A new approach to measure the volume scattering function

Instrument for in situ synchronous measurement of the multi-angle volume scattering function and attenuation coefficient

An instrument named as Volume Scattering and Attenuation Meter (VSAM) is presented. The VSAM can simultaneously measure the attenuation coefficient and the volume scattering function (VSF) from 10° to 170° with an interval of 10° at 659 nm. Using ultrapure water and NCRM-traceable polystyrene microsphere beads, the VSAM was calibrated, and the conversion factor χ_bθ for estimating the backscattering coefficient from the backward VSF was obtained based on Mie theory in the laboratory. For χ_bθ, the average relative deviation was no more than 7.77% in the range of 100°-160° between the modeled result based on VSAM and the theoretical result by Boss. Subsequently, the VSAM and ECO-VSF3 were deployed in situ in Zhanjiang Bay. The backscattering coefficient and VSF at the same angles measured by the two instruments were quite consistent. Some remarkable changes in the shape and magnitude of the VSF profile at different stations were found, with land-based pollutants composing an important suspicious source of these changes.

Forward volume scattering function (0.03°-60°) measured using an oblique-incidence particle sizer

The forward volume scattering function (VSF) is an inherent optical property important in ocean lidar and underwater imaging and communication. The scattered power within 60° contains >90% of total scattered power, making it essential for determining the asymmetry parameter g. Thus, the new oblique-incidence-design Bettersize BT-3000 particle sizer was utilized to measure forward VSF (0.03°-60°) synchronously. A double-exponential model was then used to construct the full-angle-range VSF (0°-180°). The g value calculated therefrom had an uncertainty of <1%. Calibration was implemented using 11-µm beads alone, and the BT-3000's performance was validated.

Measurements of Aquatic Particle Volume Scattering Function up to 178.5° in the East China Sea

Particulate volume scattering function (VSF), especially at angles larger than 170°, is of particular importance for interpreting ocean optical remote sensing signals and underwater imagery. In this study, a laboratory-based VSF instrument (VSFlab) adopting the periscopic optical system was developed to obtain VSF measurements from 1°–178.5°. In the VSFlab, a new prism design that simply combines a single prism and a neutral density filter was proposed to more efficiently reduce the stray light in the backward direction, while a detailed calibration procedure was given. A full validation based on standard beads of various sizes and a comparison with the results from LISST-VSF and POLVSM indicated that the VSFlab can provide reliable results from 1° to 178.5°. VSFlab measurements in the East China Sea (ECS) exhibited a moderate increase (not more than 5 times) in VSF from 170° to 178.5° rather than a sharp increase of more than one order of magnitude presented in other instrument results measured in other coastal regions. The estimates of the particulate backscattering coefficient using single angle scattering measurements near 120° or 140° and suitable χp were justified. Two types of the VSFs with different size distribution and shape parameters in the ECS can be distinguished based on the variability of χp after 155°. The measured VSF could provide a basis for the parameterization of VSF in the radiative transfer model and the variability of χp in the backward direction had the potential to be used to characterize the particles in the coastal region of the ECS.

Two-term Reynolds-McCormick phase function parameterization better describes light scattering by microalgae and mineral hydrosols

The presence of hydrosols, taken as suspension of micro- or macroscopic material in water, strongly alters light propagation and thus the radiance distribution within a natural or artificial water volume. Understanding of hydrosols' impacts on light propagation is limited by our ability to accurately handle the angular scattering phase function inherent to complex material such as suspended sediments or living cells. Based on actual quality-controlled measurements of sediments and microalgae, this Letter demonstrates the superiority of a two-term five-parameter empirical phase function as recently proposed for scattering by nanoparticle layers [Nanoscale11, 7404 (2019)NANOHL2040-336410.1039/C9NR01707K]. The use of such phase function parameterizations presents new potentialities for various radiative transfer and remote sensing applications related to an aquatic environment.

Shape of particle backscattering in the North Pacific Ocean: the χ factor

Volume scattering functions were measured using two instruments in waters near the Ocean Station Papa (50°N 145°W) and show consistency in estimating the χ factor attributable to particles (χ_p). While χ_p in the study area exhibits a limited variability, it could vary significantly when compared with data obtained in various parts of the global oceans. The global comparison also confirms that the minimal variation of χ_p is at scattering angles near 120°. With an uncertainty of <10%, χ_p can be assumed as spectrally independent. For backscatter sensors with wide field of view (FOV), the averaging of scattering within the FOV reduces the values of χ_p needed to compute the backscattering coefficient by up to 20% at angles <130^∘.

