Journal of Plankton Research Vol.18 no. 12 pp.2223-2249, 1996
Refractive index of phytoplankton derived from its
metabolite composition
Eyvind Aas
Department of Geophysics, University of Oslo, PO Box 1022 Blindern, N-0315
Oslo, Norway
Abstract. The refractive index of phytoplankton is calculated from its metabolite composition. The
mean index of the algal dry mass, relative to the index of water, seems to vary from 1.146 for green
algae to 1.167 for coccolithophonds. This difference of 0.021 reduces to 0.007 and 0.003 when the
partial water volumes of the algae are 0.6 and 0.8, respectively. The most important factor for the
variation of the refractive index is the algal water content. If a reasonable average range of the partial
water volume is 0.6 ± 0.2, the corresponding range of the refractive index relative to sea water
becomes 1.06 ±0.04. This result is in excellent agreement with estimates based on optical measurements of pure algal cultures. The normal dispersion of the refractive index is negligible, but anomalous dispersion in the vicinity of strong absorption bands may be of importance for the light
scattering properties of small phytoplankton.
Introduction
Concept of a mean refractive index
The ratio between the phase velocity of light in a vacuum and in a certain
medium defines the refractive index n of the medium. In many calculations the
absorption index K may be regarded as the imaginary part of a complex refractive index m. The total refractive index is then written m — n±i>c, where n is
the real part of the index, and / is yT—\. The choice of the sign + or - in the
definition depends on how the phase of the light wave is written.
In the sea the vertical attenuation of downward irradiance is influenced more
by light absorption than by scattering. The absorption of a particle depends on
its absorption index as well as its refractive index, and also the scattering process
depends on both indices. Consequently knowledge of both indices becomes
necessary if one wants to estimate the optical properties of the particle and the
influence of the particle on the light conditions.
If one is dealing with particles of irregular forms, like those found in the
ocean, it may be practical to define a significant refractive index (Zaneveld and
Pak, 1973). This is done by comparing the scattering properties of the natural
particle with those of a homogeneous sphere of the same volume, and then
determining which refractive index the sphere must have in order to produce
the same scattering. The basic idea or assumption behind this method is that a
sample of irregular particles, oriented at random, will scatter light like spheres
of the same volume or projected area. The works of Hodkinson (1963), Holland
and Gagne (1970, 1971) and Plass and Kattawar (1971) have often been referred
to in support of this assumption. However, Holland and Gagne (1971) drew the
conclusion that 'the limited results we have achieved so far . . . do indicate large
deviations between the scattering properties of spheres and our sample particles'.
The significant refractive index defined by this method should then be regarded
O Oxford University Press
2223
E.Aas
Table I. Real part of the refractive index relative to water of inorganic, mixed, and organic marine
particles (X: wavelength; ri: refractive index; p\9): volume scattering function of the angle 8; b: scattering coefficient of particles; JVO: particle concentration; Qc: attenuation efficiency; Q,: absorption
efficiency)
Ref.
Particles or area
1
1
1
1
2
3
4
5
6
7
7
8
8
9
10
11
12
10
13
13
14
15
15
15
16
17
18
19
18
20
21
21
22
23
24
25
26
27
18
18
24
27
25
28
28
28
25
18
18
18
18
18
24
27
29
Quartz
Feldspar
Mica
Clay minerals
Near Japan Trench
Central North Pacific
Off Equador
Sargasso Sea
Sargasso Sea
Sarg. S.: diam. >2.5 nm
Sarg. S.: diam. <2.5 fim
Sarg. S.: inorg. particles
Sarg. S.: organic particles
Bahama Islands
Mediterranean
Different areas
North Sea
Baltic Sea
Oregon, nearshore
Oregon, inshore
Chesapeake Bay
Spinach chloroplast
Spinach chloroplast
Spinach chloroplast
Marine bacteria
Marine bacteria
Synechococcus sp.
Synechococcui
Synechocystis sp.
Synechocystis
Synechocystis
Synechocystis
Diatoms
Skeletonema sp.
Thalassiosira pseudonana
Thalassiosira pseudonana
Thalassiosira pseudonana
Skeletonema coslatum
Chaetoceros curvisetum
Chaetoceros lauderi
Emiliana huxleyi
Emiliana huxleyi
Emiliana huxleyi
Isochrysis galbana
Isochrysis galbana
fsochrysis galbana
Pavlova sp.
Pavlova pingnis
Pavlova lutheri
Prymnesium parvum
Porphyridium cruenlum
Dunaliella salina
Dunaliella lertiolecta
Plalymonas suecica
Chlorella
2224
Method
X (nm)
fW
589
589
589
589
521, 652
436-578
436, 546
633
633
b
#45°)
436
fW
flow cytometry
PW
QcQ.
QcQ.
&
immersion
refractometer
Qc
QcQ,
QcQ.
QcQ.
QcQ.
QcQ.
QcQ.
QcQ.
QcQ.
immersion
immersion
flow cytometry
QcQ.
QcQ.
QcQ.
QcQ.
QcQ.
flow cytometry
QcQ.
QcQ.
#45°, X)
#45°, X)
#45°, X)
QcQ.
QcQ.
QcQ.
QcQ.
QcQ.
QcQ.
flow cytometry
QcQ.
flow cytometry
488
633
488
488
400-800
1.15
1.13-1.18
1.15-1.25
1.11-1.22
1.20-1.25
1.03-1.05
1.01-1.05
1.20
1.05
1.15
1.01
1.15
1.05-1.075
1.15-1.20
1.20
1.02-1.05
1.079-1.092
1.04
1.016-1.055
1.040-1.054
1.15
1.060
1.030
589
350-750
400-740
350-750
400-740
400-720
400
700
589
514
660
660
400-740
400-740
400-740
514
400-740
660
436
546
578
660
400-740
400-740
400-740
400-740
400-740
514
400-740
514
1.021
1.043-1.058
1.040-1.076
1.032
1.049-1.083
1.0325-1.0355
1.047-1.059
1.046-1.055
1.055-1.060
1.060-1.067
1.087
1.06-1.065
1.035-1.063
1.036-1.055
1.028
1.021
1.0045
1.05-1.058
1.044
1.093-1.095
1.023-1.031
1.026-1.035
1.027-1.035
1.067-1.075
1.050
1.045
1.048
1.057
1.092
1.062-1.065
1.071
1.047-1.086
Refractive index of pbytopknkton
Table I . (cont.)
Ref.
Particles or area
Method
X (nm)
30
30
30
31
31
32
32
33
33
ChJorella: cell wall
Chlorella: chloroplast
Chlr: cytopl. excl. chlplst.
