18 Field Radiometry and Ocean Color Remote Sensing
315
between radiance and irradiance calibrations when using the same irradiance standard for both types of calibration. With the lamp-plaque system, C L (λ) is determined
from DN(λ) related to the input radiance L(λ). Under the assumption of a radiance
sensor with narrow bandwidth centered at λ and a narrow field-of-view viewing the
plaque at an angle θ with respect to the normal to the plaque,
L(λ) = E(λ)ρ d (λ,θ )π
−1
(18.8)
where ρ d (λ,θ ) is the directional-directional reflectance of the plaque for the specific
viewing configuration (generally θ = 45 ◦ ) and E(λ) is given by Equation (18.7)
with distance d between lamp and plaque. It is recalled that while increasing d augments the homogeneity of the radiance field within the field-of-view of the sensor,
the intensity decreases with 1/d 2 . Thus, d needs to be chosen to satisfy both intensity and homogeneity requirements for the sensor under calibration. Finally, if the
directional-hemispherical reflectance ρ h (λ) is provided for the plaque as opposed
to the directional-directional reflectance ρ d (λ,θ ), a suitable correction coefficient is
required to relate these two factors.
Extended analysis of calibration uncertainties were made within the framework of the SeaWiFS Intercalibration Round Robin Experiments (SIRREX) which
addressed absolute calibrations of field radiometers (see Hooker et al., 2002b and
references therein). In particular, during SIRREX-7 comprehensive efforts were
focused on the evaluation of uncertainties of lamp radiant fluxes (based on multiple
measurements performed on a set of lamps), calibration repeatability (as affected
by power supply, lamp stability, and radiometer alignment) and plaque reflectance
(due to spatial inhomogeneity and uncertainty in directional-directional reflectance).
Results suggested ranking calibration uncertainties as primary (minimum), secondary (average) and tertiary (high) based on the difficulty of reducing the size of
uncertainties from different individual sources. These values vary from 1.1 to 3.4%
for irradiance and from 1.5 to 6.3% for radiance.
18.4.2 Cosine Response of Irradiance Sensors
Irradiance sensors should ideally collect the directional radiance contributions with
a response varying as the cosine of the incident angle. Real collectors, nevertheless,
have an angular response which deviates from this ideal cosine. Consequently, the
error in the cosine response is a source of uncertainty in irradiance measurements.
This generally increases with the angle of incidence on the collector and depends
on wavelength, sun zenith (i.e., geographic position, season and time), atmospheric
optical conditions (i.e., cloudiness, aerosol type and load), and additionally the
seawater optical properties and depth for in-water measurements.
The cosine error, denoted as f c (θ ,φ,λ) and expressed in percent, is conveniently
described through the normalized angular response – the response divided by the
cosine of the angle of incidence and by the response at normal incidence – at the
center-wavelength λ of each spectral band
315
between radiance and irradiance calibrations when using the same irradiance standard for both types of calibration. With the lamp-plaque system, C L (λ) is determined
from DN(λ) related to the input radiance L(λ). Under the assumption of a radiance
sensor with narrow bandwidth centered at λ and a narrow field-of-view viewing the
plaque at an angle θ with respect to the normal to the plaque,
L(λ) = E(λ)ρ d (λ,θ )π
−1
(18.8)
where ρ d (λ,θ ) is the directional-directional reflectance of the plaque for the specific
viewing configuration (generally θ = 45 ◦ ) and E(λ) is given by Equation (18.7)
with distance d between lamp and plaque. It is recalled that while increasing d augments the homogeneity of the radiance field within the field-of-view of the sensor,
the intensity decreases with 1/d 2 . Thus, d needs to be chosen to satisfy both intensity and homogeneity requirements for the sensor under calibration. Finally, if the
directional-hemispherical reflectance ρ h (λ) is provided for the plaque as opposed
to the directional-directional reflectance ρ d (λ,θ ), a suitable correction coefficient is
required to relate these two factors.
Extended analysis of calibration uncertainties were made within the framework of the SeaWiFS Intercalibration Round Robin Experiments (SIRREX) which
addressed absolute calibrations of field radiometers (see Hooker et al., 2002b and
references therein). In particular, during SIRREX-7 comprehensive efforts were
focused on the evaluation of uncertainties of lamp radiant fluxes (based on multiple
measurements performed on a set of lamps), calibration repeatability (as affected
by power supply, lamp stability, and radiometer alignment) and plaque reflectance
(due to spatial inhomogeneity and uncertainty in directional-directional reflectance).
Results suggested ranking calibration uncertainties as primary (minimum), secondary (average) and tertiary (high) based on the difficulty of reducing the size of
uncertainties from different individual sources. These values vary from 1.1 to 3.4%
for irradiance and from 1.5 to 6.3% for radiance.
18.4.2 Cosine Response of Irradiance Sensors
Irradiance sensors should ideally collect the directional radiance contributions with
a response varying as the cosine of the incident angle. Real collectors, nevertheless,
have an angular response which deviates from this ideal cosine. Consequently, the
error in the cosine response is a source of uncertainty in irradiance measurements.
This generally increases with the angle of incidence on the collector and depends
on wavelength, sun zenith (i.e., geographic position, season and time), atmospheric
optical conditions (i.e., cloudiness, aerosol type and load), and additionally the
seawater optical properties and depth for in-water measurements.
The cosine error, denoted as f c (θ ,φ,λ) and expressed in percent, is conveniently
described through the normalized angular response – the response divided by the
cosine of the angle of incidence and by the response at normal incidence – at the
center-wavelength λ of each spectral band