1. Introduction

Estimation of light absorption by phytoplankton is important in determination of phytoplankton productivity from bio-optical models [1, 2] and for obtaining estimates of biological variables from remote sensing. It has also been used to provide information on taxonomic composition, and to analyze community structure [3]. However, accurate estimates of phytoplankton absorption by conventional spectrophotometers are difficult due to relatively dilute concentrations of particulate matter in natural waters which are below the detection limits of laboratory spectrophotometers when measured on standard 1- or 10-cm cuvettes. A solution to this was first suggested by Yentsch, 1962 [4], and later modified by Truper and Yentsch, 1967 [5], where the latter concentrated bacterial cultures on a glass-fiber filter (GF/F) and measured the absorption directly on the wet filter. This technique known as the Quantitative Filter Technique (QFT) [6] is being widely used since then for measurement of light absorption of natural phytoplankton population [7–11]. The particulate absorption obtained from the QFT can be separated into absorption by phytoplankton and non-algal particulate matter (NAP) [9]. However, several sources of error have been identified in the QFT method that include, variations with saturation of filter paper and differential filter paper loading [6, 12], losses due to scattering (especially backscattering) [13] and correction for baseline fluctuations and null corrections [14]. The errors due to scattering can be reduced by using an integrating sphere attachment in conjunction with a double beam spectrophotometer [15]. But the issue of prime concern is pathlength amplification factor (β) (see Table 1 for list of symbols) that occurs due to multiple scattering within the filter paper. The β factor is defined as the ratio of optical to geometric pathlength (which is the ratio of volume filtered to the filter paper clearance area) [16, 17] and is the principal source of uncertainty in estimation of particulate absorption using the QFT method [12]. The β factor is instrument (spectrophotometer configuration) as well as phytoplankton species and size dependent. Both theoretical [e.g [12, 18].] and empirical corrections [e.g [6, 8, 10, 11, 19–21].] for β factor have been proposed. Most empirical corrections for β factor have been determined by measuring OD(λ) of phytoplankton suspensions and relating it to OD(λ) measured on the filters. The correction factor thus derived is then applied to field samples. Some consistency has been reported among the various empirical corrections for β factor [6, 13, 19, 20], but several studies have shown large deviations [21, 22]. There is significant uncertainty at present concerning the influence of phytoplankton/particle species/type, size, and refractive index on the β factor. The chief unresolved issues in the determination of β factor are thedivergence in the β factor at high optical densities and the ‘hysteresis effect’ (several values of β for the same value of OD(λ)) leading to a wavelength dependency of the β factor [11].

Table 1. Definitions of terms and symbols used in the text

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Taking into consideration the errors in measurement of particles concentrated on filter paper, another alternative to enhancing spectroscopic sensitivity is to increase the sample cell pathlength by means of long-path cells [23, 24] or capillary optical waveguide cells [25–27]. The reflective tube measurements have allowed in situ measurements of absorption coefficients in spite of difficulties with effects of bubbles and correction for scattering losses [28]. Using a similar principle as the reflective tube, various types of long-pathlength liquid core waveguides have been developed [29] and introduced commercially by World Precision Instruments (Ultrapath^TM, WPI) (Fig. 1 ). In such arrangements, light is guided in the liquid core, enters and passes through the capillary tubing and is reflected back into the liquid core at the glass/air or a low refractive index coating interface with optical fiber transporting light to and from the sample cell [25, 27]. Advantages of using a capillary waveguide include small sample volume (e.g., 100 μL to 10 mL) and higher sensitivity due to increased effective pathlength [30]. The liquid core waveguide systems have primarily been used to measure chromophoric dissolved organic matter (CDOM) [25] and rarely to measure particulate matter in suspension [31, 32]. These studies have shown the potential for measurement of particulate matter in suspension with the waveguide. The Ultrapath can be used to measure particles concentrated on filter paper as well, by using a portable fiber optic based GF/F filter holder (Fig. 1) [31]. This set-up is much more portable allowing convenient absorption measurements of large number of samples quickly in the field and is relatively less expensive than commercial spectrophotometers.