Chlorella: core
Chlorella: shell
Chlorella: core
Chlorella: shell
Chlorella: core
Chlorella: shell
immersion
phase contr.
phase contr.
Mueller matrix
Mueller matrix
Mueller matrix
Mueller matrix
Mueller matrix
Mueller matrix
589
589
589
442, 663
442,663
442
442
457, 514
457, 514
ri
.022
.05-1.06
.015
.05
.15
.08
.13
.06
.08
References: 1: Weast (1981); 2: Sasaki el at. (1960), 3: Sugihara and Tsuda (1979); 4: Zaneveld and Pak (1973);
5: Kullenberg (1970); 6: Gordon and Brown (1972); 7: Brown and Gordon (1973a); 8: Zaneveld el al. (1974);
9: Brown and Gordon (1973b); 10. Kullenberg and Berg CHsen (1972); 11: Morel (1973); 12: Ackleson el al.
(1988); 13: Bricaud el al. (1995); 14: Burt (1955); 15: Bryant el al. (1969); 16: Morel and Ahn (1990); 17: Stramski
and Kiefer (1990); 18: Bncaud el al. (1988); 19: Stramski el al. (1995); 20: Stramiki el al. (1988); 21: Stranuki and
Morel (1990); 22: McCrone el al. (1967); 23: Hodgson and Newkirk (1975); 24- Ackleson and Spinrad (1988), 25:
Ackleson el al. (1990); 26: Stramski and Reynolds (1993); 27: Bricaud and Morel (1986), 28 Carder el al (1972);
29: Spinrad and Brown (1986); 30: Charoey and Brackett (1961); 31: Quinby-Hunt el al. (1986); 32: Quinby-Hunt
el al. (1989); 33: Hunt el al. (1990).
as what it is: a practical way of characterizing one of the optical properties of
marine particles.
Table I illustrates how the significant refractive index may vary with the
applied particle size distribution. Kullenberg (1970), Gordon and Brown (1972),
Brown and Gordon (1973a), and Zaneveld et al. (1974) used the same volume
scattering function fi{6) from the Sargasso Sea to calculate the refractive index
which best reproduced the measurements, but they applied different size distributions. The refractive index of the particles relative to sea water, ri, is seen to vary
between 1.05 and 1.20 in one-component systems, and between 1.01 and 1.15 in
two-component systems.
The uncertainty becomes less when the size distribution is known. If also the
attenuation and absorption efficiencies Qc and Q& have been determined by optical measurements, the refractive index may be obtained by comparing the scattering efficiency Qb = Qc~ Qa with theoretical scattering models. Several of the
results in Table I have been obtained by this method. Another method based
on scatterance is the flow cytometnc technique which applies measurements of
P(ff) in the forward and sideways directions.
Table I also demonstrates the importance of the method chosen. With the
immersion method the particle is immersed in liquids of different indices, until
a liquid is found where the contours of the particle disappear. The liquid will
then have the same refractive index as the particle or vice versa. The method
is obviously less suitable for inhomogeneous particles, in particular those
with shells, since the shells seem to dominate the index (McCrone et al., 1967;
Hodgson and Newkirk, 1975). Phase contrast methods are microscope techniques based on the same principles as the immersion method. In the refractometer the phase difference of the light passing through the test liquid and a
reference medium is observed, and the refractive index may then be calculated.
The measurements on spinach chloroplast by Bryant et al. (1969) give three
2225
E.Aas
different indices of which the one obtained by the immersion method (1.06) is
the greatest, and the one calculated from scatterance measurements (1.02) the
smallest.
One may then ask whether the concept of a mean refractive index has any
unique meaning for an inhomogeneous particle. The answer seems to be that
the concept mean depends on the type of measurement it is calculated from.
The work presented here uses an indirect method and estimates the mean refractive indices of the different metabolite components of the alga, the resulting bulk
refractive index and its most likely variations.
While each water molecule within a raindrop scatters light, the molecular scatterance is negligible compared with the scatterance of the raindrop as a whole.
Similarly it is thought here that while a phytoplankton particle may consist of
different parts with different properties, these differences can be neglected compared with the integrated properties of the particle. That is, it is assumed that
the particle can be regarded as homogeneous. A more important factor for the
optical behaviour than the internal variation may be the shape of the particle,
as already suggested, but this problem shall not be further dealt with here.
This work, which is a revised version of a former institute report (Aas, 1981) is
mainly concerned with the real part of the refractive index. However, since the
imaginary part is linked to the real part, the magnitude of its influence on the
real part has also been estimated.
Significant characteristics of phytoplankton
The phytoplankton is a transparent particle which as a single cell usually is so
small that it becomes invisible, but which in greater concentrations is able to
colour the sea. Its size is of an order of magnitude ranging from 1 to lOOO^m,
or of an order of 1 to 1000 compared with the wavelength of visible light.
Colonial phytoplankton forms may obtain dimensions in the millimetre range.
The volume content of phytoplankton in sea water in the eutrophic Oslofjorden has been observed by Karl Tangen (personal communication) to reach
the extreme value 600 mm31"1 (mostly dinoflagellates), while normally a content
of 1 mm31~' must be considered to be very high (see for instance the values
quoted by Jorgensen, 1966, Table 2.15). Lisitzin (quoted by Parsons, 1963)
gives an oceanic average of 0.8-2.5mgl~' of total particular matter, and its
organic fraction as 20-60%. The ratio between organic detritus and living
phytoplankton cells will vary, but Parsons (1963) suggests a ratio in the order
5:1.
Thus, <10~3 of the water volume and usually <10~6 is likely to be occupied
by phytoplankton. The values of Lisitzin and Parsons indicate that the oceanic
average may be in the range 10~8-10~7. The meaning of these small numbers is
better understood if one considers that a fractional volume of 10~6 corresponds
to lmm 3 1" 1 .
Most of the phytoplankton volume consists of water. The main organic constituents or major metabolites are proteins, carbohydrates and fats. The pigment
content is small, but is still the only organic constituent with any significant light
absorption.
2226
Refractive index of phytoplankton
Several cellular structures are observed in the phytoplankton. Some species
have an external silica shell, while others are covered with calcite scales. Internal
silica structures may also occur. Organic cell walls may consist of cellulose,
pectin or other substances. In all algae, except the blue-green algae, the pigments
are not evenly distributed, but concentrated in chloroplasts. Many species have
only one or two chloroplasts per cell, but some may have numerous small
chloroplasts. Vacuoles are filled with a cell sap which in composition may differ
somewhat from sea water. In some species the cell walls are covered with a mucilage layer, and some colonial forms may be completely embedded in this slime or
jelly-like material. For the present computation of the mean refractive index of
the alga, however, the structure has been neglected and all constituents have
been regarded as evenly distributed.
