Abstract

A semianalytic Monte Carlo model is developed to simulate oceanic high-spectral-resolution lidar (HSRL) signals with multiple scattering. The phase function effects on oceanic HSRL retrieval are studied, e.g., the effective particulate 180° volume scattering function (VSF) and lidar attenuation coefficient that describe characteristics of backscatter and attenuation, respectively. The results demonstrate that the particulate backward and forward phase functions both have a significant influence on δ1, which is the relative difference between the effective and true particulate 180° VSF. The values of |δ1| are typically quite small for all phase functions at the water surface and increase with depth up to ~17% for the Fournier and Forand (FF) phase function but up to ~40% for the two-term Henyey-Greenstein (TTHG) phase function and ~75% for the one-term Henyey-Greenstein (OTHG) phase function. The reason that δ1 is not zero is due to broadening of backscattering angles from 180° caused by multiple scattering and uneven backward phase function. Also, the reason that maximum TTHG and OTHG |δ1| are larger than FF is due to less sharply increasing feature of FF in the backward direction. In addition, the particulate forward phase functions are closely related to δ2, which is the relative deviation between the lidar attenuation coefficient and the sum of the absorption and backscattering coefficients. The values of δ2 are small for all phase functions at the water surface and increase with depth up to ~12% for TTHG but up to ~26% for FF and ~31% for OTHG, due to the less peaked forward phase functions that result in more angular spread of the beam with depth and therefore result in less photons within the field of view of the lidar.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

2017 (2)

2016 (1)

2013 (2)

2008 (1)

2006 (1)

2002 (1)

1997 (1)

1996 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

1982 (2)

1981 (1)

1974 (1)

A. Morel, “Optical properties of pure water and pure sea water,” Opt. Aspects Oceanogr. 1, 1–24 (1974).

1968 (2)

I. L. Fabelinskii and H. B. Levine, “Molecular Scattering of Light,” Springer Berlin 37, 483–532 (1968).

G. Kullenberg, “Scattering of light by Sargasso sea water,” Deep-Sea Res. 15, 423–424 (1968).

1967 (1)

C. L. O’Connor and J. P. Schlupf, “Brillouin scattering in water: the Landau—Placzek ratio,” J. Chem. Phys. 47(1), 31–38 (1967).
[Crossref]

1941 (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Bai, J.

Behrenfeld, M. J.

Bissonnette, L. R.

L. R. Bissonnette, Lidar and Multiple Scattering (Springer, 2005).

Boss, E.

Campbell, J. W.

Chami, M.

Che, H.

Chen, S.

Cheng, Z.

Churnside, J. H.

Donaghay, P. L.

Fabelinskii, I. L.

I. L. Fabelinskii and H. B. Levine, “Molecular Scattering of Light,” Springer Berlin 37, 483–532 (1968).

Feygels, V. I.

V. I. Feygels, “Airborne lidar system with variable-field-of-view receiver for water optical properties measurement,” Proc. SPIE5155, 12–22 (2003).
[Crossref]

Fournier, G. R.

G. R. Fournier, “Computer-based underwater imaging analysis,” Proc. SPIE3761, 62–70 (1999).
[Crossref]

Gordon, H. R.

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Hair, J. W.

Harmel, T.

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Hieronymi, M.

Hostetler, C. A.

Hu, Y.

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne lidar in the study of marine systems,” Annu. Rev. Mar. Sci. 10(10), 121–147 (2018).
[PubMed]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Joelson, B. D.

Katsev, I. L.

Kattawar, G. W.

Khomenko, G.

Kopilevich, Y. I.

Kullenberg, G.

G. Kullenberg, “Scattering of light by Sargasso sea water,” Deep-Sea Res. 15, 423–424 (1968).

Lee, J. H.

Levine, H. B.

I. L. Fabelinskii and H. B. Levine, “Molecular Scattering of Light,” Springer Berlin 37, 483–532 (1968).

Leymarie, E.

Liu, C.

Liu, D.

Liu, Q.

Liu, Z.

Marchbanks, R. D.

McKee, D.

Mobley, C. D.

Morel, A.

A. Morel, “Optical properties of pure water and pure sea water,” Opt. Aspects Oceanogr. 1, 1–24 (1974).

O’Connor, C. L.

