Polarization of Light by Vegetation

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


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.


Phase Angle Leaf Surface Solid Angle Plant Canopy Reflectance Factor 
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Leaves (Sect. 2)


maximum output voltage of sensor when polarization analyzer is rotated


minimum output voltage of sensor when polarization analyser is rotated


output voltage of sensor when calibration surface is measured


output voltage of sensor when no light enters sensor

Reflectance factors of leaves measured and illuminated at 55°


maximum biconical reflectance factor when polarizer is rotated


minimum biconical reflectance factor when polarizer is rotated


bidirectional reflectance factor of calibration surface


biconical reflectance factor


polarized biconical reflectance factor

because of the arrangement of the source

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


nonpolarized biconical reflectance factor; RQ + RN = RI


degree of linear polarization, 100%RQ/RI

Canopies (Sect. 3)


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


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


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


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)]


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


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


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


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


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


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


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


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


a small finite volume of the canopy at location r


maximum output voltage of sensor when polarization analyzer is rotated


minimum output voltage of sensor when polarization analyzer is rotated


output voltage of sensor when calibration surface is measured


output voltage of sensor when no light enters sensor


direction of incident illumination in the (x1y1z1θ1φ1) coordinate system


direction of scattered light in the (x1y1z1θ1φ1) coordinate system


direction of normal to differential area of leaf


solid angle of incident flux


solid angle of normals to differential areas of leaves


solid angle of scattered flux


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

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

There are no affiliations available

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