 

Fig. 1 Schematic diagram of the Ultrapath system with a long pathlength capillary waveguide which is connected between 1 and 2 (shown in red) for measurements of suspensions, adapted from D’Sa et al., 1999 [25], and the GF/F filter holder which is connected between points 1 and 2 (shown in red) for filter paper measurements, adapted from Belz et al., 2006 [31]. Not to scale.

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In this study, a relationship between the OD(λ) of samples in suspension (OD_s(λ)) and the OD(λ) of the same sample on a GF/F filter (OD_f(λ)) are developed in order to determine the β factor correction algorithm for the two different spectrophotometers. The validity of the β factor is then tested by applying it to cultures and natural water samples. In order to test the potential of the Ultrapath to measure OD(λ) and understand the variability in the relationship between OD_s(λ) and OD_f(λ) measured on it, comparison of Ultrapath measurements to a double beam spectrophotometer equipped with an integrating sphere (Lambda 850) were evaluated. The differences in OD(λ) observed between the two spectrophotometers are discussed in terms of scattering and pigment concentration of samples.

2. Methods

Nine cultures were obtained from the Provasoli-Guillard Center for Culture of Marine Phytoplankton (CCMP) (Table 2 ) and grown in f/2 enriched sterile seawater medium [33] with an illumination of approximately 100 μmol photons m⁻² s⁻¹ under a 12:12 dark:light cycle. They were chosen to cover wide variations in the shape and size of the cells, pigment composition, structure of the cell wall, and intracellular pigment concentration. Before the spectrophotometric analysis, cultures were diluted with filtered culture media to provide a range of optical densities (OD(λ)). Natural water samples were obtained from various estuarine, coastal and open ocean regions. Since phytoplankton cells are in low density in natural samples, they were concentrated so that measurements could be made on a 1 cm cuvette. The samples were filtered on 0.22 μm Nucleopore membrane filters and resuspended in a small volume of the filtrate [11]. The above process will concentrate apart from phytoplankton all the other particulate matter present in the natural samples. The concentration process has the potential to rupture phytoplankton cells and hence alter particle optical properties, which was minimized by filtering at low pressure and gentle resuspension.

Table 2. List of phytoplankton cultures and their coefficients (a and b) obtained by applying a quadratic fit (see Eq. (1)) between optical density of phytoplankton in suspension (OD_s(λ)) and optical density of phytoplankton on filter paper (OD_f(λ)). CL is the cell length and CW is the cell width. S.E. represents the standard error.

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Measurements of optical density of suspensions (OD_s(λ)) were made with a dual grating double beam Perkin Elmer Lambda 850 spectrophotometer equipped with an integrating sphere (referred to as Lambda 850 hereafter) on a 1cm quartz cuvette and WPI Ultrapath^TM hyperspectral system (Ultrapath, WPI Inc., Sarasota, FL, USA) (referred to as Ultrapath hereafter) at 2 nm interval. The Ultrapath is a spectrophotometer together with a waveguide and has a user-selectable pathlength (2, 10, 50 and 200 cm) through a fiber optic cable (Fig. 1). A peristaltic pump is used to inject water samples from a beaker containing the suspension into the sample cell at low rate. The incident light is provided by Deuterium and Halogen light sources that is coupled to the sample cell via a fiber optic cable. The light travels by internal reflection within the waveguide and after exiting the waveguide is collected by a fiber optic cable connected to a photodiode array fiber optic spectrometer. The spectrophotometer is specified to have a dynamic range of 0.002-231 m⁻¹, with a maximum deviation in replicate spectra < 0.001 OD units [30]. The sample cell was cleaned between measurements using successive rinses of methanol, 10% HCL and Milli-Q water. OD_s(λ) were measured on the Ultrapath by setting the pathlength to 2 cm and using culture filtrates as the blank. The OD_s(λ) for the Lambda 850 was determined by placing phytoplankton culture in a 1 cm quartz cuvette with the same volume of culture filtrate serving as a blank. For concentrated natural samples, the measurements were similar to those mentioned above except filtrates of concentrated natural samples were used as the blank.