Another point which has not been taken into account here is that the phytoplankton particle may aggregate with inorganic particles of sizes ranging from
ionic dimensions to silt. The smaller particles may be taken up by the algae and
become a part of their structure. Vinogradov (1953) quotes ferro oxide (Fe2(>3)
contents from 0.5 to 2.0% in the dry matter of diatoms, and aluminium oxide
(AI2O3) contents of the same order. Since metallic minerals have absorption
indices of order of magnitude 1, similar to the absorption bands of pigments, it
is possible that their influence on the optical properties of the plankton particle
under certain conditions may equal that of the pigments. According to Harvey
(1937) particles of ferro hydroxide are readily adsorbed on the surface of
diatoms to such an extent that the algae may appear coated with the brown
material. It has, however, been assumed here that such cases are rare, and only
the 'pure' phytoplankton composition has been considered.
Method
Composition of phytoplankton
Table II gives some examples of the major metabolite composition of phytoplankton: proteins, carbohydrates, and fats. (The original taxonomy has been
retained.) The table does not pretend to show all possible variations, but it is
hoped that some idea of the mean values may be obtained from the numbers.
An interesting result is that the total pigment content in these examples only
varies between 1 and 3% of the dry mass.
The content of inorganic material, except silica and calcite, has been neglected.
The ash content of many marine algae does not exceed 10% of the dry mass,
and consists mainly of sea salts (Strickland, 1960), which here have been
assumed as already included in the water content.
The water content is the greatest factor of uncertainty in our estimates of the
refraction index. Table III presents some observations of water and dry mass
content. Numbers without parentheses have been observed, while numbers in
parentheses have been calculated. The relations between the partial dry mass
m^, the dry mass concentration C, and the partial water volume vw in Table III
are
2227
E.Aas
Table II. Dry mass composition of phytoplankton
A: Algae with organic surface
Species
Reference
(and series
of measurement)
Protein
Carbohydrate
Fat
Pigment
[% of dry mass]
Dinoflagellates
mainly Ceralium
mainly Ceratium
mainly Ceratium
mainly Ceratium
mainly Ceratium
mainly Ceratium
mainly Ceratium
Amphidinium carterae
Exuviaella sp.
52
82
79
84
78
73
73
35
37
45
12
13
8
14
19
18
39
44
3
6
8
8
8
8
9
23
18
3
1
2
Brown flagellates
Monochrysis lutheri
53
34
12
1
2
Blue-green algae
Agmenellum quadrup.
44
38
16
2
3
3
4
4
4
4
2
2
(Day
(Day
(Day
(Day
Green algae
Chlorella pyrenoidosa
Chlorella vulgaris
Chlorella vulgaris
Chlorella vulgaris
Chlorella vulgaris
Chlorella vulgaris
Tetraselmis maculata
Dunaliflla salina
48
48
30
21
21
15
72
58
27
32
44
48
46
49
21
32
25
20
23
28
31
34
4
7
3
3
2
2
3
3
4
4
4
4
(A8)
(A20)
(A26)
(B20)
Red algae
Porphyridium cruentum
Porphyridium cruentum
Porphyridium cruentum
Porphyridium cruentum
40
33
39
26
47
55
45
65
10
10
14
8
1
1
1
1
1
1
1
2
2
(An.
(An.
(An.
(An.
(An.
(An.
(An.
IV)
X)
XIa)
b)
c)
d)
e)
11)
18)
25)
32)
3
2
2
1
B: Algae with mineralized surface
Reference
Species
(and series
of measurement)
1
1
1
1
(An.
(An.
(An.
(An.
Ill)
VI)
VII)
V)
1
1
1
1
2
2
2
(An.
(An.
(An.
(An.
Villa)
b)
c)
d)
2228
Diatoms
mainly Rhizosolenia
mainly Skeletonema
mainly Skeletonema
mainly Skel. <£
Thalassiothrix
mainly diatoms
mainly diatoms
mainly diatoms
mainly diatoms
Skeletonema costatum
Coscinodiscus sp.
Phaeodactylum tricom.
SUka shell
Silica
Protein
Fat
Carbohydrate
[% of dry rnass]
46
28
24
30
32
42
20
33
27
4
7
7
41
35
37
29
23
32
67
1
48
57
49
63
64
39
24
49
5
1
1
2
5
22
6
36
6
7
13
6
8
5
2
10
Pigment
2
1
4
Refractive index of phytoplankton
Table II. (cont.)
B: Algae with mineralized surface
Silica shell
Silica
Protein
Reference
Species
(and series
of measurement)
5
5
6
6
6
6
6
(Day
(Day
(Day
(Day
(Day
(Day
(Day
12)
15)
12)
14)
16)
18)
20)
Diatoms
mainly diatoms
mainly diatoms
mainly diatoms
mainly diatoms
mainly diatoms
mainly diatoms
mainly diatoms
49
47
30
36
42
40
40
Carbohydrate
[%ofdry
11
23
5
6
12
21
21
31
21
59
51
38
32
30
Cakite scales
Calcite
Protein
Reference
Species
(and series
of measurement)
Coccolithophondes
Syracosphaera carterae 23
Pigment
Fat
6
6
4
4
6
6
8
3
3
2
3
2
1
1
CarboFat
hydrate
[% of dry mass]
Pigment
17
54
References 1: Brandt and Raben (1920); 2: Parsons el al. (1961), 3: Ketchum and Redfield (1949); 4: Collyer and
Fogg (1955); 5 McAllister el al. (1961); 6: Antia el al. (1963).
dry mass
total mass
dry mass
total volume
water volume
total volume
)
Pi
=
PdO - vw)
(2)
Pw/
m
(1 -ma) Pi
Pi
(3)
Dry mass has been converted to volume and vice versa by assuming that the dry
mass of diatoms has the density p<i = l-5gcm~3, that other species have
Pi = 1.3gcm~3, that mixed populations have pi = 1.4gcm~3 (see Table VIII),
and that the density of water is p* = l.Ogcirr3.
A factor of uncertainty is that sea salts may be included in the dry mass, but
the error, as mentioned earlier, is probably not large.
