1. Introduction

Since the first approaches to determine the light absorption by phytoplanktonic particles in water [1–3], the absolute quantification of particulate absorption in natural waters has remained difficult. The determination of particulate absorption at low concentrations in most natural waters requires sensitive methods, but the ability of particles to scatter light adversely affects these measurements at all concentrations. Only recently has the use of integrating-cavity absorption meters (ICAM), insensitive to scattering errors, provided more accurate determination in oceanic waters [4,5]. However, filter pad techniques have been routinely and widely used for many decades, and it is desirable to further improve these methods and to validate their performance with the more accurate ICAM methods. Most of the lab techniques used to determine particulate absorption are simple and can be conducted using a dual-beam spectrophotometer (for summary see [6]). One approach to determining phytoplankton absorption is to measure the attenuation of an algal suspension in a photometric cuvette [2,7,8] when the cuvette is positioned in front of the detector, in front of a diffusive plate placed between cuvette and detector, or in front of an integrating sphere, such that all forward-scattered light can be measured by the detector. However, the backscattered and sidewards-scattered light is lost and, thus, is a source for significant errors. Different methods have been developed to correct for these losses [9,10], but typically the attenuation determined at $>750\mathrm{nm}$ (assuming negligible absorption by particles in this spectral region and a wavelength-independent scattering) is subtracted from the attenuation values of all other wavelengths and the result taken as absorption (null-point correction). To avoid errors by backscattered light, the cuvette can be positioned in the center of an integrating sphere [7,11–16]. These techniques are applicable for samples with relatively high particle concentrations; on the other hand they are limited to low, optically thin concentrations of particles to avoid errors by multiple scattering in the cuvette. Particles in natural aquatic samples have to be concentrated to obtain a sufficient optical density. This is done by retaining particles on a filter. The attenuation of this filter is measured in a photometer by determining the transmittance of the filter when placed directly in front of the detector window or in front of an integrating sphere [3,17,18]. A special method of this quantitative filter technique (QFT) [19] is the “transmittance–reflectance” (T-R) technique of Tassan and Ferrari [20,21], where the attenuation by particles on a filter is derived from light, which is transmitted through and reflected by the filter. This method allows the correction of errors induced by backscattering by the filter and the particles itself. Furthermore, it is assumed that this method is more accurate compared to simple transmission methods in waters with high concentrations of mineral particles [16,21] that adversely change the scattering properties of the sample/filter composite. However, the method needs additional measurements with the same filter in the “reflectance” mode and some assumptions for its calculation (for details see [20,21]. Glass-fiber filters, which are used for the QFT, have a high scattering coefficient. Thus, a collimated light beam is scattered inside the filter and transformed into a diffuse light field. As a result, these filters strongly amplify the optical path length because of multiple internal scattering and the fact that the particles are distributed in the depth of the filter, not just on its surface. Normally, the amplification factor ($\beta$), which is the ratio of the real optical to the geometric path length [22], is determined empirically. These determinations have been done, e.g., by comparison with measurements in a cuvette using algal cultures [19,20,23–27]. Errors in the determination of $\beta$ occur because the cuvette measurements and/or the QFT could be susceptible to significant wavelength-dependent scattering errors [28]. Furthermore, $\beta$ might be variable and dependent on the particle distribution in the filter depth. Additional errors are introduced by sample filtration, freezing, and storage procedures [29–32]. Some errors of the QFT discussed above are related to (multiple) light scattering and thereby to incomplete capture of scattered light when the filter is measured in front of an integrating sphere or in front of the detector window. These errors can be compensated to some extent by measuring backscatter losses, as in the T-R technique [20,21], but could be completely avoided by placing the filter in the center of an integrating sphere (e.g., [33]) to directly determine its absorptance. The required special integrating spheres were custom-made instruments until a few years ago, and consequently, this kind of measurement has been made in well equipped optical laboratories only. For a few years they have been commercially available as accessory equipment for many common spectrophotometers and are already used in a number of laboratories, e.g., to measure absorption in a cuvette placed in their center (see above), as well as to measure particulate absorption on filters [34]. To the best of our knowledge there has been no methodological work done to standardize the procedure, to perform an error and sensitivity analysis, or to analyze the necessary amplification corrections for conducting measurements with filters inside an integrating sphere. Some measurements of particulate absorption of dust particles in suspension [14,15] showed significant particulate absorption in the near IR (NIR) region of 700–900 nm. Significant absorption in the NIR spectral region would preclude using these wavelengths for null-point correction. Tassan and Ferrari [16] showed significant absorption up to 750 nm in natural samples measured by the T-R method, but the regular “transmittance” method is highly susceptible to filter-to-filter variations (e.g., due to filter wetness), making exact determination of the reference background difficult. This is also a problem for the “reflectance” measurement, but the T-R technique can partly correct for these filter-to-filter differences. We will show the advantages of filter measurement in the center of an integrating sphere, e.g., that the overall precision and accuracy of the QFT are strongly improved, and describe the necessary correction for path-length amplification, which is also much changed compared to a transmittance measurement. As the scattering error for the absorption determination inside an integrating sphere is insignificantly small and, hence, no scattering offset (null-point) correction is required, this setup can be used to measure the low particulate absorption in the NIR spectral region.

