Abstract

The cosine error of in situ seven-channel radiometers designed to measure the in-air downward irradiance for ocean color applications was investigated in the 412683  nm spectral range with a sample of three instruments. The interchannel variability of cosine errors showed values generally lower than ±3% below 50 degrees incidence angle with extreme values of approximately 4–20% (absolute) at 50–80 degrees for the channels at 412 and 443  nm. The intrachannel variability, estimated from the standard deviation of the cosine errors of different sensors for each center wavelength, displayed values generally lower than 2% for incidence angles up to 50 degrees and occasionally increasing up to 6% at 80 degrees. Simulations of total downward irradiance measurements, accounting for average angular responses of the investigated radiometers, were made with an accurate radiative transfer code. The estimated errors showed a significant dependence on wavelength, sun zenith, and aerosol optical thickness. For a clear sky maritime atmosphere, these errors displayed values spectrally varying and generally within ±3%, with extreme values of approximately 4–10% (absolute) at 40–80 degrees sun zenith for the channels at 412 and 443  nm. Schemes for minimizing the cosine errors have also been proposed and discussed.

© 2007 Optical Society of America

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  1. J. L. Mueller and R. W. Austin, "Ocean optics protocols for SeaWiFS for validation, Revision 1," Vol. 25 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, 1995).
  2. C. R. McClain, G. C. Feldman, and S. B. Hooker, "An overview of the seawifs project and strategies for producing a climate research quality global ocean bio-optical time-series," Deep-Sea Res. 51, 5-42 (2004).
    [CrossRef]
  3. S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).
  4. G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).
  5. R. G. Grainger, R. E. Basher, and R. L. McKenzie, "UV-B Robertson-Berger meter characterization and field calibration," Appl. Opt. 32, 343-349 (1993).
    [CrossRef] [PubMed]
  6. G. Seckmeyer and G. Bernhard, "Cosine error correction of spectral uv-irradiances," in Proc. SPIE 2049, 140-151 (1993).
    [CrossRef]
  7. A. de La Casiniére, T. Cabot, and S. Benmansour, "Measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers," Sol. Energy 54, 173-182 (1995).
    [CrossRef]
  8. J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, "Cosine response characteristics of some radiometric and photometric sensors," Sol. Energy 38, 397-402 (1995).
    [CrossRef]
  9. P.-M. Nast, "Measurements on the accuracy of pyranometers," Sol. Energy 31, 279-282 (1983).
    [CrossRef]
  10. J. Groebner, "Improved entrance optics for total irradiance measurements with a brewer spectrophotometer," Appl. Opt. 42, 3516-3521 (2003).
    [CrossRef]
  11. L. Harrison, J. Michalsky, and J. Berndt, "Automated multifilter rotating shadow-band radiometer: an instrument for optical depth and radiation measurements," Appl. Opt. 33, 5118-5125 (1994).
    [CrossRef] [PubMed]
  12. M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
    [CrossRef]
  13. J. Groebner, M. Blumthaler, and W. Ambach, "Experimental investigation of the spectral total irradiance measurement errors due to a non cosine response," Geophys. Res. Lett. 23, 2493-2496 (1996).
    [CrossRef]
  14. U. Feister, R. Grewe, and K. Gericke, "A method for the correction of cosine errors in measurements of spectral uv irradiance," Solar Energy 60, 313-332 (1997).
    [CrossRef]
  15. F. Bais, S. Kazadzis, D. Balis, C. Zerefos, and M. Blumthaler, "Correcting total solar ultraviolet spectra recorded by a brewer spectroradiometer for its angular response error," Appl. Opt. 37, 6339-6344 (1998).
    [CrossRef]
  16. G. Zibordi and K. J. Voss, "Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements," Remote Sens. Environ. 27, 343-358 (1989).
    [CrossRef]
  17. J. H. Morrow, M. S. Duhig, and C. R. Booth, "Design and evaluation of a cosine collector for a SeaWiFS-compatible Marine Reflectance Radiometer," in Proc. SPIE 2258, 879-886 (1994).
    [CrossRef]
  18. G. Bernhard and G. Seckmeyer, "New entrance optics for solar spectral uv measurements," Photochem. Photobiol. 65, 923-930 (1997).
    [CrossRef]
  19. German Institute of Standardization, "DIN 5032 Teil 1," Deutsche Normen Series (Beuth Verlag, 1978).
  20. B. Bulgarelli, V. Kisselev, and L. Roberti, "Radiative transfer in the atmosphereocean system: the finite-element method," Appl. Opt. 38, 1530-1542 (1999).
    [CrossRef]
  21. B. Bulgarelli and G. Zibordi, "Remote sensing of ocean color: accuracy assessment of an approximate atmospheric correction method," Int. J. Remote Sens. 24, 491-509 (2003).
    [CrossRef]
  22. B. Bulgarelli, G. Zibordi, and J. F. Berthon, "Measured and modeled radiometric quantities in coastal waters: towards a closure," Appl. Opt. 42, 5365-5381 (2003).
    [CrossRef] [PubMed]
  23. IAMAPRC, "A preliminary cloudless standard atmosphere for radiation computation," Technical Report WCP-112, WMO/TD-No. 24 (International Association for Meteorology and Atmospheric Physics, Radiation Commission, World Climate Programme, 1984).
  24. G. W. Kattawar, "A three-parameter analytic phase function for multiple scattering calculations," J. Quant. Spectrosc. Radiat. Transfer 15, 839-849 (1975).
    [CrossRef]
  25. A. Ångström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
    [CrossRef]
  26. G. Zibordi and G. Ferrari, "Instrumental self-shading in underwater optical measurements: experimental data," Appl. Opt. 34, 2750-2754 (1995).
    [CrossRef] [PubMed]
  27. J. P. Doyle and G. Zibordi, "Optical propagation within a 3-dimensional shadowed atmosphere-ocean field: application to large deployment structures," Appl. Opt. 41, 4283-4306 (2002).
    [CrossRef] [PubMed]

