## Abstract

The paper presents a new experimental method that measures light absorption and backscattering by aquatic particles, combining the innovative features of the ‘modified filter–transfer–freeze’ (FTF) and ‘transmittance–reflectance’ (T-R) techniques, namely no path-length amplification and accuratecorrection for scattering loss, respectively. This method (in short: the FTF/T-R method) measures both the transmittance and the reflectance of particles deposited on a glass slide, using a double-beam spectrophotometer equipped with an integrating-sphere attachment. The data are interpreted by an algorithm that yields both the absorption and the backscattering coefficients of the particle sample. The paper includes a summary of results of validation tests, that have been performed using samples ranging from pure phytoplankton (low light scattering) to pure detrital particles (high light scattering), as well as a detailed analysis of the experimental error. The FTF/T-R measurement is somewhat more laborious than the standard transmittance measurement of particles retained on glass fibre filters. However, it has the important asset of permitting the simultaneous determination of light absorption and backscattering and it yields more accurate absorption data in situations where the magnitude of path amplification by glass fibre filters is uncertain and light scattering by the particles is high.

## INTRODUCTION

The study of marine ecosystems using remote sensing data requires extensive application of bio-optical models for the prediction of such basic quantities as phytoplankton concentration, carbon fixation rates, algal growth and primary productivity (Morel and Bricaud Platt and Sathyendranath, 1988; Sathyendranath et al., 1989; Morel, 1991). The effectiveness of these water optics models relies on the precise description of the individual contributions of the various substances contained in water. This implies a need for accurate measurements of optical properties, such as the light absorption and backscattering co-efficients of suspended particulate matter, which includes phytoplankton and both organic and inorganic detritus.

At present only laboratory measurements of light absorption by particulates are carried out routinely. The standard method used (Yentch, 1962; Mitchell and Kiefer, 1988) is based on the light transmittance measurement of particles retained on glass-fibre filters, that is carried out using a double-beam spectrophotometer. Filtration is required to concentrate particles that are naturally too dilute to measure with adequate accuracy. In the following, this method is referred to as the ‘transmittance method’ or ‘T method’. The measured quantity is the optical density, OD(λ), defined as the base 10 logarithm of the inverse transmittance (λ is the wavelength). The spectral range of the measurement covers the visible region and it often extends to the ultraviolet and near infrared.

Light scattered by the particles outside the reception angle of the spectrophotometer detector contributes to the measured optical density. This spurious contribution is corrected for by subtracting from the data the optical density measured at the upper end of the spectral range, usually 750 nm (Mitchell and Kiefer, 1988). The correction is based on the assumptions that (i) the particle absorption at this wavelength is negligible, and (ii) the effect of scattering is wavelength-independent. These assumptions are acceptable for phytoplankton (negligible pigment absorption in the near infrared range, low scattering), but may be inadequate when the particle sample contains a large fraction of light scattering detritus (Tassan and Ferrari, 1995).

A problem with filter-retained particles is that their absorption is amplified owing to the increase of the optical path length caused by multiple scattering in the filter medium. Thus the measured optical density values (ODf) must be converted into optical density values of the suspension with the same geometrical pathlength (ODsus). The conversion is performed by means of empirical expressions that are obtained by averaging measurements performed on samples of algal cultures in suspension and retained on filter (Mitchell, 1990; Cleveland and Weidemann, 1993; Arbones et al., 1996). The amplification factor ODf/ODsus is often referred to as the ‘β factor’, following the terminology of Butler (Butler, 1962). The volume absorption coefficient of the particulate, ap (λ) in m−1, is determined from ODsus(λ) as

(1)
$a_{p}({\lambda})\ {=}\ 2.3\ OD_{sus}({\lambda})/X$
where X is the ratio of the filtered volume to the filter clearance area (in m).

