Abstract

Instead of the conventionally atmospheric correction algorithms using the near-infrared and shortwave infrared wavelengths, an alternative practical atmospheric correction algorithm using the ultraviolet wavelength for turbid waters (named UV-AC) is proposed for satellite ocean color imagery in the paper. The principle of the algorithm is based on the fact that the water-leaving radiance at ultraviolet wavelengths can be neglected as compared with that at the visible light wavelengths or even near-infrared wavelengths in most cases of highly turbid waters due to the strong absorption by detritus and colored dissolved organic matter. The UV-AC algorithm uses the ultraviolet band to estimate the aerosol scattering radiance empirically, and it does not need any assumption of the water’s optical properties. Validations by both of the simulated data and in situ data show that the algorithm is appropriate for the retrieval of the water-leaving radiance in turbid waters. The UV-AC algorithm can be used for all the current satellite ocean color sensors, and it is especially useful for those ocean color sensors lacking the shortwave infrared bands. Moreover, the algorithm can be used for any turbid waters with negligible water-leaving radiance at ultraviolet wavelength. Based on our work, we recommend the future satellite ocean color remote sensors setting the ultraviolet band to perform the atmospheric correction in turbid waters.

© 2012 OSA

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2012 (2)

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

M. Wang, W. Shi, and L. Jiang, “Atmospheric correction using near-infrared bands for satellite ocean color data processing in the turbid western Pacific region,” Opt. Express20(2), 741–753 (2012).
[CrossRef] [PubMed]

2011 (3)

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Evaluation of the aerosol models for SeaWiFS and MODIS by AERONET data over open oceans,” Appl. Opt.50(22), 4353–4364 (2011).
[CrossRef] [PubMed]

J. H. Ryu, J. K. Choi, J. Eom, and J. H. Ahn, “Temporal variation in Korean coastal waters using Geostationary Ocean Color Imager,” J. Coast. Res.SI64, 1731–1735 (2011).

M. Doron, S. Bélanger, D. Doxaran, and M. Babin, “Spectral variations in the near-infrared ocean reflectance,” Remote Sens. Environ.115(7), 1617–1631 (2011).
[CrossRef]

2010 (2)

M. Zhang, J. Tang, J. Dong, Q. Song, and J. Ding, “Retrieval of total suspended matter concentration in the Yellow and East China Seas from MODIS imagery,” Remote Sens. Environ.114(2), 392–403 (2010).
[CrossRef]

S. W. Bailey, B. A. Franz, and P. J. Werdell, “Estimation of near-infrared water-leaving reflectance for satellite ocean color data processing,” Opt. Express18(7), 7521–7527 (2010).
[CrossRef] [PubMed]

2009 (2)

M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009).
[CrossRef]

W. Shi and M. Wang, “An assessment of the black ocean pixel assumption for MODIS SWIR bands,” Remote Sens. Environ.113(8), 1587–1597 (2009).
[CrossRef]

2008 (2)

2007 (3)

2005 (2)

S. J. Lavender, M. H. Pinkerton, G. F. Moore, J. Aiken, and D. Blondeau-Patissier, “Modification to the atmospheric correction of SeaWiFS ocean colour images over turbid waters,” Cont. Shelf Res.25(4), 539–555 (2005).
[CrossRef]

M. Wang and W. Shi, “Estimation of ocean contribution at the MODIS near infrared wavelengths along the east coast of the U.S.: two case studies,” Geophys. Res. Lett.32(13), L13606 (2005), doi:.
[CrossRef]

2004 (1)

X. Q. He, D. L. Pan, and Z. H. Mao, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Acta Oceanol. Sin.23(4), 609–615 (2004).

2003 (1)

2002 (1)

D. Doxaran, J. M. Froidefond, S. Lavender, and P. Castaing, “Spectral signature of highly turbid water application with SPOT data to quantify suspended particulate matter concentrations,” Remote Sens. Environ.81(2), 149–161 (2002).
[CrossRef]

2000 (3)

1999 (1)

G. F. Moore, J. Aiken, and S. J. Lavender, “The atmospheric correction of water colour and quantitative retrieval of suspended particulate matter in Case II waters: application to MERIS,” Int. J. Remote Sens.20(9), 1713–1733 (1999).
[CrossRef]

1997 (1)

H. R. Gordon, “Atmospheric correction of ocean color imagery in the Earth Observing System era,” J. Geophys. Res.102(D14), 17081–17106 (1997).
[CrossRef]

1994 (3)

1993 (1)

1992 (1)

1988 (1)

Ahmed, S.