The problem of measuring the true wet weight or total mass of algae has been
discussed by Strickland (1960). According to him, the experimental wet weight
will rarely be less than twice the true algal weight, due to the presence of interstitial water. His own estimate of a mean dry mass concentration C is nevertheless 0.35gcm~3 in accordance with the mean value 0.3gcm~3 obtained in Table
III without any corrections. Also Jergensen (1966) has discussed this problem
2229
E.Aas
Table III. Water content of algae
Reference
Species
"id
C (g cm" 3 )
Vw
1
seaweeds
(Fucus, Laminaria)
diatoms
other species
mixed population
organic part
green algae
green algae
green algae
mainly diatoms
0.18-0.24
(0.43-0.66)
(0.19-0.37)
(0.35)
(0.26)
(0.22 ± 0.03)
0.25
0.20-0.33
0.16 ±0.06
(0.19-0.25)
0.50-0.85
0.20-0.40
0.39
0.28
0.23 ± 0.03
(0.27)
(0.21-0.36)
(0.17 ±0.07)
(0.8O-O.86)
(0.43-0.67)
(0.69-0.85)
(0.72)
(0.79)
(0.82 ± 0.03)
(0.80)
(0.73-0.84)
(0.89 ± 0.05)
0.3
0.1
0.3
0.2
0.8
0.1
2
2
3
3
4
5
6
7
Mean value
Standard deviation
References: 1: Quoted by Atkins (1923), 2: Gnm (1939), 3: Riley (1941); 4: Ketchum and Redfield (1949): 5: Myers
and Johnston (1949); 6: Spoehr and Milner (1949), 7: Harris and Riley (1956).
and quotes some additional data in the same range as Table III. The mean value
of mi in Table III, 0.3, is about four times the value that was once recommended
by ICES (Cushing et al., 1958).
However, it is likely that the numbers in Table III overestimate the wet
weight, and thus the partial water volume. If Strickland is right all values of m&
in the table should be multiplied by 2, and the resulting range of vw would then
become 0.6 ± 0.2 rather than the estimate value 0.8 ±0.1 in the table.
Refractive index and density of the constituents
Diatom cells are enclosed in walls composed of hydrated amorphous silica
(Lewin, 1962a), which in this form (SiO2-nH2O) is called opal. Some data
for the density p and refractive index n of opal and quartz (SiC>2), as well as of
diatoms, are presented in Table IV. The values p = (2.7±0.1)gcm~3 and
n = 1.48 ± 0.07 have been chosen to represent the dry state of the silica.
Table IV. Density and refractive index of silica
Reference
Silica
1
2
2
3
4
5
4
6
2
opal
opal
opal
diatom opal
diatoms
Skelelonema
devitrified diatoms
vitreous quartz
crystal quartz
P (g m" 3 )
2.17-2.20
1.73-2.16
2.00-2.07
-2.0
~2.7
2.64-2.66
i7
.406
.41-1.46
.41-1.46
.40-1.43
.42-1.43
.457
-1.486
.485
.547
References. 1: Forsythe (1954); 2: West (1981); 3: quoted by Lewin (l%2a); 4: McCrone et al. (1967); 5: Hodgson
and Newkirk (1975); 6: Jenkins and White (1957).
2230
Refractive index of phytoplankton
Table V. Density and refractive index of CaCO 3
Reference
Form
p (g cm 3 )
n
1
2
2
1
2
2
calcite
calcite
calcite
aragonite
aragonite
aragonite
2.71
2.71
2.72-2.94
2.94
2.93
2.94-2.95
1.601
1.601
1.601-1.677
1.633
1.632
1.632-1.633
References: 1: McCrone el al. (1967); 2: Weast (1981).
Some algae bear small scales, coccoliths, or anhydrous crystalline CaCC>3.
Usually each coccolith comprises only one crystal type, either uniaxial calcite
or biaxial aragonite (Lewin, 1962b) [see equations (22) and (23)]. Table V gives
the densities and mean refractive indices of these crystal forms. The values
p = (2.71 ± 0.01) g cm~3 and n = 1.60 ± 0.01 have been chosen to represent the
calcite of the coccolithophorids.
Armstrong et al. (1947) found that lipid-free proteins had a refractive index
n = 1.60, while proteins with 75% lipid content had n = 1.51. Protein and nonprotein indices of cellular constituents have also been discussed by Barer (1966)
and Ross (1967). Based on the indices of Armstrong et al. and the densities of
Oncley et al. (1947), the resulting estimates are p = (1.22 ±0.02) gcm~ 3 and
n= 1.57 ±0.01.
Table VI gives densities and refractive indices of some algal carbohydrate
forms: cellulose and starch [(QHioOs),,], sucrose (C12H22O11), and glucose
(C6H12O6). The values which have been chosen to represent all carbohydrates
are p = (1.53 ±0.04)gem" 3 and n = 1.55 ±0.02.
Table VI. Density and refractive index of carbohydrate
Reference
Form
1
2
3
4
4
5
1
6
7
1
5
4
6
1
4
cellulose,
cellulose,
cellulose,
cellulose,
starch
starch
starch
starch
starch
sucrose
sucrose
sucrose
sucrose
glucose
glucose
p (g cm" 3 )
crystalline
crystalline
amorphous
fibers
.27-1.61
.55
.482-1.489
.48-1.55
.53
.50
.53
.581
.588
.588
.562
.544
.563-1.573
.53-1.56
.53
.53
.51-1.54
.538
.558
.56
.557
.55
Reference*: 1: Weast (1981); 2. Steelier (1968); 3: Treiber (1955); 4: McCrone el at. (1967); 5: Davies el al. (1954); 6:
Gibbs (1942); 7: Chamot and Mason (1944).
2231
E-Aas
Table VII. Density and refractive index of pigments
Reference
Form
p (g cm" 3 )
1
2
1
2
2
See
3
See
See
See
cr-carotene
or-carotene
/(-carotene
0-carotene
xanthophyll
xanthophyll
chlorophyll a
chlorophyll a
chlorophyll b
chlorophyll c
1.00
text
text
text
text
1.451
1.00
1.453
1.448
(1.06)
1.11
(1.13)
(1.31)
(1.52)
(1.52)
(1.54)
Refereoces: 1: Weast (1981); 2: Euler and Jansson (1931); 3: Ketelaar and Hanson (1937).
Mean values and standard deviations for the densities and refractive indices of
plant oil quoted by Weast (1981) have been calculated. Temperature effects were
neglected, since the coefficient of volume expansion is only ~0.0007deg~'
(Clark, 1962). The results become p = (0.93 ± 0.02)gem"3 and n = 1.47 ± 0.01,
and it has been assumed that these values may represent the algal fat.
Very little information about densities and refractive indices of pigments is
given in the literature. The few obtainable data are presented in Table VII. The
numbers in parentheses are 'educated guesses', which will be explained later in
connection with equation (13). In an investigation by Antia et al. (1963) of a
population of mainly diatoms, the ratios chlorophyll a:chlorophyll c:carotenoids were crudely 1:0.5:1. From the table the values p « (1.12 ±0.06)gcm~ 3
and n = 1.50 ± 0.04 have then been chosen to represent pigment. It should be
noted, however, that due to the small pigment content, the chosen values have
little influence on the mean refractive index of the algae.
