Geology Reference
In-Depth Information
noted, however, that a smooth surface may lead to diffuse
reflection if scattering is caused by crystallites, impurities,
or inhomogeneous inclusions within a layer immediately
under the surface. The fraction of the reflected to the
incident energy at the surface is determined by the Fresnel
equation (introduced later).
There is a lack of standardization regarding the use of
the term “reflection” and its products in the field of
remote sensing. Erroneous or ambiguous nomenclature
regarding this term has led to misunderstanding of data
and inability of comparing measured or modeled quanti-
ties. Schaepman‐Strub et al. [2006] present recommenda-
tions to standardize the concept and the description of
the term reflection in remote sensing observations. The
definitions adopted in this topic entail that reflectance
and reflectivity are expressions of the power (i.e., inten-
sity) fraction of the reflected to the incident wave. This is
a scalar quantity. On the other hand, the reflection coef-
ficient, which is the amplitude ratio, is a complex number
determined by Fresnel's equations for a single layer reflec-
tor. There is a difference, however, between reflectance
and reflectivity (though both are power ratio and assume
a smooth surface to satisfy the condition for specular
reflection). Reflectance takes into consideration the scat-
tering within the volume and the possible reflection at the
opposite surface if they reach back to reflective surface
and refract across it. If the medium is thin, contribution
of this “internal scattering” causes reflectance to vary
with thickness. Reflectivity, on the other hand, does not
take into account the internal scattering. Therefore, it is
the limit value of reflectance as the medium becomes
thick, i.e., it is the intrinsic reflectance of the surface.
Reflectivity is a property of the material itself while
reflectance is the fraction of EM power reflected from a
specific sample, depending on its thickness. The term
reflectance is usually used when addressing the reflection
off the ice or any surface.
EM beam is propagating in a medium with refractive
index n i and strikes another medium with a different
refractive index n t at an incidence angle θ i , the two com-
ponents are given by
2
n
n
n
cos
n
1
i
s
in
i
i
t
i
n
cos
n
cos
t
i
i
t
t
R
h
n
cos
n
cos
2
n
n
i
i
t
t
n
cos
n
1
i
sin
i
i
t
i
t
(7.4)
2
n
n
n
1
i
sin
n
cos
i
i
t
i
n
cos
n
cos
t
i
t
t
i
R
v
n
cos
n
cos
2
n
n
i
t
t
i
n
1
i
sin
n
cos
i
i
t
i
t
(7.5)
where θ t is the local angle of refraction at the interface.
The second form in each one of the above two equations
is derived from the first by eliminating θ t using Snell's
law (also known as the law of refraction), which has the
following expression:
sin
sin
n
n
i
t
(7.6)
t
i
The refractive index is a complex number and is related
to the complex permittivity  [equation (3.36)] and per-
meability μ by the equation
n
(7.7)
For most natural materials, μ is very close to 1 at optical
frequencies; therefore
7.3.2.2. Fresnel Equations
Unlike diffuse reflection, specular reflection at an
interface can be modeled in terms of the refractive indi-
ces (in optical bands) or the complex permittivity (in
microwave bands) of the two media at the opposite sides
of an interface. The interface must feature a quasi‐steady
smooth surface. For sea ice applications it can be a
smooth ocean or a level ice surface. The model, known
as  Fresnel reflection equations, involves also the angles
of the incident and refracted beams. It determines the
reflection coefficient of the two orthogonal polarization
components, when the electric field of the reflected
radiation is in the plane of incidence ( R v ) and when it is
perpendicular to that plane ( R h ). These two components
are referred to by some as the parallel (||) and perpen-
dicular (⊥) components. For optical radiation, when an
n
(7.8)
Equations (7.4) and (7.5) show that the reflection
increases as the contrast in the refractive index or the per-
mittivity between the two media increase. Fresnel's law is
directional, i.e., it determines only the specular reflection.
It is applicable whether the incident EM wave is polarized
or unpolarized but it determines the reflection coefficient
of the two reflected polarization components for any
given incidence angle.
For incident radar signals the complex dielectric con-
stant of the incident and transmitted waves  i and  t ,
respectively, are used instead of the refractive indices n i
 
Search WWH ::




Custom Search