2004

C. R. McClain, G. C. Feldman, and S. B. Hooker, "An overview of the seawifs project and strategies for producing a climate research quality global ocean bio-optical time-series," Deep-Sea Res. 51, 5-42 (2004).
[CrossRef]

2003

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

J. Groebner, "Improved entrance optics for total irradiance measurements with a brewer spectrophotometer," Appl. Opt. 42, 3516-3521 (2003).
[CrossRef]

B. Bulgarelli and G. Zibordi, "Remote sensing of ocean color: accuracy assessment of an approximate atmospheric correction method," Int. J. Remote Sens. 24, 491-509 (2003).
[CrossRef]

B. Bulgarelli, G. Zibordi, and J. F. Berthon, "Measured and modeled radiometric quantities in coastal waters: towards a closure," Appl. Opt. 42, 5365-5381 (2003).
[CrossRef] [PubMed]

2002

J. P. Doyle and G. Zibordi, "Optical propagation within a 3-dimensional shadowed atmosphere-ocean field: application to large deployment structures," Appl. Opt. 41, 4283-4306 (2002).
[CrossRef] [PubMed]

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

1999

1998

1997

G. Bernhard and G. Seckmeyer, "New entrance optics for solar spectral uv measurements," Photochem. Photobiol. 65, 923-930 (1997).
[CrossRef]

U. Feister, R. Grewe, and K. Gericke, "A method for the correction of cosine errors in measurements of spectral uv irradiance," Solar Energy 60, 313-332 (1997).
[CrossRef]

1996

M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, and W. Ambach, "Experimental investigation of the spectral total irradiance measurement errors due to a non cosine response," Geophys. Res. Lett. 23, 2493-2496 (1996).
[CrossRef]

1995

J. L. Mueller and R. W. Austin, "Ocean optics protocols for SeaWiFS for validation, Revision 1," Vol. 25 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, 1995).

A. de La Casiniére, T. Cabot, and S. Benmansour, "Measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers," Sol. Energy 54, 173-182 (1995).
[CrossRef]

J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, "Cosine response characteristics of some radiometric and photometric sensors," Sol. Energy 38, 397-402 (1995).
[CrossRef]

G. Zibordi and G. Ferrari, "Instrumental self-shading in underwater optical measurements: experimental data," Appl. Opt. 34, 2750-2754 (1995).
[CrossRef] [PubMed]

1994

J. H. Morrow, M. S. Duhig, and C. R. Booth, "Design and evaluation of a cosine collector for a SeaWiFS-compatible Marine Reflectance Radiometer," in Proc. SPIE 2258, 879-886 (1994).
[CrossRef]

