151
ex is the size parameter, relative to the wavelength in the surrounding medium (Aw in water,
Ao in vacuo), and p and p' combine the relative size ex with the real part or the imaginary part
of the relative refraction index. By combining Eq. 8 with Eq. 2, it is clear that p' can also
be defined as
(8')
the product of the absorption coefficient of the substance forming the particle with its
diameter.
Absorption cross section
In the frame of the van de Hulst approximation, the efficiency factor for absorption is only
a function of p'
-1
-2
Qa- 1 +2[exp(-p')] P' + 2[exp(-p')-I] P'
(10)
This function asymptotically approaches 1 when p' approaches 00 ,meaning that in such a
case, the particle is able to absorb all the energy impinging on its geometrical cross section
and then is a black body. The behavior of this function (see Fig. 1) is at the origin of the socalled package effect (Kirk, 1975 a, b), or discreteness effect (Morel and Bricaud, 1981). This
effect is experienced by most of the phytoplankters, which often are rather strongly absorbing
bodies. The practical consequence is that the actual absorption capability of an algal cell is
not simply proportional to its pigment content, as easily seen in Fig. 1. For instance, if we
assume that a certain cell has an initial p' value equal to 2 before doubling its pigment
content, p' becomes 4 after the doubling, whereas the absorption capability, depicted by Qa
(which goes from about 0.7 to 0.9), is only increased by about 30 %. The ratio of actual
absorption to pigment concentration is no longer a constant, as it depends on the initial p'
value (hence Beer's Law does not apply in this case).
The "flattening" of the absorption spectrum is another aspect of the same phenomenon. If, by
changing the wavelength, as is found to be doubled (and thus p' doubled), Qa in general is not
doubled and the amplitude of the absorption peak for a discrete absorbing substance is not
doubled as it would be in a continuous medium (a "solution" of the same substance).
ex is the size parameter, relative to the wavelength in the surrounding medium (Aw in water,
Ao in vacuo), and p and p' combine the relative size ex with the real part or the imaginary part
of the relative refraction index. By combining Eq. 8 with Eq. 2, it is clear that p' can also
be defined as
(8')
the product of the absorption coefficient of the substance forming the particle with its
diameter.
Absorption cross section
In the frame of the van de Hulst approximation, the efficiency factor for absorption is only
a function of p'
-1
-2
Qa- 1 +2[exp(-p')] P' + 2[exp(-p')-I] P'
(10)
This function asymptotically approaches 1 when p' approaches 00 ,meaning that in such a
case, the particle is able to absorb all the energy impinging on its geometrical cross section
and then is a black body. The behavior of this function (see Fig. 1) is at the origin of the socalled package effect (Kirk, 1975 a, b), or discreteness effect (Morel and Bricaud, 1981). This
effect is experienced by most of the phytoplankters, which often are rather strongly absorbing
bodies. The practical consequence is that the actual absorption capability of an algal cell is
not simply proportional to its pigment content, as easily seen in Fig. 1. For instance, if we
assume that a certain cell has an initial p' value equal to 2 before doubling its pigment
content, p' becomes 4 after the doubling, whereas the absorption capability, depicted by Qa
(which goes from about 0.7 to 0.9), is only increased by about 30 %. The ratio of actual
absorption to pigment concentration is no longer a constant, as it depends on the initial p'
value (hence Beer's Law does not apply in this case).
The "flattening" of the absorption spectrum is another aspect of the same phenomenon. If, by
changing the wavelength, as is found to be doubled (and thus p' doubled), Qa in general is not
doubled and the amplitude of the absorption peak for a discrete absorbing substance is not
doubled as it would be in a continuous medium (a "solution" of the same substance).