Abstract

A new system to measure the natural skylight polarized radiance distribution has been developed. The system is based on a fish-eye lens, CCD camera system, and filter changer. With this system sequences of images can be combined to determine the linear polarization components of the incident light field. Calibration steps to determine the system’s polarization characteristics are described. Comparisons of the radiance measurements of this system and a simple pointing radiometer were made in the field and agreed within 10% for measurements at 560 and 670 nm and 25% at 860 nm. Polarization tests were done in the laboratory. The accuracy of the intensity measurements is estimated to be 10%, while the accuracy of measurements of elements of the Mueller matrix are estimated to be 2%.

© 1997 Optical Society of America

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References

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  1. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, Hampton, Va., 1988).
  2. A. T. Young, “Rayleigh scattering,” Phys. Today 35(1), 42–48 (1982).
    [CrossRef]
  3. K. L. Coulson, “Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity. I: degree of polarization,” Appl. Opt. 19, 3469–3480 (1980).
    [CrossRef] [PubMed]
  4. H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).
  5. T. Prosch, D. Hennongs, E. Raschke, “Video polarimetry: a new imaging technique in atmospheric science,” Appl. Opt. 22, 1360–1363 (1983).
    [CrossRef] [PubMed]
  6. T. W. Cronin, N. Shashar, L. Wolff, “Portable imaging polarimeters,” in Proceedings of the Twelfth IAPR International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers Computer Society, Los Alamitos Calif., 1994), pp. 606–609.
    [CrossRef]
  7. H. Povel, “Imaging stokes polarimetry with modulators and charge coupled-device image sensors,” Opt. Eng. 34, 1870–1878 (1995).
    [CrossRef]
  8. K. J. Voss, A. L. Chapin, “Next generation in-water radiance distribution camera system,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 384–387 (1992).
    [CrossRef]
  9. K. J. Voss, G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fish-eye’ camera radiance distribution system,” J. Atmos. Oceanic Tech. 6, 652–662 (1989).
    [CrossRef]
  10. Y. Kiu, K. J. Voss, “Polarized radiance distribution measurement of skylight. II. Experiment and data,” Appl. Opt.36 (1997), to be published.
  11. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  12. G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 233–258 (1852).
  13. G. W. Kattawar, X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 222–233 (1994).
    [CrossRef]
  14. K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).
    [CrossRef]
  15. P. J. Johnson, Manual on Starscape II CCD Cameras (First Magnitude Inc., Laramie, Wyo., 1992).
  16. J. S. Campbell, “TC271 characterization report,” in Area Array Image Sensor Products (Texas Instruments, Dallas, Tex., 1994).
  17. G. R. Sims, M. B. Denton, “Spatial pixel crosstalk in a charge-injection device,” Opt. Eng. 26, 999–1007 (1987).
    [CrossRef]
  18. C. L. Wyatt, Radiometric Calibration: Theory and Methods (Academic, New York, 1978).
  19. B. J. Howell, “Measurement of the polarization effects of an instrument using partially polarized light,” Appl. Opt. 18, 809–812 (1979).
    [CrossRef] [PubMed]
  20. E. H. Land, “Some aspects of the development of sheet polarizers,” J. Opt. Soc. Am. 41, 957–963 (1951).
    [CrossRef]
  21. G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
    [CrossRef]
  22. W. H. Wilson, “Measurements of atmospheric transmittance in a maritime environment,” in Atmospheric Effects on Radiative Transfer, C. B. Ludwig, ed., Proc. SPIE195, 153–159 (1979).
    [CrossRef]

1995 (1)

H. Povel, “Imaging stokes polarimetry with modulators and charge coupled-device image sensors,” Opt. Eng. 34, 1870–1878 (1995).
[CrossRef]

1989 (3)

K. J. Voss, G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fish-eye’ camera radiance distribution system,” J. Atmos. Oceanic Tech. 6, 652–662 (1989).
[CrossRef]

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).
[CrossRef]

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

1987 (1)

G. R. Sims, M. B. Denton, “Spatial pixel crosstalk in a charge-injection device,” Opt. Eng. 26, 999–1007 (1987).
[CrossRef]

1983 (1)

1982 (1)

A. T. Young, “Rayleigh scattering,” Phys. Today 35(1), 42–48 (1982).
[CrossRef]

1980 (1)

1979 (1)

1951 (1)

1913 (1)

H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).

1852 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 233–258 (1852).

Adams, C. N.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Campbell, J. S.

J. S. Campbell, “TC271 characterization report,” in Area Array Image Sensor Products (Texas Instruments, Dallas, Tex., 1994).

Chapin, A. L.

K. J. Voss, A. L. Chapin, “Next generation in-water radiance distribution camera system,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 384–387 (1992).
[CrossRef]

Coulson, K. L.

Cronin, T. W.