Ahn, J. H.

J. H. Ryu, J. K. Choi, J. Eom, and J. H. Ahn, “Temporal variation in Korean coastal waters using Geostationary Ocean Color Imager,” J. Coast. Res.SI64, 1731–1735 (2011).

Aiken, J.

S. J. Lavender, M. H. Pinkerton, G. F. Moore, J. Aiken, and D. Blondeau-Patissier, “Modification to the atmospheric correction of SeaWiFS ocean colour images over turbid waters,” Cont. Shelf Res.25(4), 539–555 (2005).
[CrossRef]

G. F. Moore, J. Aiken, and S. J. Lavender, “The atmospheric correction of water colour and quantitative retrieval of suspended particulate matter in Case II waters: application to MERIS,” Int. J. Remote Sens.20(9), 1713–1733 (1999).
[CrossRef]

Babin, M.

M. Doron, S. Bélanger, D. Doxaran, and M. Babin, “Spectral variations in the near-infrared ocean reflectance,” Remote Sens. Environ.115(7), 1617–1631 (2011).
[CrossRef]

Bai, Y.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Evaluation of the aerosol models for SeaWiFS and MODIS by AERONET data over open oceans,” Appl. Opt.50(22), 4353–4364 (2011).
[CrossRef] [PubMed]

Bailey, S. W.

Bélanger, S.

M. Doron, S. Bélanger, D. Doxaran, and M. Babin, “Spectral variations in the near-infrared ocean reflectance,” Remote Sens. Environ.115(7), 1617–1631 (2011).
[CrossRef]

Blondeau-Patissier, D.

S. J. Lavender, M. H. Pinkerton, G. F. Moore, J. Aiken, and D. Blondeau-Patissier, “Modification to the atmospheric correction of SeaWiFS ocean colour images over turbid waters,” Cont. Shelf Res.25(4), 539–555 (2005).
[CrossRef]

Brown, J. W.

Carder, K. L.

C. Hu, K. L. Carder, and F. E. Muller-Karger, “Atmospheric correction of SeaWiFS imagery over turbid coastal waters: a practical method,” Remote Sens. Environ.74(2), 195–206 (2000).
[CrossRef]

Castaing, P.

D. Doxaran, J. M. Froidefond, and P. Castaing, “Remote-sensing reflectance of turbid sediment-dominated waters. Reduction of sediment type variations and changing illumination conditions effects by use of reflectance ratios,” Appl. Opt.42(15), 2623–2634 (2003).
[CrossRef] [PubMed]

D. Doxaran, J. M. Froidefond, S. Lavender, and P. Castaing, “Spectral signature of highly turbid water application with SPOT data to quantify suspended particulate matter concentrations,” Remote Sens. Environ.81(2), 149–161 (2002).
[CrossRef]

Chen, J. S.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

Choi, J. K.

J. H. Ryu, J. K. Choi, J. Eom, and J. H. Ahn, “Temporal variation in Korean coastal waters using Geostationary Ocean Color Imager,” J. Coast. Res.SI64, 1731–1735 (2011).

Cui, Q. F.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

Ding, J.

M. Zhang, J. Tang, J. Dong, Q. Song, and J. Ding, “Retrieval of total suspended matter concentration in the Yellow and East China Seas from MODIS imagery,” Remote Sens. Environ.114(2), 392–403 (2010).
[CrossRef]

Dong, J.

M. Zhang, J. Tang, J. Dong, Q. Song, and J. Ding, “Retrieval of total suspended matter concentration in the Yellow and East China Seas from MODIS imagery,” Remote Sens. Environ.114(2), 392–403 (2010).
[CrossRef]

Dong, X.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

Doron, M.

M. Doron, S. Bélanger, D. Doxaran, and M. Babin, “Spectral variations in the near-infrared ocean reflectance,” Remote Sens. Environ.115(7), 1617–1631 (2011).
[CrossRef]

Doxaran, D.