The application of the ODsus vs. ODf relationship measured for algal cultures to natural samples of varying composition that include mineral and organic detritus, is a generally accepted procedure (Bricaud and Stramski, 1990; Mitchell, 1990; Cleveland and Weidemann, 1993; Arbones et al., 1996). However, recent measurements have shown important variations of the absorption amplification factor for picoplankton cultures, such as Synechococcus and Prochlorococcus (Moore et al., 1995). A similar change of the β factor has been observed with natural phytoplankton populations in the oligotrophic water of the Sargasso Sea (Allali et al., 1997), apparently associated with the abundance of Prochlorophytes. Both results suggest a dependence of the amplification factor on the phytoplankton cell size, even if there is some evidence that at least part of the observed variability may be due to the approximate correction for light scattering performed by the T method (Tassan and Ferrari, 1998; Tassan et al., 2000). If confirmed by further experimentation, this dependence might increase significantly the uncertainty of absorption measurements performed in waters where small phytoplankton species are abundant.

Recently, two new methods have been proposed to improve the peformance of the measurement of light absorption by aquatic particles, namely the ‘modified filter–transfer–freeze’ method and the ‘transmittance–reflectance’ method. The ‘modified filter–transfer–freeze’ (FTF) method (Allali et al., 1995) avoids the absorption amplification due to multiple scattering in the glass-fibre medium, by concentrating particles into a polycarbonate filter and transferring them to a glass slide using liquid nitrogen freezing. The measurement is performed by the T method and yields directly the absorption of the particle suspension. The ‘transmittance-reflectance’ (T-R) method (Tassan and Ferrari, 1995) measures the light transmitted and reflected by the filter-retained particles, using an integrating-sphere attachment to the spectrophotometer. The data analysis is performed by atheoretical model that eliminates the effect of light backscattering by the particles.

This paper presents the results of an attempt to merge the advantages of these two approaches (i.e. no absorption amplification, accurate correction for light scattering) into a combined FTF/T-R method, that also permits determination of the backscattering coefficient of the particle suspension.

## METHOD

Preparation of the samples was performed by the FTF routine and consisted of the following steps: (i) filtering the chosen water volume through a 25 mm diameter polycarbonate Millipore membrane (type HTTP with 0.6 μm pore size), (ii) transferring the membrane, particle side down, onto 5 μl of filtered (0.2 μm pore) water lying on a 1-mm-thick Superfrost glass slide, (iii) quick freezing of the slide by placing it onto an aluminium block cooled in liquid nitrogen, (iv) peeling off the filter, leaving the particle layer adhering to the slide, (v) trapping the particles by means of a 25 mm diameter, 0.1 mm thick, glass cover slip, and (vi) waiting until the preparation has thawed and the water condensed on the cover slip has completely evaporated. The reader is referred to (Allali et al., 1995) for additional details on the FTF technique. In the following text the experimental assembly, consisting of the water film containing the particles and trapped between the Superfrost slide and the glass cover, is called the ‘sample’.

The measurements in the transmission and reflection modes were carried out on the ‘sample’ placed against one port of the integrating-sphere, with the thin glass cover slip facing the light beam. An identical assembly without particles (in short: ‘reference’) was placed against the port of the spectrophotometer crossed by the other beam. A schematic view of sample and reference position on the integrating-sphere is shown in Fig. 1 of the paper presenting the T-R method (Tassan and Ferrari, 1995). The measurement yielded the ratio, ρ(λ), of radiant fluxesincident on the detector inside the sphere that weretransmitted (measurement in the transmission mode) or reflected (measurement in the reflection mode) by ‘sample’ and ‘reference’. The instrument used was a Perkin-Elmers Lambda 19 dual-beam spectrophotometer, equipped with a 60 mm diameter, barium sulphate-coated integrating-sphere attachment. The unit was operated in the wavelength range from 400 to 750 nm, with 1 nm spectral band width and 1 nm spectral increments.

The theoretical model yielding the particle absorption from the T-R data [equations (5) to (11)] in Tassan and Ferrari (Tassan and Ferrari, 1995) required a substantial modification, to account for the fact that the particles were inside a water film, sandwiched between two glass slides. In fact, contrary to measurements on particles embedded in GF/F filters, where the angular distribution of scattered light is determined by the diffusing properties of the glass-fibre medium, in the FTF/T-R measurements the collimated light beam impinging normally on the ‘reference’ glass is not refracted, while the beam crossing the ‘sample’ is diffused by the particles. The angular distribution of the scattered light is determined by the particle scattering phase function, which is strongly forward peaked. The light fraction scattered outside the glass-to-air Brewster angle (∼49°) does not go out of the ‘sample’ and is not measured by the detector.

