Abstract

The polarimetric characteristics of a class of hyperspectral radiometers commonly applied for above-water radiometry have been investigated by analyzing a sample of sensors. Results indicate polarization sensitivity increasing with wavelength and exhibiting values varying from sensor to sensor. In the case of radiance sensors, the maximum differences increase from approximately 0.4% at 400 nm to 1.3% at 750 nm. In the case of irradiance sensors, due to depolarizing effects of the diffusing collector, the maximum differences between horizontal and vertical polarization sensitivities vary from approximately 0.3% at 400 nm to 0.6% at 750 nm. Application of the previous results to above-water radiometry measurements performed in sediment dominated waters indicates that neglecting polarization effects may lead to uncertainties not exceeding a few tenths of a percent in remote sensing reflectance RRS determined in the 400–570 nm spectral interval. Conversely, uncertainties spectrally increase toward the near infrared, reaching several percent at 750 nm in the case of oligotrophic waters.

© 2016 Optical Society of America

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References

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    [Crossref]
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  5. H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997).
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  8. D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2016).
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    [Crossref]
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    [Crossref]
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2016 (3)

2015 (2)

C. D. Mobley, “Polarized reflectance and transmittance properties of windblown sea surfaces,” Appl. Opt. 54, 4828–4849 (2015).
[Crossref]

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

2014 (1)

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

2011 (1)

2010 (1)

1999 (1)

1998 (1)

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

1994 (1)

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, 222–233 (1994).
[Crossref]

1981 (1)

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 200114 (1981).
[Crossref]

1958 (1)

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

Ansko, I.

Antoine, D.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Banks, A. C.

Belmar da Costa, L.

Berndt, J.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Bhandari, A.

Bojinski, S.

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

Bruegge, C. J.

D’Alimonte, D.

DeLuisi, J.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Disterhoft, P.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Early, E.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

Franz, B. A.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Frette, Ø.

Goldstein, D. H.

D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2016).

Hamre, B.

Haner, D. A.

Harrison, L.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Hayes, D. S.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Huot, J.-P.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Ivanoff, A.

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

Johnson, C.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Kajiyama, T.

Kattawar, G. W.

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, 222–233 (1994).
[Crossref]

Kildemo, M.

Kostkowski, H. J.

H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997).

Kuusk, J.

Kwiatkowska, E.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Lucas, T.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

McGuckin, B. T.

Melin, F.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Mestechkina, T.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Mobley, C. D.

Mou, W.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Peterson, T. C.

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

Richter, C.

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

Schott, J. R.

J. R. Schott, Fundamentals of Polarimetric Remote Sensing (SPIE, 2009), Vol. TT81.

Simmons, A.

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

Souaidia, N.

Stamnes, J. J.

Sun, Y.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Talone, M.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

Thompson, A.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Verstraete, M.

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

Voss, K. J.

K. J. Voss and L. Belmar da Costa, “Polarization properties of FEL lamps as applied to radiometric calibration,” Appl. Opt. 55, 8829–8832 (2016).
[Crossref]

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

K. J. Voss and N. Souaidia, “POLRADS: polarization radiance distribution measurement system,” Opt. Express 18, 19672–19680 (2010).
[Crossref]

G. Zibordi and K. J. Voss, “In situ optical radiometry in the visible and near infrared,” in Optical Radiometry for Oceans Climate Measurements, G. Zibordi, C. Donlon, and A. Parr, eds., Experimental Methods in the Physical Sciences (Elsevier and Academic, 2014), Vol. 47.

Walraven, R.

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 200114 (1981).
[Crossref]

Wang, M.

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Wardle, D.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Waterman, T. H.

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

Wu, E.

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Wyatt, C. L.

C. L. Wyatt, Radiometric System Design (MacMillan, 1987).

Xu, X.

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, 222–233 (1994).
[Crossref]

Zemp, M.

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

Zhao, L.

Zibordi, G.

M. Talone, G. Zibordi, I. Ansko, A. C. Banks, and J. Kuusk, “Stray light effects in above-water remote-sensing reflectance from hyperspectral radiometers,” Appl. Opt. 55, 3966–3977 (2016).
[Crossref]

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

G. Zibordi and K. J. Voss, “In situ optical radiometry in the visible and near infrared,” in Optical Radiometry for Oceans Climate Measurements, G. Zibordi, C. Donlon, and A. Parr, eds., Experimental Methods in the Physical Sciences (Elsevier and Academic, 2014), Vol. 47.

