Download polarization of light by vegetation

May 8, 2000
POLARIZATION OF LIGHT BY VEGETATION
Vern C. Vanderbilt and Lois Grant
I. INTRODUCTION
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.
Here we shall examine the phenomenon of surface-scattered light from both leaves and plant canopies.
Results from measurements will show that this surface-scattered light — a quasi-specular reflection if the leaves
appear shiny — originates at the interface between the air and the cuticle wax layer. Unlike light that is diffusely
reflected by the interior of a leaf, the surface-scattered light never enters the leaf; it is reflected from the first surface
encountered. This light is partially polarized and may be described by the Stokes vector. The results show that
remotely sensed polarization measurements of a plant canopy contain information about leaf surfaces —
information that is independent of the information in the light absorbed or scattered from the leaf mesophyll. The
polarized, surface-scattered light does not penetrate the leaf to be absorbed by the metabolic constituents of cells,
e.g., cell pigments, or to be multiply scattered at the dielectric boundaries in leaf tissue, e.g., the cell wall and water
interfaces.
While the measurements provide evidence that there is potentially useful information in remotely sensed
polarization data, they represent only a beginning. More research is needed to gain fuller understanding of the light
polarizing process in plant canopies and to improve leaf and canopy polarization models. The books by Egan
(1985) and Coulson (1988), the book chapter by Vanderbilt, Grant and Ustin (1991) and the articles by Rondeaux
and Guyot (1990) and Rondeaux and Herman (1991) provide an introduction to this research area.
II. WHAT IS POLARIZED LIGHT?
From physics we know that a light wave can 'vibrate' in two directions at once. The two directions are
mutually perpendicular and they are in the plane perpendicular to the propagation direction.
So why is that so important? It's important because observations show a light wave sometimes vibrates
preferentially in only one of those two directions. And that is the definition of polarized light. (In comparison,
unpolarized light displays no preferred vibration direction, vibrating equally often in each direction.)
In contrast to a light wave, consider a wave in water (a ‘gravity wave’) — for example, one created by
dropping a pebble in the center of a smooth pond. A ring wave will expand outward, propagating radially away
from the center. You may determine the amplitude of the water wave from its trough-to-crest height as it passes
some point. Of course you only measure the height vertically (which is perpendicular to the direction of
propagation) and not horizontally. This is because water waves 'vibrate' in only one direction — vertically. They
do not vibrate horizontally. How would water waves appear if they vibrated in both directions?
Unlike water and light, sound waves vibrate in three directions — a compression wave travels in the
direction of propagation of the sound while displacement waves vibrate in the plane perpendicular to that direction.
Thus, while water waves, light waves and sound waves 'vibrate,' light waves — unlike water waves and
sound waves — are able to vibrate in only two directions. In the case of light if the amplitude of the vibration
measured in one of the directions is greater than that measured in the other direction, then the light wave is partially
polarized. (Often the word 'partially' is dropped and such light is described simply as 'polarized light.') In the
unusual situation when the amplitude is zero in one direction — the horizontal direction for example, then the light
beam is 100% polarized — in this case in the vertical direction. Only rarely will you discover a light beam to be
100% polarized; most often it will be partially polarized, displaying some power in each vibration direction.
To measure the polarization of the light beam, you will need a photodetector and a polarization filter or
‘analyzer,’ which is an optical device that transmits light vibrating in one of the two directions but absorbs light
vibrating in the second, perpendicular direction. After placing the polarization filter in the light beam, measure the
transmitted light with the aid of the photodetector.
polarization
filter
»»»
»»»
»»»
>
photodetector
light beam
|
By slowly rotating the filter while monitoring the output of the photodetector, you will observe that the measured
light varies between maximum and minimum values — provided the beam is at least partially polarized. (If the
beam is unpolarized, then the photodetector output will remain constant as you rotate the polarizer.) You may
compute the degree of linear polarization (%) from the minimum and maximum voltage readings of the
photodetector output:
{ Degree of linear polarization}
=
100%
Vmax - Vmin
Vmax + Vmin
(1)
III. OCCURRENCE OF POLARIZED LIGHT
Specular Reflection
Shiny surfaces such as desk tops, drinking glasses, window panes — and shiny leaves — specularly reflect
light. The amount of light reflected from a shiny surface may be calculated with the aid of Snells’s law and the
Fresnel equations from optics. Snell’s law provides a method for calculating the speed of light in a substance
merely by measuring the angles of incidence and transmittance, θi and θt, respectively, of an incident light beam —
or, in our case, the angle of transmittance assuming the index of refraction is known.