Variability of relationship between the volume scattering function at 180° and the backscattering coefficient for aquatic particles

Properly interpreting lidar (light detection and ranging) signal for characterizing particle distribution relies on a key parameter, χ_p(π), which relates the particulate volume scattering function (VSF) at 180° (β_p(π)) that a lidar measures to the particulate backscattering coefficient (b_bp). However, χ_p(π) has been seldom studied due to challenges in accurately measuring β_p(π) and b_bp concurrently in the field. In this study, χ_p(π), as well as its spectral dependence, was re-examined using the VSFs measured in situ at high angular resolution in a wide range of waters. β_p(π), while not measured directly, was inferred using a physically sound, well-validated VSF-inversion method. The effects of particle shape and internal structure on the inversion were tested using three inversion kernels consisting of phase functions computed for particles that are assumed as homogenous sphere, homogenous asymmetric hexahedra, or coated sphere. The reconstructed VSFs using any of the three kernels agreed well with the measured VSFs with a mean percentage difference <5% at scattering angles <170^∘. At angles immediately near or equal to 180°, the reconstructed β_p(π) depends strongly on the inversion kernel. χ_p(π) derived with the sphere kernels was smaller than those derived with the hexahedra kernel but consistent with χ_p(π) estimated directly from high-spectral-resolution lidar and in situ backscattering sensor. The possible explanation was that the sphere kernels are able to capture the backscattering enhancement feature near 180° that has been observed for marine particles. χ_p(π) derived using the coated sphere kernel was generally lower than those derived with the homogenous sphere kernel. Our result suggests that χ_p(π) is sensitive to the shape and internal structure of particles and significant error could be induced if a fixed value of χ_p(π) is to be used to interpret lidar signal collected in different waters. On the other hand, χ_p(π) showed little spectral dependence.

Calibration of the LISST-VSF to derive the volume scattering functions in clear waters

The recently commercialized LISST-VSF instrument measures the volume scattering function (VSF) from 0.1° to 15° with a traditional laser diffraction unit (LISST) and from 15° to 155° with an eyeball component. Between these two optical components, only the LISST unit is calibrated. The eyeball measurements are scaled using the VSFs at 15° that are measured by both components. As this relative calibration relies on a valid measurement at 15° by the LISST, it might fail in clear oceanic waters, where the forward scattering is relative weak either due to a lack of large particles or an overall low concentration of all particles. In this study, we calibrated the LISST-VSF eyeball component through a series of lab experiments using standard polystyrene beads. Validation with the beads of two different sizes showed a median difference of 11.1% between theoretical and calibrated values. Further evaluations with in situ data collected by the LISST-VSF and an ECO-BB3 meter indicated that the new calibration worked well in both turbid and clear waters, while the relative calibration method tended to overestimate VSFs in clear waters.

Measurements of the Volume Scattering Function and the Degree of Linear Polarization of Light Scattered by Contrasting Natural Assemblages of Marine Particles

The light scattering properties of seawater play important roles in radiative transfer in the ocean and optically-based methods for characterizing marine suspended particles from in situ and remote sensing measurements. The recently commercialized LISST-VSF instrument is capable of providing in situ or laboratory measurements of the volume scattering function, β p ( ψ ) , and the degree of linear polarization, DoLP p ( ψ ) , associated with particle scattering. These optical quantities of natural particle assemblages have not been measured routinely in past studies. To fully realize the potential of LISST-VSF measurements, we evaluated instrument performance, and developed calibration correction functions from laboratory measurements and Mie scattering calculations for standard polystyrene beads suspended in water. The correction functions were validated with independent measurements. The improved LISST-VSF protocol was applied to measurements of β p ( ψ ) and DoLP p ( ψ ) taken on 17 natural seawater samples from coastal and offshore marine environments characterized by contrasting assemblages of suspended particles. Both β p ( ψ ) and DoLP p ( ψ ) exhibited significant variations related to a broad range of composition and size distribution of particulate assemblages. For example, negative relational trends were observed between the particulate backscattering ratio derived from β p ( ψ ) and increasing proportions of organic particles or phytoplankton in the particulate assemblage. Our results also suggest a potential trend between the maximum values of DoLP p ( ψ ) and particle size metrics, such that a decrease in the maximum DoLP p ( ψ ) tends to be associated with particulate assemblages exhibiting a higher proportion of large-sized particles. Such results have the potential to advance optically-based applications that rely on an understanding of relationships between light scattering and particle properties of natural particulate assemblages.

