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194 Algae: Anatomy, Biochemistry, and Biotechnology

elemental cone. This gives us the definition of radiant intensity:

dF
I ¼ (5:17)
dv

where dv is the infinitesimal solid angle of the elemental cone containing the given direction. From
the definition of an infinitesimal solid angle, we get:

dF I
2 2
I ¼ r or I ¼ r E or E ¼ (5:18)
dA r 2
where the infinitesimal surface area dA is on the surface of a sphere centered on the source and at a
distance r from the source and E is the irradiance of that surface. More generally, the radiant flux
will intercept dA at an angle u from the surface normal. This gives us the inverse square law for
point sources:

I u cos u
E ¼ (5:19)
d 2
where I u is the intensity of the source in the u direction and d is the distance from the source to the
surface element dA.
Radiant intensity is measured in watts per steradian (W sr 21 ). Combining the definitions of
radiance [Equation (5.13)] and radiant intensity [Equation (5.17)] gives us an alternative definition
of radiance:

d I u
L ¼ (5:20)
d A cos u
where dI u is the infinitesimal intensity of the point source in the u direction with the surface normal.

SPECTRAL RADIANT INTENSITY
Spectral radiant intensity is radiant intensity per unit wavelength interval at wavelength l.It is
defined as:

d I
I l ¼ (5:21)
dl
and is measured in watts per steradian per nanometer (W sr 21 nm 21 ).

PHOTOMETRY
Photometry is the science of measuring visible light in units that are weighted according to the
sensitivity of the human eye. It is a quantitative science based on a statistical model of the
human visual response to light under carefully controlled conditions. We cannot apply this
model to the “perception” of light by algae, because we should substitute the sensitivity of the
algal photoreception systems for that of the human eye as quantified by action spectroscopy in
Chapter 2.
For the human perception, the Commission International d’Eclairage (CIE) photometric curves
(photopic and scotopic) provide a weighting function that can be used to convert radiometric
into photometric measurements. In scotopic curve, yellowish-green light receives the greatest
weight because it stimulates the eye more than blue or red light of equal radiant power
(l max ¼ 555 nm) (Figure 5.11, Table 5.3); in photopic curve blue-green light receives the greatest