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Applied Optics

Applied Optics


  • Vol. 37, Iss. 9 — Mar. 20, 1998
  • pp: 1465–1476

Digital imaging of clear-sky polarization

Raymond L. Lee, Jr.  »View Author Affiliations

Applied Optics, Vol. 37, Issue 9, pp. 1465-1476 (1998)

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If digital images of clear daytime or twilight skies are acquired through a linear polarizing filter, they can be combined to produce high-resolution maps of skylight polarization. Here polarization P and normalized Stokes parameter Q are measured near sunset at one inland and two coastal sites. Maps that include the principal plane consistently show that the familiar Arago and Babinet neutral points are part of broader areas in which skylight polarization is often indistinguishably different from zero. A simple multiple-scattering model helps explain some of these polarization patterns.

© 1998 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(100.2000) Image processing : Digital image processing
(260.5430) Physical optics : Polarization
(290.4210) Scattering : Multiple scattering

Original Manuscript: May 22, 1997
Revised Manuscript: August 11, 1997
Published: March 20, 1998

Raymond L. Lee, "Digital imaging of clear-sky polarization," Appl. Opt. 37, 1465-1476 (1998)

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  1. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (Deepak, Hampton, Va., 1988), pp. 375–391.
  2. J. W. Strutt, “On the light from the sky, its polarization and colour,” Philos. Mag. 41, 107–120, 274–279 (1871).
  3. Reference 1, pp. 269–270, lists skylight polarization studies by several of Rayleigh’s contemporaries.
  4. S. Chandrasekhar, D. Elbert, “The illumination and polarization of the sunlit sky on Rayleigh scattering,” Trans. Am. Philos. Soc. 44, Pt. 6, 643–728 (1954).
  5. H. Neuberger, Introduction to Physical Meteorology, Revised ed. (Pennsylvania State University, University Park, Pa., 1957), pp. 194–206.
  6. Z. Sekera, “Light scattering in the atmosphere and the polarization of sky light,” J. Opt. Soc. Am. 47, 484–490 (1957). [CrossRef]
  7. K. L. Coulson, “Effects of the El Chichon volcanic cloud in the stratosphere on the polarization of light from the sky,” Appl. Opt. 22, 1036–1050 (1983). [CrossRef] [PubMed]
  8. F. E. Volz, “Volcanic turbidity, skylight scattering functions, sky polarization, and twilights in New England during 1983,” Appl. Opt. 23, 2589–2593 (1984). [CrossRef] [PubMed]
  9. See Ref. 1, pp. 377–378.
  10. E. de Bary, “Influence of multiple scattering of the intensity and polarization of diffuse sky radiation,” Appl. Opt. 3, 1293–1303 (1964). The atmospheric principal plane is also called the Sun’s vertical.
  11. R. S. Fraser, “Atmospheric neutral points outside of the principal plane,” Contrib. Atmos. Phys. 54, 286–297 (1981).
  12. K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” Adv. Geophys. 10, 99–260 (1964). Polarization measurements that span half of the sky dome appear on pp. 212–215 (Figs. 49 and 50). Also see Ref. 1, pp. 216–218, 311, 325, 327. [CrossRef]
  13. T. Prosch, D. Hennings, E. Raschke, “Video polarimetry: a new imaging technique in atmospheric science,” Appl. Opt. 22, 1360–1363 (1983). Also see Ref. 1, p. 554.
  14. E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles (Wiley, New York, 1976), pp. 213, 268.
  15. D. J. Gambling, B. Billard, “A study of the polarization of skylight,” Aust. J. Phys. 20, 675–681 (1967). [CrossRef]
  16. F. S. Harris, “Calculated Mie scattering properties in the visible and infrared of measured Los Angeles aerosol size distributions,” Appl. Opt. 11, 2697–2705 (1972). [CrossRef] [PubMed]
  17. For examples, see Ref. 1, pp. 256–261.
  18. Ref. 5, p. 197.
  19. Ref. 1, p. 233. Also see E. Collett , Polarized Light: Fundamentals and Applications (Marcel Dekker, New York, 1993), pp. 34–39.
  20. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 50–53.