2. Materials and Methods

A. General Procedure

Measurements were performed with two types of glass-fiber filters, GF/F (Whatman) and GF-5 (Macherey and Nagel), in a dual-beam UV/VIS spectrophotometer (Lambda 800, Perkin Elmer) that was equipped with a 150 mm integrating sphere (Labsphere Inc.). The sphere was made from Spectralon (Labsphere Inc.) and allowed placement of a sample in its center with the help of special center-mount sample holders, as well as placement of a sample in front of (transmission port) and behind (reflection port) the integrating sphere. For all measurements inside the sphere we used a custom-made, clip-style, center-mount filter holder that allowed arrangement of different angles between the sample and the incident light beam. We performed measurements in three different modes (in front, behind, and at the center of the integrating sphere). These three modes can be considered as measurements of the optical properties transmittance ($T$), reflectance ($R$), and absorptance ($A$). Theoretically we should find that $T+R+A=1$. Transmittance is measured by placing the filter in front of the entrance of the integrating sphere. Absorptance is measured by placing the filter at the center of the sphere. In both cases the reflectance ports are closed with a white Spectralon reflectance standard. Reflectance is measured by placing the filter behind the integrating sphere without placing a white reflectance plate behind the filter, so the black cover behind the port acts as a light trap. In all cases the reference reflectance port is covered by the reflectance standard. The filters used had a diameter of at least 47 mm (47 or 55 mm). The transmittance and reflectance measurements were performed with complete filters. For absorptance measurements each filter was cut in up to four rectangular pieces of about $1\times 2\mathrm{cm}$. During measurement the filters were never completely soaked with water, to avoid any water droplets that might fall down inside the sphere and damage the detectors at the bottom of the sphere. The general procedure was to soak the filter with water for at least 1 h and then briefly put it on a tissue to remove free water. We will show later that filter wetness has a minor effect on the overall attenuation of the filter when placing a filter inside an integrating sphere. The filter was placed at the center of the integrating sphere by the use of a clip-style filter holder (Labsphere Inc., USA). Filters were placed perpendicular to the light beam, and the wavelength scan with the spectrophotometer was started promptly. Spectral measurements were performed from 300 to 900 nm (occasionally only 350 to 750 nm) with a resolution of 2 nm (slit width: 2–4 nm; scan speed: $60–200\mathrm{nm}/\min$). We checked the effects of slit width and scan speed on the overall optical density (OD) spectrum and the signal-to-noise ratio. In the range of 1 to 4 nm and 100 to $500\mathrm{nm}/\min$ these effects were insignificant for the spectral range of 350 to 750 nm. At shorter and longer wavelengths the signal-to-noise ratio decreased with decreasing slit width and increasing scan speed. Our software permits use of different settings for scan speed and slit width for different spectral regions, and thus, the whole scan was optimized for all wavelengths for good signal-to-noise level and minimal total scanning time to avoid drying of wet filters during the scan. For the spectral region between 830 and 900 nm we used a slit width of 4 nm and a slow scan speed of $60\mathrm{nm}/\min$, and for 300 to 830 nm we used 2 nm and $200\mathrm{nm}/\min$. Before each set of measurements the instrument was allowed to warm up for at least 1 h. The positions of the two light beams were checked after the optical compartment and the sphere were cleaned of dust using ultraclean compressed air. This ensured that the sample light beam passed through the filter for both situations, when the filter was in front of or in the center of the sphere, that the reference beam illuminated exactly the center of the respective reflectance standards that cover the reflectance ports, and that the sample beam crossed the filter patch approximately 5–10 mm distance from the clip holder. The baseline of the spectrophotometer is adjusted by performing an “autozero” run either without any filter or with a dry filter in the center of the integrating sphere. For this run the entrance ports were open, and the reflectance ports were covered with Spectralon reflectance standards. Between measurements the baseline was checked either by performing a scan with the same setup as during the “autozero” scan or by verifying the value at 750 nm.

B. Filter Preparation

We observed specific spectral characteristics of some Whatman GF/F filter batches [Fig. 1(a)] that indicated contamination of the filters with an unknown chemical compound originating from the blue plastic tray that contains the filter. The contamination was observed on filters from new filter packs, was highly variable between filters from any given pack, and was observable in different packs from the same batch of filters. The contaminant was soluble in water as well as in organic solvents and, hence, could influence all kinds of measurements. If detectable in the absorption, it was, e.g., detected by high-performance liquid chromatography (HPLC) analysis techniques, which are used for measuring phytoplankton pigments, or as dissolved matter in the chromophoric dissolved organic matter (CDOM) fraction (pers. observations). It should be noted that the peak was not as obvious when the filters were measured in front of the integrating sphere. In this case the attenuation of the filter is high, so the fractional contribution from the contamination is significantly less. A much lower peak was also seen in original GF-5 filters [Fig. 1(b)]. Combustion of the filters at 450 °C for 4 h removed this contamination and was, hence, used for filter preparation. This combustion did not influence the optical properties of uncontaminated filters significantly [Fig. 1(b)]. In the following, all measurements were made with combusted GF-5 filters. Saldanha-Correa et al. [35] showed that this filter type has the same particle retention characteristics as the commonly used GF/F filter type.

 

Fig. 1. (a) Optical density, ${\mathrm{OD}}_f$, as a function of wavelength for different GF/F filters (Whatman) showing contamination (dirty filter) with an absorption maximum around 420 nm; (b) the ${\mathrm{OD}}_f$ of uncombusted and combusted GF-5 filters.

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C. Cultures and Samples

Cultures of several microalgal species were provided by the Alfred Wegener Institute for Polar and Marine Research (AWI), Bremerhaven, or isolated from the North Sea. These cultures include different diatom species isolated from the North Sea, as well as cultures of Prymnesium parvum, Isochrysis galbana, Trichodesmium erythreum, and Nannochloropsis species. A culture of Prochlorococcus marinus was provided by the University of Freiburg, Germany. The cultures were cultivated as batch cultures in 1 l glass bottles (Duran, Schott) at 20 °C, with an illumination of approximately $20\mathrm{\mu m}\text{photons}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ with 24 h of light. Samples from natural water were collected on a variety of cruises from the River Elbe, the North Sea, the Baltic Sea, and the Atlantic Ocean.

3. Assessment

The absorption coefficient, $a$ [$m^{-1}$], of a particle suspension retained on a filter is calculated from the OD of a sample and a reference filter, ${\mathrm{OD}}_s$ and ${\mathrm{OD}}_r$, respectively, as