Index of Refraction = n
=
velocity of light in air
velocity of light in leaf
=
sinθi
sinθt
(2)
Having found θt, we may use the Fresnel equations to calculate the reflectance of a beam of light polarized in
mutually orthogonal directions. The reflectance of the component parallel to the surface and perpendicular to the
direction of propagation is
=
 sin(θi-θt) 


 sin(θi+θt) 
2
(3)
The reflectance of the component perpendicular to the directions of both propagation and of (eq.3) is
=
 tan(θi-θt) 


 tan(θi+θt) 
2
(4)
If the incident beam of light is unpolarized, then the reflectance of the surface is the average of the two
reflectances.
These equations show that the reflectance of an 'optically smooth' surface depends upon the angle of
incidence, the index of refraction of the surface and the vibration direction of the incident light. (An 'optically
smooth' surface displays no surface roughness capable of scattering light away from the specular direction.)
In other words the reflectance of a surface depends upon the polarization of the incident light! In fact, for
light incident on an optically smooth surface at one angle (the Brewster angle, approximately 55°), the reflectance
of the surface is zero for light vibrating in the plane of incidence — defined by the surface normal vector and the
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direction of propagation. Thus, an optically smooth surface reflects zero light that is (a) incident at the Brewster
angle and both (b) 100% linearly polarized and (c) vibrating in the plane of incidence. The Brewster angle is
derived by setting (eq. 4) equal to zero and solving for the angle of incidence for which the reflectance is zero.
Brewster angle = Angle of zero reflectance
= tan-1 n
(5)
The reflectance of an optically smooth surface is non-zero in all other situations: when the incidence angle
≠ Brewster angle, or when the incident light is partially polarized, or when the vibration direction of the incident
light is not in the plane of incidence. This also means that unpolarized light (such as sunlight) incident at the
Brewster angle upon an optically smooth surface is 100% polarized after reflection. At other incidence angles —
except 0° and 90°, the light reflected by an optically smooth surface is partially polarized.
Shiny leaf surfaces, although not optically smooth, are sufficiently smooth to partially polarize the incident
sunlight light over a large range of incidence angles.
You may observe the polarized light reflected by a leaf surface with the aid of a photographic polarization
filter commonly available in camera stores. The surface reflected light will appear to blink on and off as you
observe the leaf through the filter while rapidly rotating it about its optical axis. The effect is most pronounced
when you face the sun and the incident light hits the shiny surface at an angle approximately 55° to the surface
normal, approximately the Brewster angle.
Other Examples of Polarized Light
Besides the light reflected by shiny leaves, other examples of polarized light in nature include the light
scattered by minerals, wet soils, the water droplets in both clouds and rainbows and particles both large and small
compared to the wavelength of light. For example, blue skylight, the result of small particle (molecular) scattering
in the atmosphere, is highly polarized if it is observed 90° to the direction of illumination. Why? (Hint: Which
component of the incident light does the observer see?) G.P. Können’s extraordinary book Polarized light in
Nature (1985) presents other examples including the case of glitter (specular reflection) from snow clouds observed
in the subsolar direction.
IV. SCATTERING BY SINGLE LEAVES
Air-Epicuticular Wax Interface
Knowing the biophysical properties of a foliage surface allows us to understand how that surface might
modify the polarization of incident light. The surface is the air-plant cuticle interface, the first refractive
discontinuity encountered by light incident on a leaf (or, for that matter, incident on a plant canopy). The cuticle is
an extracellular, multi-layered membrane of pectin, cellulose, cutin, and wax which forms a continuous and
protective skin at the air-plant interface (Please refer to The Cuticles of Plants by Martin and Juniper (1970).
