1. Introduction

Knowledge about water temperature, in both freshwater and marine environments, is of great importance in fields such as oceanography, climate change, waterway health and defense. Satellite imagery is routinely used for measurement of sea surface temperature, yet methods for vertical profiling of water temperature are typically limited to the use of expendable probes or submersing strings of thermocouples. Hence a practical remote sensing method compatible with surface, subsurface or airborne platforms for rapid depth-resolved water temperature measurement would benefit many fields. One such approach to achieving this is remote sensing based on Raman spectroscopy of water, using methods that were first investigated by Chang and Young in 1972 [1].

The Raman spectra of liquid water exhibit subtle but significant changes depending on water temperature [2, 3]. This temperature dependence is observed in the broad spectral band from 2900 to 3900 cm⁻¹, which arises from symmetric and asymmetric stretching vibrations of OH bonds within clusters of hydrogen-bonded H₂O molecules. It is the instability of the hydrogen bonds, which are continually breaking and re-forming that is generally understood to give rise to temperature-dependent spectra [4]. As the temperature increases, the Raman spectra are altered around isosbestic points in each spectra [5, 6]. The spectra for Raman-scattered light polarized parallel and perpendicular to the polarization of the excitation laser are different; the spectra with parallel polarization are dominated by two peaks at approximately 3250 cm⁻¹ and 3400 cm⁻¹, while the perpendicular polarization has one dominant peak at around 3460 cm⁻¹. There are two main techniques that have been used for analyzing water Raman scattering to deduce temperature, and these are known as the “two-color” technique and the “depolarization” technique. In the former, unpolarized Raman-scattered light is analyzed to measure the ratio of amplitudes corresponding to the two main peaks which is then analyzed to estimate water temperature. For the latter technique, the Raman signal is separated according to polarization and the ratio of emission intensities for orthogonal polarization states is measured. In both of these techniques a ratio is measured which varies proportionally with water temperature, enabling calibration to independently-measured reference temperatures in order to produce predictive models.

The application of Raman spectroscopy to remotely sense water temperature has been investigated by several research groups, for example [7–10], with detailed investigations reported by Chang [1, 11] and Leonard [12, 13] in the 1970s. Chang et al reported temperature sensitivities of the measurands to be approximately 1-1.7% per °C, and it was predicted that it would be feasible to measure water temperature to depths of 10-100 m from an airborne platform. Leonard et al [13] investigated practical considerations for airborne remote sensing. However the potential of this early work has not to our knowledge been realized in practice, and we note that there have been major advances in detectors, LIDAR and statistical methods since those times.

In most studies, full Raman spectra have been recorded to which a series of Gaussian or Voigt line-shapes are fitted, and these are then analyzed to determine water temperature. However such an approach is not suited to rapid vertical profiling of water temperature. Recently a detailed investigation was reported by Oh et. al. [7] who recorded and analyzed full Raman spectra using two methods (with and without spectral decomposition) to compare the accuracy with which water temperature could be predicted, and achieving temperature accuracies of ± 0.2 °C.

In this paper we report detailed experimental measurements of unpolarized Raman spectra as a function of water temperature. In the first (main) part of the paper, the unpolarized Raman spectra temperature-dependence has been carefully analyzed to identify the spectral features which are most sensitive to changes in temperature, and those which can be used to predict temperature most accurately, without the need for spectral decomposition. This analysis has then been used to inform the design of a simple, two-channel optical system which will ultimately be used to explore the prospects for near real-time depth-resolved field measurements of water temperature. The second part of the paper concerns a “proof of concept” study, in which a two-channel Raman spectrometer has been constructed and used to predict/determine temperature in a 1 m length cell of mains supply water with an accuracy of ± 0.5 °C. This preliminary finding is a first step towards practical implementation of the main findings in this paper.