Thus the terms of the radiation balance equation for the ‘sample’:

(2)
$fraction\ transmitted\ (TR)\ {+}\ fraction\ backscattered\ (BK)\ {+}\ fraction\ absorbed\ (AP)\ {=}\ 1$
were modelled as (minimal glass absorption neglected, wavelength dependence omitted):
(3)
$TR\ {=}\ {\rho}_{{T}}\ (1\ {+}\ L_{f})\ T_{r}$

(4)
$BK\ {=}\ {\rho}_{R}\ (1\ {+}\ L_{b})\ R_{r}$

(5)
$AP\ {=}\ (1\ {-}\ R_{ag,n})\ (1\ {+}\ {\rho}_{T}\ R_{ga,f})\ {\alpha}_{p},$
where: ρT = result of transmittance measurement, Tr = transmittance of the ‘reference’, Lf = fraction of light forward scattered outside the Brewster angle, ρR = result of reflectance measurement, Rr = reflectance of the ‘reference’, Lb = fraction of light backscattered outside the Brewster angle, Rag,n = Snell reflectance at the air–glass interface of the sample (ag pedice) for normally incident light (n pedice), Rga,f = mean value of Snell reflectance at the glass–air interface of the sample (ga pedice) for light forward scattered within the Brewster angle (f pedice), αp = absorption by the particles due to an incident unitary light beam on a single through-way. All symbols are listed in a table of notation (Table I).

(6)
${\alpha}_{p}\ {=}\ \{1\ {-}\ {\rho}_{T}\ (1\ {+}\ L_{f})\ {+}\ R_{r}\ [{\rho}_{T}\ (1\ {+}\ L_{f}){-}\ {\rho}_{R}\ (1\ {+}\ L_{b})]\}/[(1\ {-}\ R_{ag,n})\ (1\ {+}\ {\rho}_{T}\ R_{ga,f})]$

(7)
$L_{b}\ {=}\ (1\ {-}\ R_{ag,n})\ B_{p}\ BR_{b}\ ({\rho}_{R}\ R_{r})^{{-}1}$
where: Bp = light fraction backscattered by the particles, BRb = fraction of backward scattered light that is scattered outside the Brewster angle.

(8)
$R_{r}\ {=}\ R_{ag,n}\ {+}\ (1\ {-}\ R_{ag,n})^{2}\ R_{ga,n}\ {+}\ {...}$

The validity of the model was tested experimentally. Being Rag,n = Rga,n (Maul, 1985), equation (8) was linearized, yielding Rag,n = 0.525 Rr.

The Snell reflectances at the glass–air interfaces of the sample for the angular distribution of light scattered by the particles within the Brewster angle in the forward andbackward directions, i.e. Rga,f and Rga,b, were estimated averaging results of computations using two very different hydrosol phase functions [phase functions labelled A and C in (Gordon, 1973)], that were expressed by two-term Henyey–Greenstein functions, defined by the parameters g1 = 0.95, g2 = 0.360, α = 0.98, and g1 = 0.94, g2 = 0.365, α = 0.91, respectively. The same phase functions were used to compute mean values for the fractions of forward and backward scattered light that are scattered outside the glass-to-air Brewster angle, obtaining BRf = 0.035 ± 0.005 and BRb = 0.55 ± 0.04 (the quoted uncertainty is one half the difference of the values computed by the two phase functions).

The term Bp was estimated modelling the measured sample reflection, ρR Rr, as the sum of three terms (in each term the order of factors follows the light path):

(i) light fraction reflected at the air–glass interface of the sample:

(9)
$R_{ag,n}$

(ii) light fraction backscattered by the particles:

(10)
$(1\ {-}\ R_{ag,n})\ B_{p}\ (1\ {-}\ BR_{b})\ (1\ {-}\ R_{ga,b})$

(iii) light fraction transmitted by the particles and reflected at the glass–air interface of the sample:

