS Postlaunch Technical Report Series, Vol. 10, , S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2000).
  4. H. R. Gordon, “Remote sensing of ocean color: a methodology for dealing with broad spectral bands and significant out-of-band response,” Appl. Opt. 34, 8363–8374 (1995).
    [CrossRef] [PubMed]
  5. H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
    [CrossRef] [PubMed]
  6. H. R. Gordon, M. Wang, “Influence of oceanic whitecaps on atmospheric correction of ocean-color sensor,” Appl. Opt. 33, 7754–7763 (1994).
    [CrossRef] [PubMed]
  7. R. Frouin, M. Schwindling, P. Y. Deschamps, “Spectral reflectance of sea foam in the visible and near infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14,361–14,371 (1996).
    [CrossRef]
  8. K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: their contribution to water-leaving radiance,” J. Geophys. Res. 105, 6493–6499 (2000).
    [CrossRef]
  9. M. Wang, “A sensitivity study of SeaWiFS atmospheric correction algorithm: effects of spectral band variations,” Remote Sens. Environ. 67, 348–359 (1999).
    [CrossRef]
  10. H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
    [CrossRef] [PubMed]
  11. J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
    [CrossRef]
  12. H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
    [CrossRef]
  13. H. R. Gordon, A. Y. Morel, Remote Assessment of Ocean Color for Interpretation of Satellite Visible Imagery: A Review (Springer-Verlag, New York, 1983).
    [CrossRef]
  14. F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
    [CrossRef] [PubMed]

2000 (2)

D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
[CrossRef]

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: their contribution to water-leaving radiance,” J. Geophys. Res. 105, 6493–6499 (2000).
[CrossRef]

1999 (2)

M. Wang, “A sensitivity study of SeaWiFS atmospheric correction algorithm: effects of spectral band variations,” Remote Sens. Environ. 67, 348–359 (1999).
[CrossRef]

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

1998 (1)

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

1996 (1)

R. Frouin, M. Schwindling, P. Y. Deschamps, “Spectral reflectance of sea foam in the visible and near infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14,361–14,371 (1996).
[CrossRef]

1995 (1)

1994 (2)

1988 (1)

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

1981 (1)

Baker, K. S.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Barnes, R. A.

M. Wang, B. A. Franz, R. A. Barnes, Analyses of the SeaWiFS Spectral Bandpass Effects, SeaWiFS Postlaunch Technical Report Series, Vol. 10, , S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2000).

Brown, J. W.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Brown, O. B.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Carder, K. L.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Chavez, F. P.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Clark, D. K.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

Deschamps, P. Y.

R. Frouin, M. Schwindling, P. Y. Deschamps, “Spectral reflectance of sea foam in the visible and near infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14,361–14,371 (1996).
[CrossRef]

Esaias, W. E.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Evans, R. H.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Feely, R. A.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Feldman, G. C.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Foley, D. G.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Franz, B. A.

M. Wang, B. A. Franz, R. A. Barnes, Analyses of the SeaWiFS Spectral Bandpass Effects, SeaWiFS Postlaunch Technical Report Series, Vol. 10, , S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2000).

Friederich, G. E.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Frouin, R.

R. Frouin, M. Schwindling, P. Y. Deschamps, “Spectral reflectance of sea foam in the visible and near infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14,361–14,371 (1996).
[CrossRef]

Garver, S. A.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Gordon, H. R.

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: their contribution to water-leaving radiance,” J. Geophys. Res. 105, 6493–6499 (2000).
[CrossRef]

H. R. Gordon, “Remote sensing of ocean color: a methodology for dealing with broad spectral bands and significant out-of-band response,” Appl. Opt. 34, 8363–8374 (1995).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Influence of oceanic whitecaps on atmospheric correction of ocean-color sensor,” Appl. Opt. 33, 7754–7763 (1994).
[CrossRef] [PubMed]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

H. R. Gordon, D. K. Clark, “Clear water radiances for atmospheric correction of coastal zone color scanner imagery,” Appl. Opt. 20, 4175–4180 (1981).
[CrossRef] [PubMed]

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

Gregg, W. W.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Hooker, S. B.

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

Kahru, M.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Maritorena, S.

D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

McClain, C. R.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

McPhaden, M. J.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Mitchell, B. G.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Moore, K. D.

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: their contribution to water-leaving radiance,” J. Geophys. Res. 105, 6493–6499 (2000).
[CrossRef]

Morel, A. Y.

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

O’Reilly, J. E.

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Robinson, W.

Schwindling, M.

R. Frouin, M. Schwindling, P. Y. Deschamps, “Spectral reflectance of sea foam in the visible and near infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14,361–14,371 (1996).
[CrossRef]

Siegel, D. A.

D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
[CrossRef]

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

Smith, R. C.

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

Strutton, P. G.

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Voss, K. J.

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: their contribution to water-leaving radiance,” J. Geophys. Res. 105, 6493–6499 (2000).
[CrossRef]

Wang, M.