A. Filter-to-Filter Variations

In a first set of experiments, the OD of empty, dry filters was measured using the different setups ($T$, $A$, and $R$), followed by measurements of empty, wet filters that were soaked in purified water and subsequently measured over a period of 40 min to follow changes in OD when the filters were drying. The transmittance of an empty, dry filter was very low ($<6\%$), the corresponding OD for this measuring mode, ${\mathrm{OD}}_f^T$, was, hence, $>1.2$ [Fig. 2(a)]. Accordingly, the reflectance of this filter was high, between 94 and $\sim 100\%$, and the corresponding OD, ${\mathrm{OD}}_f^R$, between 0.029 and 0.003 [Fig. 2(a)]. The absorptance of an empty, dry filter was very low ($<1\%$ and partly negative), and the corresponding OD, ${\mathrm{OD}}_f^A$, was between $-0.01$ and 0.003 [Fig. 2(b)]; the artificial negative values were observed mainly at shorter wavelengths. The ${\mathrm{OD}}_f^T$ of an empty filter that was soaked in purified water was between 0.36 and 0.60 [Fig. 2(a)] and the ${\mathrm{OD}}_f^R$ between 0.14 and 0.24 [Fig. 2(a)]. This corresponds to a transmittance of 24% to 41% and a reflectance of 72% to 58%. Thus, soaking the filter with water increases the transmittance of the filter, with a corresponding decrease in reflectance. Hence, the T/R ratio of a filter changes when the filter is soaked in water. The ${\mathrm{OD}}_f^A$ of such a wet filter was only slightly different from that of a dry filter and was between 0.001 and 0.02, mainly below 0.006 [Fig. 2(b)]. The corresponding absorptance was $<5\%$, mainly $<1.5\%$. It has previously been observed that transmittance decreased slightly over time when filters were soaked in water but eventually stabilized when the filter was soaked for more than 1 h (see [21]). These changes for transmittance and reflectance were observed here as well (data not shown). Reference filters for $T$, $R$, and T-R measurements should be soaked in water for more than 1 h as proposed by Tassan and Ferrari [21]. However, when filters were measured inside the integrating sphere, no significant differences in absorptance were observed with time after soaking for the spectral region measured (data not shown). In addition, differences in the ${\mathrm{OD}}_f^A$ between the two structurally different filter sides were tested and found to be insignificant for dry and for wet filters (data not shown). Changes in optical density between dry and wet filters were examined in more detail by conducting repetitive measurements with five to seven filters that were first measured shortly after filtering 100 mL purified water through them, and then again every 10 min for 40 min in total, with the filters left to dry in air on an open petri slide between measurements. The ${\mathrm{OD}}_f^T$ of a soaked filter increased with time at all wavelengths [Fig. 2(a)] approaching the values of a dry filter, whereas the ${\mathrm{OD}}_f^A$ of the same filter changed only slightly, with pronounced changes at wavelengths $<350\mathrm{nm}$ only [see Fig. 2(b)]. Next we reexamined the variability in the ${\mathrm{OD}}_f$ of different filters, and how the ${\mathrm{OD}}_f$ varies with the water content of the filter, as these variations determine the quality of empty filters when used as reference blanks. This has been examined earlier for $T$ and T-R measurements [20,21,28] (see Table 1). Repetitive measurements with different filters ($n=5-14$) were used to determine standard deviations ($\sigma$) for measurements of empty, dry filters and empty, wet filters (in this case measured immediately after soaking with purified water). Figure 3(a) shows ${\sigma }_{\mathrm{OD}}$ for dry filters that were used to determine the variability of filters from one filter batch. The mean ${\sigma }_{\mathrm{OD}}$ in the spectral range of 300–890 nm was similar when measured as transmittance and reflectance, with a value of $\sim 0.005$ (range: 0.004–0.012). That when measured as absorptance was 0.0003, about one order of magnitude lower [range: 0.0001–0.0010, Fig. 3(a)], a value just two to three times the noise level of the spectrophotometer for the settings used. The mean ${\sigma }_{\mathrm{OD}}$ for the T-R method (0.0041, range: 0.003–0.010) was slightly lower than that for transmittance or reflectance alone. The highest values were observed in all cases at shorter, UV and at longer, IR wavelengths and were mainly a function of the spectrophotometric precision. For wet filters [Fig. 3(b)], the mean ${\sigma }_{\mathrm{OD}}$ for transmittance was 0.0022 (range: 0.0015–0.005), whereas that for absorptance was again lower (mean: 0.0004, range: 0.0002–0.0010), and only slightly higher than the respective ${\sigma }_{\mathrm{OD}}$ for dry filters. For the T-R measurements the mean ${\sigma }_{\mathrm{OD}}$ was 0.0006 (range: 0.0004–0.0009), and at some wavelengths it was still higher than that for absorptance but significantly lower than that for transmittance alone and lower than the respective ${\sigma }_{\mathrm{OD}}$ for dry filters. A second set of experiments was conducted with filters prepared from different algal cultures to examine the variability in sample filters. The observed variability includes errors related to the filtration procedure (like filter homogeneity, filtered volume precision, and filter wetness) and to any filter-to-filter variability of the path-length amplification inside the filter. We measured seven to ten different filters through which the same volume of an algal culture was filtered. The regular procedure for the T-R technique was followed in such a way that we prepared filters with an ${\mathrm{OD}}_f^T$ between 0.1 and 0.3. For absorptance measurements we prepared filters with an ${\mathrm{OD}}_f^A$ between 0.01 and 0.1 (see below). The mean ${\sigma }_{\mathrm{OD}}$ for absorptance measurements of a particle sample was 0.0009 (range: 0.0003–0.0020, $n=10$) and was OD-dependent [Fig. 3(c)]. The mean relative error was 3.0% (range: 1.6%–5%) and less OD-dependent (note that the OD was $>0.01$ at all wavelengths used for this calculation). The mean ${\sigma }_{\mathrm{OD}}$ for the ${\mathrm{OD}}_f^T$ was 0.0051 (range: 0.0025–0.0076, $n=7$), and that for the ${\mathrm{OD}}_f^{TR}$ was 0.0023 (range: 0.0005–0.0057, $n=7$). In the NIR spectral region, for which no significant absorption is expected for an algal culture, the observed error for a sample filter was nearly the same as that for an empty, wet filter. In summary, in all cases (dry and wet, empty and sample-loaded filters) the highest variability, and thereby the largest error in determining OD, was observed for the transmittance and reflectance measurement, and the lowest for the absorptance measurement, with the error of the T-R method being lower than that for the transmittance measurement alone and slightly higher than that for the absorptance measurement. The error of the T-R method was notably higher than that of the absorptance measurement in the NIR spectral region, where it is particularly important to distinguish between absorption and scattering for baseline correction purposes. A smaller error would make the absorption measurement more accurate, potentially to the point where a null-point correction could be avoided. The relative errors of the ${\mathrm{OD}}_f^A$ and ${\mathrm{OD}}_f^{TR}$ were similar as higher filter loads were used for the T-R measurements. We will show later that lower filter loads are preferable to decrease influence of particle density on the path-length amplification.