Ocean Color Analytical Model Explicitly Dependent on the Volume Scattering Function

An analytical radiative transfer (RT) model for remote sensing reflectance that includes the bidirectional reflectance distribution function (BRDF) is described. The model, called ZTT (Zaneveld-Twardowski-Tonizzo), is based on the restatement of the RT equation by Zaneveld (1995) in terms of light field shape factors. Besides remote sensing geometry considerations (solar zenith angle, viewing angle, and relative azimuth), the inputs are Inherent Optical Properties (IOPs) absorption a and backscattering bb coefficients, the shape of the particulate volume scattering function (VSF) in the backward direction, and the particulate backscattering ratio. Model performance (absolute error) is equivalent to full RT simulations for available high quality validation data sets, indicating almost all residual errors are inherent to the data sets themselves, i.e., from the measurements of IOPs and radiometry used as model input and in match up assessments, respectively. Best performance was observed when a constant backward phase function shape based on the findings of Sullivan and Twardowski (2009) was assumed in the model. Critically, using a constant phase function in the backward direction eliminates a key unknown, providing a path toward inversion to solve for a and bb. Performance degraded when using other phase function shapes. With available data sets, the model shows stronger performance than current state-of-the-art look-up table (LUT) based BRDF models used to normalize reflectance data, formulated on simpler first order RT approximations between rrs and bb/a or bb/(a + bb) (Morel et al., 2002; Lee et al., 2011). Stronger performance of ZTT relative to LUT-based models is attributed to using a more representative phase function shape, as well as the additional degrees of freedom achieved with several physically meaningful terms in the model. Since the model is fully described with analytical expressions, errors for terms can be individually assessed, and refinements can be readily made without carrying out the gamut of full RT computations required for LUT-based models. The ZTT model is invertible to solve for a and bb from remote sensing reflectance, and inversion approaches are being pursued in ongoing work. The focus here is with development and testing of the in-water forward model, but current ocean color remote sensing approaches to cope with an air-sea interface and atmospheric effects would appear to be transferable. In summary, this new analytical model shows good potential for future ocean color inversion with low bias, well-constrained uncertainties (including the VSF), and explicit terms that can be readily tuned. Emphasis is put on application to the future NASA Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission.

Chlorophyll-a specific volume scattering function of phytoplankton

Chlorophyll-a specific light volume scattering functions (VSFs) by cultured phytoplankton in visible spectrum range is presented. Chlorophyll-a specific VSFs were determined based on the linear least squares method using a measured VSFs with different chlorophyll-a concentrations. We found obvious variability of it in terms of spectral and angular shapes of VSF between cultures. It was also presented that chlorophyll-a specific scattering significantly affected on spectral variation of the remote sensing reflectance, depending on spectral shape of b. This result is useful for developing an advance algorithm of ocean color remote sensing and for deep understanding of light in the sea.

Understanding the contribution of phytoplankton phase functions to uncertainties in the water colour signal

The accurate description of a water body's volume scattering function (VSF), and hence its phase functions, is critical to the determination of the constituent inherent optical properties (IOPs), the associated spectral water-leaving reflectance, and consequently the retrieval of phytoplankton functional type (PFT) information. The equivalent algal populations (EAP) model has previously been evaluated for phytoplankton-dominated waters, and offers the ability to provide phytoplankton population-specific phase functions, unveiling a new opportunity to further understanding of the causality of the PFT signal. This study presents and evaluates the wavelength dependent, spectrally variable EAP particle phase functions and the subsequent effects on water-leaving reflectance. Comparisons are made with frequently used phase function approximations e.g. the Fournier Forand formulation, as well as with phase functions inferred from measured VSFs in coastal waters. Relative differences in shape and magnitude are quantified. Reflectance modelled with the EAP phase functions is then compared against measured reflectance data from phytoplankton-dominated waters. Further examples of modelled phytoplankton-dominated waters are discussed with reference to choice of phase function for two PFTs (eukaryote and prokaryote) across a range of biomass. Finally a demonstration of the sensitivity of reflectance due to the choice of phase function is presented. The EAP model phase functions account for both spectral and angular variability in phytoplankton backscattering i.e. they display variability which is both spectral and shape-related. It is concluded that phase functions modelled in this way are necessary for investigating the effects of assemblage variability on the ocean colour signal, and should be considered for model closure even in relatively low scattering conditions where phytoplankton dominate the IOPs.

Laboratory experiments for inter-comparison of three volume scattering meters to measure angular scattering properties of hydrosols

Measurements of the volume scattering function (VSF) of hydrosols is of primary importance to investigate the interaction of light with hydrosols and to further interpret in situ and remote sensing data of ocean color. In this paper, a laboratory inter-comparison experiment of three recently developed VSF meters that are able to measure the scattered light for a wide range of scattering angle at 515 nm wavelength is performed using phytoplankton cultures and mineral-like hydrosols. A rigorous measurement protocol was employed to ensure good quality data. In particular, the protocol enabled removing the influence of bacteria on the hydrosols within the sample. The differences in the VSF measurements between the instruments vary from 10 to 25% depending on the composition of the hydrosols. The analysis of the angular features of the VSF revealed a sharp increase of the VSF beyond the scattering angle of 150° for some phytoplankton species. Such behavior is observed for two of the three VSF meters, thus suggesting that it is not due to instrumental artifacts but more likely to phytoplankton optical properties themselves. Moreover, comparisons with currently used theoretical phase functions show that the models are not able to reproduce satisfactorily the directional patterns in the backscattering region. This study suggests that a better modelling of the VSF shape of phytoplankton at high scattering angles is required to correctly represent the angular shape of the VSF in the backscattering hemisphere. Tabulated values of the measured phase functions are provided for scattering angles from 0.1 to 175°.