  21. Ref. 20, p. 53.
  22. B. W. Fitch, R. L. Walraven, D. E. Bradley, “Polarization of light reflected from grain crops during the heading growth stage,” Remote Sensing Environ. 15, 263–268 (1984). [CrossRef]
  23. See Ref. 1, p. 254 and Ref. 20, p. 50.
  24. Ref. 20, pp. 46, 50. χ has the same direction as skylight’s plane of polarization but avoids the conceptual difficulties that a plane of (partial) polarization entails.
  25. For examples, see Ref. 1, pp. 554–555 and 565–566.
  26. For example, see Ref. 5, pp. 194–197. Lines of zero Q are still called neutral lines (Ref. 1, pp. 254–258).
  27. ϕrel ranges between 0° and 360°, with values increasing clockwise from the Sun’s azimuth.
  28. Ref. 1, p. 254.
  29. Ref. 20, pp. 382–383. Equation (4) also defines polarization for specular reflection from planar surfaces. χ is horizontal for linear polarization by reflection from horizontal surfaces (e.g., calm water). To measure this polarization, once again set Eq. (4)’s 0° direction parallel to χ (i.e., horizontal).
  30. Ref. 20, p. 54.
  31. Ref. 14, pp. 198–199.
  32. Ref. 14, pp. 136–139. Note that 475 nm is a dominant wavelength typical of clear skies.
  33. R. L. Lee, “Colorimetric calibration of a video digitizing system: algorithm and applications,” Color Res. Appl. 13, 180–186 (1988). [CrossRef]
  34. For a remote-sensing application of P derived from photographs, see K. L. Coulson, V. S. Whitehead, C. Campbell, “Polarized views of the earth from orbital altitude,” in Ocean Optics VIII, M. A. Blizard, ed., Proc. SPIE637, 35–41 (1986). Narrow-FOV photographic polarimetry that uses a Savart plate is discussed in R. Gerharz, “Polarization of scattered horizon light in inclement weather,” Arch. Meteorol. Geophys. Bioklimatol. Ser. A 26, 265–273 (1977).
  35. For example, see Ref. 1, p. 261 (Fig. 4.36). θv is 0° at the astronomical horizon, except in Figs. 10–13, where θv is 0° at the slightly higher mean topographic horizon (see Fig. 3).
  36. My polarizer’s H90 is fairly uniform at visible wavelengths, although crossed pairs of such polarizers do transmit a dim violet from a white-light source. Because skylight dominant wavelengths at the Earth’s surface typically are 475 nm or more, the increase in photographic polarizers’ H90 at shorter wavelengths is unlikely to appreciably bias observations of skylight polarization.
  37. See Ref. 1, p. 582, for the general form of these Mueller matrix calculations.
  38. As noted above, P measured by the four-image technique depends only on a polarizer’s relative (rather than absolute) directions of 0°, 45°, 90°, and 135°. In other words, the four-image 0° direction can differ arbitrarily from χ.
  39. R. Gerharz, “Self polarization in refractive systems,” Optik 43, 471–485 (1975). Coulson calls self-polarization parasitic polarization (Ref. 1, p. 556).
  40. See Ref. 1, pp. 254–258.
  41. R. S. Fraser, “Atmospheric neutral points over water,” J. Opt. Soc. Am. 58, 1029–1031 (1968). Also see Ref. 1, pp. 381–382. [CrossRef]
  42. See Ref. 1, pp. 522–525, for a discussion of partial polarization on reflection by water.
  43. Ref. 1, p. 311 (Fig. 5.22). Large near-horizon pQ gradients at 90° from a low Sun appear consistently in my polarization maps.
  44. Usually red pixels in Figs. 2–4 are the result of identical 24-bit colors in the original digital images; so, in a limited sense, the maps do include points where pQ and P = 0.0 exactly, but this equality is just an artifact of the resolution with which the slide scanner quantized scene radiances.
  45. For example, K. F. Evans, G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transfer 46, 413–423 (1991). [CrossRef]
  46. R. L. Lee, “Horizon brightness revisited: measurements and a model of clear-sky radiances,” Appl. Opt. 33, 4620–4628, 4959 (1994).
  47. Ref. 20, pp. 112–113.
  48. Ref. 1, pp. 391–393.

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