2. Measurement of temperature-dependent water Raman spectra

Polarized and unpolarized Raman spectra for reverse osmosis filtered water (Boss Watermax RO) were measured for water temperatures ranging from 10 to 50 °C. Reverse osmosis filtered water was used rather than deionized water to minimize sample variability over the time taken to acquire the full set of spectra. A custom-built aluminum cell with an AR coated BK7 window and a volume of ~1 mL was used to contain samples during spectral measurements. The water temperature was actively controlled using a Peltier element attached to the cell in combination with a temperature controller (Newport 350B), and a 10 kΩ thermistor for feedback with an accuracy of ± 0.2 °C. Spectra were collected using a dispersive Raman spectrometer (Enwave EZRaman-I) which has a spectral resolution of 8 cm⁻¹, and uses a frequency-doubled, linearly polarized, CW Nd:YAG laser (30 mW at 532 nm) for excitation. An aspheric lens with 0.3 NA and a 7 mm working distance was used to couple excitation light into the sample and collect the Raman signal.

The signal detection path was collinear with excitation, i.e. the 180° backscattered Raman signal was collected, and polarizers could be introduced into the Raman signal beam path to obtain polarized spectra, i.e. the Raman signals having polarization parallel or orthogonal to the polarization of the excitation laser. Figure 1 shows the experimental setup used.

 

Fig. 1 Experimental setup for collection of water Raman spectra.

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Wavelength calibration of the spectrometer was carried out using an acetonitrile (CH₃CN) reference sample. The acquisition time for each spectrum was 30 seconds, and the corresponding RMS standard deviation for several acquisitions at peak signal was ~35 counts. Three scans were averaged for consistency. Spectral data were smoothed with a Savitsky-Golay algorithm to reduce noise (2nd order, 25 point window).

Both linearly polarized and unpolarized Raman spectra exhibit temperature-dependence, as detailed in [5], and accordingly there is potential to relate water temperature to a ratio of the signals at two emission wavelengths (one on each side of the isosbestic point) or the ratio of the integrated polarized Raman signals, as denoted in the introduction as the two-color ratio method and the depolarization ratio method. For our particular Raman spectrometer, in which it was necessary to physically exchange polarizing filters in order to select the polarization, there were errors of repeatability which were found to have a significant adverse impact on the accuracy with which temperature could be determined. As a consequence, we focused our studies on an analysis of the unpolarized Raman spectra, with a view to using the two-color ratio method to determine temperature.

Unpolarized Raman spectra displaying the OH stretching band for eight temperatures are shown in Fig. 2(a). The vertical axes of plotted spectra are given in terms of signal counts registered by the spectrometer (more specifically, these correspond to the CCD counts corrected for grating and detector spectral response), and have not been normalized in any way. The behavior of the stretching band is clearly defined in response to temperature change, with an isosbestic point (point of equal scattering) observed at ~3422 cm⁻¹, which is consistent with the published value of 3425 cm⁻¹ found in the literature [6, 14]. The temperature isosbestic point is relatively insensitive to the angle between excitation and scattering axes [14]. The rate of change of Raman intensity variation with water temperature is shown in Fig. 2(b) where it can be seen that the points of greatest temperature response are observed at 3182 cm⁻¹ and 3542 cm⁻¹. We will refer to these as the “A” wavenumber pair. The largest change of intensity with increasing temperature was negative, −171 counts per °C, which occurred at 3182 cm⁻¹, while at 3542 cm⁻¹, a positive intensity change of 85 counts per °C was observed.

 

Fig. 2 (a) Unpolarized Raman spectra of RO filtered water with varying temperature. (b) Variation in unpolarized Raman signal intensity in response to temperature change.

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Based on these observations, there are multiple means by which temperature may be quantitatively deduced from the Raman spectra of water. The simplest possible scheme would be a measurement of intensity at a single point, or over some wavelength range, with a regression relating Raman intensity to reference temperature values. Practically however, this approach would have serious failings because spontaneous Raman scattering in water is relatively weak, and ambient light, scattering from suspended particulates and fluorescence from organic matter would adversely impact the accuracy of temperature determination.

Accordingly, it is desirable to use some sort of ratio of quantities in order to overcome these issues, and in the remainder of this paper we focus on the two-color ratio method, which involves a ratio of Raman signals corresponding to Raman shifts on either side of the isosbestic point. This approach is well suited to our long-term goal of near-real-time remote sensing of water temperature because a ratio of signals at two wavelengths can be readily acquired using filters and high-speed photodetectors.

