Advertisement

Polarization of Light by Vegetation

  • V. C. Vanderbilt
  • L. Grant
  • S. L. Ustin

Abstract

The amount of sunlight specularly reflected by plants such as sunflower, sorghum, ivy, ponderosa pine, American elm, California laurel, various oaks, and citrus is sometimes so large that canopies may appear white instead of green when viewed obliquely toward the sun. Surface-scattered light is often a significant part of the total light reflected by plants of many diverse species.

Keywords

Phase Angle Leaf Surface Solid Angle Plant Canopy Reflectance Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Symbols

Leaves (Sect. 2)

Voltagemax

maximum output voltage of sensor when polarization analyzer is rotated

Voltagemin

minimum output voltage of sensor when polarization analyser is rotated

Voltagecal

output voltage of sensor when calibration surface is measured

Voltagedark

output voltage of sensor when no light enters sensor

Reflectance factors of leaves measured and illuminated at 55°

Rmax

maximum biconical reflectance factor when polarizer is rotated

Rmin

minimum biconical reflectance factor when polarizer is rotated

Rcal

bidirectional reflectance factor of calibration surface

RI

biconical reflectance factor

RQ

polarized biconical reflectance factor

because of the arrangement of the source

leaf-polarizer/detector, RU = 0 and therefore RQ = RQU

RN

nonpolarized biconical reflectance factor; RQ + RN = RI

πpol

degree of linear polarization, 100%RQ/RI

Canopies (Sect. 3)

(x1y1z1θ1φ1)

canopy coordinate system. Fig. 1; z1 axis is vertical, x1 is sun azimuth

(x2y2z2θ2φ2)

leaf facet coordinate system, z2 axis is toward sun, plane x2z2 is scattering plane

(xyzθφ)

leaf facet coordinate system, Fig. 4; plane xz is scattering plane

ε = [εs, εQU]T

efficiency, compared to an optically smooth surface, by which a plant canopy specularly redirects (εs) and polarizes and redirects (εQU) incident sunlight from direction Ω̱′ to direction Ω̱

α′ = α

angle of incidence of ray on facet = angle of specular reflection = Θ/2

αr

angle of the ray refracted (transmitted) into the leaf facet

gL(rL, Ω̱)′ 1/2π

probability density function for leaf angles Integers (l,m,n) indicate the volume V(l,m,n) centered at r[x1(l),y1(m),z1(n)]

K

probability that a ray incident on a leaf surface will be specularly reflected. K is a measure of the leaf surface roughness

L, L′

radiance (incident) and radiance (scattered)

N(Ω̱′, Ω̱) a 3 × 3

matrix representing the polarized light scattering process in the canopy as Rscene = NR′cal

P(Ω̱′ → Ω̱)/4π

phase function

Φ′, φ

incident and scattered fluxes

p′, p

probability of a canopy gap in the direction Ω̱′ and Ω̱

πpol

degree of linear polarization, 100%RQU/RI

r(x1, y1, z1)

a location in the (x1y1z1θ1φ1) canopy coordinate system

R = [RI, RQ, RU]T

biconical reflectance factor corresponding to the Stokes vector S = [SI, SQ, SU]T

RQU

linearly polarized portion of RI; RQU = {RQ 2 + RU 2|1/2 angle between the plane of polarization and the direction of RU

b0

angle between the plane of polarization and the direction of RU

Rscene(Ω̱′, Ω̱)

biconical reflectance factor, R, of a scene such as a plant canopy or leaf

R′IcaI(Ω̱′, Ω̱)

biconical reflectance factor of calibration surface, first component of R

RQscene(Ω̱′, Ω̱)

biconical reflectance factor of scene, second component of R

RUscene(Ω̱′, Ω̱)

biconical reflectance factor of scene, third component of R

RQUscene(Ω̱′, Ω̱)

RQU of a Scene

RQUglass(Ω̱′, Ω̱) RQU

of an optically smooth glass surface

SFRS

specular reflectance of optically smooth dielectric interface; computed from the Fresnel equations of optics

SFRQ

polarized part of specular reflectance of dielectric interface; from the Fresnel equations

S′ = [Sl, SQ, SU]T

Stokes vector

Sscene(Ω̱′, Ω̱)

Stokes vector S, of a scene

S′Ical(Ω̱′, Ω̱)