Another extraordinary reference source, this book contains much information still relevant today more than 30 years
after publication). Trichomes, outgrowths such as hairs from epidermal cells, are covered by the cuticle and affect
the surface morphological properties.
The outermost portion of all cuticles consists of epicuticular wax. The wax may be amorphous,
semicrystalline, or crystalline in form and exhibit geometric configurations ranging from simple rods to complex
dendrites (Hall et al. 1965). That the facets of crystalline waxes range widely in size and shape is illustrated by the
surface waxes of Sorghum bicolor L. (sorghum), which include small flakes 0.1-0.16 µm thick and 0.21-1.58 µm in
diameter and wax filaments 0.5-1.25 µm in diameter and up to 140 µm long (Atkin and Hamilton 1982a, b). In
general the crystalline waxes form complex microscale structures arrayed on the leaf surface (Hull et al. 1978;
Sargeant 1983).
The morphology of trichomes and both the cuticle and the epicuticular wax provide most of the surface
detail of plant tissue on a microscopic and optical scale. Electron micrographs of a leaf surface often reveal the
small, crystalline wax structures such as found on Sorghum bicolor. These structures, having dimensions
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sometimes smaller than the wavelength of light, are arrayed on a comparatively smooth substrate which displays
roughness on a scale of sometimes 1000 wavelengths.
Thus, the interface between the air and the cuticle, the first dielectric discontinuity encountered by light
incident on the canopy, is an optically rough surface. The light scattering and light polarizing properties of this
surface depend on its roughness properties – its surface morphology.
Reflection: Leaf Surface vs. Leaf Interior
One might assume that the various optical properties of a leaf should depend upon both its surface and
interior. Yet one optical property, the linear polarization of the reflected light, may depend primarily on the leaf
surface properties. Research on 20 plant species suggests that the linearly polarized part of the leaf reflectance
factor in the visible and near-infrared wavelength regions depends on the properties of the leaf surface but not on
those of its interior (Grant et al. 1992).
The emphasis in previous research investigating the light polarizing properties of single leaves has been the
variation with view and illumination angles. Here in discussing the polarization properties of single leaves we shall
emphasize instead variation with wavelength. Our approach builds upon the contributions found in Shul'gin and
Khazanov (1961), Shul'gin and Moldau (1964), Rvachev and Guminetskii (1966), Egan et al. (1968), Egan and
Hallock (1969), Knipling (1970), Egan (1970), Woolley (1971), Breece and Holmes (1971), Egan (1985), Grant et
al. (1987a, b), and Coulson (1988). Grant (1987) reviewed this research.
Typical of the results from 20 species investigated (Grant et al. 1992) are those of two variegated hybrids
of the common house plant, Coleus blumei, Benth.
Results (Fig. 1) show the reflectance (or more correctly, the bidirectional reflectance factor)
RI(55°,0°;55°,180°) of the variegated leaves depends upon leaf pigmentation. For the green portion of the leaf, the
reflectance curve is characteristic of green leaves for which chlorophyll is the dominant pigment. The reflectance
for the redish-purple portion of the leaf is small throughout the visible region due to absorption not only by
chlorophyll but also by anthrocyanin, both important pigments in this leaf tissue. Anthrocyanin absorbs in the
green spectral region. The reflectance of the white portion of the leaf is large throughout much of the visible,
decreasing only toward the shorter blue wavelengths. Although the tissue appeared white and therefore to lack
pigments, the reflectance decrease toward the shorter blue wavelengths suggests it did contain some carotenoid
pigments which absorb in the UV, blue, and blue-green regions of the spectrum.
Just as RI varies spectrally according to the constituent pigments in each leaf, so too does the nonpolarized part of the reflectance, RN. As shown in Fig. 1, the RI and RN curves representing any one leaf type
display almost identical variation with wavelength.
In contrast, the polarized component of the bidirectional reflectance factor, RQ,displays no spectral
dependence. Statistical tests show there is no significant change in RQ with wavelength; spectrally RQ is flat.
