International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
irradiated under the same conditions. For measurement
purposes, a Spectralon panel commonly approximates the
ideal diffuse standard surface. Reflectance factors may reach
values beyond 1, especially for highly specular reflecting
surfaces.
2.2 Geometrical considerations of the incident and
reflected fluxes
The basic concept describing the reflectance anisotropy of a
surface is the BRDF. Conceptual quantities of reflectance
include the assumption that the size/ distance ratio of the
illuminating source (usually the sun or lamp) and the
observing sensor is assumed to be zero and are usually
labelled directional in the general terminology. Since
infinitesimal elements of solid angle do not include
measurable amounts of radiant flux, and unlimited small
light sources and sensor field of views do not exist, all
measurable quantities of reflectance are performed in the
conical or hemispherical domain of geometrical
considerations. Thus, actual measurements always involve
non-zero intervals of direction and the underlying basic
quantity for all radiance and reflectance measurements is the
conical case, including the special case of a cone of
hemispherical extent. In the case of hemispherical
illumination under field conditions, the irradiance can be
divided into a direct sunlight component and a second
irradiance component scattered by the atmosphere and
terrain, which leads to an anisotropic, diffuse sky
illumination. Being a function of wavelength, the ratio of
diffuse/direct incident irradiance highly influences the
spectral dependence of directional effects as shown in the
snow case study below.
According to Nicodemus (1977), the angular characteristics
of the incoming radiance are named first in the term and are
followed by the angular characteristics of the reflected
radiance. This leads to the following nomenclature of
reflectance quantities (Table 1):
| Reflected Directional | Conical Hemispherical
|! Incoming
| Directional | Bidirectional | Directional- | Directional-
| conical hemispherical
| Case 1 Case 2 Case 3
| Conical Conical- Biconical Conical-
| directional hemispherical
| = Case 4 Case 5 Case 6
| Hemispheri Hemispherica| Hemispherica| Bihemispherica
| cal l-directional | l-conical ]
| Case 7
Case 8 Case 9
Tablel: Relation of incoming and reflected radiance
terminology used to describe reflectance
quantities. The labelling with ‘Case’ corresponds
to Nicodemus (1977). Grey fields correspond to
measurable quantities, whereas the others denote
conceptual quantities.
2.3 Examples for measurable quantities and derived
products
Referring to Table 1, typical measurement instrumentation
with resulting reflectance products can be listed for the
individual cases. The biconical reflectance (Case 5) is a
typical laboratory setup, where a collimated light source
illuminates a target that is measured using a non-imaging
spectroradiometer. A special case is the conical-
hemispherical reflectance (Case 6), where in the laboratory
the sensor is replaced using a cosine receptor for
hemispherical measurement. The hemispherical-conical
reflectance (Case 8) corresponds to the most common
measurement of satellites or airborne and field instruments
(e.g., MERIS, ASD FieldSpec). Finally, bihemispherical
reflectance (Case 9) is measured using albedometers.
Even though measurable quantities only reflect Cases 5, 6, 8
and 9 in Table | above, the non-zero interval of the sensor’s
field of view may be neglected and resulting quantities are
reported as being bidirectional or hemispherical-directional
measurements. Most satellite reflectance products delivered
after atmospheric correction procedures are labelled ‘surface
reflectance’ (e.g., MODIS (Vermote, 1999)). Nevertheless, in
many cases the underlying concept of the used reflectance
nomenclature is unclear or undocumented, resulting in
significant difficulties to assign the proper terminology to
the delivered data product. As long as data from satellite or
airborne sensors and field spectrometers are not corrected for
the hemispherical angular extent of the incoming radiance,
the reflected measured quantity always depends on the
actual direct and diffuse components of the irradiance over
the whole hemisphere. As a consequence, data without a
proper specification of the corresponding beam geometries
are subject to misinterpretation and subsequently lead to
larger uncertainties.
Table 2 shows typical reflectance products and their
derivation from the satellite measurement. The integration of
the HDRF (Case 7) over the viewing hemisphere results in
the BHR (Case 9). Using a modelling approach (e.g,
Martonchik 1994; Lyapustin, 1999), the HDRF data (Case 7)
is further used to derive BRF (Case 1), and finally, DHR
(Case 3) can be derived from BRF (Casel) by hemispherical
integration over the viewing hemisphere. A special case is
the derivation of the BRDF from the BRF (again Case 1),
which is simply scaling the BRF by 1/JT.
f
Measurement Derived Products
BRDF
Bidirectional
Reflectance
BRE Distribution
HDRF Bidirectional Function
: Hemispherie Reflectance Case 1
Hemispherical als Factor DHR
„Conical Directional Gad Directional-
Reflectance c Hemispherica
Case 8 Re ctun | Reflectance
Factor Mies
Case 7 | Case 3
BHR
Bihemispheri
cal
Reflectance
Table 2: Conceptual data processing chain of airborne and
satellite measurements. The table is read from the
left to the right side.
The abovementioned derivations of conceptual reflectance
quantities from measured reflectance data include the
application of a BRDF model. Thus, derived conceptual
quantities depend not only on the sampling scheme,
availability and accuracy of measured data, but also on the
model itself.
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