L. Harrison, J. Michalsky, and J. Berndt, "Automated multifilter rotating shadow-band radiometer: an instrument for optical depth and radiation measurements," Appl. Opt. 33, 5118-5125 (1994).
[CrossRef] [PubMed]

1993

R. G. Grainger, R. E. Basher, and R. L. McKenzie, "UV-B Robertson-Berger meter characterization and field calibration," Appl. Opt. 32, 343-349 (1993).
[CrossRef] [PubMed]

G. Seckmeyer and G. Bernhard, "Cosine error correction of spectral uv-irradiances," in Proc. SPIE 2049, 140-151 (1993).
[CrossRef]

1989

G. Zibordi and K. J. Voss, "Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements," Remote Sens. Environ. 27, 343-358 (1989).
[CrossRef]

1984

IAMAPRC, "A preliminary cloudless standard atmosphere for radiation computation," Technical Report WCP-112, WMO/TD-No. 24 (International Association for Meteorology and Atmospheric Physics, Radiation Commission, World Climate Programme, 1984).

1983

P.-M. Nast, "Measurements on the accuracy of pyranometers," Sol. Energy 31, 279-282 (1983).
[CrossRef]

1978

German Institute of Standardization, "DIN 5032 Teil 1," Deutsche Normen Series (Beuth Verlag, 1978).

1975

G. W. Kattawar, "A three-parameter analytic phase function for multiple scattering calculations," J. Quant. Spectrosc. Radiat. Transfer 15, 839-849 (1975).
[CrossRef]

1961

A. Ångström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
[CrossRef]

Ambach, W.

M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, and W. Ambach, "Experimental investigation of the spectral total irradiance measurement errors due to a non cosine response," Geophys. Res. Lett. 23, 2493-2496 (1996).
[CrossRef]

Ångström, A.

A. Ångström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
[CrossRef]

Austin, R. W.

J. L. Mueller and R. W. Austin, "Ocean optics protocols for SeaWiFS for validation, Revision 1," Vol. 25 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, 1995).

Bais, F.

Balis, D.

Basher, R. E.

Benmansour, S.

A. de La Casiniére, T. Cabot, and S. Benmansour, "Measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers," Sol. Energy 54, 173-182 (1995).
[CrossRef]

Berkheiser, W. E.

J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, "Cosine response characteristics of some radiometric and photometric sensors," Sol. Energy 38, 397-402 (1995).
[CrossRef]

Berndt, J.

Bernhard, G.

G. Bernhard and G. Seckmeyer, "New entrance optics for solar spectral uv measurements," Photochem. Photobiol. 65, 923-930 (1997).
[CrossRef]

G. Seckmeyer and G. Bernhard, "Cosine error correction of spectral uv-irradiances," in Proc. SPIE 2049, 140-151 (1993).
[CrossRef]

Berthon, J. F.

Blumthaler, M.

F. Bais, S. Kazadzis, D. Balis, C. Zerefos, and M. Blumthaler, "Correcting total solar ultraviolet spectra recorded by a brewer spectroradiometer for its angular response error," Appl. Opt. 37, 6339-6344 (1998).
[CrossRef]

J. Groebner, M. Blumthaler, and W. Ambach, "Experimental investigation of the spectral total irradiance measurement errors due to a non cosine response," Geophys. Res. Lett. 23, 2493-2496 (1996).
[CrossRef]

M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
[CrossRef]

Booth, C. R.

J. H. Morrow, M. S. Duhig, and C. R. Booth, "Design and evaluation of a cosine collector for a SeaWiFS-compatible Marine Reflectance Radiometer," in Proc. SPIE 2258, 879-886 (1994).
[CrossRef]

Brown, J. W.

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

Bulgarelli, B.

Cabot, T.

A. de La Casiniére, T. Cabot, and S. Benmansour, "Measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers," Sol. Energy 54, 173-182 (1995).
[CrossRef]

D'Alimonte, D.

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

de La Casiniére, A.

A. de La Casiniére, T. Cabot, and S. Benmansour, "Measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers," Sol. Energy 54, 173-182 (1995).
[CrossRef]

Doyle, J. P.

Duhig, M. S.

J. H. Morrow, M. S. Duhig, and C. R. Booth, "Design and evaluation of a cosine collector for a SeaWiFS-compatible Marine Reflectance Radiometer," in Proc. SPIE 2258, 879-886 (1994).
[CrossRef]

Feister, U.