How can light reflected by a leaf not display at least some evidence of interaction with leaf pigments, especially
pigments with a spectral presence so evident in RI and RN? The answer appears to be that the polarized part of the
reflected light never entered the leaf tissue to interact with the leaf pigments. RQ represents solely light reflected at
the leaf surface.
The conclusion, derived from polarization data of Coleus and the leaves of 20 other species, is that the
light reflected by a leaf can be separated into two components with the aid of polarization measurements. One
component originates at the surface of the leaf and contains no information about leaf pigments, while the other
emanates primarily, but not entirely, from the interior leaf tissue. Its magnitude is determined by leaf pigments and
other energy absorbing metabolites.
This conclusion, that linear polarization of visible and near-infrared light reflected by leaves is apparently a
first surface phenomena unaffected by cellular pigments, metabolites and structure, remains to be tested on a wider
variety of species and most importantly at longer wavelengths outside the visible. Presumably the surface reflected
light and its polarization will include evidence of interaction with cellular structure and metabolites when the
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wavelength of the incident light is a large fraction of, or greater than, the thickness of the cuticle, a criteria which
applies at wavelengths longer than 0.8 µm for many species.
V. MODELING SCATTERING FROM CANOPIES
Introduction
After correction for the effects of the disturbing atmospheric, data obtained from satellite-borne sensors,
which measure the ensemble of surfaces – the leaves, stems, and fruits and the litter, soil and rocks – of the plant
canopy and its environs, potentially includes the effects due to three phenomena (1) the light scattering and
polarizing properties of each scatterer, (2) the architectural arrangement of the scatterers in the canopy, and (3) the
directions of view and illumination. Research on polarization of the light scattered by plant canopies has been
reviewed by Talmage and Curran (1986) and Rondeaux and Guyot (1990). The book chapter by Vanderbilt et al.,
(1990) and the books by Egan (1985) and Coulson (1988) consider the research in detail. More recently specular
reflection has been included in models for the total light scattered by a canopy.
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 that is described by an index of refraction (of the
epicuticular wax), a probability of gap, leaf area index, leaf angle probability density function, and sometimes other
biophysical parameters.
Layer Model, Definitions
Development of the model begins with an analysis of the quasi-specular reflecting properties of the leaf
area in layer ∆z at height z in the canopy and illuminated from direction (θi,φi). Light is scattered from layer ∆z
into direction (θr,φr). Just as would be true for the normal of any specular reflector - a small mirror, for example the direction of the normals to those foliage areas specularly redirecting sunlight toward an observer is unique. As
with all specular reflectors, the angle of incidence γ must equal the angle of reflection and the three vectors (formed
by the incident light ray i, the redirected light ray r and the normal nL to the leaf) must be coplanar. ("The two rules
of specular reflection!!!") The phase angle Θ between i and r must equal 2γ. These conditions are satisfied by the
three equations involving the vector dot products
( i
•
( nL •
•
( i
n )
L
r )
= cosγ,
(6a)
= cosγ,
(6b)
r
= cos 2γ.
(6c)
)
For a specific sun direction and reflection, these equations may be solved to obtain the angle of incidence
and the direction of the normal to each foliage facet specularly redirecting sunlight to the observer:
γ
=
-1
0.5 cos { sinθr cosφi sinθi + cosθi cosθr }
(7)
θL
=
-1  (cosθi + cosθr) 
cos 
,
(2cosγ)


(8)
φL
=
-1  (sinθi + sinθr cosφr) 
cos 
(2cosγ sinθL)


(9)
Neither sunlight nor the light received by an observer is parallel. The sizes of the solar disk and the
entrance optic of the observer plus the distance from the sun and the distance from the observer to a small
specularly reflecting leaf area define two solid angles, ∆ωi and ∆ωr respectively [Note that ∆ωr depends on the areal
size of the entrance optic divided by the square of the distance to the leaf; ∆ωr is not the field-of-view (FOV) of the
5
measuring instrument]. From geometric optics, an incident sun ray specularly redirected by the leaf to the observer
must originate somewhere within the solid angle ∆ωr and it must be reflected into any direction within ∆ωr. The
direction of the normal to the leaf to satisfy these criteria is not unique; the range of these directions defines a solid
angle ∆ωL. By the rules of specular reflection, any one set of the vectors i and r within the respective solid angles
∆ωi and ∆ωr represents the specular reflection of one light ray by a surface having a normal nL within a solid
angle ∆ωL. The transformation between directions within the solid angles ∆ωi, ∆ωr , and ∆ωL does not provide a
1:1 correspondence, as multiple directions of incidence i and directions of scattering r may map to the same n .
