Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles

Daniel Koestner; Dariusz Stramski; Rick A. Reynolds

doi:10.1364/AO.396709

Applied Optics
Vol. 59,
Issue 27,
pp. 8314-8334
(2020)
•https://doi.org/10.1364/AO.396709

Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles

Daniel Koestner, Dariusz Stramski, and Rick A. Reynolds

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Daniel Koestner, Dariusz Stramski, and Rick A. Reynolds, "Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles," Appl. Opt. 59, 8314-8334 (2020)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: May 11, 2020
- Revised Manuscript: August 1, 2020
- Manuscript Accepted: August 2, 2020
- Published: September 16, 2020

Abstract

Polarized light scattering measurements have the potential to provide improved characterization of natural particle assemblages in terms of particle size and composition. However, few studies have investigated this possibility for natural assemblages of marine particles. In this study, seawater samples representing contrasting assemblages of particles from coastal environments have been comprehensively characterized with measurements of angle-resolved polarized light scattering, particle size distribution, and particle composition. We observed robust trends linking samples containing higher proportions of large-sized particles with lower values of the maximum degree of linear polarization and the second element of the scattering matrix at a scattering angle of 100°, ${p_{22}}({{{100}}^\circ})$. In contrast, lower values of ${p_{22}}({{{20}}^\circ})$ were found in more non-phytoplankton—or inorganic--dominated samples. We also determined that three measurements involving the combinations of linearly polarized incident and scattered beams at two scattering angles (110° and 18°) have the potential to serve as useful proxies for estimating particle size and composition parameters.

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Corrections

Daniel Koestner, Dariusz Stramski, and Rick A. Reynolds, "Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles: erratum," Appl. Opt. 60, 380-382 (2021)
https://opg.optica.org/ao/abstract.cfm?uri=ao-60-2-380

2 October 2020: A correction was made to Eq. (1).

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Appl. Opt. 60(36) 11161-11179 (2021)

Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles: erratum

Daniel Koestner, Dariusz Stramski, and Rick A. Reynolds
Appl. Opt. 60(2) 380-382 (2021)

Polarized light scattering measurements as a means to characterize particle size and composition of natural assemblages of marine particles: publisher’s note

Daniel Koestner, Dariusz Stramski, and Rick A. Reynolds
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Symbol	Description [units]
$ψ$	Scattering angle with 0 defined as direction of initial propagation [deg]
$⊥$ or $∥$	Indicates polarization perpendicular or parallel to a reference plane
$β_{p} (ψ)$	Particulate volume scattering function [ $m^{- 1} {s r}^{- 1}$ ] (Eq. (10))
$β_{p}^{ϵ ϵ} (ψ)$	Polarized light scattering by particles where $ϵ = ⊥$ or $∥$ [ $m^{- 1} {s r}^{- 1}$ ]
${C F}_{f}^{ϵ ϵ} (ψ)$	Correction functions for polarized light scattering combinations (Fig. 2)
${C F}_{f} (ψ)$	Correction function for $β_{p} (ψ)$ from [25]
$b_{p}$	Particulate scattering coefficient [ $m^{- 1}$ ]; $2 π \int_{0^{\circ}}^{180^{\circ}} β_{p} (ψ) \sin (ψ) d ψ$
$b_{bp}$	Particulate backscattering coefficient [ $m^{- 1}$ ]; $2 π \int_{90^{\circ}}^{180^{\circ}} β_{p} (ψ) \sin (ψ) d ψ$
${\tilde{b}}_{bp}$	Particulate backscattering ratio; $b_{bp} / b_{p}$
${D o L P}_{p} (ψ)$	Degree of linear polarization of light scattered by particles (Eq. (11))
${D o L P}_{p, max}$	Maximum value of ${D o L P}_{p} (ψ)$
$ψ_{m a x}$	Scattering angle of ${D o L P}_{p, m a x}$ [deg]
FWHM	The angular width of ${D o L P}_{p} (ψ)$ at half of ${D o L P}_{p, m a x}$ [deg]
${D o L P}_{p}$ symmetry	Symmetry of ${D o L P}_{p} (ψ)$ about $ψ_{m a x}$ ; ${D o L P}_{p} (ψ_{m a x} - 45^{\circ}) / {D o L P}_{p} (ψ_{m a x} + 45^{\circ})$
$p_{22} (ψ)$	Normalized scattering matrix element row 2 column 2 (Eq. (12))
$a_{p} (λ)$ and $a_{ph} (λ)$	Spectral absorption coefficients of particles and phytoplankton [ $m^{- 1}$ ]
SPM	Dry mass concentration of suspended particulate matter [ $g m^{- 3}$ ]
POC	Particulate organic carbon mass concentration [ $g m^{- 3}$ ]
Chla	Chlorophyll-a mass concentration [ $g m^{- 3}$ ]
PSD	Particle size distribution [number or volume concentration]
$D_{v}^{50}$ and $D_{v}^{90}$	50th and 90th percentile diameter of the cumulative volume PSD [µm]