T. W. Cronin, N. Shashar, L. Wolff, “Portable imaging polarimeters,” in Proceedings of the Twelfth IAPR International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers Computer Society, Los Alamitos Calif., 1994), pp. 606–609.
[CrossRef]

Denton, M. B.

G. R. Sims, M. B. Denton, “Spatial pixel crosstalk in a charge-injection device,” Opt. Eng. 26, 999–1007 (1987).
[CrossRef]

Hennongs, D.

Howell, B. J.

Johnson, P. J.

P. J. Johnson, Manual on Starscape II CCD Cameras (First Magnitude Inc., Laramie, Wyo., 1992).

Kattawar, G. W.

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

G. W. Kattawar, X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 222–233 (1994).
[CrossRef]

Kimball, H. H.

H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).

Kiu, Y.

Y. Kiu, K. J. Voss, “Polarized radiance distribution measurement of skylight. II. Experiment and data,” Appl. Opt.36 (1997), to be published.

Land, E. H.

Povel, H.

H. Povel, “Imaging stokes polarimetry with modulators and charge coupled-device image sensors,” Opt. Eng. 34, 1870–1878 (1995).
[CrossRef]

Prosch, T.

Raschke, E.

Shashar, N.

T. W. Cronin, N. Shashar, L. Wolff, “Portable imaging polarimeters,” in Proceedings of the Twelfth IAPR International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers Computer Society, Los Alamitos Calif., 1994), pp. 606–609.
[CrossRef]

Sims, G. R.

G. R. Sims, M. B. Denton, “Spatial pixel crosstalk in a charge-injection device,” Opt. Eng. 26, 999–1007 (1987).
[CrossRef]

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 233–258 (1852).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Voss, K. J.

K. J. Voss, G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fish-eye’ camera radiance distribution system,” J. Atmos. Oceanic Tech. 6, 652–662 (1989).
[CrossRef]

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).
[CrossRef]

K. J. Voss, A. L. Chapin, “Next generation in-water radiance distribution camera system,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 384–387 (1992).
[CrossRef]

Y. Kiu, K. J. Voss, “Polarized radiance distribution measurement of skylight. II. Experiment and data,” Appl. Opt.36 (1997), to be published.

Wilson, W. H.

W. H. Wilson, “Measurements of atmospheric transmittance in a maritime environment,” in Atmospheric Effects on Radiative Transfer, C. B. Ludwig, ed., Proc. SPIE195, 153–159 (1979).
[CrossRef]

Wolff, L.

T. W. Cronin, N. Shashar, L. Wolff, “Portable imaging polarimeters,” in Proceedings of the Twelfth IAPR International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers Computer Society, Los Alamitos Calif., 1994), pp. 606–609.
[CrossRef]

Wyatt, C. L.

C. L. Wyatt, Radiometric Calibration: Theory and Methods (Academic, New York, 1978).

Xu, X.

G. W. Kattawar, X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 222–233 (1994).
[CrossRef]

Young, A. T.

A. T. Young, “Rayleigh scattering,” Phys. Today 35(1), 42–48 (1982).
[CrossRef]

Zibordi, G.

K. J. Voss, G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fish-eye’ camera radiance distribution system,” J. Atmos. Oceanic Tech. 6, 652–662 (1989).
[CrossRef]

Appl. Opt. (3)

Bull. Mt. Weather Obs. (1)

H. H. Kimball, “The effect of the atmospheric turbidity of 1912 on solar radiation intensities and skylight polarization,” Bull. Mt. Weather Obs. 5, 295–312 (1913).

J. Atmos. Oceanic Tech. (1)

K. J. Voss, G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fish-eye’ camera radiance distribution system,” J. Atmos. Oceanic Tech. 6, 652–662 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Limnol. Oceanogr. (1)

G. W. Kattawar, C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere-ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34, 1453–1472 (1989).
[CrossRef]

Opt. Eng. (3)

K. J. Voss, “Electro-optic camera system for measurement of the underwater radiance distribution,” Opt. Eng. 28, 241–247 (1989).
[CrossRef]

G. R. Sims, M. B. Denton, “Spatial pixel crosstalk in a charge-injection device,” Opt. Eng. 26, 999–1007 (1987).
[CrossRef]

H. Povel, “Imaging stokes polarimetry with modulators and charge coupled-device image sensors,” Opt. Eng. 34, 1870–1878 (1995).
[CrossRef]

Phys. Today (1)

A. T. Young, “Rayleigh scattering,” Phys. Today 35(1), 42–48 (1982).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 233–258 (1852).

Other (10)

G. W. Kattawar, X. Xu, “Detecting Raman scattering in the ocean by use of polarimetry,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 222–233 (1994).
[CrossRef]

Y. Kiu, K. J. Voss, “Polarized radiance distribution measurement of skylight. II. Experiment and data,” Appl. Opt.36 (1997), to be published.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

C. L. Wyatt, Radiometric Calibration: Theory and Methods (Academic, New York, 1978).

P. J. Johnson, Manual on Starscape II CCD Cameras (First Magnitude Inc., Laramie, Wyo., 1992).

J. S. Campbell, “TC271 characterization report,” in Area Array Image Sensor Products (Texas Instruments, Dallas, Tex., 1994).