Stokes vector of the light scattered by the calibration surface, first component

Θ

phase angle between directions Ω̱′ and Ω̱ (Θ equals 2α)

σL

leaf area in volume V, leaf area index is the sum ΣσLv for Ω̱ in z1 (vertical direction in the canopy

σ′v, σv

cross-sectional area of volume V projected in directions Ω̱′ and Ω̱

V(r)

a small finite volume of the canopy at location r

Voltagemax

maximum output voltage of sensor when polarization analyzer is rotated

Voltagemin

minimum output voltage of sensor when polarization analyzer is rotated

VoltagecaI

output voltage of sensor when calibration surface is measured

Voltagedark

output voltage of sensor when no light enters sensor

Ω̱′(θ11)

direction of incident illumination in the (x1y1z1θ1φ1) coordinate system

Ω̱(θ11)

direction of scattered light in the (x1y1z1θ1φ1) coordinate system

Ω̱L

direction of normal to differential area of leaf

ΔΩ̱′

solid angle of incident flux

ΔΩ̱L

solid angle of normals to differential areas of leaves

ΔΩ̱

solid angle of scattered flux

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atkin DSJ, Hamilton RJ (1982a) The changes with age in the epicuticular wax of Sorghum bicolor. J Nat Prod 45:697–703CrossRefGoogle Scholar
  2. Atkin DSJ, Hamilton RJ (1982b) The surface of Sorghum bicolor. In: Cutler EF, Alvin KL, Price CE (eds) The plant cuticle. Academic Press, Lond New York, pp 231–236Google Scholar
  3. Baker EA (1982) Chemistry and morphology of plant epicuticular waxes. In: Cutler DF, Alvin KL, Price CE (eds) The plant cuticle. Academic Press, Lond New York, pp 139–166Google Scholar
  4. Banks JCG, Whitecross MI (1971) Ecotypic variations in Eucalyptus viminalis, Labill. I. Leaf surface waxes, a temperature X origin interaction. Aust J Bot 19:327–334CrossRefGoogle Scholar
  5. Breece HT, Holmes RH (1971) Bidirectional scattering characteristics of healthy green soybeans and corn in vivo. Appl Opt 10:119–127CrossRefGoogle Scholar
  6. Carr SGM, Milkovits L, Carr DJ (1971) Eucalypt phytoglyphs. The microanatomical features of the epidermis in relation taxonomy. Aust J Bot 19:173–190CrossRefGoogle Scholar
  7. Coulson KL (1988) Polarization and Intensity of light in the atmosphere. Deepak Publ, Hampton, Virginia, USAGoogle Scholar
  8. Egan WG (1970) Optical Stokes parameters for farm crop identification. Remote sens environ 1:165–180CrossRefGoogle Scholar
  9. Egan WG (1985) Photometry and polarization in remote sensing. Elsevier, New YorkGoogle Scholar
  10. Egan WG, Hallock HB (1969) Coherence polarization phenomena in remote sensing. Proc IEEE 57:621–628CrossRefGoogle Scholar
  11. Egan WG, Grusauskas J, Hallock HB (1968) Optical depolarization properties of surfaces illuminated by coherent light. Appl Opt 7:1529–1534PubMedCrossRefGoogle Scholar
  12. Fobes JF, Mudd JB, Marsden MP (1985) Epicuticular lipid accumulation on the leaves of Lycopersicon pennelli (Corr.) D’Arcy and Lycopersicon esculentum Mill. Plant Physiol 77:567–570PubMedCrossRefGoogle Scholar
  13. Grant L (1987) Review article. Diffuse and specular characteristics of leaf reflectance. Remote Sens Environ 22:309–322CrossRefGoogle Scholar
  14. Grant L, Daughtry CST, Vanderbilt VC (1987a) Polarized and non-polarized leaf reflectances of Coleus blumei. Environ Exp Bot 27:139–145CrossRefGoogle Scholar
  15. Grant L, Daughtry CST, Vanderbilt VC (1987b) Variations in the polarized leaf reflectance of Sorghum bicole. Remote Sens Environ 21:333–339CrossRefGoogle Scholar
  16. Hall DM, Matus AI, Lamberton JA, Barber HN (1965) Infraspecific variation in wax on leaf surfaces. Aust J Biol Sci 18:323–332Google Scholar