(11)
$(1\ {-}\ R_{ag,n})\ {\rho}_{T}\ R_{ga,f}\ {\rho}_{T}\ (1\ {-}\ R_{ga,f})$
with Rga,b = mean value of Snell reflectance at the glass–air interface of the sample for light backward scattered within the Brewster angle. Equation (10) is the product of the light fractions transmitted through the air–glass interface of the sample [i.e. (1 – Rag,n)], backscattered by the particles within the Brewster angle [i.e. Bp (1 – BRb)] and transmitted through the glass–air interface of the sample on the way back [i.e. (1 – Rga,b)]. Equation (11) is the product of the light fractions transmitted through the air–glass interface of the sample [i.e. (1 – Rag,n)], transmitted by the particles (ρT), reflected by the glass–air interface of the sample (Rga,f), transmitted by the particles on the way back (ρT), transmitted through the glass–air interface of the sample on the way back [i.e. (1 – Rga,f)].

(12)
$B_{p}\ {=}\ [{\rho}_{R}\ R_{r}\ {-}\ R_{ag,n}{-}\ (1\ {-}\ R_{ag,n})\ {\rho}_{T}^{2}\ R_{ga,f}\ (1\ {-}\ R_{ga,f})]\ /[(1\ {-}\ R_{ag,n})\ (1\ {-}\ BR_{b})\ (1\ {-}\ R_{ga,b})]$

With all the terms in the right hand side determined, equation (6) was solved for αp, yielding the optical density of the particle suspension

(13)
$OD_{sus}\ =\ log[1/(1\ {-}\ {\alpha}_{p})],$
that was converted to the volume absorption coefficient of the particles, ap, by equation (1). As shown in detail elsewhere (Tassan and Ferrari, 1995), the optical density yielded by the T-R model is accurately corrected for the effect of light backscattering.

When measuring absorption of aquatic particles it is important to separate pigment from detritus absorption. In this measurement pigment absorption was discriminated from detritus absorption by subtracting from the measured optical density of the sample the optical density measured after pigment absorption removal by the oxidizer NaClO (Tassan and Ferrari, 1995; Ferrari and Tassan, 1999). Specifically, after the first measurement the particle deposit was resuspended in 5 ml of water with the addition of a few drops of a NaClO solution (1% active chlorine, 5 min action time), and the FTF procedure was repeated as described previously, rinsing the polycarbonate membrane by filtered water before step (ii). Filtration of the depigmented particles did not require membranes with smaller pore size (e.g. 0.22 μm), because the oxidation by NaClO does not disrupt the phytoplankton cells (Ferrari and Tassan, 1999). Alternatively, the NaClO solution could be added to the particles retained on the polycarbonate filter. Note that the usual solvent extraction procedure by means of methanol (Kishino et al., 1985) is not recommended for use with polycarbonate membranes, that might contain pigments which are also extracted and then adsorbed by the particles (Allali et al., 1995).

To obtain the backscattering coefficient of the particle suspension, bpb in m−1, the measured particle transmittance corrected for the forward scattering loss, T0 = ρT (1 + Lf), was written as (wavelength dependence omitted):

(14)
$T_{0}\ {=}\ exp[{-}\ (a_{p}\ {+}\ b_{pb})\ X]\ {=}exp({-}\ a_{p}\ X)\ exp({-}\ b_{pb}\ X)\ {=}T_{a}\ exp({-}\ b_{pb}\ X)$
with Ta = transmittance due to absorption. Since ODsus measured by the FTF/T-R method is only due to absorption (being scattering-free), Ta = 10−oDsus. Solving equation (14) yielded:
(15)
$b_{pb}\ {=}\ 1/X\ ln(T_{a}/T_{0})$

Incidentally, the backscattering coefficient of the par-ticle suspension cannot be obtained by a similar model applied to results of transmittance and reflectance measurements performed using filters, because light backscattering of the particles embedded in the filter cannot be converted by a simple formalism to that of the particle suspension.

## RESULTS AND DISCUSSION

The proposed FTF/T-R method for measuring absorption was tested against the validated FTF and T-R methods. The basic criteria for the tests were the following.

Firstly, with samples characterized by very small light scattering, where the approximate correction for scattering loss performed by the T method holds, the FTF/T-R and FTF methods should yield optical density spectra within the combined experimental error margin. Typical samples of this kind are healthy phytoplankton cultures with minimum detritus content.

