One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater

Vladimir I. Haltrin

doi:10.1364/AO.41.001022

One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater

Vladimir I. Haltrin

Applied Optics
Vol. 41,
Issue 6,
pp. 1022-1028
(2002)
•https://doi.org/10.1364/AO.41.001022

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Vladimir I. Haltrin, "One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater," Appl. Opt. 41, 1022-1028 (2002)

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Previously assigned OCIS codes
- Atmospheric and oceanic optics (010.0010)
- Oceanic optics (010.4450)
- Water (010.7340)
- Scattering (290.0290)
- Turbid media (290.7050)

About this Article
History
- Original Manuscript: April 24, 2001
- Revised Manuscript: August 31, 2001
- Published: February 20, 2002

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Abstract

A one-parameter two-term Henyey-Greenstein (TTHG) phase function of light scattering in seawater is proposed. The original three-parameter TTHG phase function was reduced to the one-parameter TTHG phase function by use of experimentally derived regression dependencies between integral parameters of the marine phase functions. An approach to calculate a diffuse attenuation coefficient in the depth of seawater is presented.

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B/ω₀	Eigenvalue
B/ω₀	0.20	0.30	0.40	0.50	0.60	0.70	0.80	0.90	0.99
0.005	0.862038	0.716817	0.670190	0.521512	0.447405	0.323231	0.222598	0.120107	0.021534
0.050	0.860399	0.778234	0.692595	0.603911	0.512142	0.416768	0.316303	0.205647	0.060727
0.100	0.893488	0.823050	0.747403	0.667069	0.581793	0.490387	0.389641	0.269236	0.084465
0.150	0.919372	0.859252	0.792536	0.719673	0.640036	0.551622	0.449466	0.318981	0.102089
0.200	0.940713	0.890095	0.831655	0.765632	0.690945	0.604749	0.500527	0.360395	0.116453
0.250	0.958529	0.916864	0.866245	0.806596	0.736330	0.651806	0.545203	0.396069	0.128689
0.300	0.973240	0.940149	0.897057	0.843465	0.777248	0.694039	0.584946	0.427481	0.139393
0.350	0.984925	0.960157	0.924468	0.876781	0.814398	0.732298	0.620730	0.455566	0.148921
0.400	0.993398	0.976777	0.948583	0.906861	0.848265	0.767197	0.653247	0.480965	0.157513
0.450	0.998330	0.989516	0.969196	0.933815	0.879178	0.799195	0.683010	0.504138	0.165335
0.500	0.999909	0.997414	0.985624	0.957504	0.907332	0.828635	0.710412	0.525430	0.172511

ω₀	γ₀(ω₀)	γ₁(ω₀)	γ₂(ω₀)	γ₃(ω₀)	γ₄(ω₀)	γ₅(ω₀)	r ²
0.05	0.95609	0.41762	1.8653	5.3139	9.0900	6.6281	0.99992
0.10	0.90763	0.73428	3.2760	10.415	18.715	13.196	0.99991
0.15	0.85958	0.97587	4.1853	13.523	24.053	16.382	0.99995
0.20	0.81145	1.1718	4.7173	14.839	25.423	16.520	0.99996
0.25	0.76304	1.3459	5.1578	15.933	26.616	16.805	0.99996
0.30	0.71437	1.5039	5.5563	17.038	28.177	17.665	0.99997
0.35	0.66548	1.6481	5.9213	18.146	30.012	18.943	0.99997
0.40	0.61639	1.7788	6.2421	19.151	31.795	20.297	0.99998
0.45	0.56712	1.8959	6.5105	19.966	33.270	21.463	0.99998
0.50	0.51768	1.9995	6.7251	20.552	34.304	22.303	0.99998
0.55	0.46807	2.0895	6.8909	20.910	34.870	22.774	0.99998
0.60	0.41827	2.1657	7.0186	21.070	35.006	22.899	0.99998
0.65	0.36826	2.2278	7.1237	21.092	34.810	22.741	0.99999
0.70	0.31802	2.2744	7.2282	21.069	34.447	22.413	0.99999
0.75	0.26751	2.3030	7.3619	21.149	34.188	22.102	0.99999
0.80	0.21670	2.3080	7.5606	21.546	34.462	22.112	0.99999
0.85	0.16560	2.2753	7.8495	22.521	35.857	22.886	0.99999
0.90	0.11433	2.1659	8.1620	24.143	38.785	24.816	0.99998
0.95	0.063265	1.8473	7.9291	24.867	41.055	26.660	0.99996
0.97	0.042914	1.5580	7.1137	22.981	38.530	25.250	0.99993
0.99	0.021309	0.97834	4.7437	15.778	26.869	17.777	0.99989