U. Feister, R. Grewe, and K. Gericke, "A method for the correction of cosine errors in measurements of spectral uv irradiance," Solar Energy 60, 313-332 (1997).
[CrossRef]

Feldman, G. C.

C. R. McClain, G. C. Feldman, and S. B. Hooker, "An overview of the seawifs project and strategies for producing a climate research quality global ocean bio-optical time-series," Deep-Sea Res. 51, 5-42 (2004).
[CrossRef]

Ferrari, G.

Gericke, K.

U. Feister, R. Grewe, and K. Gericke, "A method for the correction of cosine errors in measurements of spectral uv irradiance," Solar Energy 60, 313-332 (1997).
[CrossRef]

Grainger, R. G.

Grewe, R.

U. Feister, R. Grewe, and K. Gericke, "A method for the correction of cosine errors in measurements of spectral uv irradiance," Solar Energy 60, 313-332 (1997).
[CrossRef]

Groebner, J.

J. Groebner, "Improved entrance optics for total irradiance measurements with a brewer spectrophotometer," Appl. Opt. 42, 3516-3521 (2003).
[CrossRef]

M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, and W. Ambach, "Experimental investigation of the spectral total irradiance measurement errors due to a non cosine response," Geophys. Res. Lett. 23, 2493-2496 (1996).
[CrossRef]

Harrison, L.

Harrison, L. C.

J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, "Cosine response characteristics of some radiometric and photometric sensors," Sol. Energy 38, 397-402 (1995).
[CrossRef]

Hooker, S. B.

C. R. McClain, G. C. Feldman, and S. B. Hooker, "An overview of the seawifs project and strategies for producing a climate research quality global ocean bio-optical time-series," Deep-Sea Res. 51, 5-42 (2004).
[CrossRef]

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

Huber, M.

M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
[CrossRef]

Kattawar, G. W.

G. W. Kattawar, "A three-parameter analytic phase function for multiple scattering calculations," J. Quant. Spectrosc. Radiat. Transfer 15, 839-849 (1975).
[CrossRef]

Kazadzis, S.

Kisselev, V.

Lazin, G.

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

McClain, C. R.

C. R. McClain, G. C. Feldman, and S. B. Hooker, "An overview of the seawifs project and strategies for producing a climate research quality global ocean bio-optical time-series," Deep-Sea Res. 51, 5-42 (2004).
[CrossRef]

McKenzie, R. L.

McLean, S.

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

Michalsky, J.

Michalsky, J. J.

J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, "Cosine response characteristics of some radiometric and photometric sensors," Sol. Energy 38, 397-402 (1995).
[CrossRef]

Morrow, J. H.

J. H. Morrow, M. S. Duhig, and C. R. Booth, "Design and evaluation of a cosine collector for a SeaWiFS-compatible Marine Reflectance Radiometer," in Proc. SPIE 2258, 879-886 (1994).
[CrossRef]

Mueller, J. L.

J. L. Mueller and R. W. Austin, "Ocean optics protocols for SeaWiFS for validation, Revision 1," Vol. 25 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, 1995).

Nast, P.-M.

P.-M. Nast, "Measurements on the accuracy of pyranometers," Sol. Energy 31, 279-282 (1983).
[CrossRef]

Roberti, L.

Seckmeyer, G.

G. Bernhard and G. Seckmeyer, "New entrance optics for solar spectral uv measurements," Photochem. Photobiol. 65, 923-930 (1997).
[CrossRef]

G. Seckmeyer and G. Bernhard, "Cosine error correction of spectral uv-irradiances," in Proc. SPIE 2049, 140-151 (1993).
[CrossRef]

Sherman, J.

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

Small, M.

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

van der Linde, D.

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

Voss, K. J.

G. Zibordi and K. J. Voss, "Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements," Remote Sens. Environ. 27, 343-358 (1989).
[CrossRef]

Zerefos, C.

Zibordi, G.

B. Bulgarelli, G. Zibordi, and J. F. Berthon, "Measured and modeled radiometric quantities in coastal waters: towards a closure," Appl. Opt. 42, 5365-5381 (2003).
[CrossRef] [PubMed]

B. Bulgarelli and G. Zibordi, "Remote sensing of ocean color: accuracy assessment of an approximate atmospheric correction method," Int. J. Remote Sens. 24, 491-509 (2003).
[CrossRef]

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

J. P. Doyle and G. Zibordi, "Optical propagation within a 3-dimensional shadowed atmosphere-ocean field: application to large deployment structures," Appl. Opt. 41, 4283-4306 (2002).
[CrossRef] [PubMed]

G. Zibordi and G. Ferrari, "Instrumental self-shading in underwater optical measurements: experimental data," Appl. Opt. 34, 2750-2754 (1995).
[CrossRef] [PubMed]

G. Zibordi and K. J. Voss, "Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements," Remote Sens. Environ. 27, 343-358 (1989).
[CrossRef]

Appl. Opt.