K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, Hampton, Va., 1988).

K. J. Voss, A. L. Chapin, “Next generation in-water radiance distribution camera system,” in Ocean Optics XI, G. D. Gilbert, ed., Proc. SPIE1750, 384–387 (1992).
[CrossRef]

T. W. Cronin, N. Shashar, L. Wolff, “Portable imaging polarimeters,” in Proceedings of the Twelfth IAPR International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers Computer Society, Los Alamitos Calif., 1994), pp. 606–609.
[CrossRef]

W. H. Wilson, “Measurements of atmospheric transmittance in a maritime environment,” in Atmospheric Effects on Radiative Transfer, C. B. Ludwig, ed., Proc. SPIE195, 153–159 (1979).
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

Block diagram of the RADS-IIP instrument.

Fig. 2
Fig. 2

Dark counts along a row and column, illustrating the nonuniformity of the dark signal on the detector. Integration time was 1 s; sensor temperature was -34.5 °C.

Fig. 3
Fig. 3

Dark counts as a function of integration time and sensor temperature, illustrating the linear relation of dark counts to integration time and exponential relation to sensor temperature.

Fig. 4
Fig. 4

Cross-talk experiment that illustrates the suppression of counts from pixels in the same row as a bright pixel.

Fig. 5
Fig. 5

Linearity calibration. Line is a power fit to the data and fits well over 3 orders of magnitude of light intensity (exponent is 1.04).

Fig. 6
Fig. 6

Typical roll-off curve found through the calibration process.

Fig. 7
Fig. 7

Measured principal transmittances for the dichroic polarizer used as a function of wavelength.

Fig. 8
Fig. 8

Nonzero matrix elements for the reflected and transmitted light due to interaction with a glass (index of refraction of 1.5) surface.

Fig. 9
Fig. 9

Reduced matrix element M14 as a function of off-axis angle and polarization filter position (W1–W4).

Fig. 10
Fig. 10

Reduced matrix element M12 as a function of off-axis angle and polarization filter position.

Fig. 11
Fig. 11

Reduced matrix element M13 as a function of off-axis angle and polarization filter position.

Fig. 12
Fig. 12

Almucantar comparison of HHCRM and RADS.

Fig. 13
Fig. 13

Principal plane comparison of HHCRM and RADS.

Fig. 14
Fig. 14

Relative difference between HHCRM and RADS measurements in the principal plane at each wavelength.

Fig. 15
Fig. 15

M 12 direct measurement and matrix transformation method, illustrating how well the matrix transformation method works to estimate the system Mueller matrix. Measurements were performed at 560 nm.

Fig. 16
Fig. 16

M 13 direct measurement and matrix transformation method, illustrating how well the matrix transformation method works to estimate the system Mueller matrix. Measurements were performed at 560 nm.

Fig. 17
Fig. 17

Sample contour plot of M12(W2).

Fig. 18
Fig. 18

Sample contour plot of M12(W3).

Equations (21)

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

Lλθ, ϕ=d2Pλθ, ϕcos θ dAdΩdλ.
E=Ell+Err.
El=al coskz-ωt+δl,Er=ar coskz-ωt+δr,
I=ElEl*+ErEr*, Q=ElEl*-ErEr*,U=ElEr*+ErEl*,V=-iElEr*-ErEl*.
I2=Q2+U2+V2.
I=Il+Ir,Q=Il-Ir=I cos 2β cos 2χ, U=I cos 2β sin 2χ, V=I sin 2β.
I2Q2+U2+V2.
P+=Q2+U2+V21/2/I
Plinear=Q2+U21/2/I.
tan 2χ=U/Q,
sin 2β=V/Q2+U2+V21/2.
IQUV=Q2+U2+V21/2QUV+I-Q2+U2+V21/2000.
IQUV=M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44IoQoUoVo.
Mp=k1+k2k1-k2cos 2ψk1-k2sin 2ψ0k1-k2cos 2ψk1+k2cos2 2ψ+2k1k2sin2 2ψk1+k2-2k1k2cos 2ψ sin 2ψ0k1-k2sin 2ψk1+k2-2k1k2cos 2ψ sin 2ψk1+k2sin2 2ψ+2k1k2cos2 2ψ00002k1k2,
I1=Io+Qoψ=0°,I2=Io+Uoψ=45°I3=Io-Qoψ=90°.
A=IoIoOO, B=Io-IoOO, C=IoOIo0, D=I0OOIo,
A=1k1-k2k1+k200, B=1k1+k2k1+k200, C=10k1-k2k1+k2O.
M=M3M2M1,
1α-ηα+η00α-ηα+η10000γα+η0000γα+η,
M=MpMs.
%difference=100HHCRM-RADSHHCRM+RADS/2

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