To measure the optical density of particles on filter paper (OD_f(λ)), samples were filtered onto 25 mm GF/F filters under low vacuum. Culture and natural samples volumes were chosen so that the geometric pathlength of the filtered samples matched the pathlength in the cuvette [20, 21]. For measurements of particles on filters, the Ultrapath had an attachment for mounting filter papers which connected the light source and detector by fiber optic cables [31] (Fig. 1). A collimated light beam incident perpendicular to the GF/F filter is transmitted or scattered through the GF/F filter and collected by a second collimating lens behind the filter and coupled into an exit fiber [31]. Similarly, the Lambda 850 had a special filter holder which was placed at the entrance of the integrating sphere. Recently, Rottgers and Gehnke, 2011 [34], have shown that the percentage error for samples placed at the entrance and center of the integrating sphere is 4.5% and 3%, respectively. Such a difference in percentage error will have little effect on analysis of this paper. The blank was obtained from the same volume of filtrate, filtered under low pressure onto a second filter. During the analyses, saturation was maintained between the sample and blank filter by moistening them with few drops of the filtrate [6]. The filters were placed in the spectrophotometer on a special filter holder immediately after the filtration step. All measured OD(λ) were shifted to zero near the infrared region. The pathlength amplification factor (β) can be determined by comparing OD_s(λ) and OD_f(λ). The relationships between OD_s(λ) and OD_f(λ) were fitted to a quadratic equation between 400 and 700 nm at 2 nm interval [6, 19, 20].

The coefficients a and b were determined for each of the nine cultures at different dilutions and all the cultures taken together.

The LISST‐100X (Laser In Situ Scattering and Transmissometry (LISST); Sequoia Scientific, Inc.) (referred to as LISST hereafter) is an instrument that measures light scattering of a particle suspension at small forward angles, and inverts this information to estimate the particle size distribution (PSD) [35]. A collimated laser beam (wavelength 670 nm) illuminates particles and the light scattered is sensed by a 32-ring detector. Each ring measures the scattering intensity over a range of small forward angles for 32 different size classes logarithmically spaced from 2.5 to 500 μm. The instrument has been shown to provide reasonable results for phytoplankton cultures [36, 37], and natural particles in coastal waters [38]. A manufacture supplied sample chamber was inserted into the optical head of the instrument and used for measurements of particles in suspension from cultures and natural samples. After cleaning of the optical windows with lens paper, the samples were slowly poured into the sample chamber to avoid bubble formation. Prior to sample analysis, a background scan was measured using filtered seawater corresponding to the sample. For each sample more than 100 scans were collected. With the software provided by the manufacturers, the scattering intensities measured by the detector were mathematically inverted to obtain the PSD assuming that particles are spherical. The volume scattering function (VSF) (m⁻¹ sr⁻¹) for the LISST was obtained according to the method described by Agrawal, 2005 [39]. Normalized VSF (sr⁻¹) was obtained by dividing VSF by the scattering coefficient (b(λ)) (m⁻¹). The b(λ) was obtained by subtracting the beam attenuation coefficient (c(λ)) (m⁻¹) of filtered seawater (essentially absorption coefficient (a(λ)) (m⁻¹) assuming no scattering from filtered seawater) from c(λ) of the particulate sample.

Chlorophyll-a concentrations were obtained using high-performance liquid chromatography (HPLC); samples for HPLC were filtered onto 25 mm GF/F paper and stored in liquid nitrogen until analysis.

