572 
directions of view and illumination. Research on polarization of the light scattered by plant canopies has been 
reviewed recently by Talmage and Curran (1986), Rondeaux and Guvot, (1990) and Rondeaux and Herman. ( 1991); the 
books by Egan ( 1985) and Coulson (1988) and the book chapters Vanderbilt, et al. ( 1990) and Vanderbilt et al. (1993) 
consider the research in detail. 
Several models, see for example Vanderbilt and Grant 1985. Rondeaux and Herman 1993 and Myneni and Ross (1991), 
estimate the polarization of the light scattered by plant canopies. The hypothesis underpining these models is that the 
polarization is due to a quasi-specular reflection from individual leaves, the same process as was examined above. The 
models predict the amount of sunlight specularly redirected toward an observer by leaves in a plant canopy described by 
an epicuticular wax index of refraction, a probability of gap, leaf area index, leaf angle probability density function, and 
sometimes other biophysical parameters. In a first approximation, the predicted polarized reflectance is in the form 
R((7t - 0) / 2)F(struc.) 
R = 
p 4(cos9 s + cos0 y ) 
where R is the Fresnel coefficient for polarized light for the incidence angle (here © stands for the angle between the 
sun-earth and the earth-detector directions); 0s and 0v are the solar and viewing zenith angles; the F function depends 
on the canopy structure but is reasonably near from I for moderate zenith viewing angles. 
II.B.2. Wavelength Variation. Canopy measurements provide a vehicle to test the underpinning hypothesis in 
these models which link a leaf first surface reflection with the polarization of the light reflected by the canopy. Thus, 
for example, measurements show the canopy reflectance Rj, Fig. 2, of a canopy of wheat plants with green leaves 
exhibits a characteristic green vegetation shape showing pigment absorption bands in the blue 0.5 mm and red 0.65 
mm spectral regions. Based upon the first surface reflection hypothesis, the canopy polarization models predict that 
the polarized reflectance (but not the degree of linear polarization) should display no evidence of interaction with light 
absorbing pigments and metabolites located exclusively inside the leaf. The measurements support the hypothesis, 
showing that the polarized portion of the canopy reflectance factor Rp, Fig. 2. displays no evidence of chlorophyll 
pigment absorption. The degree of polarization. Fig. 2, does show evidence of pigment absorption because it is the 
ratio of Rp which does not vary with leaf pigments divided by Rj which does. 
Fig 2. The reflectance factor. R= (Rmax+ R min)/2, and its polarized component, RQ=( R max- R minV2. 
were determined for a wheat canopy measured 60° from nadir in the principle plane looking toward the 
sun. The values R ma x und R min correspond to the reflectance factor of the canopy with the polarizer 
adjusted to transmit the maximum and minimum amounts of light. The variables R and Rq in this 
figure corresponds to Rj and Rp, respectively, in the text. 
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Figure 2 shows that Rp increases with decreasing wavelength, an increase predicted by the models based on the slight 
corresponding increase of the index of refraction of the epicuticular wax. Yet the models underestimate the size of the 
increase in Rp, Fig. 2. by an order of magnitude. The discrepancy points to the potential importance of blue skylight, 
a hemispherical light not included in the models. 
II.B.3. Phase Angle Variation The models predict that perhaps the single most important variable for 
explaining the angular variation of the polarization of the light from plant canopies is the phase angle, Q, the angle 
between the directions of illumination and observation. In order to redirect a light ray from the sun to an observer, a 
specularly rcllccting facet must be correctly oriented; in fact the direction of the normal to such a facet is unique. The 
angle of incidence of the sunlight on the leaf must equal the angle of reflection: their sum must equal the phase angle 
Q and the angle of incidence therefore equals the half phase angle, Q/2. 
The importance of the phase angle is underscored by an analysis of the wheat measurements. Fig. 3a. collected in 
approximately 33 view directions. The degree of polarization displays large variation as a function of the zenith ana 
azimuth view angles. Yet as Fig. 3b shows, much of the variation as a function of the two angles is explained by one 
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