M. Doron, S. Bélanger, D. Doxaran, and M. Babin, “Spectral variations in the near-infrared ocean reflectance,” Remote Sens. Environ.115(7), 1617–1631 (2011).
[CrossRef]

D. Doxaran, J. M. Froidefond, and P. Castaing, “Remote-sensing reflectance of turbid sediment-dominated waters. Reduction of sediment type variations and changing illumination conditions effects by use of reflectance ratios,” Appl. Opt.42(15), 2623–2634 (2003).
[CrossRef] [PubMed]

D. Doxaran, J. M. Froidefond, S. Lavender, and P. Castaing, “Spectral signature of highly turbid water application with SPOT data to quantify suspended particulate matter concentrations,” Remote Sens. Environ.81(2), 149–161 (2002).
[CrossRef]

Eom, J.

J. H. Ryu, J. K. Choi, J. Eom, and J. H. Ahn, “Temporal variation in Korean coastal waters using Geostationary Ocean Color Imager,” J. Coast. Res.SI64, 1731–1735 (2011).

Evans, R. H.

Franz, B. A.

Froidefond, J. M.

D. Doxaran, J. M. Froidefond, and P. Castaing, “Remote-sensing reflectance of turbid sediment-dominated waters. Reduction of sediment type variations and changing illumination conditions effects by use of reflectance ratios,” Appl. Opt.42(15), 2623–2634 (2003).
[CrossRef] [PubMed]

D. Doxaran, J. M. Froidefond, S. Lavender, and P. Castaing, “Spectral signature of highly turbid water application with SPOT data to quantify suspended particulate matter concentrations,” Remote Sens. Environ.81(2), 149–161 (2002).
[CrossRef]

Gentili, B.

Gilerson, A.

Gong, F.

Gordon, H. R.

Gross, B.

He, X. Q.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Evaluation of the aerosol models for SeaWiFS and MODIS by AERONET data over open oceans,” Appl. Opt.50(22), 4353–4364 (2011).
[CrossRef] [PubMed]

X. Q. He, D. L. Pan, and Z. H. Mao, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Acta Oceanol. Sin.23(4), 609–615 (2004).

Hu, C.

C. Hu, K. L. Carder, and F. E. Muller-Karger, “Atmospheric correction of SeaWiFS imagery over turbid coastal waters: a practical method,” Remote Sens. Environ.74(2), 195–206 (2000).
[CrossRef]

Hu, D. X.

D. L. Yuan, J. R. Zhu, C. Y. Li, and D. X. Hu, “Cross-shelf circulation in the Yellow and East China Seas indicated by MODIS satellite observations,” J. Mar. Syst.70(1-2), 134–149 (2008).
[CrossRef]

Huang, N. L.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

Jiang, L.

Lavender, S.

D. Doxaran, J. M. Froidefond, S. Lavender, and P. Castaing, “Spectral signature of highly turbid water application with SPOT data to quantify suspended particulate matter concentrations,” Remote Sens. Environ.81(2), 149–161 (2002).
[CrossRef]

Lavender, S. J.

S. J. Lavender, M. H. Pinkerton, G. F. Moore, J. Aiken, and D. Blondeau-Patissier, “Modification to the atmospheric correction of SeaWiFS ocean colour images over turbid waters,” Cont. Shelf Res.25(4), 539–555 (2005).
[CrossRef]

G. F. Moore, J. Aiken, and S. J. Lavender, “The atmospheric correction of water colour and quantitative retrieval of suspended particulate matter in Case II waters: application to MERIS,” Int. J. Remote Sens.20(9), 1713–1733 (1999).
[CrossRef]

Li, C. Y.

D. L. Yuan, J. R. Zhu, C. Y. Li, and D. X. Hu, “Cross-shelf circulation in the Yellow and East China Seas indicated by MODIS satellite observations,” J. Mar. Syst.70(1-2), 134–149 (2008).
[CrossRef]

Mao, Z. H.

X. Q. He, D. L. Pan, and Z. H. Mao, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Acta Oceanol. Sin.23(4), 609–615 (2004).

Maritorena, S.

Moore, G. F.

S. J. Lavender, M. H. Pinkerton, G. F. Moore, J. Aiken, and D. Blondeau-Patissier, “Modification to the atmospheric correction of SeaWiFS ocean colour images over turbid waters,” Cont. Shelf Res.25(4), 539–555 (2005).
[CrossRef]

G. F. Moore, J. Aiken, and S. J. Lavender, “The atmospheric correction of water colour and quantitative retrieval of suspended particulate matter in Case II waters: application to MERIS,” Int. J. Remote Sens.20(9), 1713–1733 (1999).
[CrossRef]

Morel, A.

Moshary, F.

Muller-Karger, F. E.