3. Spectral analysis relating to temperature sensitivity

In this section we analyze the spectral data in Fig. 2(a) with a view to identifying the pairs of wavenumber shifts whose ratio gives rise to the greatest sensitivity to temperature. We then extend the analysis to consider the case where the Raman signals are integrated over two wavenumber “channels”.

We begin by explaining the need to mean-scale the two-color ratio temperature sensitivity. Intuitively the spectral regions exhibiting maximum intensity variation with temperature might be expected to produce the two-color ratio with the maximum variation. However, it is necessary to consider that low intensity values in the denominator of the ratio will result in larger ratio values, and vice versa for the numerator. To account for this, the two-color ratio values were scaled by the mean of all two-color ratios value over the temperatures investigated. The gradient of these scaled ratios with changing temperature gives a parameter we term the “mean-scaled two-color ratio temperature sensitivity”:

where R represents the set of two-color ratio values, and T is the set of corresponding temperature values. The difference between mean-scaled and non-mean-scaled sensitivities is relatively small (typically <10%), but is significant when it comes to comparing the sensitivities achievable for different wavenumber pairs.

To determine the optimal wavenumber shifts which yield the highest mean-scaled two-color ratio, the mean-scaled two-color ratio was computed, using Matlab, for all wavenumber pairs (data interval 2 cm⁻¹). The results are mapped in Fig. 3 as a function of Raman shift on the “high” and “low” sides of 3400 cm⁻¹. The color scale on the right-hand side indicates the mean-scaled two color ratio temperature sensitivity. The maximum mean-scaled two-color ratio sensitivity is found to be 1.48% per °C for wavenumber shifts around 3120 cm⁻¹ and 3586 cm⁻¹, and we will refer to these points as the “B” wavenumber pair. For comparison, the “A” points are also indicated; the corresponding temperature sensitivity shown was slightly lower, at 1.26% per °C.

 

Fig. 3 Temperature sensitivity of the mean-scaled two-color ratio for unpolarized Raman spectra with varying shift positions. Wavenumber pairs A and B are marked.

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While the analysis presented above enables temperature sensitivity to be visualized for each spectral data point (data interval 2 cm⁻¹), a practical remote sensing system will require the Raman signal to be integrated over a “channel” of wavelengths and it is necessary to take the relative signal intensity into account when selecting the optimal bands for determining temperature. This is not such a concern for strong Raman emission under laboratory conditions, but may prove crucial in terms of in situ remote sensing, where we can anticipate a trade-off between maximum temperature sensitivity and signal intensity, depending on the signal to noise ratio in the system.

To explore this trade-off, we transition to the use of channels centered at 3120 cm⁻¹ and 3586 cm⁻¹, i.e. the “B” wavenumber pair, and consider the effect of varying channel width on temperature sensitivity and signal intensity. The Raman signal was integrated over successively larger channel widths (from 2 cm⁻¹ to 300 cm⁻¹) and the integrated intensity for each channel and the mean-scaled ratio temperature sensitivity were calculated. Selected results are shown in Table 1.

Table 1. Effect of channel width on mean-scaled ratio temperature sensitivity and integrated signal intensities (channels centered on the “B” wavenumber pair).

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Increasing the channel width over the range shown here reduces temperature sensitivity by a factor of 2.8, while the integrated signal intensities for both channels increase by a factor greater than 300. In practice, the optimal channel width will be a compromise between temperature sensitivity and signal strength, and selection will depend on many factors including laser source, receiver and detector characteristics.

A map of mean-scaled temperature sensitivity with 200 cm⁻¹ (~8 nm) channel widths is shown in Fig. 4. This channel width was selected to represent realistic channels which might be employed in a practical temperature sensing system. The maximum sensitivity was ~1.18%/°C, compared with 1.48%/°C for the single-point intensity ratio map in Fig. 3. The maximum temperature sensitivity occurs for bands centered near 3000 cm⁻¹ on the low (left) side of the isosbestic point, and 3720 cm⁻¹ on the high (right) side. We will call these the “C” wavenumber pair. It can also be seen from Fig. 3 and Fig. 4 that for the larger channel widths, the precise location of channel centers has less impact on values for the two-color temperature sensitivity ratio.