B/ω₀	Eigenvalue
B/ω₀	0.20	0.30	0.40	0.50	0.60	0.70	0.80	0.90	0.99
0.005	0.862038	0.716817	0.670190	0.521512	0.447405	0.323231	0.222598	0.120107	0.021534
0.050	0.860399	0.778234	0.692595	0.603911	0.512142	0.416768	0.316303	0.205647	0.060727
0.100	0.893488	0.823050	0.747403	0.667069	0.581793	0.490387	0.389641	0.269236	0.084465
0.150	0.919372	0.859252	0.792536	0.719673	0.640036	0.551622	0.449466	0.318981	0.102089
0.200	0.940713	0.890095	0.831655	0.765632	0.690945	0.604749	0.500527	0.360395	0.116453
0.250	0.958529	0.916864	0.866245	0.806596	0.736330	0.651806	0.545203	0.396069	0.128689
0.300	0.973240	0.940149	0.897057	0.843465	0.777248	0.694039	0.584946	0.427481	0.139393
0.350	0.984925	0.960157	0.924468	0.876781	0.814398	0.732298	0.620730	0.455566	0.148921
0.400	0.993398	0.976777	0.948583	0.906861	0.848265	0.767197	0.653247	0.480965	0.157513
0.450	0.998330	0.989516	0.969196	0.933815	0.879178	0.799195	0.683010	0.504138	0.165335
0.500	0.999909	0.997414	0.985624	0.957504	0.907332	0.828635	0.710412	0.525430	0.172511

ω₀	γ₀(ω₀)	γ₁(ω₀)	γ₂(ω₀)	γ₃(ω₀)	γ₄(ω₀)	γ₅(ω₀)	r ²
0.05	0.95609	0.41762	1.8653	5.3139	9.0900	6.6281	0.99992
0.10	0.90763	0.73428	3.2760	10.415	18.715	13.196	0.99991
0.15	0.85958	0.97587	4.1853	13.523	24.053	16.382	0.99995
0.20	0.81145	1.1718	4.7173	14.839	25.423	16.520	0.99996
0.25	0.76304	1.3459	5.1578	15.933	26.616	16.805	0.99996
0.30	0.71437	1.5039	5.5563	17.038	28.177	17.665	0.99997
0.35	0.66548	1.6481	5.9213	18.146	30.012	18.943	0.99997
0.40	0.61639	1.7788	6.2421	19.151	31.795	20.297	0.99998
0.45	0.56712	1.8959	6.5105	19.966	33.270	21.463	0.99998
0.50	0.51768	1.9995	6.7251	20.552	34.304	22.303	0.99998
0.55	0.46807	2.0895	6.8909	20.910	34.870	22.774	0.99998
0.60	0.41827	2.1657	7.0186	21.070	35.006	22.899	0.99998
0.65	0.36826	2.2278	7.1237	21.092	34.810	22.741	0.99999
0.70	0.31802	2.2744	7.2282	21.069	34.447	22.413	0.99999
0.75	0.26751	2.3030	7.3619	21.149	34.188	22.102	0.99999
0.80	0.21670	2.3080	7.5606	21.546	34.462	22.112	0.99999
0.85	0.16560	2.2753	7.8495	22.521	35.857	22.886	0.99999
0.90	0.11433	2.1659	8.1620	24.143	38.785	24.816	0.99998
0.95	0.063265	1.8473	7.9291	24.867	41.055	26.660	0.99996
0.97	0.042914	1.5580	7.1137	22.981	38.530	25.250	0.99993
0.99	0.021309	0.97834	4.7437	15.778	26.869	17.777	0.99989

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Equations (33)

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