L
If the solid angles ∆ωi and ∆ωr are square or circular in cross section, then it can be shown that
∆ωL =
{(∆w )
i
+ (∆wr ) 0.5
4 cos γ
0.5
}
2
(10)
As light sources, such as the solar disk, tend to be round and most sensors have circular fields-of-view (or
circular instantaneous fields-of-view), this result is applicable to many measurement situations. Eq. (10)
approaches the equation of Rense (1950) in the limit as the solid angular size of the source ∆ωi approaches zero, as
when the source is well collimated. Thus, in general
 ∆w r
 4 cos γ if

∆ωL ≈ 
 ∆wi
if

 4 cos γ
∆wr >> ∆wi ,
(11)
∆wr << ∆wi .
We define the probability density function gL(z,θL,φL)/2π for the angular directions of normals to facets
of plant foliage in a layer ∆z at height z such that the probability that a differential foliage surface area has a normal
within a solid angle ∆ωL about direction n (θL,φL) is ∆ωL⋅gL(z,θL,φL)/2π (dimensionless). The units of gL/2π are
L
reciprocal steradians, sr-1.
We define pi(z,θi,φi) as the probability that layer ∆z at height z is illuminated directly by the sun as
opposed to being shaded by intervening foliage. We define a second probability pr(z,θr,φr) as the probability that
layer ∆z at height z is observable from above the canopy and in a specific direction (θr,φr). The terms pi and pr are
the probabilities of a canopy gap — transmittances — and represent the attenuation due to foliage in layers above
the layer at z. The probabilities will approach unity for a volume containing the topmost leaves of a dense,
preheaded wheat canopy if the aggregation of these leaves forms a horizontal mono-layer one leaf thick which is
essentially impenetrable to direct illumination. The probabilities will be less than unity for most canopies — which
are not closed. For non-closed canopies having foliage dispersed in a layer the probabilities pi and pr decrease with
cumulative leaf area into the canopy. As described in Ross (1981), they may be measured or estimated from
models.
We shall assume that the specular light reflection from the leaf occurs principally at the air-wax boundary
of the leaf. This assumption requires that comparatively negligible amounts of light are reflected specularly from
the boundaries between the various cuticle layers and from boundaries between the cuticle, epidermal cell
walls, and cell membranes located near the cuticle. The assumption is reasonable because, first, the boundaries
between these materials are indistinct and often appear optically rough in electron micrographs, suggesting that
diffuse reflection rather than specular reflection is more important at these boundaries within the cuticle. Second,
even if two dielectric materials form an optically smooth boundary, the amount of light specularly reflected at the
boundary will be significant only if the indices of refraction of the two materials are dissimilar; the greater the
dissimilarity, the greater will be the amount of light specularly reflected at the boundary. For the optical system
formed by the air-wax-cuticle layers-cell membrane, by far the greatest discontinuity between the indices of
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refraction is across the air-wax boundary; the organic mixtures forming the other boundaries have more
comparable indices of refraction.
If leaf surfaces were optically smooth, the Fresnel equations could be used to compute the amounts of
specularly reflected and polarized light from a leaf, provided the angle of the incident light on the leaf and the index
of refraction of the epicuticular wax were known. However, leaf surfaces are rarely, if ever, optically smooth.
Instead they support the small crystalline wax structures previously discussed, which diffusely scatter light that
would otherwise be specularly reflected. To account for this reduction in the amount of specularly reflected and
polarized light, we shall modify the Fresnel equations by a factor K. The value of K varies between zero and one.