  17. Hallam ND (1982) Fine structure of the leaf cuticle and the origin of leaf waxes. In: Cutler DF, Alvin KL, Price CE (eds) The plant cutice. Academic Press, Lond New York, pp 197–214Google Scholar
  18. Holloway PJ (1981) Structure and histochemistry of plant cuticular membranes an overview. In: Cutler EF, Alvin KL, Price CE (eds) The plant cuticle. Academic Press, Lond New YorkGoogle Scholar
  19. Hull HM, Wright LN, Beckmann CA (1978) Epicuticular wax ultrastructure among lines of Eragrostis lehmann, Ness, developed for seeding drought tolerance. Crop Sci 19:699–704CrossRefGoogle Scholar
  20. Jordan WR, Monk RL, Miller FR, Rosenow DT, Clark LE, Shouse PJ (1983) Environmental physiology of sorghum. I. Environmental and genetic control of epicuticular wax load. Crop Sci 23:552–558CrossRefGoogle Scholar
  21. Juniper BE, Jeffree CE (1983) Plant surfaces. Edward Arnold, LondGoogle Scholar
  22. Knipling EB (1970) Physical and physiological basis for the reflectance of visible and near-infrared radiation from vegetation. Remote sens environ 1:155–159CrossRefGoogle Scholar
  23. Martin JT, Juniper BE (1970) The cuticles of plants. St Martin’s, New YorkGoogle Scholar
  24. Rao JVS, Reddy KR (1980) Seasonal variation on leaf epicuticular wax of some semi-arid shrubs. Indian J Exp Biol 18:495–499Google Scholar
  25. Rense WA (1950) Polarization studies of light diffusely reflected from ground and etched glass surfaces. J Opt Soc Am 40:55–59CrossRefGoogle Scholar
  26. Ross J (1981) The radiation regime and architecture of plant stands. Junk, The HagueGoogle Scholar
  27. Rvachev VP, Guminetskii SG (1966) The structure of light beams reflected by plant leaves. J Appl Spectrosc 4:415–421Google Scholar
  28. Sargeant JA (1983) The preparation of leaf surfaces for scanning electron microscopy. A comparative study. J Microsc 129:103–110CrossRefGoogle Scholar
  29. Shul’gin I A, Khazanov VS (1961) On the problem of light conditions in plant associations. ABIS Dokl Bot Sci 141:210–212Google Scholar
  30. Shul’gin IA, Moldau KA (1964) On coefficients of brightness of leaves in nature and polarized light. ABIS Dokl Bot Sci 162:99–101Google Scholar
  31. Talmage DA, Curran P (1986) Remote sensing using partially polarized light. Int J Remote Sens 7:47–64CrossRefGoogle Scholar
  32. Tulloch AP (1973) Composition of leaf surface waxes of Triticum species variation with age and tissue. Phytochem 12:2225–2232CrossRefGoogle Scholar
  33. Vanderbilt VC, Grant L (1985a) Polarization photometer to measure bidirectional reflectance factor R (55°, 0°; 55°, 180°) of leaves. Opt Eng 25:566–571Google Scholar
  34. Vanderbilt VC, Grant L (1985b) Plant canopy specular reflectance model. IEEE trans geosci remote sens GE-23:722–730CrossRefGoogle Scholar
  35. Vanderbilt VC, Grant L, Daughtry CST (1985a) Polarization of light scattered by vegetation. Proc IEEE 73:1012–1024CrossRefGoogle Scholar
  36. Vanderbilt VC, Grant L, Biehl LL, Robinson BF (1985b) Specular, diffuse and polarized light scattered by two wheat canopies. Appl Opt 24:2408–2418PubMedCrossRefGoogle Scholar
  37. Weast RC (1989) CRC Handbook of Chemistry and Physics. CRC Press, Boca Raton, FloridaGoogle Scholar
  38. Whitecross MI, Armstrong DJ (1972) Environmental effects on epicuticular waxes of Brassica napus, L. Aust J Bot 20:87–90CrossRefGoogle Scholar
  39. Woolley JT (1971) Reflectance and transmittance of light by leaves. Plant Physiol 47:656–662PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • V. C. Vanderbilt
  • L. Grant
  • S. L. Ustin

There are no affiliations available

Personalised recommendations