C. Hu, K. L. Carder, and F. E. Muller-Karger, “Atmospheric correction of SeaWiFS imagery over turbid coastal waters: a practical method,” Remote Sens. Environ.74(2), 195–206 (2000).
[CrossRef]

Oo, M.

Ovidio, F.

Pan, D. L.

X. Q. He, Y. Bai, D. L. Pan, N. L. Huang, X. Dong, J. S. Chen, and Q. F. Cui, “Using geostationary satellite ocean color data to map the diurnal dynamics of suspended particulate matter in coastal waters,” Remote Sens. Environ. (to be published) (2012).

X. Q. He, D. L. Pan, Y. Bai, Q. K. Zhu, and F. Gong, “Evaluation of the aerosol models for SeaWiFS and MODIS by AERONET data over open oceans,” Appl. Opt.50(22), 4353–4364 (2011).
[CrossRef] [PubMed]

X. Q. He, D. L. Pan, and Z. H. Mao, “Atmospheric correction of SeaWiFS imagery for turbid coastal and inland waters,” Acta Oceanol. Sin.23(4), 609–615 (2004).

Pinkerton, M. H.

S. J. Lavender, M. H. Pinkerton, G. F. Moore, J. Aiken, and D. Blondeau-Patissier, “Modification to the atmospheric correction of SeaWiFS ocean colour images over turbid waters,” Cont. Shelf Res.25(4), 539–555 (2005).
[CrossRef]

Rijkeboer, M.

Robinson, W.

Ruddick, K. G.

Ryu, J. H.

J. H. Ryu, J. K. Choi, J. Eom, and J. H. Ahn, “Temporal variation in Korean coastal waters using Geostationary Ocean Color Imager,” J. Coast. Res.SI64, 1731–1735 (2011).

Shi, W.

M. Wang, W. Shi, and L. Jiang, “Atmospheric correction using near-infrared bands for satellite ocean color data processing in the turbid western Pacific region,” Opt. Express20(2), 741–753 (2012).
[CrossRef] [PubMed]

M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009).
[CrossRef]

W. Shi and M. Wang, “An assessment of the black ocean pixel assumption for MODIS SWIR bands,” Remote Sens. Environ.113(8), 1587–1597 (2009).
[CrossRef]

M. Wang, J. Tang, and W. Shi, “MODIS-derived ocean color products along the China east coastal region,” Geophys. Res. Lett.34(6), L06611 (2007), doi:.
[CrossRef]

M. Wang and W. Shi, “The NIR-SWIR combined atmospheric correction approach for MODIS ocean color data processing,” Opt. Express15(24), 15722–15733 (2007).
[CrossRef] [PubMed]

M. Wang and W. Shi, “Estimation of ocean contribution at the MODIS near infrared wavelengths along the east coast of the U.S.: two case studies,” Geophys. Res. Lett.32(13), L13606 (2005), doi:.
[CrossRef]

Siegel, D. A.

Son, S.

M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009).
[CrossRef]

Song, Q.

M. Zhang, J. Tang, J. Dong, Q. Song, and J. Ding, “Retrieval of total suspended matter concentration in the Yellow and East China Seas from MODIS imagery,” Remote Sens. Environ.114(2), 392–403 (2010).
[CrossRef]

Tang, J.

M. Zhang, J. Tang, J. Dong, Q. Song, and J. Ding, “Retrieval of total suspended matter concentration in the Yellow and East China Seas from MODIS imagery,” Remote Sens. Environ.114(2), 392–403 (2010).
[CrossRef]

M. Wang, J. Tang, and W. Shi, “MODIS-derived ocean color products along the China east coastal region,” Geophys. Res. Lett.34(6), L06611 (2007), doi:.
[CrossRef]

Vargas, M.

Wang, M.

M. Wang, W. Shi, and L. Jiang, “Atmospheric correction using near-infrared bands for satellite ocean color data processing in the turbid western Pacific region,” Opt. Express20(2), 741–753 (2012).
[CrossRef] [PubMed]

W. Shi and M. Wang, “An assessment of the black ocean pixel assumption for MODIS SWIR bands,” Remote Sens. Environ.113(8), 1587–1597 (2009).
[CrossRef]

M. Wang, S. Son, and W. Shi, “Evaluation of MODIS SWIR and NIR-SWIR atmospheric correction algorithm using SeaBASS data,” Remote Sens. Environ.113(3), 635–644 (2009).
[CrossRef]