 

Fig. 2. Optical density of empty glass-fiber filters, ${\mathrm{OD}}_f$, as a function of wavelength. Wet filters were soaked in water and then left drying for 10 to 40 min (dot-dashed lines). (a) Measurements against air of dry and wet filters in transmittance (upper six curves) and reflectance mode (lower two curves); (b) the same filters measured in absorptance mode inside an integrating sphere. Note the differences in the $y$ axis.

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Table 1. Standard Deviations of the Optical Density, ${\sigma }_{\mathrm{OD}}$, for Various Error Sources Given for the Full Wavelength Range and the Mean Over All Wavelengths^a

View Table

 

Fig. 3. Variation in optical density as a function of wavelength for filters from the same filter batch depicted as standard deviation, ${\sigma }_{\mathrm{OD}}$, for multiple measurements of (a) dry filters, (b) wet filters, and (c) filters prepared from an algal culture sample, measured as transmittance, $T$, as absorptance, $A$, and by the T-R method.

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B. NIR Absorption

The results described above make it obvious that simple transmittance measurements will generally only give correct absorption results if filter-to-filter variations are null-point corrected, using the OD at a wavelength at which negligible absorption can be assumed. The validity of this assumption can be assessed from measurements we performed during this exercise. We show results of the ${\mathrm{OD}}_f^A$ for an algal culture and a sample from the North Sea together with that of a reference filter (Fig. 4). Two different sample volumes were used for each sample: (1) to obtain a maximal OD below 0.1 [Fig. 4(a)] and (2) to obtain $\mathrm{OD}\gg 0.1$ [Fig. 4(b)] to increase the sensitivity in spectral regions with low absorption (i.e., NIR). The original measurements are shown without any corrections. It is evident that the algal culture does not posses any significant absorption at wavelengths $>730\mathrm{nm}$, as the OD at those wavelengths is not different from that of the reference filter even when high sample volumes are used, as in Fig. 4(b). In contrast, the natural sample showed significant absorption in the NIR spectral region, and in this case using higher sample volumes gave an OD up to 0.1 in the NIR region. A negligible NIR absorption can only be shown for pure algal cultures. Natural samples always contain higher amounts of detrital material that seems to absorb in the NIR region strongly. A scatter error correction (null-point correction) would, hence, always result in an underestimation of absorption. Considering the extent of the scattering error and the significant absorption in the NIR, simple transmission measurements of the particulate absorption can hardly be correct. At longer wavelengths the relative error of this method can be much larger.

 

Fig. 4. Raw OD versus wavelength spectra of an algal culture and a natural sample measured inside an integrating sphere (absorptance mode). Shown are filters of both samples with (a) a low filter load, and (b) an approximately $10\times$ higher filter load, together with the spectrum of a wet reference filter. No corrections were applied. Significant absorptance is observed in the NIR spectral region for the natural sample.

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C. Path-Length Amplification