Secondly, with samples characterized by large light scattering, where the correction for scattering loss performed by the T method fails, the FTF/T-R and FTF methods are expected to give different results, but the FTF/T-R and T-R methods should yield optical density spectra within the combined experimental error margin (provided that an appropriate β factor is used to convert to ODsus the ODf measured by the T-R method). Typical samples of this kind are those consisting of pure mineral detrital particles.

A typical result of the tests performed with reference to the T-R method (second criterion above) is presented in Figure 4, displaying optical density spectra of mineral particles suspended in the water of River Toce (Italy). To perform this test the particles used for the FTF/T-R measurement were resuspended and deposited on a GF/F filter. The ODf values yielded by the T-R measurement were converted to ODsus by equation (18) in Tassan and Ferrari (Tassan and Ferrari, 1995). Although this equation was obtained from measurements performed on a single laboratory culture of Scenedesmus obliquus, it was tested to have a wide validity range, including very small algal cells for which the standard T method gave varying β factors (Tassan and Ferrari, 1998). In particular, the same equation (18) was shown to apply to mineral detritus samples taken from River Toce (ibid.). The figure displays the ODf(λ) and ODsus(λ) spectra yielded by the T-R method, together with the ODsus(λ) spectrum directly measured by the FTF/T-R method: the two ODsus spectra are hardly distinguishable.

As expected, with this particle sample characterized by large backscattering the approximate correction for the scattering loss applied by the FTF method is inadequate, so that the optical density spectra yielded by the FTF and FTF/T-R methods are quite different (Figure 5). The FTF/T-R spectrum shows significant absorption up to the infrared end of the wavelength range, as is frequently observed with mineral particles. The FTF method, the correction of which for light scattering shifts down the OD spectrum by the measured OD(750), underestimates the optical density by a factor varying from 1.15 to 2 as the wavelength increases from 400 to 650 nm. The evidence offered by the experimental results plotted in Figure 5 shows the need to shift from FTF to FTF/T-R for absorption measurements of highly scattering samples.

The conclusion of our tests was that the results of the backscattering measurements by the FTF/T-R method were within the variation range of previously published data. In addition, indirect validation of the model for the backscattering measurement was provided by internal consistencies found between absorption and backscattering measured by the FTF/T-R method. An example is given in Figure 6, displaying the volume backscattering coefficient [bpb(λ) in m−1] measured for the same particle sample whose OD spectra are shown in Figure 3, before and after pigment oxidation. Consistently with the indication derived from the optical density plots of Figure 3, the scattering spectra exhibit only a minor wavelength dependence. Besides, the fact that the two bpb(λ) spectra differ less than the combined experimental error (see the error analysis presented at the end of this Section) indicates that (i) as expected, scattering was due almost totally to the detrital particles, and (ii) the NaClO addition had no significant effect on light scattering by the particles [this is in agreement with the observation that sodium hypochlorite causes trivial changes to the particle size, see Ferrari and Tassan (Ferrari and Tassan, 1999)]. A complete assessment of the validity and limitations of the proposed backscattering measurement will be possible only after extensive use of the FTF/T-R method in in situ campaigns.

The perfomance of the measurements by the FTF/T-R method does not present practical problems that go beyond the usual care necessary in experimental work, once the manual skill needed for the particle transfer from filter to glass has been acquired. One must be aware that the use of the FTF technique demands that the optical thickness of the sample be low enough to avoid important non-linear effects induced by multiple scattering (this is not the case when measuring filter-retained particles, because non-linearity is accounted for by the empirical equation converting ODf to ODsus). Other details of the FTF technique related to the experimental error (homogeneity of the particle deposit, transfer efficiency from filter to glass, etc.) are treated in the paper presenting the method (Allali et al., 1995). The use of the oxidizer NaClO for pigment absorption removal has confirmed its effectiveness (in particular the minimal effect on light scattering by the particles). It is worth mentioning that NaClO also acts on water soluble pigments that are not extracted by methanol, including the important class of the phycobilins. A thorough analysis of this technique is presented elsewhere (Ferrari and Tassan, 1999).