Symbol	Description
$N$	Number of samples
$x_{i}$ or $y_{i}$	Measured value for sample $i$ of $N$
$\bar{x}$ or $\bar{y}$	Mean value; $\bar{x} = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$ , and likewise for $\bar{y}$
$P_{i}$ or $O_{i}$	Model-predicted or observed value for sample $i$ of $N$
$R$	Pearson correlation coefficient; $\frac{\sum_{i = 1}^{N} (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt{\sum_{i = 1}^{N} {(x_{i} - \bar{x})}^{2}} \sqrt{\sum_{i = 1}^{N} {(y_{i} - \bar{y})}^{2}}}$
$ρ$	Spearman correlation coefficient; calculated as $R$ with numerical rank values
Model-performance variables
RMSD	Root mean square deviation; $\sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(P_{i} - O_{i})}^{2}}$
MdAPD	Median absolute percent difference; 50th percentile of $\| \frac{P_{i} - O_{i}}{O_{i}} \| \times 100 %$
MdR	Median ratio; 50th percentile of $\frac{P_{i}}{O_{i}}$
${M B}_{l o g}$	Mean bias of log-transformed data; $10^{N^{- 1} \sum_{i = 1}^{N} (\log P_{i} - \log O_{i})}$

Particle Parameter	Min	Max	$N$
$c_{p}$ [ $m^{- 1}$ ] ^a	0.41	21	46
SPM [ $g m^{- 3}$ ]	0.24	74	27
POC [ $g m^{- 3}$ ]	0.063	2.9	27
Chla [ $m g m^{- 3}$ ]	0.53	6.0	15
POC/SPM	0.039	0.64	27
$D_{v}^{50}$ [µm]	4.5	25	41
$D_{v}^{90}$ [µm]	8.1	37	41

Regression						Model Performance
Optical Parameter	Particle Parameter	Eq.	m	b	R	RMSD	MdAPD	MdR	${M B}_{l o g}$
${D o L P}_{p, max}^{10}$	$D_{V}^{90}$	Linear	$- 117.50$	104.13	$- 0.73$	5.83 µm	22.9 %	1.02	1.00
${D o L P}_{p, max}^{50}$	$D_{V}^{90}$	Linear	$- 146.32$	137.02	$- 0.60$	7.19 µm	29.1 %	1.04	0.99
${D o L P}_{p, max}^{90}$	$D_{V}^{90}$	Linear	$- 129.06$	133.14	$- 0.42$	8.66 µm	36.8 %	0.96	0.98
$\frac{β^{∥ ⊥} (110^{\circ})}{β_{p}^{∥ ∥} (110^{\circ})}$	$D_{V}^{90}$	Linear	$- 23.47$	156.16	$- 0.66$	6.62 µm	21.5 %	0.98	1.00
$\frac{β_{p}^{∥ ⊥} (110^{\circ})}{β_{p}^{∥ ∥} (18^{\circ})}$	POC/SPM	Exp	$- 352.87$	4.57	$- 0.88$	0.10	17.0 %	0.98	1.00
${\tilde{b}}_{bp}$	POC/SPM	Exp	$- 145.45$	2.19	$- 0.74$	0.12	23.6 %	0.96	1.00

Symbol	Description [units]
$ψ$	Scattering angle with 0 defined as direction of initial propagation [deg]
$⊥$ or $∥$	Indicates polarization perpendicular or parallel to a reference plane
$β_{p} (ψ)$	Particulate volume scattering function [ $m^{- 1} {s r}^{- 1}$ ] (Eq. (10))
$β_{p}^{ϵ ϵ} (ψ)$	Polarized light scattering by particles where $ϵ = ⊥$ or $∥$ [ $m^{- 1} {s r}^{- 1}$ ]
${C F}_{f}^{ϵ ϵ} (ψ)$	Correction functions for polarized light scattering combinations (Fig. 2)
${C F}_{f} (ψ)$	Correction function for $β_{p} (ψ)$ from [25]
$b_{p}$	Particulate scattering coefficient [ $m^{- 1}$ ]; $2 π \int_{0^{\circ}}^{180^{\circ}} β_{p} (ψ) \sin (ψ) d ψ$
$b_{bp}$	Particulate backscattering coefficient [ $m^{- 1}$ ]; $2 π \int_{90^{\circ}}^{180^{\circ}} β_{p} (ψ) \sin (ψ) d ψ$
${\tilde{b}}_{bp}$	Particulate backscattering ratio; $b_{bp} / b_{p}$
${D o L P}_{p} (ψ)$	Degree of linear polarization of light scattered by particles (Eq. (11))
${D o L P}_{p, max}$	Maximum value of ${D o L P}_{p} (ψ)$
$ψ_{m a x}$	Scattering angle of ${D o L P}_{p, m a x}$ [deg]
FWHM	The angular width of ${D o L P}_{p} (ψ)$ at half of ${D o L P}_{p, m a x}$ [deg]
${D o L P}_{p}$ symmetry	Symmetry of ${D o L P}_{p} (ψ)$ about $ψ_{m a x}$ ; ${D o L P}_{p} (ψ_{m a x} - 45^{\circ}) / {D o L P}_{p} (ψ_{m a x} + 45^{\circ})$
$p_{22} (ψ)$	Normalized scattering matrix element row 2 column 2 (Eq. (12))
$a_{p} (λ)$ and $a_{ph} (λ)$	Spectral absorption coefficients of particles and phytoplankton [ $m^{- 1}$ ]
SPM	Dry mass concentration of suspended particulate matter [ $g m^{- 3}$ ]
POC	Particulate organic carbon mass concentration [ $g m^{- 3}$ ]
Chla	Chlorophyll-a mass concentration [ $g m^{- 3}$ ]
PSD	Particle size distribution [number or volume concentration]
$D_{v}^{50}$ and $D_{v}^{90}$	50th and 90th percentile diameter of the cumulative volume PSD [µm]

Abstract

Corrections

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Tables (4)

Equations (16)

Applied Optics