3. Results and Discussion

3.1 Pathlength amplification factor for Lambda 850 and Ultrapath

Following Mitchell, 1990 [6] pathlength amplification were determined by fitting a quadratic equation to each pair of OD_s(λ) and OD_f(λ) between 400 and 700 nm at 2 nm interval for both Lambda 850 and Ultrapath. Values of OD_s(λ) were restricted to <0.4 to reduce the influence of multiple scattering on the OD_s(λ) and OD_f(λ) relationship and as field data usually do not exceed this value [6, 20]. In some samples OD_s(λ) and OD_f(λ) relation showed the ‘hysteresis effect,’ where for the same value of OD_f(λ) multiple values of OD_s(λ) were observed depending on the wavelength [11, 12, 19]. The hysteresis did not show any species dependence but was rather dependent on the concentration of the samples, mainly occurring at low absorbing regions of the spectra (~540-590 nm - range depended on the species) and was more severe at lower culture concentration (Fig. 2(a,b) ). The hysteresis effect was much higher in the Ultrapath measurements and was almost negligible for majority of the Lambda 850 measurements (Fig. 2(a,b)). To avoid biasing our results due to this effect, we either removed the regions of low absorption from the spectra where the hysteresis was present [40] or excluded spectra with very large hysteresis loops from the analysis. The above exclusions were mainly applicable to the Ultrapath measurements and not as much for the Lambda 850 measurements (5 samples only). The results of fitting a quadratic equation for all pairs of OD_s(λ) and OD_f(λ) for Lambda 850 are shown in Fig. 2(c) and Table 2. The variation of coefficients from species to species and for all data pooled together is similar to that observed by other studies on β factor [6, 19, 20, 40]. The fit for all data pooled together was robust with no effect of removal or addition of certain species data. Significant differences were found between the β corrections of individual species (F-test, p<0.001) consistent with other studies [19, 21, 22]. Within the species the coefficient ‘a’ was less variable relative to coefficient ‘b’ (Table 2). The coefficient ‘a’ was not significantly different for species, but the coefficient ‘b’was significantly different (F-test, p<0.001). Further the coefficient ‘b’ was inversely correlated to the HPLC chlorophyll-a concentration (r² = 0.65; p<0.001) and to average particle size estimated from LISST (r² = 0.55; p<0.001) (data not shown). Thus much of the variations in the β correction arise from the concentration of phytoplankton pigments and their size. The variability in phytoplankton species and size influence β by mainly influencing the OD_s(λ) measurements as stronger scattering due smaller cell sizes and cell shape or material would be overshadowed by the scattering of the filter, but would significantly affect the cuvette measurements. Especially for smaller particle size the VSF will have relatively more scattering at larger angles which is not collected by the detector optics even an integrating sphere. Similar to previous studies [e.g [19, 21, 22].], the significance of cell size and species composition on the β correction is corroborated by this study. Although these studies are consistent in terms of differences observed in species composition and β correction, the exact reason for these differences is still under debate. For e.g. inconsistency exists in the coefficient ‘b’; Moore et al., 1995 found ‘b’ coefficients are low for small sized cells (Synechococcus sp. and Prochlorococcus marinus), while in this and Finkel & Irwin, 2001 study, the ‘b’ coefficients were lower for larger sized cells (Table 2). The reasons for these contradictions are not clear at present and warrant further research.

 

Fig. 2 Relationship between optical density of particles in suspension (OD_s(λ)) and optical density of particles on filter paper (OD_f(λ)) measured on Lambda 850 (left panel) and Ultrapath (right panel), (a,b) for representative high and low concentration samples, (c,d) for all samples, the black solid line is the quadratic fit to the data, and (e,f) at 443 nm (solid black circles) and 676 nm (solid gray circles). The black and gray dashed lines represent the quadratic fit for 443 nm and 676 nm, respectively.

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The β correction strongly depended on the range of OD(λ), with flatter relationships when higher OD(λ) were ignored and steeper relationship when higher OD(λ) were included [6]. The sensitivity of β correction to the ranges in OD(λ) becomes more apparent while testing the wavelength dependency of β correction algorithm [20]. To check if there is a wavelength dependency of the β correction we applied the quadratic fit (Eq. (1)) to wavelengths between 400 and 700 nm at every 10 nm. The coefficient ‘a’ showed little variation and was within 95% confidence intervals, but coefficient ‘b’ varied depending on the OD(λ) within the spectra, with wavelengths between 400 and 490 nm and 650-680 nm showing similar relationships. Results at two specific wavelengths (443 nm and 676 nm) are shown in Fig. 2(e). The fits for these two wavelengths are almost identical emphasizing that for similar ranges of OD(λ) the β was identical with no apparent wavelength dependency.