C. L. O’Connor and J. P. Schlupf, “Brillouin scattering in water: the Landau—Placzek ratio,” J. Chem. Phys. 47(1), 31–38 (1967).
[Crossref]

Petzold, T. J.

T. J. Petzold, Volume scattering functions for selected ocean waters (Scripps Institution of Oceanography, 1972).

Polonsky, I. N.

Poole, L. R.

Prikhach, A. S.

Röttgers, R.

Roullier, F.

Schlupf, J. P.

C. L. O’Connor and J. P. Schlupf, “Brillouin scattering in water: the Landau—Placzek ratio,” J. Chem. Phys. 47(1), 31–38 (1967).
[Crossref]

Schulien, J. A.

Shen, Y.

Slade, W.

Su, L.

Sullivan, J. M.

Sundman, L. K.

Surkov, A.

Tang, P.

Twardowski, M. S.

Venable, D. D.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Wu, L.

Xu, P.

Yang, L.

Zege, E. P.

Zhang, Y.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Zhou, Y.

Annu. Rev. Mar. Sci. (1)

C. A. Hostetler, M. J. Behrenfeld, Y. Hu, J. W. Hair, and J. A. Schulien, “Spaceborne lidar in the study of marine systems,” Annu. Rev. Mar. Sci. 10(10), 121–147 (2018).
[PubMed]

Appl. Opt. (7)

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Deep-Sea Res. (1)

G. Kullenberg, “Scattering of light by Sargasso sea water,” Deep-Sea Res. 15, 423–424 (1968).

J. Chem. Phys. (1)

C. L. O’Connor and J. P. Schlupf, “Brillouin scattering in water: the Landau—Placzek ratio,” J. Chem. Phys. 47(1), 31–38 (1967).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Technol. (1)

Opt. Aspects Oceanogr. (1)

A. Morel, “Optical properties of pure water and pure sea water,” Opt. Aspects Oceanogr. 1, 1–24 (1974).

Opt. Eng. (1)

J. H. Churnside, “Review of profiling oceanographic lidar,” Opt. Eng. 53(5), 051405 (2013).
[Crossref]

Opt. Express (4)

Springer Berlin (1)

I. L. Fabelinskii and H. B. Levine, “Molecular Scattering of Light,” Springer Berlin 37, 483–532 (1968).

Other (7)

J. Hair, C. Hostetler, Y. Hu, M. Behrenfeld, C. Butler, D. Harper, R. Hare, T. Berkoff, A. Cook, and J. Collins, “Combined atmospheric and ocean profiling from an airborne high spectral resolution lidar,” in EPJ Web of Conferences, 22001 (EDP Sciences, 2016).
[Crossref]

L. R. Bissonnette, Lidar and Multiple Scattering (Springer, 2005).

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic Press, 1994).

V. I. Feygels, “Airborne lidar system with variable-field-of-view receiver for water optical properties measurement,” Proc. SPIE5155, 12–22 (2003).
[Crossref]

T. J. Petzold, Volume scattering functions for selected ocean waters (Scripps Institution of Oceanography, 1972).

V. I. Haltrin, “Two-term Henyey-Greenstein light scattering phase function for seawater,” in Proceedings. IEEE International Geoscience and Remote Sensing Symposium (IEEE, 1999), pp. 1423–1425.
[Crossref]