Thus, for a real leaf with a wax surface that is not optically smooth, the amounts of quasi-specularly reflected and
polarized light are KρI and KρQ, respectively.
K is conceptually related to the probabilities of gap, pi and pr, but at the scale of the leaf surface rather
than the canopy. In general, K (dimensionless) is a function of the leaf surface morphology and varies with several
leaf-level parameters - the directions i and r, wavelength, side (adaxial or abaxial), lateral position, and both the
type of and, as appropriate, the direction of venation. Rather than retain this complexity in the model, we shall
make the simplifying, but optional assumptions that K is a constant for all foliage surfaces belonging to one plant
cultivar and that it is neither a function of lateral position on the foliage surface nor the type and direction of the
venation.
The leaf area index (LAI) is the integral over the canopy profile of D(z), the leaf area density, the leaf area
per unit volume. The leaf area within a unit volume of layer ∆z with normals directed within ∆ωL about direction
(θL,φL) is
(D( z )∆z )  g L ( z,θ L , φ L ) ∆ω L  .
2π

1 
Layer Radiance
A leaf facet of area ∆Af in a layer ∆z at height z receives flux Ei(z) cosγ ∆Af from a ∆ωi neighborhood
about the source direction θi and specularly reflects Ei(z) cosγ ∆Af Kρ flux in the sensor direction θi where Εi(z) is
the irradiance of the source attenuated by passage through the canopy to height z. Eq. 12 provides the area of all
facets in a unit volume of layer ∆z specularly redirecting source light to the sensor if the variables (θL,φL) and ∆ωL
are given by eqs. 6 and 10. Thus, the flux scattered by an area ∆A of the layer is
∆Φr(z) = ∆A D(z) ∆z
g L ( z,θ L , φ L )
∆ωL EL(z) cosγ Kρ
2π
The radiance of the canopy layer is found
∆Lr(z)
=
∆Φ r ( z )
∆A cos θ r ∆ω r
∆AD ( z )∆z
=
D ( z ) ∆z
=
g L ( z,θ L , φ L )
∆ω L Ei ( z ) cos γ Kρ
2π
∆A cos θ r dω r
g L ( z,θ L , φ L )
Ei ( z ) KS
2π
.
4 cos θ r
7
.
The radiance of the canopy is the layer radiance integrated over the canopy profile. Thus,
canopy top
∫
dLr ( z ′)
z
canopy top
=
∫
D(z ′)
g L ( z ′,θ L , φ L )
E 0 KS Pj ( z ′) Pr ( z ′)
2π
dz ′
4 cosθ r
z
where Eo is the solar irradiance at the top of the canopy.
VI. TESTING THE CANOPY MODEL
Wavelength Variation
Canopy measurements provide a vehicle to test the underpinning hypothesis in these models, which
mathematically link the surface reflection from a leaf to the polarization of the light reflected by the canopy. Thus,
for example, measurements (Vanderbilt et al. 1985) show the canopy reflectance RI, 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 µm and red 0.65 µm 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 RQU,
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 RQU, which does not vary with leaf pigments divided by
RI, which does.
Figure 2 shows that RQU 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 RQU, Fig. 2, by an order of magnitude. The discrepancy points to the
potential importance of blue skylight, a hemispherical light source not included in the models.
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, Θ , the angle between the directions of
illumination and observation. In order to redirect a light ray from the sun to an observer, a specularly reflecting
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 Θ and the angle
of incidence therefore equals the half phase angle, Θ /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 and azimuth view angles. Yet as Fig. 3b shows, much of the variation as a function of the two angles is
explained by one angle, the half-phase angle or the angle of incidence of the sunlight on the leaf. The data for the
preheaded display markedly less scatter than those of the headed canopy.
Specular Reflecting Efficiency
The efficiency of a plant canopy as a specular reflector is small compared to an optically smooth glass
surface similarly viewed and illuminated. The glass surface provides an excellent standard for comparison provided
the index of refraction of the glass is the same as the epicuticular wax of the leaf. No interface between two
dielectrics would be able to specularly reflect more than such a hypothetical glass surface. It serves as a
hypothetical specular calibration target just as a hypothetical perfectly white, perfectly diffuse surface often serves
as a diffuse calibration target.