 

Fig. 4 Temperature sensitivity of the mean-scaled two-color ratio for all pairs of wavenumber channel centers (200 cm⁻¹ channel widths).

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4. Spectral Analysis relating to temperature accuracy

In this section, we analyze the spectra in Fig. 2(a) to predict the accuracy with which temperature can be predicted using the two-color method. As in Section 3, we begin by considering all data points in the spectra (2 cm⁻¹ data intervals), and then extend the analysis to consider the case where the Raman signal is integrated over two wavenumber channels.

When the measured two-color ratio is plotted against the reference temperature, a linear relationship is found, with coefficients which can then be applied to estimate the temperature of other water samples. By applying these coefficients to the reference data, an estimate of the best-case temperature uncertainty may be obtained. A least squares regression was performed using Matlab, for each combination of wavenumbers (data interval 2 cm⁻¹) for ratio values against reference temperature for each wavenumber pair. This produced sets of coefficients for simple linear expressions:

where T is the temperature and (a,b) are regression coefficients. By rearranging these expressions to predict temperature in terms of the two-color ratio and coefficients, a predictive model was produced for each wavenumber pair, and an RMS temperature error was calculated.

The map in Fig. 5 shows the RMS temperature error values obtained by this method. The color bar shows RMS temperature error (°C). The temperature error is quite variable over the range covered by the map, and the color bar on the right shows that low error/high accuracy is indicated by lighter tones, while high error/low accuracy is indicated by darker tones. The isosbestic point falls in the dark region in the lower left corner of the map. The minimum RMS temperature error was ± 0.1 °C with a low shift of 3386 cm⁻¹ and high shift of 3478 cm⁻¹. The regions of lower RMS error were found close to the isosbestic point, and did not align with the region of highest temperature sensitivity. The A and B wavenumber pairs each exhibited similar RMS temperature error values of ± 0.6 °C. Most likely, the lowest errors being observed near the isosbestic point is due to these regions lying near the peak of the OH stretching band, where the Raman intensity (and signal to noise ratio) is greatest.

 

Fig. 5 Map of RMS temperature errors computed for all pairs of wavenumber shifts (data interval 2 cm⁻¹).

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Next the spectra in Fig. 2(a) were analyzed in terms of wavenumber channels having 200 cm⁻¹ channel width, this being more consistent with practical remote sensing scenarios. Figure 6 shows the same spectral data used above recalculated with 200 cm⁻¹ channel widths. The 200 cm⁻¹ channel width map shows more consistent and smoother behavior than the single-point intensity map in Fig. 5. The minimum RMS temperature error was approximately ± 0.1 °C, which occurred for channels centered at approximately 3240 cm⁻¹ and 3400 cm⁻¹. The higher channel center is very close to the isosbestic point, and the two channels overlap by ~50 cm⁻¹.

 

Fig. 6 RMS temperature error map computed for all pairs of wavenumber channel centers (200 cm⁻¹ channel widths).

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While this is somewhat counter-intuitive in terms of temperature sensitivity, this does not preclude such an arrangement providing better temperature accuracy. RMS temperature error of ± 0.2 °C is found with high-side channel center positions up to ~3450 cm⁻¹, where no overlap occurs between the two channels. For comparison, the ‘A’ and ‘B’ wavenumber pairs produced RMS temperature errors of ± 0.3 °C and ± 0.4 °C, while the ‘C’ wavenumber pair RMS temperature error was ± 0.6 °C.

Larger channel widths have the effect of compensating for intensity fluctuations (noise) in the Raman spectra. These variations are small in comparison with the integrated spectral channels, and are reduced in their impact as channel widths are increased. Hence increased channel width should provide for more consistent temperature prediction, assuming the loss in temperature sensitivity can be coped with.

5. Laboratory remote temperature sensing using two-channel Raman spectroscopy

The preceding spectral analyses have been used to inform the design of a simple two-channel Raman spectrometer, predict its performance, and evaluate its potential as a means for near real-time temperature measurement. The experimental configuration is shown in Fig. 7, and we emphasize that there was no acquisition of the full Raman spectra in these experiments.