It has been assumed that the water of the algae has the same density and
refractive index as sea water. Values for these can be found in most textbooks,
and the ones used here are p = 1.025gcm~3 and n= 1.339 (corresponding to
the salinity 35.0p.s.u., the temperature 20.0°C, and the wavelength 589 nm).
Refractive index of mixtures
A simple equation for the refractive index of a mixture, supported by experiments with liquids, was proposed in 1863 by Gladstone and Dale:
m-\)=Vm(nm-l)
(4)
The subscript j refers to the j-th component, while m refers to the homogeneous
mixture. V is volume, n is refractive index, and p is density. This equation takes
into account the possibility that
2232
Refractive index of phytopianktoo
For the case that
V
S = V™
£
(6)
j
and by means of the partial volume
' m
equation (4) reduces to
^ V j = n
(8)
m
j
For a two-component system the last equation yields
nm =n]v] +n2v2 = « i ( l -v2) + n2v2 =n\ + {n2-n\)v2
(9)
By introducing the concentration C of the second component
C=V2PI
(10)
equation (9) may be written
nm=n\+?±—^C
= nx +aC
(11)
Pi
In this form the Gladstone-Dale equation is used by cell biologists to determine
the concentration of cellular constituents (e.g. Ross, 1967). a is called the specific
refraction increment.
Some years after the Gladstone-Dale equation another relation was derived
theoretically by Lorenz (1880) and Lorentz (1880):
02)
Lorentz (1915) says that 'This equation is found to hold as a rough approximation for various liquid mixtures', and adds that the same may be said of the
Gladstone-Dale equation. Many textbooks, however, describe equation (12) as
superior to equation (4).
One of the advantages of the Lorenz-Lorentz equation is that it may be used
to estimate the refractive index of a chemical compound. It will then have the
form
n) - 1 Mj
v
nj-l
Mm
M is the molecular or atomic weight of the constituent. The term R, defined by
2233
E.Aas
is called the molar refraction. Some values of R are listed by the CRC Handbook
of Chemistry and Physics (Weast, 1981). Equation (13) may be applied to
estimate the refractive indices of the algal pigments, as has been done for the
numbers in parentheses in Table VII. The molecular structure of xanthophyll
or luteol (C40H56O2) is very similar to ^-carotene (C40H56) (e.g. Rabinowitch,
1945). Roughly speaking, the difference is an oxygen atom added at each end
of the molecule. If the volume remains practically the same, the ratio between
the densities should be equal to the ratio between the molar masses, and the
density of xanthophyll should be p » (1.00 g cm" 3 ) 569/537 = 1.06 gcm~ 3 . The
refractive index of chlorophyll a ( C s s F ^ M g ^ O s ) is obtained by observing
that the molecule consists of a phytol tail (C20H40O) and a head
(C35H32MgN4O4). The tail has a molar mass of 297 g, a density of 0.85 gcm" 3 ,
a refractive index of 1.460 (Weast, 1981), and consequently a molar refraction
of R = 95.7 cm 3 . The constituents of the head (Wolken, 1973) have the ^-contributions:
C35
2.591 cm3 x 35 = 90.7 cm 3
H32
1.028 cm3 x 32 = 32.9 cm 3
aromatic N 4
3.550 cm3 x 4 = 14.2 cm 3
double bond O 2 2.122 cm3 x 2 = 4.2 cm 3
single bond O2
1.643 cm 3 x 2 = 3.3 cm 3
Mg
3.000 cm3 x 1 = 3.0 cm 3
/? head = 148.3 cm 3
The values are from Weast (1981), except the value for magnesium which has
been estimated here. Since
rttoui = ^head + ^taii = 138.3 cm 3 + 95.7 cm 3 = 244 cm 3
and since equation (14) yields
n2 + 2 1.11 gcm~3
= 244 cm 3
we obtain n = 1.52 for chlorophyll a. If chlorophyll b (C5sH7oMg06N4) occupies
the same volume as chlorophyll a, the ratio between their densities should equal
the ratio between their molar masses, and the density of chlorophyll b should be
p — (1.11 g cm"3) 907/893 = 1.13 g cm"3. In the same way as for chlorophyll a,
the refractive index of chlorophyll b may be estimated to n = 1.52. Chlorophyll
c is a mixture of C35H28MgN4O5 and C35H3oMgN405 (Dougherty et al., 1966),
and its structure resembles the head of chlorophyll a. It is then not unlikely
that it will also occupy approximately the same volume. If the volumes of the
head and tail of chlorophyll a are additive, that is (M/p)totai «
(M/p\ead + (M/p)xaii, we find that the molar volume of the head should be
= 464 cm3. Since the molar mass of chlorophyll c is ~609g, its density
2234
Refractive index of phytoplankton
will then become 1.31 gcm~3. As for chlorophyll a, we may estimate its R value
to ~146.4cm3, and its refractive index may be estimated to 1.54.
Equations (4) and (12) were criticized by Wiener (1912) according to whom, a
mixture of spheres with refractive index n-i in a liquid of index n\ should have a
mean refractive index nm given by the relation
For fibres fa) in a liquid («i) he obtained that
-2
_ ~2
«2 _
M2
when the direction of the electric vector in the polarized light was normal to the
optical axis, that is normal to the fibre axis, and
< , = "i«? + V2»i
(17)
when the direction was parallel with the optical axis.
When the constituents were arranged in parallel layers, and the electric vector
of the polarized light was normal to the optical axis, that is, parallel with the
layers, Wiener obtained
When the electric vector was parallel with the optical axis (normal to the layers),
the relation became
"mp
«i
n
2
Wiener's equations require that equation (6) is valid, but on a molecular scale
this is not necessarily true. In his criticism of equation (12) he seemed to overlook that he was working on a dimensional scale quite different from that of
Lorenz and Lorentz. His structures consisted of ordered arrangements of optically isotropic material, with dimensions which were small when compared to
the wavelength of light, but still large compared to the size of the molecules.
Lorenz and Lorentz, on the other hand, were working on the atomic scale. The
distinction between spheres and liquid in Wiener's equation (15), for instance,
becomes meaningless when the spheres are of molecular size. However, his equations (16) and (17) have proved to give a description of the so-called textural
(Oster, 1955) or form (Born and Wolf, 1975) birefringence of fibres. Some calculations result in (Oster, 1955)
that is
(21)
2235
E.Aas
In fact, for natural cellulose fibres it has been observed that nmp = 1.58-1.60,
while rim, = 1.53-1.54 (Frey, 1926; McCrone et al., 1967). In an analysis of 11
phytoplankton species, Parsons et al. (1961) found that 0.3-14%, with a mean
value of 3%, of the total dry mass content was crude fibres. Birefringence effects
due to fibres should then be negligible. [The formulae become far more complicated if one of the constituents is light absorbing (Wiener, 1927), but such cases
will not be discussed here.]