Appl. Opt. (5)

Bull. Am. Meteorol. Soc. (1)

S. Bojinski, M. Verstraete, T. C. Peterson, C. Richter, A. Simmons, and M. Zemp, “The concept of essential climate variables in support of climate research, applications, and policy,” Bull. Am. Meteorol. Soc. 95, 1431–1443 (2014).
[Crossref]

J. Mar. Res. (1)

A. Ivanoff and T. H. Waterman, “Elliptical polarization of submarine illumination,” J. Mar. Res. 16, 255–282 (1958).

J. Res. Natl. Inst. Stand. Technol. (1)

E. Early, A. Thompson, C. Johnson, J. DeLuisi, P. Disterhoft, D. Wardle, E. Wu, W. Mou, Y. Sun, T. Lucas, T. Mestechkina, L. Harrison, J. Berndt, and D. S. Hayes, “The 1995 North American interagency intercomparison of ultraviolet monitoring spectroradiometers,” J. Res. Natl. Inst. Stand. Technol. 103(1), 15–62 (1998).
[Crossref]

Opt. Eng. (1)

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 200114 (1981).
[Crossref]

Opt. Express (2)

Proc. SPIE (1)

G. W. Kattawar and X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” Proc. SPIE 2258, 222–233 (1994).
[Crossref]

Remote Sens. Environ. (1)

G. Zibordi, F. Melin, K. J. Voss, C. Johnson, B. A. Franz, E. Kwiatkowska, J.-P. Huot, M. Wang, and D. Antoine, “System vicarious calibration for ocean color climate change applications: requirements for in situ data,” Remote Sens. Environ. 159, 361–369 (2015).
[Crossref]

Other (8)

C. L. Wyatt, Radiometric System Design (MacMillan, 1987).

H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997).

National Bureau of Standards (NBS), “Self-study manual on optical radiation measurements,” in Technical Notes 910-1 through 910-8, F. E. Nicodemus, ed. (U.S. Government Printing Office, 1976–1985).

D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2016).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

“Implementation plan for the global observing system for climate in support of the UNFCCC,” (2010, update) , [available online at http://www.wmo.int/pages/prog/gcos/Publications/gcos-138.pdf ].

G. Zibordi and K. J. Voss, “In situ optical radiometry in the visible and near infrared,” in Optical Radiometry for Oceans Climate Measurements, G. Zibordi, C. Donlon, and A. Parr, eds., Experimental Methods in the Physical Sciences (Elsevier and Academic, 2014), Vol. 47.

J. R. Schott, Fundamentals of Polarimetric Remote Sensing (SPIE, 2009), Vol. TT81.

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Figures (24)