M. Wang, J. Tang, and W. Shi, “MODIS-derived ocean color products along the China east coastal region,” Geophys. Res. Lett.34(6), L06611 (2007), doi:.
[CrossRef]

M. Wang, “Remote sensing of the ocean contributions from ultraviolet to near-infrared using the shortwave infrared bands: simulations,” Appl. Opt.46(9), 1535–1547 (2007).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

H. R. Gordon and M. Wang, “Retrieval of water-leaving radiance and aerosol optical thickness over the oceans with SeaWiFS: a preliminary algorithm,” Appl. Opt.33(3), 443–452 (1994).
[CrossRef] [PubMed]

M. Wang and H. R. Gordon, “Radiance reflected from the ocean-atmosphere system: synthesis from individual components of the aerosol size distribution,” Appl. Opt.33(30), 7088–7095 (1994).
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[CrossRef]

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[CrossRef]

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Other (2)

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Figures (9)

Fig. 1
Fig. 1

Normalized water-leaving radiance (Lwn) measured in the Changjiang River Estuary, Mississippi River Estuary and Orinoco River Estuary. (a) Location of the sampling stations, with pink and black circles in the Changjiang River Estuary represent stations of spring and autumn cruises, respectively; (b) Lwn at Changjiang River Estuary in spring of 2003; (c) Lwn at Changjiang River Estuary in autumn of 2003; (d) Lwn at Mississippi River Estuary; (e) Lwn at Orinoco River Estuary. The above-water methods are used to measure the Lwn. The remote sensing reflectance data sets at Mississippi River Estuary and Orinoco River Estuary were downloaded from the SeaBASS, and were converted to Lwn by multiplying the mean extraterrestrial solar irradiance.

Fig. 2
Fig. 2

Simulated aerosol multiple-scattering reflectance for solar and satellite zenith angles of 30°, relative azimuth angle of 120°, and aerosol multiple-scattering reflectance at 865nm of 0.008. Individual curves mean the 12 aerosol models from SeaDAS.

Fig. 3
Fig. 3

Comparison of the water-leaving reflectance retrieved by the UV-AC algorithms and the in situ measured water-leaving reflectance. (a) scatter plot for the UV-AC algorithm based on 365nm; (b) scatter plot for the UV-AC algorithm based on 412nm; (c) spectral distributions of the mean value and standard deviation of water-leaving reflectance. Points in the red ellipses in (a) and (b) correspond to the same sample with maximal L wn (865nm) shown in Fig. 1(b).

Fig. 4
Fig. 4

The L wn retrieved by Aqua/MODIS on 5 April 2003 using the UV-AC(412nm) algorithm (unit: mW/(cm2⋅μm⋅sr)). Arrows in the sub-image of 412nm indicate the Subei Coastal Current (SCC) and the Taiwan Warm Current (TWC).

Fig. 5
Fig. 5

The L wn retrieved by Aqua/MODIS on 5 April 2003 using the SeaDAS 6.3 based on the SWIR/NIR-AC algorithm (unit: mW/(cm2⋅μm⋅sr)).

Fig. 6
Fig. 6

Comparisons between satellite retrieved and in situ measured normalized water-leaving radiances. (a) Locations of the in situ measurement of normalized water-leaving radiances on 5 April 2003 (marked as stars); (b) comparison at station HD34; (c) comparison at station HD35; (d) comparison at station HD36; (e) comparison at station HD37.

Fig. 7
Fig. 7

GOCI-retrieved L wn (660nm) (unit: mW/(cm2⋅μm⋅sr)) using the UV-AC(412nm) algorithm on 5 April 2011. The time labels on (a)-(h) are the corresponding observing time in Beijing time. (i) is the comparison of L wn (660nm) along the section AB in the sub-image (a).

Fig. 8
Fig. 8

Variation of α (765nm,865nm) with the concentration of suspended particulate matter.

Fig. 9
Fig. 9

α (745nm,865nm) and C TSM retrieved by GOCI data at 12:28 (Beijing time) on 5 April 2011. (a) α (745nm,865nm) , (b) C TSM with unit of mg/l.