Textural birefringence behaves like the birefringence of uniaxial crystals, with
an ordinary refractive index a> and an extraordinary refractive index e. nmB corresponds to u> and nmp to e. It may be shown that for random orientations of
uniaxial crystals, the mean refractive index will be approximately
n « (2a> +1)/3
(22)
Biaxial crystals like aragonite, with refractive indices a, ft and y, will have the
mean refractive index (Dana, 1950):
n*(a
+ p+y)/3
(23)
Refractive indices, if not otherwise stated, are usually given at the yellow Dline (589 run).
Normal dispersion of the refractive index
The refractive index of a transparent particle will usually decrease monotonously
from UV towards the red part of the spectrum. This behaviour is called the
normal dispersion of the refractive index. If the matter has absorption bands in
the visible part of the spectrum, the refractive index in this region will vary in a
way which is called the anomalous dispersion of the coefficient.
The normal dispersion may be described by the Sellmeier equation in its most
simple form:
"2 =
l
+
^
<24>
where A and \\ are constants, X\ < X. The equation can be expanded in series to
give the Cauchy equation
n p+ +
(25)
= i*
where P, Q and R are constants (Jenkins and White, 1957). In the visible region
the two first terms on the right side may suffice to describe the dispersion. The
refractive index relative to water may then be written
ri=
T
2236
= P>Jr
%
(26)
Refractive index of phytoplaoktoa
Anomalous dispersion of the refractive index
The Helmholtz theory of 1875, based on a mechanical analogy, gives a relation
between the absorptions bands and the anomalous dispersion of the refractive
index. The resulting equations between n and K, which have been presented by
for example Jenkins and White (1957), will in a wavelength region where only
one dominating abosrption band has to be taken into account, be simplified to
(X2 - X2) + X2G2
(27)
(28)
where N is the refractive index outside the actual band, Xi is the wavelength of
the absorption peak, and A and G are physical constants. The absorption index
*: is related to the absorption coefficient a by
The indices n and K may be found as functions of X, Xi, A, and G from equations (27) and (28), but these functions are not easily interpreted. Simpler expressions may be obtained by making the following approximations close to the
absorption band
X2 - X2 = (X - X,)(X -|- Xi) as (X - Xi)2X,
(30)
X 2 «X 2
(31)
X3 * X 3
(32)
It may also be assumed that the absorption index K is small compared with the
refractive index n
K<^n^N
(33)
but that its relative variation in wavelength is larger
K
dX
n dX
(34)
and that
2
n
-M2 = (n- N)(n + N)f*(n- N)2N
(35)
By means of equations (30)-(35) the equations (27) and (28) may now be
approximated to
4(X-X,) 2 + G2
(36)
2237
E-Aas
(37)
From equation (37) the constant A may be expressed as a function of the peak
value of K at Xj, *i, and if this function is substituted for A, the two last equations may be written
lKXG{kXx)
n—N —
r
4 ( A X ) 2 + G2
(38)
(39)
These expressions are more suitable for our discussions than equations (27) and
(28). It can be seen from equation (38) that n — N is antisymmetric around
A. = X\, where n — N = 0, while equation (39) shows that *: is a symmetric function around X.\. G is the width of the absorption band where K — K\/2. The
extreme values of n are n = N ± K\/2, and they occur at X — X\ ± G/2.
Optical efficiencies of particles
In the case when there are p particles of equal size and shape per volume unit,
with an average geometrical cross section G, and bp is the scattering coefficient
due to the particles of the suspension, it is possible to define a scattering efficiency Qb as
Gb=-^
(40)
pG
Similarly an absorption efficiency Qa may be defined as
2a = ^
(41)
pG
where ap is the part of the absorption coefficient of the suspension which is due
to particles. Van de Hulst (1957) has obtained some approximate expressions
for 2a and Qb of spheres, where the refractive index of the spheres is close to
that of the surrounding medium, and the diameter is much larger than the wavelength. Even when the particles are not much larger than the wavelength, the
expressions may be used without too serious errors. For a suspension of absorbing particles in water the expressions of Van de Hulst may be written:
<2a = 2 ( - + —
- (2a
2238
(43)
Refractive index of phytoplankton
where
p* =
(44)
p-iy
2JID
(n - nw)
(45)
Inl)
v
(46)
—— •
D is the particle diameter, and n and nw are the refractive indices of the particles
and the water, respectively.
If the pigments are not homogeneously distributed within the particle, 'sieve
effects' may occur (Duysen, 1956) so that the total influence of the pigments
will be reduced. Such effects are neglected here.
Results and discussion
Mean refractive index and density of phytoplankton
In the last section several equations for the refractive index of mixtures were
presented. The possible error due to the choice of equation has been estimated
by calculating the indices of the equations (9), (12), and (15)—(19), as functions
of the partial water volume vi = vw. The index ni — 1.542 of particle dry mass
1.40
J— l a y e r s
=
£ffcfes
'layers
^~~ ^fibres ~ ^spheres
1.36
0.7
0.8
0.9
PARTIAL WATER VOLUME
Fig. 1. The refractive index of a two-component system, as a function of the partial water volume.
The subscript GD refers to equation (9), LL to equation (12). n,^^, is based on equation (15),
<i>fibra = "mn on (16), ffibra = imp on (17), to^ym = / ! M on (18), «hytn = /imp on (19), and /ifibre, and
n t a > o , on (22).
2239
E.Aas
1.45
\
X
LU
Q
Z
LU
>
1.40
o
<
rr
LU
LU
rr
\
\
1.35
\
.5
.6
.7
.8
.9
1.0
PARTIAL WATER VOLUME
Fig. 2. The mean refractive index of different phytoplanlcton species, based on Table II, as a function
of the partial water volume. The curves represent from top to bottom: coccolithophorids; dinoflagellates, brown flagellates; red algae or blue-green algae or diatoms; green algae.
was used together with n\ — nw = 1.339 of sea water. The partial volumes were
assumed to be additive [equation (6)]. The results are presented in Figure 1. In
the illustrated range of vw there is an almost linear relation between the refractive index and vw. If we can assume that the incident light is unpolarized and
that the internal structures are oriented at random so that textural birefringence
effects are smoothed out, then the maximum difference between the indices
resulting from the different equations or internal structures seems to be only
~0.004 for vw = 0.6. Thus the choice between equation (9) and (12) is not crucial
for the present results.