 

Fig. 7 Simple two-channel experimental setup for remote temperature sensing.

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A 1 meter length cylindrical water cell with uncoated glass windows at both ends was filled with mains supply water heated to ~60 °C. The cell was placed in the path of a linearly-polarized 532 nm pulsed Nd:YAG laser (Coherent µFlare-532) which produced 25 µJ pulses having pulse duration (FWHM) of 0.9 ns at a pulse repetition rate of 4.5 kHz. The green laser output was coupled into the water cell via DM, a dichroic mirror with high reflectivity (R~94%) at 532 nm and high transmission (T~98%) between 620 nm and 670 nm. The backscattered Raman signal passed through DM, and a long-pass filter LP (R~99.9% at 532 nm and T~98% at 620-670 nm) provided further rejection of Rayleigh scattered light at 532 nm. A non-polarizing beam splitting cube (BS) separated the Raman signal into two beams of near-equal intensity, and each of these was then passed through a band-pass filter (BP1 or BP2) before being detected by photomultipliers (PMT) modules (Hamamatsu H10721-20) and recorded with an oscilloscope (Tektronix DPO4104B). The band-pass filters used were a compromise between the optimal wavelengths as determined by the spectral analyses above, and commercial availability. BP1 (Smock FF01-642/10-25) had a center wavelength of 642 nm and a band-pass at FWHM of 16.2 nm. Filter BP2 (Smock FF01-660/13-25) had a center wavelength of 660 nm and a band-pass at FWHM of 20.2 nm. The spectral widths (FWHM) of the two detection channels were 393 cm⁻¹ for Channel 1 (BP1) and 464 cm⁻¹ for Channel 2 (BP2).

Raman signals on both channels were acquired simultaneously and averaged over 512 laser pulses. Measurements were made every few degrees as the cell temperature dropped from 50 °C to 30 °C over several hours. Measurements were made every few degrees as the cell temperature dropped from 50 °C to 30 °C over several hours. The reference temperature was measured using a temperature probe (Digitron 2024T) having an accuracy of ± 0.1 °C. Additional sources in measuring the reference temperature included spatial variations in water temperature throughout the water cell, and the finite time between recording oscilloscope traces and reading the temperature probe, and accordingly we estimate the error in measuring the reference temperature to be ± 0.3 °C.

Figure 8 shows a set of signals (averaged over 512 laser pulse acquisitions) from each of the two PMT channels for ten water temperature levels. The main peak evident in each sub-figure is consistent with the Raman return signal generated as the excitation beam passes through the water cell. The shoulder in the waveform is attributed to a Raman signal excited by the small but significant reflection of the excitation beam from the uncoated end window which passes back through the cell. A reflection of ~0.4% from the water-glass interface and ~4% from the glass-air interface is expected, assuming a glass refractive index of 1.5.

 

Fig. 8 Temperature dependence of channel 1 (top) and channel 2 (bottom) PMT signals (averaged over 512 pulses) for two-color channels.

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Temperature dependence is evident in the region around the apex of the peak for both channels, and the two-color ratio for each temperature was determined by taking the ratio of the signals integrated over a ~5 ns segment as shown in Fig. 8. The S/N ratio for each PMT voltage signal was greater than 29 dB for a single acquisition, and given the averaging over 512 acquisitions, we estimate the uncertainty in determining the two-color ratio to be ± 0.003.

The ratio of signals from the two Raman channels is plotted in Fig. 9(a) as a function of the measured reference temperature. The RMSE of the ratio values is ± 0.004. From the slope of this data, the two color ratio temperature sensitivity was found to be ~0.6% per °C. Figure 9(b) shows the predicted vs. reference temperature fit for this data, from which the RMSTE was determined to be ± 0.5 °C. Much of this error can be attributed to the ± 0.3 °C uncertainty associated with measuring the reference temperature.

 

Fig. 9 (a) Ratio of signals from the 2 Raman channels as a function of measured reference temperature and (b) Predicted temperatures as a function of measured temperatures (r² = 0.98).

