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

Hiroyuki Tan; Tomohiko Oishi; Akihiko Tanaka; Roland Doerffer

doi:10.1364/AO.54.007718

Applied Optics
Vol. 54,
Issue 25,
pp. 7718-7733
(2015)
•https://doi.org/10.1364/AO.54.007718

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

Hiroyuki Tan, Tomohiko Oishi, Akihiko Tanaka, and Roland Doerffer

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Hiroyuki Tan, Tomohiko Oishi, Akihiko Tanaka, and Roland Doerffer, "Accurate estimation of the backscattering coefficient by light scattering at two backward angles," Appl. Opt. 54, 7718-7733 (2015)

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- Scattering
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About this Article
History
- Original Manuscript: May 1, 2015
- Revised Manuscript: July 6, 2015
- Manuscript Accepted: July 27, 2015
- Published: August 28, 2015
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 10, Iss. 9

Abstract

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.

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Water samples	$N$		90°	100°	110°	120°	130°	140°	150°	160°	170°
River Elbe	18	$χ_{p, avg} (θ)$	0.81	0.99	1.11	1.16	1.21	1.17	1.08	0.88	0.54
River Elbe	18	$σ^{*}$ , %	4.6	5.7	4.8	3.7	2.7	2.5	4.2	8.9	23.6
Lake Schaalsee	16	$χ_{p, avg} (θ)$	0.94	1.09	1.17	1.14	1.13	1.04	0.91	0.71	0.52
Lake Schaalsee	16	$σ *$ , %	5.2	5.7	4.7	4.9	3.7	2.6	5.3	10.5	17.8
P. minimum	54	$χ_{p, avg (θ)}$	0.99	1.19	1.31	1.30	1.27	1.10	0.88	0.65	0.34
P. minimum	54	$σ^{*}$ , %	9.9	8.5	7.1	5.9	5.3	5.7	7.5	7.9	12.0
R. baltica	54	$χ_{p, avg} (θ)$	1.35	1.63	1.78	1.64	1.57	1.28	0.96	0.60	0.22
R. baltica	54	$σ^{*}$ , %	14.8	16.7	18.3	13.9	11.1	8.3	8.8	9.1	22.4
Synechococcus spp.	54	$χ_{p, avg} (θ)$	1.15	1.39	1.48	1.44	1.35	1.12	0.84	0.53	0.25
Synechococcus spp.	54	$σ^{*}$ , %	25.0	13.9	11.3	10.8	11.1	9.7	8.7	9.0	12.4
Nannochloropsis spp.	54	$χ_{p, avg} (θ)$	1.36	1.76	1.96	1.88	1.79	1.51	1.12	0.69	0.21
Nannochloropsis spp.	54	$σ *$ , %	13.7	16.8	18.4	19.8	17.6	15.3	14.6	11.0	22.3
T. weissflogii	54	$χ_{p, avg} (θ)$	1.18	1.37	1.39	1.30	1.23	1.06	0.85	0.62	0.32
T. weissflogii	54	$σ^{*}$ , %	8.9	9.6	9.0	8.1	4.9	4.4	6.5	9.4	19.2
Natural waters	34	$χ_{p, avg} (θ)$	0.87	1.04	1.14	1.15	1.17	1.11	1.00	0.80	0.53
Natural waters	34	$σ^{*}$ , %	8.9	7.4	5.4	4.3	4.6	6.8	9.9	14.1	20.9
Cultures	270	$χ_{p, avg} (θ)$	1.21	1.47	1.58	1.51	1.44	1.22	0.93	0.62	0.27
Cultures	270	$σ^{*}$ , %	19.4	19.8	21.6	20.3	18.9	17.4	15.0	13.0	26.8

	$φ_{p, avg} (120)$	$G_{p, avg} (120)$	$G_{p, avg} (170)$
Lake Schaalsee	1.14	1.34	0.61
River Elbe	1.16	1.31	0.60
P. minimum	1.30	1.17	0.91
T. weissflogii	1.30	1.18	1.00
Synechococcus spp.	1.44	1.07	1.24
R. baltica	1.64	0.94	1.48
Nannochloropsis spp.	1.88	0.84	1.54

			Conversion Factor Used for $b_{b p} (λ)$ Estimation
Types of Waters	$N$		$ν_{p} [R_{p} (120 ∶ 170, λ)]$	$χ_{p, ave} (120)$
Junge PSD	450	RMSE relative to $b_{b p, in tegral} (λ)$	0.033	0.031
		Average of $\| Δ b_{b p, ν p} \|$ or $\| Δ b_{b p, χ p} \|$	1.9%	1.7%
		Frequency within $\pm 5 %$ of $Δ b_{b p, ν p}$ or $Δ b_{b p, χ p}$	90%	93%
Gauss PSD	972	RMSE relative to $b_{b p, in tegral} (λ)$	0.134	0.129
		Average of $\| Δ b_{b p, ν p} \|$ or $\| Δ b_{b p, χ p} \|$	9.6%	9.3%
		Frequency within $\pm 5 %$ of $Δ b_{b p, ν p}$ or $Δ b_{b p, χ p}$	39%	22%

			Conversion Factor Used for $b_{b p} (λ)$ Estimation
Types of Waters		N	$ν_{p} [R_{p} (120 ∶ 170, λ)]$	$χ_{p, mean (120)}$
Natural waters with the historical VSFs	141	RMSE relative to $b_{b p, in tegral} (λ)$	0.047	0.080
		Average of $\| Δ b_{b p, ν p} \|$ or $\| Δ b_{b p, χ p} \|$	3.4%	6.1%
		Frequency within $\pm 5 %$ of $Δ b_{b p, ν p}$ or $Δ b_{b p, χ p}$	74%	52%
Cultures	270	RMSE relative to $b_{b p, in tegral} (λ)$	0.040	0.238
		Average of $\| Δ b_{b p, ν p} \|$ or $\| Δ b_{b p, χ p} \|$	3.2%	19.7%
		Frequency within $\pm 5 %$ of $Δ b_{b p, ν p}$ or $Δ b_{b p, χ p}$	79%	13%

			Conversion Factor Used for $b_{b} (λ)$ Estimation
Types of Waters	N		$ν_{t} [R (120 ∶ 170, λ)]$	$χ_{t} (120)$
Natural waters with the historical VSFs	154	RMSE relative to $b_{b, in tegral} (λ)$	0.039	0.080
		Average of $\| Δ b_{b, ν t} \|$ or $\| Δ b_{b, χ t} \|$	3.1%	6.9%
		Frequency within $\pm 5 %$ of $Δ b_{b, ν t}$ or $Δ b_{b, χ t}$	84%	33%
Cultures	270	RMSE relative to $b_{b, in tegral} (λ)$	0.032	0.239
		Average of $\| Δ b_{b, ν t} \|$ or $\| Δ b_{b, χ t} \|$	2.5%	21.1%
		Frequency within $\pm 5 %$ of $Δ b_{b, ν t}$ or $Δ b_{b, χ t}$	88%	4%

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Applied Optics