The relative dry mass composition of Table II and a varying water content
were used with the Lorenz-Lorentz equation (12) to calculate the mean refractive index n of the phytoplankton. The results are presented in Figure 2 and
Table VIII. The density p of the phytoplankton was, by equation (6), calculated
from
~~, P>v> = Ai - (Pd - Pw)vV
P = L
w
(47)
where pa and p w are the densities of dry mass and water, respectively. The subscript m of nm in equation (12) has been omitted in the following discussion.
It should be noted that the 'mean' values presented in Table VIII are the
means based on Table II, and not necessarily the mean values found in nature.
Still it is hoped that the numbers may represent the natural values which are
2240
Refractive index of pfaytopUnkton
Table VOL Mean values of the refractive index and density of phytoplankton, based oni Table I 1, at
different partial water volumes
0
0.6
0.8
0
0.6
p (g cm" 3 )
n
Species
0.8
Coccolithophorids
Dinoflagellates
Brown flagellates
Red algae
Blue-green algae
Diatoms
Green algae
1.562
1.552
1.548
1.545
1.541
1.538
1.535
1.424
1.420
1.419
1.418
1.416
1.415
1.414
.381
.379
.378
.378
.377
.377
.376
.426
.240
.258
.317
.252
.536
.229
1.185
1.111
1.118
1.142
1.116
1.229
1.107
1.105
1.068
1.072
1.083
1.070
1.076
1.066
Mean from Table II
Standard deviation
1.542
0.023
1.417
0.009
.377
0.004
.342
0.046
1.152
0.015
1.088
0.011
most likely to occur. The mean refractive index of the algal dry mass increases
from 1.535 for the green algae to 1.562 for the coccolithophorids, or from
1.146 to 1.167 relative to the index of water, which is a difference of 0.021. If a
reasonable mean value of vw is 0.8 for all species (Table III), Table VIII shows
that the mean refractive index n will only vary between 1.376 for the green
algae and 1.381 for the coccolithophorids, which is a difference of only 0.003.
Relative to the index of water the difference is also ~0.003. If vw « 0.6 is a
better estimate of the partial water volume, the same difference becomes 0.010,
or 0.007 relative to water.
Figure 2 illustrates that h becomes an almost linear function of vw in the range
vw = 0.5-1.0. The mean value, based on Table II, is in this range described by
1.533-0.194v w
(48)
For vw = 0.8 ± 0 . 1 the corresponding mean value of n becomes ~ 1.38 ±0.02,
according to the last equation, that is 1.03 ±0.02 relative to water. If the possible overestimation of the wet weight is taken into account and vw = 0.6 ± 0.2
is applied, the corresponding refractive index increases to 1.42 ± 0.04, or
1.06 ± 0.04 relative to water.
The density corresponding to vw = 0.8±0.1 becomes 1.09 ± 0.03 g cm" 3
[equation (47)]. If only species with organic surfaces are considered, the density
will be 1.07 ±0.02 gcm~ 3 , which accords well with the often quoted density
range 1.03-1.10gcm~3 of cytoplasm (e.g. Boney, 1975). If the estimate
vw = 0.6 ± 0.2 is applied, the mean density of the species with organic surfaces
increases to 1.12±0.05gcm~ 3 . This result indicates that the partial water
volume is larger than 0.6, or that the quoted density range of cytoplasm is too
low.
A correlation analysis performed on the values of Table VIII showed that
there was a better correlation between refractive index and partial water
volume than between refractive index and density.
While the maximum difference in n resulting from the use of different equations was estimated to be ~0.004 for vw = 0.6, the possible error in n due to
errors in refractive indices and densities of the algal constituents is larger. With
2241
E.Aas
Table IX. Dispersion constants for the main algal constituents
Based on
data from
1
2
3
4
5
6
Q (nm 2 )
P'
Q' (nm2)
7530
6070
4410
4530
3510
3170
1.192
1.197
1.146
1.101
1.073
1
2840
1720
590
790
90
0
Constituent
protein
calcite
carbohydrate
fat
opal
water
.578
.584
.517
.457
.420
.324
References: 1: Timasheft" (1976); 2 Weast (1981); 3: Kontnig (1962); 4: Washbura (1927); 5- Jenkins and White
(1957); 6: quoted by Jerlov (1976).
the standard deviations or possible errors estimated earlier, it can be calculated
by means of Table II that the standard deviation of n, at a partial water
volume of 0.6, has an average value of ~0.016. The standard deviation of n
due to the individual differences in composition is likewise found to be ~0.014.
The variation due to species seems to be less important, since the standard deviation of n of the species is ~0.003 when vw = 0.6. The largest factor of variation
in our estimate of n, however, is the algal water content, and as shown in the discussion of equation (48), the variation in h due to water content may be estimated to be about ±0.04.
Normal dispersion
Some values of the constants P, /", Q, and Q' in equations (25) and (26) are
given in Table IX. The relative refractive index ri as a function of A. is shown
Protein
X 1.20
LLJ
Q
UU
rr
Calcite
1.15
Carbohydrate
LL
LLJ
rr
LLJ
Fat
1.10
LLJ
rr
Opal
1.05
300
400
500
600
700 nm
WAVELENGTH
Fig. 3. Wavelength dispersion of the refractive index relative to water for the main algal constituents.
2242
Refractive index of phytopUoktoo
K
h
i i
a .
0.01
1
/
^^/
0
/
'
i
i
'
i
i b
i
i
i
i
j\
b1\ a
/'I \
v\
400
Jj^ \
500
600
700 nm
60Q
700 nm
WAVELENGTH
n-N
0.01
,
500
,' WAVELENGTH
\,
-0.01
Fig. 4. Absorption index * of chlorophyll a and b in ethyl ether, at a concentration of lOmgcm" 3 ,
and the corresponding variation of the refractive index difference n — N.
in Figure 3. The difference «'(300 nm) - n'(700 nm) reaches a maximum of 0.025
for protein, and for the other constituents the difference is <0.008. When ~80%
of the phytoplankton consists of water, the difference for the algal particle will
be <0.005. This variation of n' is small, and for many problems it may be
neglected.
Influence of anomalous dispersion on optical efficiencies
Figure 4 shows absorption indices for chlorophyll a and b in ethyl ether, at a
concentration of lOgT 1 or lOmgcm"3 (Zscheile and Comar, 1941; Harris and
Zscheile, 1943), as well as the variation of n — N according to equation (38).
From Tables I and II it may seem as if common cell concentrations of total pigments are ~0.5-l% of the total mass volume, or 5-10mgcm~3. This may perhaps correspond to a chlorophyll a content of 2-10mgcm~3. Rabinowitch
(1945) quotes as an extreme value of chlorophyll a the concentration 1.7% of
the total mass, or 17mgcm~3. The variation of the refractive index due to
chlorophyll a is then likely to be ~0.001-0.005, in extreme cases 0.008.
