308
G. Zibordi and K.J. Voss
validation of space derived radiometric products. Impetus for these developments,
which led to unprecedented accuracy in marine optical radiometry through the
definition and assessment of new measurement methods and protocols, were the
recent space missions for the global mapping of marine biomass (Robinson, 2004):
the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), the Moderate Resolution
Imaging Spectroradiometer (MODIS), the Global Imager (GLI) and the Medium
Resolution Imaging Spectrometer (MERIS).
This work is a brief introduction to in-situ marine optical radiometry with a view
to its application to ocean color remote sensing.
18.2 Terminology
Optical radiometry is the science and technology of measuring radiant energy in the
electromagnetic spectrum from the ultraviolet to the infrared wavelengths. Basic
radiometric quantities are the solid angle, irradiance and radiance.
In the ideal case of a cone in a 3-dimensional space that resembles the typical
geometry for radiometric measurements, the solid angle is the area intercepted by
the cone on the surface of a unit sphere centered at the vertex of the cone itself.
By indicating with φ and θ the azimuth and zenith angles in spherical coordinates,
the solid angle in units of sr for a right cone with vertex angle 2 and axis
oriented in the direction θ = 0, is obtained by integrating the element of solid angle
d = sin θ dθ dφ according to
=
2π
0
dφ
0
sin θ dθ =2π (1 − cos ).
(18.1)
For a full hemisphere, = 2πsr.
Irradiance and radiance are commonly expressed as spectral quantities. Spectral
irradiance at the wavelength λ, denoted as E(λ) and generally provided in units
of W/m 2 /nm, is the radiant flux incident on, passing through, or emerging from a
surface per unit surface area and per unit wavelength interval:
E(λ) =
d 2
dS 0 dλ
(18.2)
where d is the element of radiant flux (the time rate of flow of radiant energy),
dS 0 is an element of area at the surface and dλ is an element of wavelength centered
at λ.
Spectral radiance, denoted by L(λ) and generally provided in units of
W/m 2 /sr/nm, is the radiant flux at a given point and direction per unit solid angle,
per unit projected area and per unit wavelength interval:
L(θ ,φ,λ) =
d 3
d dS 0 cos θ dλ
(18.3)
G. Zibordi and K.J. Voss
validation of space derived radiometric products. Impetus for these developments,
which led to unprecedented accuracy in marine optical radiometry through the
definition and assessment of new measurement methods and protocols, were the
recent space missions for the global mapping of marine biomass (Robinson, 2004):
the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), the Moderate Resolution
Imaging Spectroradiometer (MODIS), the Global Imager (GLI) and the Medium
Resolution Imaging Spectrometer (MERIS).
This work is a brief introduction to in-situ marine optical radiometry with a view
to its application to ocean color remote sensing.
18.2 Terminology
Optical radiometry is the science and technology of measuring radiant energy in the
electromagnetic spectrum from the ultraviolet to the infrared wavelengths. Basic
radiometric quantities are the solid angle, irradiance and radiance.
In the ideal case of a cone in a 3-dimensional space that resembles the typical
geometry for radiometric measurements, the solid angle is the area intercepted by
the cone on the surface of a unit sphere centered at the vertex of the cone itself.
By indicating with φ and θ the azimuth and zenith angles in spherical coordinates,
the solid angle in units of sr for a right cone with vertex angle 2 and axis
oriented in the direction θ = 0, is obtained by integrating the element of solid angle
d = sin θ dθ dφ according to
=
2π
0
dφ
0
sin θ dθ =2π (1 − cos ).
(18.1)
For a full hemisphere, = 2πsr.
Irradiance and radiance are commonly expressed as spectral quantities. Spectral
irradiance at the wavelength λ, denoted as E(λ) and generally provided in units
of W/m 2 /nm, is the radiant flux incident on, passing through, or emerging from a
surface per unit surface area and per unit wavelength interval:
E(λ) =
d 2
dS 0 dλ
(18.2)
where d is the element of radiant flux (the time rate of flow of radiant energy),
dS 0 is an element of area at the surface and dλ is an element of wavelength centered
at λ.
Spectral radiance, denoted by L(λ) and generally provided in units of
W/m 2 /sr/nm, is the radiant flux at a given point and direction per unit solid angle,
per unit projected area and per unit wavelength interval:
L(θ ,φ,λ) =
d 3
d dS 0 cos θ dλ
(18.3)