Equations (22)

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ρ t ( λ )= ρ r ( λ )+ ρ a ( λ )+ t v ( λ ) ρ w ( λ ),
ρ= πL / ( F 0 cos θ 0 ) ,
ρ rc ( λ )= ρ t ( λ ) ρ r ( λ )= ρ a ( λ )+ t v ( λ ) ρ w ( λ );
ρ a (e) ( NI R L )= ρ a (e) ( UV ) [ ε (NI R S ,NI R L ) (e) ] (NI R L UV) / (NI R L NI R S ) ,
α (NI R S ,NI R L ) = t v ( NI R S ) ρ w ( NI R S ) t v ( NI R L ) ρ w ( NI R L ) .
{ ε (NI R S ,NI R L ) = ρ a ( NI R S ) ρ a ( NI R L ) ε (NI R S ,NI R L ) (e) = ρ rc ( NI R S ) ρ rc ( NI R L ) = ρ a ( NI R S )+ t v ( NI R S ) ρ w ( NI R S ) ρ a ( NI R L )+ t v ( NI R L ) ρ w ( NI R L ) .
ε (NI R S ,NI R L ) (e) =[ 1 t v ( NI R L ) ρ w ( NI R L ) ρ rc ( NI R L ) ] ε (NI R S ,NI R L ) + t v ( NI R L ) ρ w ( NI R L ) ρ rc ( NI R L ) α (NI R S ,NI R L ) .
ρ w = π t s ( 1ρ )( 1 ρ ˜ )R n w 2 Q( 1rR ) ,
R=f( 0.5 b w + b ˜ s b s * C TSM a w + a s * C TSM ),
α (NI R S ,NI R L ) ρ w ( NI R S ) ρ w ( NI R L ) [ a w ( NI R L )+ a s * ( NI R L ) C TSM rf b ˜ s ( NI R L ) b s * ( NI R L ) C TSM a w ( NI R S )+ a s * ( NI R S ) C TSM rf b ˜ s ( NI R S ) b s * ( NI R S ) C TSM ].
α (NI R S ,NI R L ) a w ( NI R L )+ a s * ( NI R L ) C TSM a w ( NI R S )+ a s * ( NI R S ) C TSM .
ρ a VIS = ρ a NI R L ε ( NI R L VIS ) / ( NI R L NI R S ) .
( ρ a VIS ) (e) = ρ rc UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) =( ρ a UV + t v UV ρ w UV ) [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) .
Δ( t v VIS ρ w VIS )= ( ρ a VIS ) (e) ρ a VIS = ρ a UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) + t v UV ρ w UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) ρ a NI R L ε ( NI R L VIS ) / ( NI R L NI R S ) .
Δ( t v VIS ρ w VIS ) ρ a UV ε ( NI R L UV ) / ( NI R L NI R S ) + t v UV ρ w UV ε ( NI R L UV ) / ( NI R L NI R S ) ρ a NI R L ε ( NI R L VIS ) / ( NI R L NI R S ) = ρ a NI R L + t v UV ρ w UV ε ( NI R L UV ) / ( NI R L NI R S ) ρ a NI R L ε ( NI R L VIS ) / ( NI R L NI R S ) ,
Δ( t v VIS ρ w VIS ) ρ a UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) + t v UV ρ w UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) ρ a NI R L ε ( NI R L UV ) / ( NI R L NI R S ) = ρ a UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) + t v UV ρ w UV [ ε (e) ] ( NI R L UV ) / ( NI R L NI R S ) ρ a UV .
ε x =1.0+x( ε1 )+Δ.
Δ( t v VIS ρ w VIS ) t v UV ρ w UV [ 1( ε1 ) ( NI R L UV ) / ( NI R L NI R S ) ] ρ a NI R L ( ε1 ) ( NI R L VIS ) / ( NI R L NI R S ) ,
Δ( t v VIS ρ w VIS ) t v UV ρ w UV [ 1( ε (e) 1 ) ( NI R L UV ) / ( NI R L NI R S ) ] ρ a UV ( ε (e) 1 ) ( NI R L UV ) / ( NI R L NI R S ) .
{ Δ( t v VIS ρ w VIS ) ρ a NI R L ( ε1 )( 865VIS )/100 t v UV ρ w UV ( 65ε ) Δ( t v VIS ρ w VIS )5 ρ a UV ( ε (e) 1 ) t v UV ρ w UV ( 65 ε (e) ) .
{ Δ( t v VIS ρ w VIS ) t v UV ρ w UV Δ( t v VIS ρ w VIS ) ρ a UV .
{ Δ( t v VIS L w VIS )( F 0 VIS / F 0 UV ) t v UV L w UV Δ( t v VIS L w VIS )( F 0 VIS / F 0 UV ) L a UV .

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