The features of chlorophyll a in Figure 4 can be used to illustrate the influence
of the absorption and refractive indices on the absorption and scattering efficiencies. The values *i = 0.012, K\ - 622 nm, G = 22 nm, JV= 1.38, and nw = 1.34
have been applied. Equations (42) and (43) then produce the solid lines for Qa
and Q\, in Figure 5. With a particle diameter of 1 ^m the scattering efficiency
2243
E.Aas
1Or
100 nm
K - K (X), n - n (X)
K - K (X), n - N
n-N
K-0,
0.1
0.01
0.001
600
700 nm
WAVELENGTH
0.01
600
700 nm
WAVELENGTH
Fig. 5. Absorption and scattering efficiencies for different particle diameters, when the particle content of chlorophyll a is lOmgcm" 3 .
has a minimum at the short wavelength side and a maximum at the long wavelength side of the absorption peak. This effect depends entirely on the anomalous dispersion of the refractive index. If n is assumed constant (n = N), but *:
is allowed to vary as before, a monotonous decrease of the scattering efficiency
with increasing wavelength will be the result, as shown by the dotted line of
Figure 5. In fact, at this small particle diameter (1 £im), the absorption index
has practically no influence on the scattering efficiency. The dashed curve,
which gives Qb when n is assumed constant and K zero, is seen to coincide with
the former curve. Another way to express this is to say that the amplitude
decrease of the ray passing through the sphere is too small to influence the
scattering.
With increasing particle size the absorption, which is an exponential function
of the diameter, becomes more pronounced. When the diameter is 10/Am and
*•] is 0.012, as in Figure 5, absorption has become the dominating effect, and
the dispersion of the refractive index can be neglected.
If the concentration of chlorophyll a is reduced to lmgcm" 3 , so that
K\ =0.0012, the scattering efficiency will be almost the same as in the nonabsorbing case, as shown by Figure 6. Only for large phytoplankton, with diameter 100/mi, is a small influence of the absorption band found.
We may then conclude that the anomalous dispersion of the refractive index
will probably only influence the scattering properties of small phytoplankton in
the vicinity of strong absorption bands.
2244
Refractive index of phytopUniton
10
•
10fim
100 (im
A
A
/
onm
600
—
—.
100 nm
1
/ 10iun \
A
\
\
\
/.A \
/
/
—
\
700 nm
WAVELENGTH
0.1
^—-
1 \im
m
600
.
.
700 nm
WAVELENGTH
Fig. 6. Absorption and scattering efficiencies for different particle diameters, when the particle content of chlorophyll a is 1 mgcm .
Comparison with other methods
The refractive indices of the common minerals are in the range 1.11-1.25 relative
to water (Table I), and some of the scatterance measurements (Burt, 1955;
Sasaki et al., 1960; Kullenberg, 1970; Kullenberg and Berg Olsen, 1972) indicate
that an inorganic type of particle, with n' = 1.15-1.25, has been dominant. In
other measurements of scatterance (Kullenberg and Berg Olsen, 1972; Morel,
1973; Zaneveld and Pak, 1973; Sugihara and Tsuda, 1979) the results definitely
suggest that the dominant type of particle has been organic, with ri = 1.011.05. However, indices in the range 1.05-1.09 may indicate mixed particles as
well as phytoplankton, as we shall see below.
Very few refractive index measurements of pure algal cultures were made
before 1980 (Table I). The indices of diatoms obtained by the immersion
method, n' = 1.060-1.087 (McCrone et al., 1967; Hodgson and Newkirk, 1975),
may represent the silica shells more than the mean index of the particles. In an
investigation of the spherical flagellate Isochrysis galbane (Carder et al., 1972)
the mean refractive index was derived from scatterance observations as
n' — 1.031. Phase contrast measurements of the spherical green alga Chlorella
pyrenoidosa (Charney and Brackett, 1961) showed that the chloroplast had a
refractive index 1.05-1.06 while the rest of the cytoplasm had the index 1.015.
If about 1/3 to 1/2 of the cell is occupied by the chloroplast, the mean refractive
index of the total cytoplasm will be in the range 1.027-1.038. If the refractive
index of the cell wall, 1.022, is included, the mean index of the alga becomes
2245
E.Aas
slightly lower and accords well with the range ri = 1.03 ± 0.02 estimated for
vw = 0.8 ± 0 . 1 in this work.
However, the bulk refractive indices obtained for all the pure algal cultures in
Table I are in the range n' = 1.06 ± 0.04, which coincides exactly with the present estimated range of n' for vw = 0.6 ± 0.2. This result supports the assumption
that the mean partial water volume in Table III may be overestimated and that
vw = 0.6 is a more representative value for the partial water volume.
Drastic changes in the optical properties of algal cultures can be caused by differences in environmental conditions and algal age (Spinrad and Yentsch, 1987;
Ackleson et al., 1990; Olson et al., 1990; Stramski and Morel, 1990; Stramski
and Reynolds, 1993). Even on a time-scale of hours these changes become significant. Probably most of the variation of the metabolite compositions and water
contents presented in Tables II and III are due to such effects.
In Table VIII the largest refractive index is obtained for the coccolithophorids
and the smallest for the diatoms and green algae. This result is confirmed by the
observations presented in Table I (Bricaud and Morel, 1986; Ackleson and Spinrad, 1988; Bricaud et al., 1988; Ackleson et ai, 1990; Stramski and Reynolds,
1993). It may also be noted that the difference between the mean indices for
algal species with vw = 0.6-0.8 in Table VIII is less than 0.05, and that the difference between the mean values for the different species in Table I is less than 0.03.
Table VIII estimates the mean refractive index for the algal dry mass to 1.542, or
1.152 relative to water, while the refractive index of the outer shell in the twolayered Chlorella models of Quinby-Hunt et al. (1986, 1989) and Hunt et al.
(1990) obtains values in the range 1.08-1.15 (Table I). Possibly the refractive
indices estimated for the different metabolite components in the present work
may be applied to construct more detailed algal models.
The normal dispersion of the algal refractive index is found to be small (Table
IX), and many of the referred works in Table I apply a constant index through
the visible part of the spectrum. The anomalous dispersion is supposed to lead
to a minimum in the scattering efficiency at the short wavelength side and a
maximum at the long wavelength side of the absorption peak. A similar selective
scattering from the green alga Chlorella, as well as from other algae, has been
observed by Latimer and Rabinowitch (1959) and Charney and Brackett
(1961). The effect also seems to be present in the observations of Platymonas
suecica by Morel and Bricaud (1986).
Acknowledgements
Thanks are due for all the help received from the Department of Marine Botany
at the University of Oslo, in particular from Karl Tangen and Jahn Throndsen.
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Received on July 14. 1995; accepted on July 5. 1996
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