Obtaining a relationship between OD_s(λ) and OD_f(λ) measured on the Ultrapath is more complex, as the measurement of OD_s(λ) in the Ultrapath is different from conventional spectrophotometers (Fig. 1). Large hysteresis loops observed in this relationship hindered the ability to determine accurate β for the Ultrapath (Fig. 2(b)). Further, β correction differences between species were more noticeable in Ultrapath, with differences present within species for different dilutions. However, a statistically significant quadratic fit could be obtained albeit with large scatter (Fig. 2(d)). This relationship showed significant wavelength dependency (Fig. 2(f)), with flatter relationship at 443 nm and steeper relationship at 676 nm. The relationship was sensitive to addition and removal of certain spectra, such a relationship is not applicable for β correction of particulate absorption. An insight into the variability of OD_s(λ) and OD_f(λ) measured on the Ultrapath can be obtained by comparisons with Lambda 850 measurements (next section). Such an analysis would serve dual purpose, firstly it would assist in obtaining an accurate pathlength amplification correction factor for the Ultrapath and secondly the potential of the Ultrapath to measure OD_s(λ) and OD_f(λ) could be tested relative to Lambda 850.

3.2 Lambda 850 and Ultrapath comparisons

Previous studies have shown that the absorption measured using a spectrophotometer in conjunction with an integrating sphere (similar to Lambda 850 in this study) is very close to the true absorption [41], hence the performance of the Ultrapath is tested by making comparisons between the Ultrapath and Lambda 850 measured OD_f(λ) and OD_s(λ) for cultures and natural samples. Representative OD_f(λ) for culture samples measured on the Ultrapath with a filter holder and Lambda 850 are shown in Fig. 3(a) . A very good agreement was observed between the two, with locations of primary absorption bands of chlorophyll-a at 443 nm and 676 nm as well as the other absorption bands between 450 and 500 nm corresponding to accessory pigments evident in both the spectra. However, the Ultrapath values showed an underestimation at the chlorophyll-a absorbance bands (443 nm and 676 nm) for all the species. The underestimation was greater at the red wavelengths relative to the blue wavelengths (Fig. 3). Although the OD_f(λ) was underestimated by the Ultrapath relative to the Lambda 850, it was small being on average 5% and never exceeded 10% (about 15 samples) for all the samples and at all wavelengths analyzed. A strong linear relationship was observed between OD_f(λ) at 443 and 676 nm (Fig. 3(b,c)), which was also observed over the entire visible domain from 400 to 700 nm at 2 nm interval (data not shown).

 

Fig. 3 Comparison of spectral shape of optical density of particles on filter paper (OD_f(λ)) (a) and suspension (OD_s(λ)) (d) for Lambda 850 (solid lines) and Ultrapath (dotted lines) for two different cultures. OD_f(λ) and OD_s(λ) for Lambda 850 and Ultrapath at two wavelengths 443 nm (solid black circles) and 676 nm (solid gray circles) for (b,e) all cultures, and (c,f) natural samples, respectively. The black solid line is the best fit line and the black dashed line is the 1:1 fit.