G. R. Fournier, “Computer-based underwater imaging analysis,” Proc. SPIE3761, 62–70 (1999).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of oceanic HSRL: (a) structure diagram of oceanic HSRL and the signal spectra for the (b) combined channel and (c) molecular channel.
Fig. 2
Fig. 2 Characteristics of the phase functions: (a) phase functions; (b) integrations of phase functions; (c) relative deviations of phase functions from their 180° values. The term “molecule” refers to the molecular phase function, and the terms “OTHG”, “TTHG”, “FF” and “Petzold” refer to different analytical forms of the particulate phase function.
Fig. 3
Fig. 3 Comparison of the particulate and molecular signals under Case B (coastal ocean, FOV of 50 mrad) between the semianalytic MC and standard MC methods introduced in Section 2 under (a) OTHG, (b) TTHG and (c) FF phase functions.
Fig. 4
Fig. 4 Characteristics of the particulate and molecular signals under Case B (coastal ocean, FOV of 50 mrad): (a) normalized lidar signals; (b) ratios of multiple-scattering signal to single-scattering signal; (c) ratios of total signal to attenuation-minimum signal.
Fig. 5
Fig. 5 Phase function effects on the effective particulate 180° VSF under (a) Case A (clear ocean, FOV of 50 mrad), (b) Case B (coastal ocean, FOV of 50 mrad) and (c) Case C (coastal ocean, FOV of 200 mrad).
Fig. 6
Fig. 6 Phase function effects on the relative differences of the effective particulate 180° VSFs under Case A (clear ocean, FOV of 50 mrad), Case B (coastal ocean, FOV of 50 mrad) and Case C (coastal ocean, FOV of 200 mrad).
Fig. 7
Fig. 7 Phase function effects on the lidar attenuation coefficient under (a) Case A (clear ocean, FOV of 50 mrad), (b) Case B (coastal ocean, FOV of 50 mrad) and (c) Case C (coastal ocean, FOV of 200 mrad).
Fig. 8
Fig. 8 Phase function effects on the relative deviation of the lidar attenuation coefficient from (a + bb) under Case A (clear ocean, FOV of 50 mrad), Case B (coastal ocean, FOV of 50 mrad) and Case C (coastal ocean, FOV of 200 mrad).
Fig. 9
Fig. 9 HSRL signals in different depths under Case B (coastal ocean, FOV of 50 mrad) evaluated by the backscattering angle for (a) OTHG, (b) TTHG and (c) FF phase functions.
Fig. 10
Fig. 10 Phase function effects on the lidar attenuation coefficient under Case B (coastal ocean, FOV of 50 mrad) calculated from the elastic lidar (dotted-dashed lines) and HSRL (solid lines) signals.

Equations (15)

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{ S p ( z ) = C 1 ( n H + z ) 2 β p π ( z ) exp [ 2 0 z α ( ξ ) d ξ ] S m ( z ) = C 2 ( n H + z ) 2 β m π ( z ) exp [ 2 0 z α ( ξ ) d ξ ] ,
β p π ( z ) = C 2 S p ( z ) C 1 S m ( z ) β m π ( z )
α ( z ) = 1 2 d d z ln [ S m ( z ) ( n H + z ) 2 C 2 β m π ( z ) ] .
β ˜ w ( θ ) = 1 4 π [ 1 1 + ( 1 δ ) / 3 ( 1 + δ ) ] ( 1 + 1 δ 1 + δ cos 2 θ ) ,
β ˜ O T H G ( θ ) = 1 g 2 4 π ( 1 + g 2 2 g cos θ ) 3 / 2 ,
β ˜ T T H G ( θ ) = χ β ˜ O T H G ( θ , g 1 ) + ( 1 χ ) β ˜ O T H G ( θ , g 2 ) ,
{ g 2 = 0.30614 + 1.0006 g 1 0.01826 g 1 2 + 0.03644 g 1 3 χ = g 2 ( 1 + g 2 ) ( g 1 + g 2 ) ( 1 + g 2 g 1 ) .
β ˜ F F ( θ ) = 1 4 π ( 1 δ ) 2 δ v [ v ( 1 δ ) ( 1 δ v ) + [ δ ( 1 δ v ) v ( 1 δ ) ] sin 2 ( θ 2 ) ] + 1 δ 180 v 16 π ( δ 180 1 ) δ 180 v ( 3 cos 2 θ 1 ) ,
{ v = 3 μ 2 δ = 4 3 ( n 1 ) 2 sin 2 ( θ 2 ) ,
ξ ( θ ) = 2 π 0 θ β ˜ ( θ ) sin θ d θ .
Δ = β ˜ ( θ ) β ˜ ( π ) β ˜ ( π ) × 100 % .
R 1 ( z ) = S m , p ( z ) S m , p ( 0 ) e x p [ 2 0 z c ( ξ ) d ξ ] ,
R 2 ( z ) = S m , p ( z ) S m , p ( 0 ) e x p { 2 0 z [ a ( ξ ) + b b ( ξ ) ] d ξ } .
δ 1 = β p π β p π β p π × 100 % .
δ 2 = α ( a + b b ) ( a + b b ) × 100 % ,

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