Definitions
155
Hemispherical-directional reflectance: The ratio of the reflected radiance from a single view direction to the incident irradiance averaged
over the entire incident hemisphere of incoming radiation.
Bi-hemispherical reJEectance: The ratio of the reflected radiance integrated over the entire view hemisphere to the incident irradiance
averaged over the entire incident hemisphere of incoming radiation.
In remote sensing the term bi-directional reflectance distribution function (BRDF) refers to the entire distribution of bi-directional reflectances
for all possible view directions. Technically the BRDF is difficult to measure because the solid angle of the source should be infinitesimal for
the measurement. The only practical source for BDRF measurements on
soils and plant canopies is the sun, and it is not only not an infinitesimal
source, but is always accompanied by scattered radiation from the sky.
The more useful bi-directional reflectance factor (BRF) is the ratio of the
reflected radiance from a single view direction to the reflected radiance
from an ideal, perfectly diffuse surface experiencing the same irradiance.
Each of the four directional reflectances defined above can have the word
factor appended to them if the denominator of the ratio is for an ideal, perfectly diffuse surface. Emission from a surface does not involve incident
radiation so the term "directional emissivity" is appropriate.
An interesting fact is worth noting here; the bi-directional reflectance
distribution function is not limited to a maximum value of unity like the reflectivity, bi-hemispherical reflectance, and the bi-directional reflectance
factors are.
Without dealing with problems of radiation measurement, it may be
difficult to understand the applications of these terms. The following example may help. A pyranometer is an instrument sensitive to the solar
wavelength band that measures the flux density on a horizontal plane arising from the entire hemisphere above that plane. A pyranometer could
be used to measure the irradiance of a crop on a clear day when the solar
beam dominates the incident flux. The pyranometer could then be inverted
to measure the radiation reflected from the crop. The ratio of reflected to
incident radiation would be a bi-hemispherical reflectance, but because
the direct beam of the sun dominates the radiance, it would approximate a directional-hemispherical reflectance. The ratio of the same set
of measurements made on an overcast day would be a bi-hemispherical
reflectance. The two measurements would be similar, but not necessarily equal because of the directional interaction of the surface with the
directional solar beam. Instruments that have a narrow view angle, such
as aircraft and satellite remote sensing devices, make measurements that
approximate the bi-directional reflectance factors. For example, the radiance measured by a narrow IFOV radiometer from some angle divided by
the radiant flux density incident on the surface from the sun (irradiance)
would approximate the bi-directional reflectance of the surface from the
viewing angle. If this narrow IFOV radiometer were used to measure the
155
Hemispherical-directional reflectance: The ratio of the reflected radiance from a single view direction to the incident irradiance averaged
over the entire incident hemisphere of incoming radiation.
Bi-hemispherical reJEectance: The ratio of the reflected radiance integrated over the entire view hemisphere to the incident irradiance
averaged over the entire incident hemisphere of incoming radiation.
In remote sensing the term bi-directional reflectance distribution function (BRDF) refers to the entire distribution of bi-directional reflectances
for all possible view directions. Technically the BRDF is difficult to measure because the solid angle of the source should be infinitesimal for
the measurement. The only practical source for BDRF measurements on
soils and plant canopies is the sun, and it is not only not an infinitesimal
source, but is always accompanied by scattered radiation from the sky.
The more useful bi-directional reflectance factor (BRF) is the ratio of the
reflected radiance from a single view direction to the reflected radiance
from an ideal, perfectly diffuse surface experiencing the same irradiance.
Each of the four directional reflectances defined above can have the word
factor appended to them if the denominator of the ratio is for an ideal, perfectly diffuse surface. Emission from a surface does not involve incident
radiation so the term "directional emissivity" is appropriate.
An interesting fact is worth noting here; the bi-directional reflectance
distribution function is not limited to a maximum value of unity like the reflectivity, bi-hemispherical reflectance, and the bi-directional reflectance
factors are.
Without dealing with problems of radiation measurement, it may be
difficult to understand the applications of these terms. The following example may help. A pyranometer is an instrument sensitive to the solar
wavelength band that measures the flux density on a horizontal plane arising from the entire hemisphere above that plane. A pyranometer could
be used to measure the irradiance of a crop on a clear day when the solar
beam dominates the incident flux. The pyranometer could then be inverted
to measure the radiation reflected from the crop. The ratio of reflected to
incident radiation would be a bi-hemispherical reflectance, but because
the direct beam of the sun dominates the radiance, it would approximate a directional-hemispherical reflectance. The ratio of the same set
of measurements made on an overcast day would be a bi-hemispherical
reflectance. The two measurements would be similar, but not necessarily equal because of the directional interaction of the surface with the
directional solar beam. Instruments that have a narrow view angle, such
as aircraft and satellite remote sensing devices, make measurements that
approximate the bi-directional reflectance factors. For example, the radiance measured by a narrow IFOV radiometer from some angle divided by
the radiant flux density incident on the surface from the sun (irradiance)
would approximate the bi-directional reflectance of the surface from the
viewing angle. If this narrow IFOV radiometer were used to measure the