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The spectral shapes of OD_s(λ) were similar to OD_f(λ) showing the chlorophyll-a absorbance bands as well as bands corresponding to accessory pigments. However, the Ultrapath underestimated OD_s(λ) in vicinity of the absorption peaks (Fig. 3(d)). The underestimation of Ultrapath values relative to Lambda 850 values were more pronounced for OD_s(λ) compared to OD_f(λ) measurements. The average percent difference between the Ultrapath and Lambda 850 OD_s(λ) was 15% and below 28% for all the samples. Despite thedifferences in magnitude of OD_s(λ), a linear relationship was observed between Ultrapath and Lambda 850 for cultures as well as natural samples (Fig. 3(e,f)). A point to be noted here is that not all OD_s(λ) were underestimated by the Ultrapath, while OD_s(λ) around 676 nm was underestimated for all samples, some samples showed a slight overestimation between 400 and 580 nm. Since the differences in spectral shape between Ultrapath and Lambda 850 can be attributed to effects of scattering [31, 32], the above observation indicate a differential effect of scattering across the visible domain.

A better understanding of differences in magnitude at the absorption peaks of OD_s(λ) and OD_f(λ) can be elucidated by understanding the variable effects of scattering and absorption on light losses in Ultrapath measurements. The effect of scattering losses is accounted for in the Ultrapath and Lambda 850 by subtracting absorbance values near the infra-red region, under the assumption that there is negligible absorption from particulate matter at these wavelengths and scattering loss is wavelength independent [14, 32]. As the OD_f(λ) spectra from Ultrapath and the Lambda 850 matched for all the samples and wavelengths other than around the chlorophyll-a absorbance peaks, it suggests that major part of scattering is taken care of at most wavelengths. The same cannot be said about the OD_s(λ) measurements from Ultrapath. The better agreement of OD_f(λ) values compared to OD_s(λ) values can be understood by examining the optical characteristics of particles on filter paper relative to that of particles in suspension. For particles in suspension, scattering is dependent on suspended particles as well as the medium, while GF/F filter papers are inherently strong scatterers making the light field diffuse as such scattering is dependent more on filter paper than the particles on the filter paper [12]. Addition of more particles in suspensions would result in significant scattering effect, while little effect of scattering would be seen on addition of particles to filter papers.

The effect of scattering in the two instruments was evaluated by making measurements of pigment extract and Maalox (aluminum hydroxide, magnesium hydroxide and simethicone) suspensions at 5 dilutions. Pigment extracts were obtained by extracting pigments from leaves in 100 ml of methanol (100%) and diluting it serially to get 10%, 25%, 50%, and 75%. Maalox dilutions were prepared by diluting 1 ml of Maalox in 100 ml of water to obtain 100% dilution (c = 27.6 m⁻¹ at 443 nm) which was then diluted serially to obtain 10%, 25%, 50%, and 75%. The Maalox plus pigment extract was allowed to sit for some time so that the particles in Maalox could absorb some of the pigment extract. For filter paper measurements, 1-2 drops of Maalox plus pigment extract were added to the filter paper before the filter paper was scanned. Both the spectrophotometers showed a linear response for different dilutions of pigment extract and were in good agreement with each other for different wavelengths (Fig. 4(a) ). The effect of scattering on these results was evaluated by addition of known concentrations of Maalox to the pigment extract. The influence of scattering is apparent on OD_s(λ) from the responses of the two instruments (Fig. 4(b)). While the Lambda 850 showed a very small increase, the Ultrapath showed a much greater increase with increasing concentration (Fig. 4(b)). An inverse relationship was observed between difference in OD_s(λ) of Lambda 850 and Ultrapath, i.e. larger differences between the spectrophotometers were observed at shorter wavelengths (Fig. 4(b)), indicating a wavelength dependent effect of scattering. This wavelength dependent effect of scattering in the Ultrapath measurements cannot be corrected by using a single wavelength from the near-infrared. In contrast to measurements of suspension no difference between the two instruments or wavelengthdependency was observed for the filter paper measurements (Fig. 4(b)). These experimental results confirm the inherent differences between absorption measurements of particulate in suspensions and particulates on filter papers mentioned earlier.

 

Fig. 4 (a) Linear response of optical density of suspension (OD_s(λ)) for different concentration of pigment extracts measured on Lambda 850 (circle and diamond) and Ultrapath (plus and cross) at 676 nm and 443 nm, respectively, (b) response of OD_s(λ) for different concentrations of pigment extract plus Maalox measured on Lambda 850 (circle and grey square) and Ultrapath (black plus and gray triangle) at 676 nm and 443 nm, respectively. Response of optical density of particles on filter paper (OD_f(λ)) measured on Lambda 850 (hexagon) and Ultrapath (black cross) at 443 nm is shown for comparison.