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For completeness we compared these measured temperature sensitivity and RMSTE values to those predicted using the numerical analyses in Sections 3 and 4, using the channel center positions and channel widths that correspond to the filters BP1 and BP2. Reasonably good agreement was found in both cases, with mean-scaled temperature sensitivity predicted to be ~0.4% per °C, and RMSTE predicted to be ~0.5 °C.

6. Discussion

Our detailed analysis using full Raman spectra demonstrates that it is possible to use Raman spectroscopy to determine the temperature of a high-purity water sample with RMSTE below ± 0.2 °C. This is comparable to or better than the best accuracies reported previously in [7–9, 13]. To some extent, this reflects the care taken to obtain high quality Raman spectra, and the use of high purity filtered water. We believe the results are effective in providing a “best-case” scenario against which other measurements can be compared. We have shown that using high quality Raman spectra to predict the performance of a simple two-channel spectrometer is a novel and useful approach to optimising and designing a remote sensing instrument. Our analysis shows that channel bandwidths of around 200 cm⁻¹ will provide a suitable compromise between temperature sensitivity and signal strength.

Our preliminary “proof of concept” measurements show that it is feasible to measure water temperature using a two-channel Raman spectrometer. We consider its performance to be very promising, considering that the band-pass filter characteristics were not optimized. Specifically, the channel bandwidths were broader than desirable, and we anticipate both higher temperature sensitivity and lower RMSTE could be achieved using optimized filters with narrower spectral width around 200 cm⁻¹. Nevertheless our results compare favorably with estimated temperature errors in the literature [1, 8, 9, 12] which report temperature errors in the range ± 0.4 °C to ± 1 °C. It is particularly interesting to compare our results to very recent work by Oh et. al. who have compared two methods for determining temperature from measured unpolarized Raman spectra obtained using a laboratory “remote sensing” configuration where the excitation laser was focused into a small cell of ultrapure water from a distance of 7 m [7]. Specifically they compared two approaches in which (1) the measured full Raman spectra was divided into two parts, according to the center of the Raman spectra acquired at 13 °C and (2) the same spectra were decomposed into two Gaussian peaks. They found that their first approach yielded temperature errors around ± 0.2 °C while the second yielded higher errors of around ± 0.4 °C. Our two-channel Raman spectrometer has similarities to the first approach by Oh et. al. [7], except that while they have numerically separated out and integrated the 2 parts of the full Raman spectra, we have optically separated and integrated the two bands. We hope that in the future, the ± 0.5 °C accuracy of our two-channel arrangement will be improved to match the ± 0.2 °C accuracy obtained numerically in [7].

We can identify several approaches for improving the temperature accuracy in the future. First and foremost is to use customised optics in the two-channel Raman spectrometer, which will enable narrower channel bandwidths centred at the optimal wavelengths to be used. Based on the spectral analyses in sections 3 and 4, and noting that the water samples were not identical (mains water vs reverse osmosis filtered water), we anticipate that temperature errors of ± 0.3 °C could be achievable with an optimised system. We do note however that applying the methods developed here to natural water samples will present a new set of challenges, bought about for example by suspended particulates and dissolved organic matter that may absorb the Raman signal, fluoresce at wavelengths that overlap the Raman spectral band, or cause increased backscattering at the excitation wavelength [15]. The impact of these phenomena will only be fully understood when Raman spectra are acquired for a variety of natural water samples.

7. Conclusion

In this paper we have presented a new and comprehensive approach to analyzing the effect of temperature change on the backscattered Raman spectra of pure water, with a view to designing a simple multi-channel optical system for near real-time, depth resolved measurements of water temperature in the field. Our investigation was focused on the two-color ratio method applied to unpolarized Raman spectra.

Our approach enabled us first to analyze Raman spectra to find the combination of spectral parameters most sensitive to changes in water temperature, and second to find the combination of spectral parameters that gave rise to the lowest RMS temperature errors. Our approach was also used to simulate the performance of a simple optical system, explore the trade-offs between Raman signal intensity and temperature sensitivity, and optimize the design of a simple optical system.

The analytical tools and procedures presented here go beyond the scope of previous studies, and indicate the potential of the two-color method to determine water temperature from Raman spectra with a high degree of accuracy. Our future work will investigate the application of similar methods to natural water samples from fresh and saltwater locations.