Semi-analytical model for deep-water hyperspectral imaging

Håvard Snefjellå Løvås; Håvard Snefjellå Løvås; Martin Kvisvik Larsen; Oscar Pizarro; Oscar Pizarro; Oscar Pizarro; Asgeir J. Sørensen; Asgeir J. Sørensen

doi:10.1364/AO.499334

Applied Optics
Vol. 62,
Issue 33,
pp. 8832-8848
(2023)
•https://doi.org/10.1364/AO.499334

Semi-analytical model for deep-water hyperspectral imaging

Håvard Snefjellå Løvås, Martin Kvisvik Larsen, Oscar Pizarro, and Asgeir J. Sørensen

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Håvard Snefjellå Løvås, Martin Kvisvik Larsen, Oscar Pizarro, and Asgeir J. Sørensen, "Semi-analytical model for deep-water hyperspectral imaging," Appl. Opt. 62, 8832-8848 (2023)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: June 30, 2023
- Revised Manuscript: October 22, 2023
- Manuscript Accepted: October 23, 2023
- Published: November 16, 2023

Abstract

We propose a semi-analytical (SA) model for relating seafloor reflectance to measured radiance in deep-water hyperspectral imaging in artificially illuminated scenes. Using accurate sensor-seafloor geometry from photogrammetry and the principle of two-viewpoint observation, we estimate the inherent optical properties (IOPs) of the water column. We demonstrate the SA model and estimation of IOPs for hyperspectral imaging of a deep-water coral reef from a remotely operated vehicle. For the calibrated SA model, evaluation of across-viewpoint similarity demonstrates the model’s ability to compensate for water column and light source effects.

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Symbol	Meaning
$a$	Spectral absorption coefficient of the constituents (with different subscripts) or the total water body (no subscript).
$b_{s}^{}$ , $b_{l}^{}$	Specific spectral scattering coefficients of small and large particles.
$b$ , $b_{b}$ , $b_{w}$ , $b_{p}$	$b$ is the total spectral scattering coefficient, $b_{b}$ is the spectral backscattering coefficient, $b_{w}$ is the seawater scattering coefficient, and $b_{p}$ is the particle scattering coefficient.
$κ$ , $κ_{w}$	Spectral quasi-single scattering approximation beam attenuation for the water body and for pure seawater.
$λ$	Spectral wavelength in nanometers.
$B_{s}$ , $B_{l}$	Scalar particle concentration for small and large particles.
$G$	Scalar absorption of CDOM at 440 nm.
$\hat{β}$	Total or constituent scattering phase function (depending on the subscript). The total phase function is spectral and directional.
$β$	Parameter vector consisting of the three scalar IOP parameters $B_{s}$ , $B_{l}$ , and $G$ .
$η$	Spectral pure water molecular scattering fraction.
$D_{d}$ , $D_{u}$	Spectral distribution functions, or path elongation factors, for downward heading irradiance and upward heading radiance. We approximated these as scalars.
$K_{d}$ , $K_{u}$	Spectral diffuse attenuation coefficients for the downward heading (seafloor incident) irradiance and the upward heading (sensor incident) radiance. Both describe light extinction as a function of path length (not along the vertical direction).
$L$ , $E$ , $I$ , $Φ$	Spectral radiance, irradiance, radiant intensity, and radiant power.
$I_{f}$	Spectral and directional immersion factor relating the in-air radiance to the in-water radiance for the hyperspectral imager (HSI). We approximate it as a scalar.
$ρ$ , $R$	$ρ$ is the bottom spectral reflectivity specific to each point on the seafloor. $R$ is spectral apparent reflectance, meaning the measured in-water radiance normalized by the spectral shape of the light source.
$F$ , $G$	$F$ is a spectral transfer function that describes the relationship between the total radiance contributed by the sea floor and $ρ$ . $G$ is the total backscattered spectral radiance from the water column.
err	err is a scalar that quantifies the SA model’s ability of relating two corresponding measured spectra across viewpoints.