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In measurements of OD(λ) by spectrophotometer (even with an integrating sphere) the backscattered and part of the side and forward scattered light will not be captured by the detector and will account for loss due to absorption. For measurement of OD_s(λ) in the capillary waveguide, light scattered by the cell suspension at angles greater than the numerical aperture of the waveguide are lost and are a function of the VSF [42]. The scattering corrections will vary from sample to sample depending upon the particles concentration, size distribution, and scattering efficiency. We will discuss some of these factors in relation to differences in OD_s(λ) measured on the Ultrapath and Lambda 850 in the next section.

3.3 Particle size distribution and VSF measured using LISST in relation to differences between Lambda 850 and Ultrapath measured OD_s(λ)

Light scattering by particles depends on the particle’s size, index of refraction, composition, and shape [43]. PSD measurements are included in this study to understand the scattering across the visible spectrum which depends on the shape of the PSD [44]. PSD from LISST has been shown to be in good agreement with measurements from Coulter counter in laboratory studies [37]. Figure 5 shows the PSD of 9 culture samples. As we were interested in looking at the shape of PSD we normalized the PSD to the modal peak. Comparisons between LISST and FlowCAM^® (Fluid Imaging Technologies) PSD measurements done for a few samples were in good agreement, though the FlowCAM PSD were narrower than the LISST PSD. Features below a size range of ~3 μm (lower range of the detection limit of LISST) are not necessarily due to the sample, but can be artifacts due to the inversion process [45]. Most PSD’s showed a peaked distribution with mean diameter ranging from about 4-30 μm. Figure 6 shows the normalized VSFs computed from LISST measurements for 9 culture samples, andnatural samples from estuarine and coastal regions. For cultures, the increasing particle size lead to a steeper VSF, with a narrower forward scattering lobe (Fig. 5, Fig. 6(a)). Scattering intensity as a function of angle varied by 4 orders of magnitude for these suspensions (Fig. 6(b)). The general magnitude of the measured VSFs for natural samples is consistent with the Petzold curve obtained from a turbid harbor [46]. However, significant variability in the shape of the VSFs measured with the LISST is observed. In measurements of scattering suspensions in the Ultrapath, measurements greater than the true absorption a(λ) have been observed [32]. If ε is the fraction of the scattering coefficient, b(λ), that is lost, then

 

Fig. 5 Particle size distribution (PSD) obtained using LISST 100X for nine cultures (black solid circles and solid line). The results from FlowCAM done for few samples are shown for comparison (gray solid triangles and solid line). The PSD was normalized to the modal peak to facilitate comparisons.

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Fig. 6 Normalized volume scattering function (VSF) (ratio of VSF to the beam attenuation coefficient) for (a) cultures, and (b) natural samples. The Petzold, 1972 data (solid black circles and solid red line) for turbid harbor is shown for comparison.

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Values of ε range from 0 to 1, for a perfect absorption meter ε should be close to zero. In Ultrapath absorption measurements, we assume ε b(λ) = a_WG(750), so subtracting this value from a_WG(λ) at all wavelengths gives the corrected absorption,

From measurements of VSF and the acceptance angle of the capillary Ultrapath, θ_WG = 20° the fraction of scattered light (1-ε) collected by the capillary Ultrapath can be approximated as [31, 32],