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The specular reflection efficiency of the wheat canopy, Fig. 4, (Vanderbilt, et al. 1991) indicates the
canopies specularly reflect less than 10-6 (10-4%) that of a hypothetical optically smooth glass surface. The index
of refraction of both the glass and the epicuticular wax are assumed to be 1.5. The variation of the efficiency
measured at a zenith view angle of 60° (Obvious when the 60° data points in Fig. 4 are connected with a segmented
line) is an artifact of the measurement process.
The efficiency is generally smaller for the headed, as compared to the preheaded wheat canopy. The heads
reduce the efficiency by reducing the amount of sunlight which reaches the specularly reflecting leaves.
Additionally once the light is specularly reflected by the leaves, the heads intercept part of it, further reducing the
amount which arrives at a sensor.
VII. APPLICATIONS
The list of potential applications of polarization, although rapidly growing as more scientists enter the
field, remains short because remotely sensed polarization images collected from spacecraft and most specifically the
French airborne polarization sensor POLDER have only recently become available. Rondeaux and Guyot (1990)
list many more applications than can be included here.
The results shown in Fig. 4 point to one potentially important application of polarization: detection of the
heading development stage in certain wheat varieties. The results show the polarization changes dramatically with
the onset of heading. This per field information could be overlaid with meteorological data to better estimate wheat
production within large regions. Rondeaux and Guyot (1990) reported a similar change in the polarization of corn
as it tassels. Perhaps similar results will be shown for canopies with similar architectures such as grain sorghum.
Another application is estimation of two of the most important parameters needed in modeling the
architecture of plant canopies: the probability density function of leaf angles and the probability of gap. The
polarization models show that potentially these critically needed parameters may be estimated from polarization
data collected as a function of view and illumination directions.
Finally, remotely sensed polarization images will potentially provide a new source of information to
compliment that already available in images showing the visible, near infrared, middle infrared, and thermal
infrared. Potentially this new information could aid in species discrimination and assessment of the biophysical
status of plant canopies, two important goals as remote sensing matures as a discipline.
REFERENCES
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FIGURES
Fig. 1. The reflectance RI, RQ, and RN of red, green and white portions of the top and bottom of variegated coleus
leaves.
Fig. 2. In order to estimate the reflectance RI and the polarized portion of the reflectance RQU as a function of
wavelength and view direction for a wheat canopy measured just prior to the heading development stage, a
polarization analyzer was rotated in front of a spectroradiometer to determine Rmax and Rmin, representing
maximum and minimum reflectances of the canopy measured in one view direction. In turn Rmax and Rmin were
used to estimate RI, RQU, and the degree of polarization, computed as illustrated in the four larger graphs
representing data collected in one, subsolar view direction (60°,135°) when the sun direction was (31°,134°).
The two pinwheels display many individual graphs of RI and RQU, each representing data collected in one
view direction. The individual graphs are overlaid on a set of concentric circles, an r_ coordinate system which in
effect rotates, tracking the solar azimuth as it changes during the day. Each circle denotes a 10° increment in polar
view direction starting from nadir at the center. View azimuth relative to sun azimuth is indicated by angle in the
coordinate system.
Each individual graph is centered over the view direction in which data were collected. The sun signifies
the approximate direction of the hot spot, opposite the subsolar direction; Data were acquired between 2.76 h
before and 1.52 h after solar noon during which the sun polar and azimuth angles varied from (40°,113) to
(31°,226°).
Fig. 3. The degree of polarization at 0.66 _m wavelength varies for view directions in both azimuth and zenith
view angles (Fig. 3a) but one angle, the angle of incidence of the sunlight on the leaf (the half-phase angle),
explains much of the variation, especially for the preheaded canopy (Fig. 3b).
Fig. 4. Specular reflection efficiency. The specular reflectance of the preheaded and headed wheat canopies was
estimated to be less than 0.000001 that of a hypothetical optically smooth glass surface, similarly viewed and
illuminated and having the same index of refraction_
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