To determine the effects of path-length amplification by multiple scattering inside the filter, we measured the absorption of different algal cultures and of a large set of samples taken during three cruises: one on the River Elbe down to the inner German Bight, one covering open ocean and coastal areas of the Baltic and the North Sea, and one crossing the Atlantic Ocean. Sample filters were prepared with different filtration volumes to obtain a maximum ${\mathrm{OD}}_f$ between 0.02 and 0.4. Samples from algal cultures were measured immediately after filtration. Natural samples were shock-frozen in liquid nitrogen, stored at $<-20°\mathrm{C}$, and measured about 2 weeks later. The theoretical absorption coefficient ($a^{\beta =1}$) is determined using the specific sample volume and filter clearance area but ignoring path-length amplification. To determine the individual amplification factor, $\beta$, for each filter, we measured the presumably real particulate absorption coefficient, $a$ [$m^{-1}$], with a point-source integrating-cavity absorption meter (PSICAM, spectral range 400–720 nm) [5,36]. Particulate absorption with the PSICAM was determined by measuring the total absorption of all water constituents and subtracting the absorption of the specific sample filtrate (glass-fiber filter, particle size $<\sim 0.7\mathrm{\mu m}$). The filtration was done carefully under low vacuum to avoid cell breakage. The absorption of the filtrate was relatively low compared to the particulate absorption, errors in particulate absorption determination by cell breakage are considered to be negligible, and the overall error is in the range of a few percent only (see [5,36]). Figure 5 shows the absorption coefficient of a culture and the theoretical absorption, $a^{\beta =1}$, observed on a filter measured as absorptance, transmittance, and reflectance, together with that for the T-R calculation (using the tau formulation of [21]). The highest values for $a^{\beta =1}$ were obtained when the filter was measured in reflectance mode $R$, the lowest for the T-R method. Measurements in transmittance mode were higher than that of the T-R method, whereas the absorption determined as absorptance was lower than that measured as reflectance. The absorption obtained by the T-R method was more than twice the real absorption, while the absorption determined as absorptance was about five times the real absorption. These differences in $a^{\beta =1}$ are the result of differences in path-length amplification for transmitted and reflected light, the effect for reflected light being about double that for transmitted light. Next we show the results of a first experiment with different filter loads, i.e., different volumes of the same algal culture filtered onto separate filters. There is general agreement in the literature that the OD for a sample filter (compared to that of a reference filter) should not be too high (e.g., $<0.4$ [19]). On the other hand, Tassan and Ferrari [21] found indications of a nonlinear relationship between OD and the path-length amplification factor when $\mathrm{OD}>0.4$. A set of filters was prepared with the maximal ${\mathrm{OD}}_f^T$ between 0.04 and 0.3 (i.e., ${\mathrm{OD}}_f^A$: 0.06–0.46), and for each filter the transmittance and absorptance were measured [Fig. 6(a)]. The theoretical absorption coefficients calculated for each of these samples was not constant but decreased with increasing sample volume in both cases; it was between two and three times higher than the real absorption coefficient when measured as transmittance, and three to five times higher when measured as absorptance [Fig. 6(b)]. However, the relative difference between filters with different sample volumes was the same for both kinds of measurements, as the two theoretical absorption coefficients, $a_T^{\beta =1}$ and $a_A^{\beta =1}$, are linearly correlated [Fig. 6(c); for this comparison the transmittance measurements had been null-point corrected]. The amplification for absorptance measurements was again about 1.5 times higher than for transmittance independent of the filter load and, hence, absolute ${\mathrm{OD}}_f$. However, when these theoretical absorption coefficients were plotted against the real absorption coefficient, only the filter with the lowest filter load showed a good linear correlation [Fig. 6(d)], with an amplification of 4.59 ($r^2=0.9987$). With increasing filter load the relationship deviated increasingly from linearity and showed a dependence on the absolute OD (not on the wavelength), probably induced by densely packed particles. This OD-dependent amplification has been regularly observed in other studies and is normally compensated by an OD-dependent amplification correction factor, $b=1/\beta$, using, e.g., a second order polynomial function (e.g., [19,25,37]). In the experiment presented here, changes in path-length amplification with OD can already be observed in the range of 0.1 to 0.3 (${\mathrm{OD}}_f^T$), but below 0.1 the deviation from linearity is insignificant. Thus, another set of filters was prepared with lower filter loads, and the OD of these filters was then measured as transmittance, absorptance, and reflectance (Fig. 7). The maximal value of ${\mathrm{OD}}_f^A$ was now between 0.02 and 0.11 [Fig. 7(a)]. The corresponding theoretical absorption at each wavelength, $a_A^{\beta =1}$, for these samples was rather constant, with only the highest filter load showing a 10% lower value; it was about five times higher than the real absorption [Fig. 7(b)]. The absorption coefficient was also calculated using the T-R method (small deviations at $>750\mathrm{nm}$ for $T$, $R$, and T-R measurement were null-point corrected). The $T$, $R$, and T-R theoretical absorption values exhibited strong linear correlations with $A$ measurements [Fig. 7(c)], with different slopes for each set of measurements and some artifacts for $a_T^{\beta =1}$ and $a_R^{\beta =1}$ that were a consequence of the much lower OD obtained with these methods and, hence, lower signal-to-noise ratio. The T-R method showed a much better correlation to $A$ measurements than $T$ and $R$ measurements alone as a result of compensation for filter-to-filter differences. Plotting theoretical absorption coefficients against the real absorption coefficient showed good linear correlations for each measurement mode [Fig. 7(d)]. The highest correlation coefficients were obtained for absorptance measurements and for T-R, as those techniques respectively avoid or compensate for filter-to-filter variability. The resulting amplification factor was again highest for the absorptance measurement (it was higher for reflectance measurements, but these were not used here to obtain absorption), with a factor of 5, and lowest for the T-R method, with a factor of 2.3. Figure 7(d) shows that there was still some systematic effect of increasing filter load (i.e., OD) on path-length amplification even for these reduced sample loads. However, if the maximal ${\mathrm{OD}}_f^A$ of the sample filter was below 0.1, the variability in amplification was below 5%. Filter load experiments with natural samples from the Elbe River that had high amounts of detrital material showed similar results and a constant amplification for the same sample when different sample volumes were used and ${\mathrm{OD}}_f^A$ was kept below 0.1 (data not shown). The above experiments demonstrated clearly that OD needs to be kept very low in order to have a constant path-length amplification effect over all wavelengths and over all OD. Standard errors for simple transmittance measurements at low ODs are too large to use the results without a null-point correction, which we have seen may not be justifiable for natural samples. Precise measurements can only be provided by $A$ and T-R methods, the latter still being more susceptible to filter-to-filter variation in OD. The following comparison was, thus, made for the $A$ and T-R method only. A large set of sample filters was used to examine the variability of the path-length amplification in filters prepared from algal cultures and from natural water samples. The real absorption coefficient was determined again using a PSICAM. Ten different algal cultures were used for absorptance measurements, but only six cultures for the T-R measurements. Algal species were chosen that did not show any absorption artifacts induced by the filtration procedure. For example, species that contain water-soluble phycobilin proteins lose some of these pigments during filtration, and the corresponding loss in absorption induces strong artifacts in the correlation plot, sometimes observed as a hysteresis (e.g., [24,26]). We were able to observe this in detail by comparing filter absorption spectra with PSICAM spectra (data not shown). Filters were prepared in replicates with the same sample volume and averaged. In addition, different sample volumes were used to prepare several sets of filters from the same culture. In all cases the correlation between the calculated theoretical absorption and the real absorption was highly linear ($r^2=0.987-0.999$, linear regression forced through the origin). However, the slopes of these linear regressions (i.e., $\beta$) were highly variable and between 3.5 and 5.4, with a mean of 4.50 ($n=23$) for the absorptance measurements and between 2.2 and 2.8, mean 2.39 ($n=15$) for samples measured using the T-R method [Fig. 8(a)]. We did not examine species-specific differences in detail, but in both cases lowest values were observed for diatoms (Bacillariophyceae) and highest values for nondiatom species without any correlation to cell size. As the variability in the amplification factor for algal culture samples was rather large, we examined the variability from filters of natural samples in more detail. Samples from natural waters were taken from the River Elbe with high amounts of detrital material and from the Baltic Sea, the North Sea, and the Atlantic Ocean. The comparison of the T-R method was only done with samples taken in the Atlantic Ocean to minimize the influence by absorption of detrital material, thereby avoiding problems with null-point correction. Figure 8(b) shows the result of all measurements in absorptance mode ($n=31$) and with the T-R method ($n=34$). In general the linearity of the correlation for each sample was as good as for culture samples. The amplification for the T-R method varied between 2.0 and 3.2 (mean 2.50), while for the absorptance measurements it varied between 3.8 and 5.1 (mean 4.47). Compared to the amplification factors from algal cultures, the variability was higher for the T-R method, but lower for the absorptance measurements. However, the mean value was the same for absorptance measurements of algal cultures (4.47 versus 4.50), but somewhat higher for the T-R method (2.50 versus 2.39). On a relative basis the amplification for the T-R method ranged between 80% and 128% of the mean; for the absorptance measurements, it ranged between 86% and 113%. The reasons for these variations have not been examined in detail but are currently considered to be natural variability induced by the physical and optical properties of the particles collected on the filters. However, we were aware that lab measurements with cultures were done by measuring the OD of the filters directly after filtration on a dry filter, whereas for natural samples the filters were measured after the filters were stored, and the filter could be considered to be soaked in water for a much longer time. With a single culture we tested whether a longer soaking of empty filter in water has an influence on the path-length amplification by measuring samples on filters that were not soaked in water before filtration and filters that were soaked before for $>1\mathrm{h}$. The OD for the same amount of culture measured on previously soaked filters was about 10% higher than that measured on filters that were not previously soaked (data not shown), indicating that path-length amplification is depending on the optical changes in filters induced by soaking glass-fiber filters in water.