Fig. 1.
Fig. 1. Block representation of an optical radiometer.
Fig. 2.
Fig. 2. Measurement configurations applied for the determination the polarimetric characteristics of (a) radiance and (b) irradiance sensors.
Fig. 3.
Fig. 3. Flow diagram for the determination of the polarimetric characteristics of a radiometer.
Fig. 4.
Fig. 4. Flow diagram for the assessment performed to quantify the inaccuracy of the measurement setup.
Fig. 5.
Fig. 5. Background signal due to measurement inaccuracy as determined with SAM-84C3 using two independent installations (i.e., different 99% Spectralon reflectance plaques and by reinstalling the measurement setup).
Fig. 6.
Fig. 6. Parameter r 1 obtained for radiance sensors SAM-8346 and SAM-8313 (blue), SAM-82CD and SAM-82CF (red), SAM-84C2 and SAM-84C3 (light blue), and SAM-850D and SAM-8508 (green).
Fig. 7.
Fig. 7. Spectral percent change Δ of the measured signal as a function of the rotation angle φ for SAM-8346 due to the polarization sensitivity of the radiance sensor.
Fig. 8.
Fig. 8. Parameter r 1 obtained for the irradiance sensors SAM-835C (blue), SAM-82C1 (red), and SAM-84C0 (green).
Fig. 9.
Fig. 9. Spectral percent difference Δ of the measured signal as a function of the rotation angle φ for SAM-82C1 due to the polarization sensitivity of the irradiance sensor.
Fig. 10.
Fig. 10. Spectra of (a)  L T and L i and (b)  R RS from the Western Mediterranean sea oligotrophic/mesotrophic waters. Measurements were performed with radiometers SAM-8346 ( L T ) , SAM-8313 ( L i ) , and SAM-835C ( E d ) on 14 April 2014 at 12:17 GMT.
Fig. 11.
Fig. 11. Spectra of (a)  L T and L i and (b)  R RS from the northern Adriatic Sea sediment-dominated waters. Measurements were performed with radiometers SAM-8346 ( L T ) , SAM-8313 ( L i ) , and SAM-835C ( E d ) on 4 April 2015 at 8:11 GMT.
Fig. 12.
Fig. 12. Effect of the radiometer’s polarization sensitivity on (a)  L T and (b)  L i measurements from the Western Mediterranean Sea oligotrophic waters, expressed in percent of L w .
Fig. 13.
Fig. 13. Effect of radiometers polarization sensitivity on (a)  L T and (b)  L i measurements from the northern Adriatic Sea sediment-dominated waters, expressed in percent of L w . To facilitate direct comparisons, the y scale is deliberately set identical to that of Fig. 12.
Fig. 14.
Fig. 14. Effects of polarization sensitivity on R RS from the Western Mediterranean Sea oligotrophic waters. Results have been determined with DoLP L T equal to 25%, 50%, and 75% (displayed in black, blue, and red, respectively). In view of reducing the complexity of the figure, data are only presented for positive values of Δ L T , which maximize perturbations due to polarization sensitivity. Error bars refer to values of ± Δ L i determined with DoLP L i equal to 40%.
Fig. 15.
Fig. 15. Effect of polarization sensitivity on R RS spectral values from the northern Adriatic Sea sediment-dominated waters. Results have been determined with DoLP L T equal to 25%, 50%, and 75% (displayed in black, blue, and red, respectively). In view of reducing the complexity of the figure, data are only presented for positive values of Δ L T , which maximize perturbations due to polarization sensitivity. Error bars refer to values of ± Δ L i determined with DoLP L i equal to 40%. To facilitate direct comparisons, the y scale is deliberately set identical to that of Fig. 14.
Fig. 16.
Fig. 16. Measurement configuration for the determination of the polarimetric characteristics of the radiance (a) and irradiance (b) sources.
Fig. 17.
Fig. 17. Flow diagram for the determination of the polarimetric characteristics of a source.
Fig. 18.
Fig. 18. Parameters s 1 obtained for a FEL-1000 W lamp (i.e., H-96531). The error bars on the y axis indicate the standard deviation determined from the polarimetric characterization of the lamp through measurements performed with three different RAMSES-ACC irradiance sensors.
Fig. 19.
Fig. 19. Spectral percent change Δ of the measured signal as a function of the rotation angle φ determined with RAMSES SAM-82C1 pointing at the FEL-1000 W lamp.
Fig. 20.
Fig. 20. Parameter s 1 determined for the radiance source obtained with the plaque illuminated by a FEL-1000 W lamp. The error bars on the y axis indicate the standard deviation obtained from the polarimetric characterization of the plaque as determined using measurements performed with eight different RAMSES-ARC radiance sensors.
Fig. 21.
Fig. 21. Spectral percent change Δ of the measured signal as a function of the rotation angle φ determined with RAMSES SAM-8346 pointing at the radiance source.
Fig. 22.
Fig. 22. Measurement configuration for the determination of parameters s and d of polarizers F and G .
Fig. 23.
Fig. 23. Parameters s (a) and extinction ratios (b) determined for polarizers F , G , and H , displayed in blue, red, and green, respectively.
Fig. 24.
Fig. 24. Values of parameters r 1 obtained by characterizing the radiance sensor SAM-8346 (blue) and the irradiance sensor SAM-82C1 (red) without the depolarizer (denoted as r 1 ) and with the depolarizer (denoted as r 1 D ).

Equations (25)