Deep-Sea Res.

C. R. McClain, G. C. Feldman, and S. B. Hooker, "An overview of the seawifs project and strategies for producing a climate research quality global ocean bio-optical time-series," Deep-Sea Res. 51, 5-42 (2004).
[CrossRef]

Geophys. Res. Lett.

M. Blumthaler, J. Groebner, M. Huber, and W. Ambach, "Measuring spectral and spatial varaiations of uvb and uva sky radiance," Geophys. Res. Lett. 23, 547-550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, and W. Ambach, "Experimental investigation of the spectral total irradiance measurement errors due to a non cosine response," Geophys. Res. Lett. 23, 2493-2496 (1996).
[CrossRef]

Int. J. Remote Sens.

B. Bulgarelli and G. Zibordi, "Remote sensing of ocean color: accuracy assessment of an approximate atmospheric correction method," Int. J. Remote Sens. 24, 491-509 (2003).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

G. W. Kattawar, "A three-parameter analytic phase function for multiple scattering calculations," J. Quant. Spectrosc. Radiat. Transfer 15, 839-849 (1975).
[CrossRef]

Photochem. Photobiol.

G. Bernhard and G. Seckmeyer, "New entrance optics for solar spectral uv measurements," Photochem. Photobiol. 65, 923-930 (1997).
[CrossRef]

Proc. SPIE

J. H. Morrow, M. S. Duhig, and C. R. Booth, "Design and evaluation of a cosine collector for a SeaWiFS-compatible Marine Reflectance Radiometer," in Proc. SPIE 2258, 879-886 (1994).
[CrossRef]

G. Seckmeyer and G. Bernhard, "Cosine error correction of spectral uv-irradiances," in Proc. SPIE 2049, 140-151 (1993).
[CrossRef]

Remote Sens. Environ.

G. Zibordi and K. J. Voss, "Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements," Remote Sens. Environ. 27, 343-358 (1989).
[CrossRef]

Sol. Energy

A. de La Casiniére, T. Cabot, and S. Benmansour, "Measuring spectral diffuse solar irradiance with non-cosine flat-plate diffusers," Sol. Energy 54, 173-182 (1995).
[CrossRef]

J. J. Michalsky, L. C. Harrison, and W. E. Berkheiser, "Cosine response characteristics of some radiometric and photometric sensors," Sol. Energy 38, 397-402 (1995).
[CrossRef]

P.-M. Nast, "Measurements on the accuracy of pyranometers," Sol. Energy 31, 279-282 (1983).
[CrossRef]

Solar Energy

U. Feister, R. Grewe, and K. Gericke, "A method for the correction of cosine errors in measurements of spectral uv irradiance," Solar Energy 60, 313-332 (1997).
[CrossRef]

Tellus

A. Ångström, "Techniques of determining the turbidity of the atmosphere," Tellus 13, 214-223 (1961).
[CrossRef]

Other

IAMAPRC, "A preliminary cloudless standard atmosphere for radiation computation," Technical Report WCP-112, WMO/TD-No. 24 (International Association for Meteorology and Atmospheric Physics, Radiation Commission, World Climate Programme, 1984).

S. B. Hooker, S. McLean, J. Sherman, M. Small, G. Lazin, G. Zibordi, and J. W. Brown, "The Seventh SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-7)," Vol. 17 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2002).

G. Zibordi, D. D'Alimonte, D. van der Linde, S. B. Hooker, and J. W. Brown, "New laboratory methods for characerizing the immersion factors of irradiance sensors," Vol. 26 of SeaWiFS postlaunch Technical Report Series (Goddard Space Flight Center, 2003).

J. L. Mueller and R. W. Austin, "Ocean optics protocols for SeaWiFS for validation, Revision 1," Vol. 25 of SeaWiFS Technical Report Series (NASA Goddard Space Flight Center, 1995).