Measurement of the light scattering of single micrometer-sized particles captured with a microfluidic trap

Light scattering detection of a single particle is significant to both theoretical developments and application progresses of particle scattering. In this work, a new method employing the polydimethylsiloxane microfluidic catcher with self-regulation was developed to detect the light scattering of an individual micro particle (20.42, 23.75, and 31.10 μm) in a wide angular range. This system can rapidly (<2 min) immobilize single particles without aggregations and continuously analyze its light scattering ranging from 2° to 162°. The high success ratio of the capture, good agreement with the anticipation, and moderate time and cost make this method a promising candidate in single-particle-scattering applications.

OSOAA: a vector radiative transfer model of coupled atmosphere-ocean system for a rough sea surface application to the estimates of the directional variations of the water leaving reflectance to better process multi-angular satellite sensors data over the ocean

In this study, we present a radiative transfer model, so-called OSOAA, that is able to predict the radiance and degree of polarization within the coupled atmosphere-ocean system in the presence of a rough sea surface. The OSOAA model solves the radiative transfer equation using the successive orders of scattering method. Comparisons with another operational radiative transfer model showed a satisfactory agreement within 0.8%. The OSOAA model has been designed with a graphical user interface to make it user friendly for the community. The radiance and degree of polarization are provided at any level, from the top of atmosphere to the ocean bottom. An application of the OSOAA model is carried out to quantify the directional variations of the water leaving reflectance and degree of polarization for phytoplankton and mineral-like dominated waters. The difference between the water leaving reflectance at a given geometry and that obtained for the nadir direction could reach 40%, thus questioning the Lambertian assumption of the sea surface that is used by inverse satellite algorithms dedicated to multi-angular sensors. It is shown as well that the directional features of the water leaving reflectance are weakly dependent on wind speed. The quantification of the directional variations of the water leaving reflectance obtained in this study should help to correctly exploit the satellite data that will be acquired by the current or forthcoming multi-angular satellite sensors.

Accurate estimation of the backscattering coefficient by light scattering at two backward angles

Backscattering coefficients are frequently estimated from light scattering at one backward angle multiplied by a conversion factor. We determined that the shapes of the volume scattering functions (VSFs), particularly for scattering angles larger than 170°, cause significant variations in the conversion factor at 120°. Our approach uses the ratio of scattering at 170° and at 120°, which is a good indicator of the shape differences of the VSFs for most oceanic waters and wavelengths in the visible range. The proposed method provides significant accuracy improvement in the determination of the backscattering coefficients with a prediction error of 3% of the mean.

POLVSM (Polarized Volume Scattering Meter) instrument: an innovative device to measure the directional and polarized scattering properties of hydrosols

An innovative instrument dedicated to the multispectral measurements of the directional and polarized scattering properties of the hydrosols, so-called POLVSM, is described. The instrument could be used onboard a ship, as a benchtop instrument, or at laboratory. The originality of the POLVSM concept relies on the use of a double periscopic optical system whose role is (i) to separate the plane containing the light source from the scattering plane containing the sample and the receiver and (ii) to prevent from any specularly reflected light within the sample chamber. As a result, a wide range of scattering angle, namely from 1° to 179°, is covered by the detector. Another originality of the instrument is to measure the Mueller scattering matrix elements, including the degree of polarization. A relevant calibration procedure, which could be of great interest as well for other instruments, is proposed to convert the raw data into physical units. The relative uncertainty in POLVSM data was determined at ± 4.3%. The analysis of measurements of the volume scattering function and degree of polarization performed under controlled conditions for samples dominated either by inorganic hydrosols or phytoplankton monospecific species showed a good consistency with literature, thus confirming the good performance of the POLVSM device. Comparisons of POLVSM data with theoretical calculations showed that Mie theory could reproduce efficiently the measurements of the VSF and degree of polarization for the case of inorganic hydrosols sample, despite the likely non sphericity of these particles as revealed by one of the element of the Mueller matrix. Our results suggested as well that a sophisticated modeling of the heterogeneous internal structure of living cells, or at least, the use of layered sphere models, is needed to correctly predict the directional and polarized effects of phytoplankton on the oceanic radiation. The relevance of performing angularly resolved measurements of the Mueller scattering elements to gain understanding on the mechanisms processes involved in the scattering of light by marine particles, which has important implications for ocean color remote sensing studies, is demonstrated.