158
(assuming n constant) are only a first approach. Full computations making use of Eq. 12 and
involving the Ketteler - Helmoltz theory are required to account for all aspects of the optics
of these pigmented bodies. With this aim, a model has been developed (Bricaud and Morel,
1986; Stramski et al., 1988) where the input parameters are the size distribution function, the
actual Qa (}..) and Qc (}..) spectra (as derived from experiments), and its outputs, beside the
understanding of all phases of the phenomenon, are the n' (}..), n (A) and Qb (A) spectra (the
spectral efficiency factor for backscattering, Qbb (A) is also derived).
The tiny cells have some interesting scattering properties which result from the behavior of
the theoretical Qb (A) curve in its initial ascending part (Fig. 2). This portion closely
resembles a parabola, as Eq. 11. When expanded, it becomes
(11')
and can reduce to its first term (to within 5 %), provided that p remains below 0.95. This
condition is fully satisfied by free-living bacteria and almost by Synechocystis (p varies from
0.65 to 1.2 when A varies from 750 to 400 nm). For p values in this range, Qb (at given A)
is therefore proportional to the square of the size and the scattering cross section (Sg Qb)
becomes proportional to d 4 • For a given (small) size and with p inversely related to A (Eq.
7 and 9), Qb will vary as }...2. Both these properties have been perfectly confirmed by
experimental determinations carried out with bacterioplankton of changing size (0.55 to 1 J-tm,
Morel and Ahn, 1990). Synechosystis (1.15 J-tm) is also not far from exhibiting a Qb (A)
spectrum with a }..-2 dependency (Stramski and Morel, 1990).
The question of even smaller particles, i.e. smaller than the wavelength, in such a manner that
the van de Hulst approximation begins to fail, is not a purely academic one (as we shall see
later on). Such particles belong to a transition domain toward the pure Rayleigh scattering.
For a Rayleigh dipole, Qb is proportional to a 4 (i.e. to ~) or equivalently inversely
proportional to A 4 • Therefore the scattering cross section is varying as d 6 • Computations show
that the departure from the p2 dependency as predicted by Eq. 11' takes place when p falls
below about 0.3, at least for particles having a relative index smaller than 1.06 (see Fig. II.
11 and discussion in Morel, 1973; and also Figure 5 later). Detrital particles, and very small
microbes with sizes above 0.3 J-tm still will behave like "common" bacteria and are
(assuming n constant) are only a first approach. Full computations making use of Eq. 12 and
involving the Ketteler - Helmoltz theory are required to account for all aspects of the optics
of these pigmented bodies. With this aim, a model has been developed (Bricaud and Morel,
1986; Stramski et al., 1988) where the input parameters are the size distribution function, the
actual Qa (}..) and Qc (}..) spectra (as derived from experiments), and its outputs, beside the
understanding of all phases of the phenomenon, are the n' (}..), n (A) and Qb (A) spectra (the
spectral efficiency factor for backscattering, Qbb (A) is also derived).
The tiny cells have some interesting scattering properties which result from the behavior of
the theoretical Qb (A) curve in its initial ascending part (Fig. 2). This portion closely
resembles a parabola, as Eq. 11. When expanded, it becomes
(11')
and can reduce to its first term (to within 5 %), provided that p remains below 0.95. This
condition is fully satisfied by free-living bacteria and almost by Synechocystis (p varies from
0.65 to 1.2 when A varies from 750 to 400 nm). For p values in this range, Qb (at given A)
is therefore proportional to the square of the size and the scattering cross section (Sg Qb)
becomes proportional to d 4 • For a given (small) size and with p inversely related to A (Eq.
7 and 9), Qb will vary as }...2. Both these properties have been perfectly confirmed by
experimental determinations carried out with bacterioplankton of changing size (0.55 to 1 J-tm,
Morel and Ahn, 1990). Synechosystis (1.15 J-tm) is also not far from exhibiting a Qb (A)
spectrum with a }..-2 dependency (Stramski and Morel, 1990).
The question of even smaller particles, i.e. smaller than the wavelength, in such a manner that
the van de Hulst approximation begins to fail, is not a purely academic one (as we shall see
later on). Such particles belong to a transition domain toward the pure Rayleigh scattering.
For a Rayleigh dipole, Qb is proportional to a 4 (i.e. to ~) or equivalently inversely
proportional to A 4 • Therefore the scattering cross section is varying as d 6 • Computations show
that the departure from the p2 dependency as predicted by Eq. 11' takes place when p falls
below about 0.3, at least for particles having a relative index smaller than 1.06 (see Fig. II.
11 and discussion in Morel, 1973; and also Figure 5 later). Detrital particles, and very small
microbes with sizes above 0.3 J-tm still will behave like "common" bacteria and are