 

Fig. 5. Example for the influence of the path-length amplification on the absorption coefficient determined for different optical setups. The true spectral absorption coefficient as a function of wavelength of an algal culture, $a$, is shown together with theoretical absorption coefficients $a^{\beta =1}$ (i.e., not corrected for path-length amplification) for measurements in modes $A$, $T$, and $R$ and for T-R (see text for details).

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Fig. 6. Filter load experiment 1. (a) ${\mathrm{OD}}_f$ as a function of wavelength measured as absorptance, $A$, and transmittance, $T$, with increasing filtered volume, $V$. (b) Calculated theoretical absorption coefficients without correction for path-length amplification, $a^{\beta =1}$. The real absorption coefficient, $a$, measured using a PSICAM is shown for comparison. (c) $a_A^{\beta =1}$ plotted against $a_T^{\beta =1}$. (d) $a_A^{\beta =1}$ plotted against $a$. Linear regression statistics are shown. Arrows denote response to increasing filter load.

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Fig. 7. Filter load experiment 2. (a) ${\mathrm{OD}}_f$ as a function of wavelength measured as absorptance, $A$, for increasing filtered volume from 10 to 60 ml. (b) Calculated theoretical absorption coefficient without correction for path-length amplification, $a_A^{\beta =1}$. The real absorption coefficient, $a$, measured using a PSICAM, is shown for comparison. (c) $a_A^{\beta =1}$ plotted against $a_T^{\beta =1}$, $a_R^{\beta =1}$, and $a_{T\text{-}R}^{\beta =1}$, for the samples with 10, 15, and 30 ml only. (d) $a_A^{\beta =1}$, $a_T^{\beta =1}$, and $a_{T\text{-}R}^{\beta =1}$ plotted against $a$. The lower curves for each mode are those with the highest filter loads of 45 and 60 ml.

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Fig. 8. Theoretical absorption coefficient, $a^{\beta =1}$, measured as absorptance, $A$, and by the T-R method, plotted against the real absorption coefficient, $a$, (a) for algal cultures ($A$: $n=23$; T-R: $n=15$) and (b) for natural samples ($A$: $n=31$; T-R: $n=34$). Indicated are the mean slopes (i.e., the mean amplification factor). The data are normalized to the maximum of $a$ of each data set to compensate for differences in the maximum absorption of each sample.

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4. Discussion

Some optical properties of glass-fiber filters have been described elsewhere (e.g., [21,28]). A first striking difference among transmittance, reflectance, and absorptance measurements is the absolute optical density of a dry empty filter [Fig. 2(a)]. Whereas ${\mathrm{OD}}_f^T$ was very high ($>1.2$), values for the reflectance and absorptance methods were about two to three orders of magnitude lower. Dry glass-fiber filters possess strong backscattering that leads to low light transmission through the filter and high reflectance. The low absorptance of dry filters is, thus, a first indication that the setup proposed here is not sensitive to scattering by the filter. When calculating the sum of transmittance, reflectance, and absorptance at each wavelength, values between 100% and 101% were obtained, supporting the validity of the measuring concept used. When filters were soaked in water and measured wet, the transmittance decreased and the reflectance increased, whereas the absorptance changed only slightly (as a result of the change in filter reflectance relative to the reflectance standard). From this we can deduce that the overall T/R ratio of a filter is different for dry and wet filters, and as a result transmittance and reflectance measurements are highly dependent on the wetness of the filter. For $T$ and $R$ measurements, filters need to be measured fully soaked with water to have constant optical conditions; any drying of the filter needs to be avoided. Roesler [28] observed an increase in $T$ with a drying filter after about 4 min and could regain the initial $T$ by adding water to the filter. In addition, soaking a dry filter changes its T/R ratio constantly for the first 60 min after placing the filter in water before it reaches a constant value. This is known, and soaking for about1 h is recommended for the T-R method [21]. In contrast to the above, the absorptance of a filter does not change significantly with time when soaking in water, and the absorptance of a wet filter is not much different from that of a dry filter. The absorptance shows a low absorption signal from water inside the filter at wavelengths $>700\mathrm{nm}$ (clearly seen at wavelengths $>900\mathrm{nm}$ per personal observation). The overall error for sample measurements was examined for the different optical setups ($A$, $T$, and T-R). This was done with an algal culture that did not possess significant absorption in the NIR spectral region. The largest error was found for the transmittance measurement and the lowest for the absorptance measurement. As different filter loads were used for each setup, it is more appropriate to look at the relative error for those wavelengths for which significant absorption can be assumed ($\mathrm{OD}>0.01$). This relative error was again largest for the transmittance measurement (mean 4.5%) but equally low for the absorptance and T-R measurements (mean: 3.0% and 2.8%, respectively). However, the error in the NIR spectral region, where no absorption by the algal sample was observed, was lowest for the absorptance measurement, and for each method was very similar to the error for empty filters (Fig. 3). The overall error for the T-R method reported by Tassan and Ferrari [21] (see Table 1) was very similar to our measurements (${\sigma }_{\mathrm{OD}}$: 0.0020 versus 0.0023), but the variability in the ${\mathrm{OD}}_f$ of empty filters was higher (${\sigma }_{\mathrm{OD}}$: 0.0015 versus 0.0006). The errors for $T$ and $R$ measurements were also higher (e.g., ${\sigma }_{OD,T}$: 0.0050 versus 0.0022). Compared to the transmittance measurement in front of an integrating sphere, changes in attenuation induced by the water content of the filter are much lower when the filter is measured inside the sphere. Less care has to be taken with respect to the water content and soaking of a reference filter. However, differences in the water content might change multiple scattering inside the filter, and with it the path-length amplification. Because of this strong dependence on the water content of the filter and generally higher sensitivity to filter-to-filter differences, variability of ${\mathrm{OD}}_f$ in wet filters is relatively high for transmittance measurements, making the application of a null-point correction often necessary. The T-R method showed much lower variability in calculated ${\mathrm{OD}}_f$, because the additional reflectance measurement is used to compensate for filter-to-filter variability in transmittance and it compensates for changes in backscattering by sample particles like minerogenic particles (for which it was originally developed [37]). When the filters are measured inside an integrating sphere, this variability is reduced even further, the null-point correction is obsolete, and ${\mathrm{OD}}_f^A>0.0008$ can be considered as significant absorptance. As the small methodological error for measurements in the center of an integrating sphere also applies for the NIR (700–890 nm) spectral region, NIR absorption can be determined quantitatively, something that could not be achieved with this accuracy using other methods yet (e.g., [12,14,15]). However, at longer wavelengths ($>900\mathrm{nm}$), strong absorption by water itself will lead to significant error. With respect to the error in the NIR, transmittance measurements will often need a null-point correction, and the T-R method will not fully compensate for variability at NIR wavelengths, whereas the absorptance measurement will not need any null-point correction and should therefore be more accurate in the NIR spectral region. When NIR absorption is high, the T-R method can be used for measurements of absorption in the NIR region as well (see [16]). In terms of measurement effort, the T-R technique needs an additional measurement (the reflectance of the filter) and a complex calculation scheme with additional empirically measured factors (tau) and additional assumptions regarding the equality in overall transmission of sample and reference filter (see [21] for details). Furthermore, T-R measurements, even when conducted very carefully, often exhibit exceptionally strong differences in OD for particular reference filters, visible by an OD higher than the mean OD by more than 3 standard deviations. These filters were not used for the earlier calculations of ${\sigma }_{\mathrm{OD}}$ (see [21]). Differences in ${\mathrm{OD}}_f$ are wavelength independent and could therefore be compensated by null-point correction. However, that would exclude the possibility of performing measurements of absorption in the NIR spectral region. Including results from these “bad” filters in the error calculation would increase ${\sigma }_{\mathrm{OD}}$ only slightly for the T-R measurement. Therefore, we would not recommend any null-point correction for the T-R method, but when performing measurements with low NIR absorption, multiple reference and sample filters should be measured to avoid potential influence from a single “bad” filter. The ${\mathrm{OD}}_f$ of these “bad” filters when measured as absorptance was not different from other reference filters and, hence, did not represent an additional error source for this technique.