In comparison with the transmittance-reflectance measurement on particles retained on glass-fibre filters, the interpretation model is somewhat more complicated and the computation required is greater. However, this has little influence on the experimental error, since most computed correction terms are small (e.g.: BRf ∼ 0.03, Rag,n ∼ 0.05, etc.). On the other hand, several experimental conditions are favourable. For instance, the lower reflectance of the glass ‘reference’ (about 9% versus the 70% reflectance of the GF/F filter) is an advantage from the point of view of the experimental error, because it reduces the magnitude of a component of the measured signal that is not related to the particle absorption. Another advantage is the (almost) constant value of the ‘reference’ reflectance (as opposed to the reflectance of the wetted GF/F ‘reference’, whose variability contributes significantly to the overall uncertainty of the measurement).

With the present routine the experimental error (as standard deviation) of ODsus was estimated as σ(ODsus) = 0.003. This error is almost independent of the ODsus magnitude, in contrast to the error of the suspension optical density obtained from measurements of filter-retained particles, which increases with ODsus due to the error of the numerical constants of the equation converting ODf to ODsus. The overall contribution to the ODsus error by the three measured quantities, i.e. ρT, ρR and Rr in equation (6), was evaluated from reproducibility tests as σ = 0.002. Changing the values of the terms BRf and BRb within the computed variation range, i.e. ± 0.005 for BRf and ± 0.04 for BRb, causes ODsus variations within ± 0.002 and ± 0.0002, respectively. The sensitivity of ODsus to the term Bp is low: a 50% variation in Bp = 0.01 causes a 0.001–0.0015 change of ODsus. The uncertainty of the estimates of Rag,n, Rga,f and Rga,b has a minor effect on ODsus. The uncertainty of X gives a negligible contribution.

In conclusion, merging the innovative features of the FTF and T-R methods has enabled the definition of a new FTF/T-R method that is specifically suited to measure particle absorption in situations where (i) the standard transmittance method may be inadequate, e.g. when the content of highly scattering detritus is large or a precise determination of detritus absorption is needed; and (ii) there are reasons to doubt that the current equations that convert ODf of the filter-retained particle sample to ODsus are applicable to the case considered (e. g.: oligotrophic water with prevailing Prochlorophyte population). Another important asset of the FTF/T-R method is that it permits simultaneous measurement of the backscattering coefficient of the particle suspension.

Using the FTF/T-R method, one gets by means of a single, relatively simple experiment, the volume coefficients for both absorption and backscattering by the particles. The de-pigmentation technique based on NaClO-induced oxidation permits discrimination of the pigment and detritus contributions to the absorption. In this way one obtains the whole set of data needed to compute the contribution of aquatic particulate to the in-water radiation field. (Sathyendranath et al., 1989).

Table I:

Notation used in equations and throughout the text

Notation Definition
transmittance, i.e. fraction of impinging light that is transmitted
reflectance, i.e. fraction of impinging light that is reflected
OD optical density = log10(1/T)
λ wavelength (nm)
ODf optical density of particles on filter
ODsus optical density of particle suspension
ap volume absorption coefficient of the particulate (m−1
ratio of the filtered volume to the filter clearance area (m).
ρT result of transmittance measurement by T-R method
ρR result of reflectance measurement by T-R method
sample SUPERFROST glass slide with particle deposit inside water film and glass cover slip
reference SUPERFROST glass slide with water film and cover slip
Ts measured sample transmittance
Tr measured reference transmittance
Rs measured sample reflectance
Rr measured reference reflectance
TR light fraction transmitted by the sample
BK light fraction backscattered by the sample
AP light fraction absorbed by the particles
Lf light fraction forward scattered by the particles outside the Brewster angle
Lb light fraction backscattered by the particles outside the Brewster angle
Rag,n Snell reflectance at the air-glass interface of the sample (ag pedice) for normally incident light (n pedice)
Rga,f mean value of Snell reflectance at the glass-air interface of the sample (ga pedice) for light forward scattered by the particles within the Brewster angle (f pedice)
αp absorption by the particles due to an incident unitary light beam on a single through-way.
BRf fraction of forward scattered light that is scattered outside the Brewster angle
Bp light fraction backscattered by the particles
BRb fraction of backward scattered light that is scattered outside the Brewster angle
Rga,b mean value of Snell reflectance at the glass-air interface of the sample for light backward scattered by the particles within the Brewster angle
bpb volume backscattering coefficient of the particulate (m−1
T0 measured sample transmittance corrected for the forward scattering loss
Ta fraction of T0 due to absorption
Notation Definition
transmittance, i.e. fraction of impinging light that is transmitted
reflectance, i.e. fraction of impinging light that is reflected
OD optical density = log10(1/T)
λ wavelength (nm)
ODf optical density of particles on filter
ODsus optical density of particle suspension
ap volume absorption coefficient of the particulate (m−1
ratio of the filtered volume to the filter clearance area (m).
ρT result of transmittance measurement by T-R method
ρR result of reflectance measurement by T-R method
sample SUPERFROST glass slide with particle deposit inside water film and glass cover slip
reference SUPERFROST glass slide with water film and cover slip
Ts measured sample transmittance
Tr measured reference transmittance
Rs measured sample reflectance
Rr measured reference reflectance
TR light fraction transmitted by the sample
BK light fraction backscattered by the sample
AP light fraction absorbed by the particles
Lf light fraction forward scattered by the particles outside the Brewster angle
Lb light fraction backscattered by the particles outside the Brewster angle
Rag,n Snell reflectance at the air-glass interface of the sample (ag pedice) for normally incident light (n pedice)
Rga,f mean value of Snell reflectance at the glass-air interface of the sample (ga pedice) for light forward scattered by the particles within the Brewster angle (f pedice)
αp absorption by the particles due to an incident unitary light beam on a single through-way.
BRf fraction of forward scattered light that is scattered outside the Brewster angle
Bp light fraction backscattered by the particles
BRb fraction of backward scattered light that is scattered outside the Brewster angle
Rga,b mean value of Snell reflectance at the glass-air interface of the sample for light backward scattered by the particles within the Brewster angle
bpb volume backscattering coefficient of the particulate (m−1
T0 measured sample transmittance corrected for the forward scattering loss
Ta fraction of T0 due to absorption
Fig. 1.

Optical density spectra measured by the FTF/T-R and FTF methods (thick and thin line, respectively) for Scenedesmus communis.

Fig. 1.

Optical density spectra measured by the FTF/T-R and FTF methods (thick and thin line, respectively) for Scenedesmus communis.

Fig. 2.

Optical density spectra measured by the FTF/T-R and FTF methods (thick and thin line, respectively) for Dunaliella marina (A: total absorption; B: pigment absorption).

Fig. 2.

Optical density spectra measured by the FTF/T-R and FTF methods (thick and thin line, respectively) for Dunaliella marina (A: total absorption; B: pigment absorption).

Fig. 3.

Total, detritus and pigment optical density spectra (T, D and P labels) measured by the FTF/T-R and FTF methods (thick and thin lines, respectively), for a particle sample collected from coastal water of the Adriatic Sea.

Fig. 3.

Total, detritus and pigment optical density spectra (T, D and P labels) measured by the FTF/T-R and FTF methods (thick and thin lines, respectively), for a particle sample collected from coastal water of the Adriatic Sea.

Fig. 4.

Optical density spectra measured for a mineral particle sample collected from River Toce (Italy) by the FTF/T-R method (medium line), and by the T-R method (ODf: thick line; ODsus: thin line)

Fig. 4.

Optical density spectra measured for a mineral particle sample collected from River Toce (Italy) by the FTF/T-R method (medium line), and by the T-R method (ODf: thick line; ODsus: thin line)

Fig. 5.

Optical density spectra measured for a mineral particle sample collected from River Toce (Italy) by the FTF/T-R and FTF methods (thick and thin line, respectively).

Fig. 5.

Optical density spectra measured for a mineral particle sample collected from River Toce (Italy) by the FTF/T-R and FTF methods (thick and thin line, respectively).

Fig. 6.

Backscattering coefficient (bpb in m−1) measured by the FTF/T-R method for a particle sample collected from coastal water of the Adriatic Sea, before and after depigmentation by NaClO (thick and thin line).

Fig. 6.

Backscattering coefficient (bpb in m−1) measured by the FTF/T-R method for a particle sample collected from coastal water of the Adriatic Sea, before and after depigmentation by NaClO (thick and thin line).

3
Present Address: Via Milano 25, 21030, Orino (VA), Italy

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