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S = [ S 0 S 1 S 2 S 3 ] = S 0 [ 1 s 1 s 2 s 3 ] ,
T = [ T 00 T 01 T 02 T 03 T 10 T 11 T 12 T 13 T 20 T 21 T 22 T 23 T 30 T 31 T 32 T 33 ] ,
S T = [ T 00 · S 0 + T 01 · S 1 + T 02 · S 2 + T 03 · S 3 T 10 · S 0 + T 11 · S 1 + T 12 · S 2 + T 13 · S 3 T 20 · S 0 + T 21 · S 1 + T 22 · S 2 + T 23 · S 3 T 30 · S 0 + T 31 · S 1 + T 32 · S 2 + T 33 · S 3 ] .
D N = R · r · S = S 0 [ R 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] · [ R 00 R 01 R 02 R 03 R 10 R 11 R 12 R 13 R 20 R 21 R 22 R 23 R 30 R 31 R 32 R 33 ] · [ 1 s 1 s 2 s 3 ] ,
D N = S 0 · ( R 00 + s 1 · R 01 + s 2 · R 02 + s 3 · R 03 ) · R = S 0 · R 00 · ( 1 + s 1 · r 1 + s 2 · r 2 + s 3 · r 3 ) · R ,
P = [ s d · cos 2 ψ d · sin 2 ψ 0 d · cos 2 ψ s · cos 2 2 ψ + p · sin 2 2 ψ ( s p ) · sin 2 ψ · cos 2 ψ q · sin 2 ψ d · sin 2 ψ ( s p ) · sin 2 ψ · cos 2 ψ s · sin 2 2 ψ + p · cos 2 2 ψ q · cos 2 ψ 0 q · sin 2 ψ q · cos 2 ψ p ] .
s = 1 2 ( k 1 + k 2 ) ,
d = 1 2 ( k 1 k 2 ) ,
p = k 1 · k 2 · cos δ ,
q = k 1 · k 2 · sin δ .
P = [ s d 0 0 d s 0 0 0 0 p q 0 0 q p ]
S P = P · S = S 0 [ s + s 1 · d d + s 1 · s s 2 · p + s 3 · q s 2 · q · + s 3 · p ] .
M = [ 1 0 0 0 0 cos 2 φ sin 2 φ 0 0 sin 2 φ cos 2 φ 0 0 0 0 1 ] ,
S MP = M · S P = S 0 [ s + s 1 · d ( d + s 1 · s ) · cos 2 φ + ( s 2 · p + s 3 · q ) · sin 2 φ ( d + s 1 · s ) · sin 2 φ + ( s 2 · p + s 3 · q ) · cos 2 φ s 2 · q + s 3 · p ] .
D N = S 0 · R 00 · ( s + s 1 · d + r 1 · d · cos 2 φ + r 1 · s 1 · s · cos 2 φ + r 1 · s 2 · p · sin 2 φ + r 1 · s 3 · q · sin 2 φ r 2 · d · sin 2 φ r 2 · s 1 · s · sin 2 φ + r 2 · s 2 · p · cos 2 φ + r 2 · s 3 · q · cos 2 φ r 3 · s 2 · q + r 3 · s 3 · p ) · R .
D N S 0 · R 00 · ( s + s 1 · d + r 1 · d · cos 2 φ r 2 · d · sin 2 φ ) · R .
D N = r · S M · R = S 0 · R 00 · ( 1 + r 1 · s 1 · cos 2 φ + r 1 · s 2 · sin 2 φ r 2 · s 1 · sin 2 φ + r 2 · s 2 · cos 2 φ + r 3 · s 3 ) · R .
D N = S 0 · R 00 · R .
Δ ( φ ) = 100 · ( D N ( φ ) D N ¯ ) D N ¯ r 1 · d · cos 2 φ s + s 1 · d .
R RS = L w E d = 1 E d ( L T ρ L i ) ,
DoLP = S 1 2 + S 2 2 S 0 .
S M = S 0 [ 1 s 1 · cos 2 φ + s 2 · sin 2 φ s 1 · sin 2 φ + s 2 · cos 2 φ s 3 ]
S PM = P · S M = S 0 [ s + ( s 1 · cos 2 φ + s 2 · sin 2 φ ) · d d + ( s 1 · cos 2 φ + s 2 · sin 2 φ ) · s ( s 1 · sin 2 φ + s 2 · cos 2 φ ) · p + s 3 · q ( s 1 · sin 2 φ + s 2 · cos 2 φ ) · q + s 3 · p ] .
D N = r · S P M · R = S 0 · R 00 · ( s + s 1 · d · cos 2 φ + s 2 · d · sin 2 φ + r 1 · d + r 1 · s 1 · s · cos 2 φ + r 1 · s 2 · s · sin 2 φ r 2 · s 1 · p · sin 2 φ + r 2 · s 2 · p · cos 2 φ + r 2 · s 3 · q r 3 · s 1 · q · sin 2 φ r 3 · s 2 · q · cos 2 φ + r 3 · s 3 · p ) · R .
D N = S 0 · R 00 · ( s + r 1 · d + s 1 · d · cos 2 φ + s 2 · d · sin 2 φ ) · R .

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