A. Path-Length Amplification

The remaining and major uncertainty for these measurements is related to the optical path-length amplification inside the filter. The amplification factor, $\beta$, has been determined several times by determining the real absorption, mainly by using algal cultures, in a photometric cuvette (e.g., [19,20,23–27]) or using an AC-9 instrument [28]. In most cases $\beta$ was observed to be dependent on the OD, and the obtained relationships were described using, e.g., a second order polynomial. Roesler [28] proposed a constant factor of 2 for all ODs and wavelengths, arguing that any deviation from linearity in the relationship of $\beta$ versus OD or wavelength was artificial due to measurement errors related to scattering losses when determining either the real or the filter pad absorption. Several filter load experiments showed that $\beta$ was dependent on $O{D}_f$ [33,38]. This dependence is observed in our experiments as well when ${\mathrm{OD}}_f$ is high. However, when ${\mathrm{OD}}_f$ is low, the variation in amplification with ${\mathrm{OD}}_f$ is insignificant. When ${\mathrm{OD}}_f$ is high, the probability for particle self-shading is high. This self-shading can only be avoided by measuring sample filters with low ${\mathrm{OD}}_f$. The methodology used here to determine the true absorption (PSICAM) does not have a significant scattering error due to the integrating cavity design and is, as well, not affected by particle self-shading under the low particle concentrations used. The same low scattering error can be assumed for the same reason for the absorptance measurements inside the spectrophotometer’s integrating sphere. The linear correlation of the transmittance and absorptance measurement for a single filter [see Fig. 6(c); $r^2=0.9991$] shows that transmittance and T-R measurements are subject to very low wavelength-dependent scattering error. Decrease of $\beta$ with increasing OD is therefore not an artifact induced by scatter losses but is mainly induced by self-shading of the particles inside the filter when the filter load is too high. When filter load and, thus, OD are low, the ${\mathrm{OD}}_f$ is a rather linear function of absorption [Fig. 7(d)], and there is only a small range in $\beta$ for each filter absorption measurement mode. However, $\beta$ is much higher when the filter is measured inside the sphere than when it is measured using the T-R method. Path-length amplification also has a different effect on the ${\mathrm{OD}}_f$ for transmittance and reflectance measurements. Reflectance measurements showed, rather exactly, two times the amplification of transmittance measurements. In transmittance mode only light that leaves the filter in the forward direction is collected, so the absorption is determined from this signal only, as light totally reflected by the filter is not collected by the detector whether it gets absorbed after being reflected or not. When measuring in reflectance mode, the situation is the opposite. The optical situation inside a filter is complex as the parallel light beam entering the filter becomes increasingly diffuse, so, the relative amount of diffuse light collected is higher for reflected light. The path-length amplification for reflectance measurements could be higher because the particles are not homogeneously distributed inside the filter but are concentrated on one side of the filter. From the assumption that the filter acts as a good light diffuser, Roesler [28] proposed that amplification for the transmittance measurement should be about 2. Following this approach, the amplification for the filter measured in absorptance mode should theoretically be double, i.e., 4. Our measurements showed that amplification for absorptance measurements was not double compared to the transmittance mode but was instead higher by a factor of about 1.5 [see Fig. 6(c)]. Despite the differences in amplification between measurement modes, our experimental data showed that any of the modes tested provided absorption data without significant scattering error and that the only error sources were the amplification factor and the filter-to-filter variability. Thus, for algal cultures (for which it is safe to assume zero NIR absorption [12]) the transmittance measurement provides a good proxy for absorption measurements without wavelength-dependent artifacts by scattering when filter-to-filter variations are compensated by a null-point correction and the individual amplification effect is known. Proper knowledge of the amplification factor makes data from any of these measurement modes valuable. However, we showed that the variability of the amplification factor was rather large for algal cultures. For the T-R method it ranged from 2.0 to 3.2, and for the absorptance measurement it ranged from 3.5 to 5.4. For natural samples the variability in $\beta$ for the absorptance measurements was lower, with $\beta$ ranging from 3.8 to 5.1 only. At least for natural samples, the amplification effect for absorptance measurements is about double that for T-R measurements, but on a relative basis it is less variable. Only a small part of the observed variation can be explained by errors made in either the PSICAM or the QFT measurements. Under lab conditions the PSICAM is very accurate [5]. (However, in the field, calibration of the PSICAM can lead to error as large as 5%.) In this case we observed large variability in amplification factors for natural samples and cultures when PSICAM measurements were very accurate. Describing the light field inside a sample/filter composite is rather complicated and influenced by (1) the parallel light beam that becomes increasingly diffuse as it penetrates through the filter, (2) the spatial allocation of particles inside or on the filter, and (3) the individual scattering properties of the particles. As (2) and (3) influence (1), a constant amplification factor is unrealistic. It was not the intention of the work presented here to examine whether the amplification depends directly on specific optical properties of the particles sampled. Nevertheless, we observed some specific details in the measurements of algal cultures. For example, the amplification effect was always lowest for diatom species and higher for nondiatom species. The high variability in amplification observed for algal cultures could, therefore, result from the use of cultures from quite different algal groups. A second source for this larger variability could be the use of filters that were not previously soaked in water, as this pretreatment influences path-length amplification as well. Considering the possible errors, an amplification factor of 4.5 can be used for the measurements inside an integrating sphere, resulting in a maximal relative error from sample to sample variability in amplification of $\pm 14\%$ for natural samples. For the T-R method a mean amplification factor of 2.45 would have a maximal relative error of about $\pm 25\%$. The natural samples came from quite different environments, like coastal and offshore waters from the North and the Baltic Sea, from a river, and from the Atlantic Ocean. Nevertheless, when optical properties of the particles collected play a role in this variability, the overall error by this variability could be larger in other environments. The exact determination of the path-length amplification factor remains the major error source in the quantitative filter technique, as most other measurement errors can be reduced by the use of absorptance measurements inside an integrating sphere. Of course there are other, previously documented problems with the QFT that do further increase its uncertainty (see [29–32]). However, the exact path-length amplification can be determined with a PSICAM measurement for each individual sample. In coastal waters with high particle concentrations, the PSICAM would actually give better results, but in oligotrophic waters its sensitivity is limited. However, even in these waters the absorption at $\sim 442\mathrm{nm}$ is high enough to be measured with good precision with the PSICAM, and this measurement could be used to determine the individual amplification factor across the spectrum. All our results support the fact that the amplification factor is constant over wavelengths for a single filter (if ${\mathrm{OD}}_f<0.1$). Despite variability of the amplification factor, the accuracy of the whole procedure can be elucidated from measurements of an algal culture with negligible absorption in the NIR spectral region and a natural sample with significant NIR absorption. In the case of the algal culture, the OD in the NIR region does not differ from that of the reference filter, even when the maximal OD is ten times higher than recommended. For the natural sample the NIR absorption is much higher than the proposed sensitivity limit of 0.0008. We therefore propose that this method can be used to determine the particulate absorption in the NIR spectral region with high accuracy, especially considering that the path-length amplification is wavelength independent (for low OD) and is therefore the same for the VIS, UV, and NIR spectral region.