D. A. Siegel, M. Wang, S. Maritorena, W. Robinson, “Atmospheric correction of satellite ocean color imagery: the black pixel assumption,” Appl. Opt. 39, 3582–3591 (2000).
[CrossRef]

M. Wang, “A sensitivity study of SeaWiFS atmospheric correction algorithm: effects of spectral band variations,” Remote Sens. Environ. 67, 348–359 (1999).
[CrossRef]

H. R. Gordon, M. Wang, “Influence of oceanic whitecaps on atmospheric correction of ocean-color sensor,” Appl. Opt. 33, 7754–7763 (1994).
[CrossRef] [PubMed]

H. R. Gordon, M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: A preliminary algorithm,” Appl. Opt. 33, 443–452 (1994).
[CrossRef] [PubMed]

M. Wang, B. A. Franz, R. A. Barnes, Analyses of the SeaWiFS Spectral Bandpass Effects, SeaWiFS Postlaunch Technical Report Series, Vol. 10, , S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2000).

Appl. Opt. (5)

J. Geophys. Res. (4)

J. E. O’Reilly, S. Maritorena, B. G. Mitchell, D. A. Siegel, K. L. Carder, S. A. Garver, M. Kahru, C. R. McClain, “Ocean color chlorophyll algorithms for SeaWiFS,” J. Geophys. Res. 103, 24,937–24,953 (1998).
[CrossRef]

H. R. Gordon, O. B. Brown, R. H. Evans, J. W. Brown, R. C. Smith, K. S. Baker, D. K. Clark, “A semianalytic radiance model of ocean color,” J. Geophys. Res. 93, 10,909–10,924 (1988).
[CrossRef]

R. Frouin, M. Schwindling, P. Y. Deschamps, “Spectral reflectance of sea foam in the visible and near infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14,361–14,371 (1996).
[CrossRef]

K. D. Moore, K. J. Voss, H. R. Gordon, “Spectral reflectance of whitecaps: their contribution to water-leaving radiance,” J. Geophys. Res. 105, 6493–6499 (2000).
[CrossRef]

Remote Sens. Environ. (1)

M. Wang, “A sensitivity study of SeaWiFS atmospheric correction algorithm: effects of spectral band variations,” Remote Sens. Environ. 67, 348–359 (1999).
[CrossRef]

Science (1)

F. P. Chavez, P. G. Strutton, G. E. Friederich, R. A. Feely, G. C. Feldman, D. G. Foley, M. J. McPhaden, “Biological and chemical response of the equatorial Pacific Ocean to the 1997–98 El Niño,” Science 286, 2126–2131 (1999).
[CrossRef] [PubMed]

Other (3)

S. B. Hooker, W. E. Esaias, G. C. Feldman, W. W. Gregg, C. R. McClain, An Overview of SeaWiFS and Ocean Color, NASA TM 104566, Vol. 1, S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 1992).

M. Wang, B. A. Franz, R. A. Barnes, Analyses of the SeaWiFS Spectral Bandpass Effects, SeaWiFS Postlaunch Technical Report Series, Vol. 10, , S. B. Hooker, E. R. Firestone, eds. (NASA Goddard Space Flight Center, Greenbelt, Md., 2000).

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

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 (5)

Fig. 1
Fig. 1

SeaWiFS spectral response functions for SeaWiFS bands 2 (443 nm), 3 (490 nm), and 5 (555 nm).

Fig. 2
Fig. 2

Spectral distribution of the normalized water-leaving radiance [L w (λ)] N for typical case 1 water for pigment concentration of (from top to bottom) 0.03, 0.1, 0.3, 0.5, 1.0, and 3.0 (mg/m3). These are derived from Gordon et al.12

Fig. 3
Fig. 3

Spectral bandpass correction factor r i ) for SeaWiFS bands 1–5 as a function of the SeaWiFS-derived two-band ratio values in the normalized water-leaving radiances between (a) bands 2 and 5 and (b) bands 3 and 5. The data correspond to pigment concentrations of 0.03, 0.1, 0.2, 0.3, 0.5, 1.0, and 1.5 (mg/m3), respectively, from high to low ratio values. The curves are the least-squares fit.

Fig. 4
Fig. 4

Correction factor r i ) as a function of the pigment concentration for b 0 values of 0.12, 0.30, and 0.45 m-1 for SeaWiFS wavelengths of 443 and 555 nm.

Fig. 5
Fig. 5

Histograms of the SeaWiFS-retrieved chlorophyll concentrations for cases with and without spectral bandpass corrections for the eight-day global data for the case of (a) winter (17–24 January 1998) and (b) summer (12–19 July 1998), respectively.

Tables (1)

Tables Icon

Table 1 Values of the Least-Squares Fitting Coefficients for SeaWiFS Bands 1–5 in Figs. 3(a) and 3(b)

Equations (9)

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

Ltλ=Lrλ+Laλ+Lraλ+tλLwcλ+tλLwλ,
Lλi= LλSiλdλ Siλdλ,
Ltλi=Lrλi+Laλi+Lraλi+tλiLwcλi+tλiLwλi,
tλiLwcλitλiLwcλi,
Lwλi=cos θ0t0λiLwλiN,
tλiLwλitλit0λicos θ0LwλiN,
rλi=LwλiN/LwλiN.
rλi=a0j,kλi+a1j,kλiLwλjN/LwλkN+a2j,kλiLwλjN/LwλkN2,
LwλiN=rλiLwλiN.

Metrics