German Institute of Standardization, "DIN 5032 Teil 1," Deutsche Normen Series (Beuth Verlag, 1978).

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Figures (10)

Fig. 1
Fig. 1

(Color online) Schematic of the measurement configuration for the characterization of cosine response. Inset (a) displays the front view of the OCI-200 and OCR-507 radiometers, while inset (b) displays the top view of the measurement system and highlights the viewing geometry.

Fig. 2
Fig. 2

Standard deviation, σ, of cosine errors f c ( θ , λ ) determined for multiple characterizations of the same sensors.

Fig. 3
Fig. 3

Average cosine errors f ¯ c ( θ , λ ) determined at various center wavelengths.

Fig. 4
Fig. 4

Intrachannel cosine errors f c ( θ , λ ) at the reference center wavelengths 443, 555, and 665   nm (different symbols indicate different radiometers: ♢ for OCR-507 s∕n 045; ☐ for OCI-200 s∕n 099; Δ for OCI-200 s∕n 129).

Fig. 5
Fig. 5

Standard deviation, σ, of intrachannel cosine errors f c ( θ , λ ) .

Fig. 6
Fig. 6

Simulated ε c ( θ 0 , λ ) for maritime aerosol, as a function of sun zenith. Values in brackets indicate the Ångström coefficient and exponent, respectively. Symbols ♢ indicate data at the 412   nm center wavelength, Δ at 443   nm , ☐ at 490   nm , ○ at 510   nm , * at 555   nm , + for 665   nm , and × at 683   nm .

Fig. 7
Fig. 7

Simulated ε c ( θ 0 , λ ) for continental aerosol, as a function of sun zenith. Values in brackets indicate the Ångström coefficient and exponent, respectively. Symbols ♢ indicate data at the 412   nm center wavelength, ▵ at 443   nm , ☐ at 490   nm , ○ at 510   nm , * at 555   nm , + for 665   nm , and × 683   nm .

Fig. 8
Fig. 8

Simulated ε c ( θ 0 , λ ) as a function of I r ( θ 0 , λ ) at the reference center-wavelengths 443, 555, and 665   nm for maritime aerosol (symbols indicate different sun zeniths in degrees: ♢ for 10; ○ for 30; + for 40; × for 50; • for 60; Δ for 65; ☐ for 70; * for 75; ⊠ for 80).

Fig. 9
Fig. 9

Values of ε c ( θ 0 , λ ) as a function of sun zenith, computed with τ a ( λ ) for very clear ( γ = 0.02 and α = 1.0 ) and hazy ( γ = 0.15 and α = 2.0 ) atmospheres. Symbols ♢ indicate data at the 412   nm center-wavelength, Δ at 443   nm , ☐ at 490   nm , ○ at 510   nm , * at 555   nm , + for 665   nm , and × at 683   nm .

Fig. 10
Fig. 10

Differences between the values of ε c ( θ 0 , λ ) and ε c ( θ 0 , λ ) displayed in Figs. 9 and 6 for very clear ( γ = 0.02 and α = 1.0 ) and hazy ( γ = 0.15 and α = 2.0 ) sky conditions. Symbols ♢ indicate data at the 412   nm center wavelength, Δ at 443   nm , ☐ at 490   nm , ○ at 510   nm , * at 555   nm , + for 665   nm , and × at 683   nm .

Tables (2)

Tables Icon

Table 1 Average Values of | f ¯ c ( λ ) | for the Radiometers Included in the Study

Tables Icon

Table 2 Simulated ε c ( θ 0 , λ ) for Overcast Sky

Equations (5)

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f c ( ϕ , θ , λ ) = 100 [ E ( ϕ , θ , λ ) E ( ϕ , 0 , λ ) cos   θ 1 ] ,
| f ¯ c ( λ ) | = 0 0.47 π | f ¯ c ( θ , λ ) | sin ( 2 θ ) d θ .
ε c ( θ 0 , λ ) = 100 [ E ̆ d ( 0 + , λ ) E ˜ d ( 0 + , λ ) 1 ] ,
ε c ( θ 0 , λ ) = f ¯ c ( λ ) I r ( θ 0 , λ ) I r ( θ 0 , λ ) + 1 + f c ( θ , λ ) 1 I r ( θ 0 , λ ) + 1   ,
f ¯ c ( λ ) = 0 0.5 π f ¯ c ( θ , λ ) sin ( 2 θ ) d θ .

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