5. Conclusions

The commonly used technique to measure the absorption of a filter in transmittance mode performs much worse in terms of sample-to-sample (and filter-to-filter) variability than a measurement in the absorptance mode inside an integrating sphere. The transmittance mode can hardly be used for filters with low ${\mathrm{OD}}_f$ without a null-point correction of the spectrum. Unfortunately, it is precisely under the condition of low ${\mathrm{OD}}_f$ that the influence of path-length amplification is wavelength and $\mathrm{OD}$ independent. However, we did not observe any wavelength-dependent artifacts induced by scattering (see measurement of an algal culture) but a rather wavelength-independent shift that would allow a null-point correction for algal cultures that do not possess absorption in the NIR. On the other hand, we showed that the T-R method compensates for a variability that is related to differences in the T/R ratios of different filters, and of sample and reference filters. It can be used (for the UV to NIR spectral range) without a null-point correction in cases where NIR absorption is high. However, T-R measurements were found to be susceptible to the effect of “bad” filters that are occasionally encountered, and appropriate precautions are required. The proposed measurement of particles retained on glass-fiber filters inside an integrating sphere has some advantages compared to the other two techniques: (1) the overall precision is high, as many variations in the OD measurements that are related to errors due to backscattering and to varying filter scattering properties (moisture, thickness, structure, etc.) are avoided, (2) no null-point correction is needed, hence, (3) the higher precision and lower absolute error allow more precise measurements in the NIR region, where absorption is sometimes relatively low, (4) the variation of the path-length amplification and, hence, the error due to this variation is reduced to a maximum of $\pm 14\%$ for natural samples (we showed that with low filter loads $\beta$ is rather constant for a single filter; however if OD is higher, a nonlinear ${\mathrm{OD}}_f$ to $a$ relationship of $\beta$ can be used but will increase the overall error), (5) as the path-length amplification effect is a factor of 2 greater than for the T-R method, less material is needed to obtain the recommended ${\mathrm{OD}}_f$, (6) the workload is reduced to a single scan compared to the T-R method and less care has to be taken for preparing the reference and sample filters. Critical for all QFT methods is the variability and nonlinearity of the path-length amplification in the filter at higher filter loads. The sources for this variability have to be examined in more detail. As spectrophotometers with large integrating spheres are commercially available and becoming more commonplace, we expect that with the described method the overall accuracy of the determination of the particulate absorption will strongly increase and that, e.g., remote sensing data can be improved in the future, as the algorithms require highly precise measurements of the inherent optical properties, like particulate absorption. The combination with PSICAM measurements allows determination of amplification factors individually for single filters and cross-validation of both methods. It combines a method with theoretically unlimited sensitivity (QFT) with one that does not need additional sample treatment like filtration, freezing, or storage (PSICAM). The overall error for determination of particulate absorption in natural waters could most probably be reduced to values below 5%.