3.4 Applications of pathlength amplification factor

A good robust relationship was obtained between OD_s(λ) and OD_f(λ) measured on the Lambda 850 for the β correction algorithm development (Fig. 2(c)), where as a similar relationship could not be obtained for Ultrapath measurements (Fig. 2(d)). As OD_f(λ) was similar for both the spectrophotometers (Fig. 3(b)), so most of the variability in the relationship between OD_s(λ) and OD_f(λ) for the Ultrapath (Fig. 2(d)) can be attributed to the variability in OD_s(λ) measured on the Ultrapath. To get the OD_s(λ) between the Lambda 850 and Ultrapath to match, accurate corrections for scattering losses have to be applied to the Ultrapath measurements. This scattering loss in Ultrapath is a function of the VSF (previous section) and wavelength dependent. Accurate corrections of OD_s(λ) measured on the Ultrapath would require measurements of VSF and scattering (or attenuation) coefficients in addition to measurements of absorption coefficient. At present there is no accessory to measure OD_s(λ) on the Ultrapath other than the capillary waveguide system used in this study.

Taking into account this fact and the above results, it is impractical to determine β for the Ultrapath system in its present configuration and without a complete set of measurements (VSF, b(λ) or c(λ), a(λ)). Therefore, we suggest the use of β correction algorithmsdetermined for spectrophotometer with integrating sphere attachment (like Lambda 850 in this study) to be applied to OD_f(λ) measurements of Ultrapath, in view of strong linear relationship in OD_f(λ) measurements between Lambda 850 and Ultrapath. The β correction algorithm for Lambda 850 obtained for our study was similar to that obtained by Cleveland and Weidemann, 1993 [20] and Arbones et al., 1996 [19], lower than that obtained by Mitchell, 1990 and higher than that obtained by Bricaud and Stramski, 1990 [11]. All the β correction algorithms are similar at lower values and diverge at higher values of OD(λ). The validity of the β amplification developed for Lambda 850 was tested by applying the β factor to cultures, a mixture of 2 or more cultures, as well as natural samples from different environments. Figure 7 shows representative results of comparisons of OD_s(λ) for culture and natural samples. Despite the significant difference in β correction between the species, reasonable agreement was found between cuvette measured and β corrected OD_s(λ). The average percent difference for cultures (also mixture of cultures) was 9% and was always below 15%. The largest differences were seen in low green-yellow absorption regions and smallest differences were in the red region of the spectrum. Similarly, for natural samples the average percent difference was 15% and always below 20% for all samples analyzed from different environments. These results are encouraging for the use of the filter pad method as a means of estimating particulate spectral absorption from both Ultrapath and Lambda 850 taking into consideration that the study covered a wide variety of sample types and spanned a wide range of OD(λ).

 

Fig. 7 Spectral values of optical density of suspension (OD_s(λ)) measured in a cuvette on Lambda 850 (solid black line) and obtained by using β algorithm (dotted black line) developed in this study for Lambda 850 for cultures and natural samples.

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4. Conclusions

The pathlength amplification factor (β) due to multiple scattering within the filter paper is the largest source of uncertainty in the measurements of particulate absorption which needs to be taken into account for its accurate measurement. For this purpose pathlength amplification correction algorithms were developed for Ultrapath and Lambda 850 using nine cultures at various dilutions. While the Lambda 850 β algorithm was robust, the algorithm developed for Ultrapath was not as robust which was attributed to the differences seen in measurements of suspensions. The Lambda 850 algorithm did not show any wavelength dependence but differences among phytoplankton species remains an issue for the algorithm. One approach to reduce this error is by making certain it is representative of the sample to which it is being applied. As it is difficult to correct the scattering losses in the Ultrapath without ancillary measurements and given the good agreement between filter paper measurements between Ultrapath and Lambda 850, we suggest the use of pathlength amplification correction algorithms developed for spectrophotometers with integrating sphere (e.g. Lambda 850 in our study) for corrections of particulate absorption measured on the Ultrapath with the GF/F filter holder. Factors such as volume scattering function and acceptance angle of the Ultrapath detector were found to be important in measurements made on Ultrapath especially for particles in suspension.

The good performance of Ultrapath for at least the filter paper measurements and to a certain extent suspensions is encouraging as it has simplified optics, longer pathlength, high sensitivity, is very portable and easy to use. The study conducted here provides new insights to utilize and understand particulate absorption measurements on two different spectrophotometers.