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Radiometry: Scalar irradiances Prev topic | Next topic

Scalar irradiance is defined as follows (for example, Mobley 1994, Morel and Smith 1982):

E0   = ∫Δω L(ξ)  
    = ∫Δω L(θ, φ) sinθ  (1)

where Δω is the solid angle, ξ is a unit vector of direction in space, also described by the pair of polar angles: θ and φ. The scalar irradiance does not account for the orientation of the direction, ξ, of the incident ER in respect of the normal to the area in question. The base definition of the scalar irradiance refers to Δω = 4π, i.e. the full solid angle.

In analogy with the vector irradiance, one can define downwelling (downward) and uppwelling (upward) scalar irradiances:

E0d = ∫Ξd L(ξ)  (2)
E0u = ∫Ξu L(ξ)  (3)

where Ξd and Ξu are respectively the solid angles subtended by the lower and upper hemispheres in reference to a horizontal plane. It follows that:

E0 = E0d + E0u  (4)

The scalar irradiance is closely related to the spherical irradiance, Es, i.e. the power of ER per area received by the surface of a sphere in the limit when the radius of the sphere vanishes. Indeed, Es = (1/4) E0.

See also: Radiometry: Vector irradiances.

CITATION:
Jonasz M. 2006. Radiometry: Scalar irradiances (www.tpdsci.com/Tpc/RdmIrdSclER.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).
HISTORY:
Published: 22-Mar-2006
Modified: 04-Mar-2007
Peer-reviewed: 03-Sep-2006
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