Label	$n_{t o t}$ [ $\times 10^{3}$ ]	$n$ [ $\times 10^{3}$ ]	$E (l_{h, 1}) [m]$	$E (l_{h, 2}) [m]$	$E (\| l_{h, 1} - l_{h, 2} \|) [m]$
DS1	2536	68 (2.7%)	$2.25 \pm 0.31$	$2.16 \pm 0.54$	$0.50 \pm 0.23$
DS2	1272	48 (3.8%)	$2.64 \pm 0.45$	$2.55 \pm 0.45$	$0.52 \pm 0.20$

	$μ$ (median)	$σ$ (MAD)	$c (G)$	$c (B_{s})$
$G_{1}$ [1/m]	0.20 (0.20)	0.01 (0.01)	1	0.48
$G_{2}$ [1/m]	0.19 (0.19)	0.02 (0.02)	1	0.90
$B_{s, 1}$ [ ${g / m}^{3}$ ]	0.31 (0.35)	0.10 (0.07)	0.48	1
$B_{s, 2}$ [ ${g / m}^{3}$ ]	0.20 (0.19)	0.07 (0.06)	0.90	1
$B_{l, 1}$ [ ${g / m}^{3}$ ]	0.29 (0.22)	0.25 (0.15)	−0.29	−0.92
$B_{l, 2}$ [ ${g / m}^{3}$ ]	0.27 (0.27)	0.18 (0.15)	−0.90	−0.97

Symbol	Meaning
$a$	Spectral absorption coefficient of the constituents (with different subscripts) or the total water body (no subscript).
$b_{s}^{}$ , $b_{l}^{}$	Specific spectral scattering coefficients of small and large particles.
$b$ , $b_{b}$ , $b_{w}$ , $b_{p}$	$b$ is the total spectral scattering coefficient, $b_{b}$ is the spectral backscattering coefficient, $b_{w}$ is the seawater scattering coefficient, and $b_{p}$ is the particle scattering coefficient.
$κ$ , $κ_{w}$	Spectral quasi-single scattering approximation beam attenuation for the water body and for pure seawater.
$λ$	Spectral wavelength in nanometers.
$B_{s}$ , $B_{l}$	Scalar particle concentration for small and large particles.
$G$	Scalar absorption of CDOM at 440 nm.
$\hat{β}$	Total or constituent scattering phase function (depending on the subscript). The total phase function is spectral and directional.
$β$	Parameter vector consisting of the three scalar IOP parameters $B_{s}$ , $B_{l}$ , and $G$ .
$η$	Spectral pure water molecular scattering fraction.
$D_{d}$ , $D_{u}$	Spectral distribution functions, or path elongation factors, for downward heading irradiance and upward heading radiance. We approximated these as scalars.
$K_{d}$ , $K_{u}$	Spectral diffuse attenuation coefficients for the downward heading (seafloor incident) irradiance and the upward heading (sensor incident) radiance. Both describe light extinction as a function of path length (not along the vertical direction).
$L$ , $E$ , $I$ , $Φ$	Spectral radiance, irradiance, radiant intensity, and radiant power.
$I_{f}$	Spectral and directional immersion factor relating the in-air radiance to the in-water radiance for the hyperspectral imager (HSI). We approximate it as a scalar.
$ρ$ , $R$	$ρ$ is the bottom spectral reflectivity specific to each point on the seafloor. $R$ is spectral apparent reflectance, meaning the measured in-water radiance normalized by the spectral shape of the light source.
$F$ , $G$	$F$ is a spectral transfer function that describes the relationship between the total radiance contributed by the sea floor and $ρ$ . $G$ is the total backscattered spectral radiance from the water column.
err	err is a scalar that quantifies the SA model’s ability of relating two corresponding measured spectra across viewpoints.

Label	$n_{t o t}$ [ $\times 10^{3}$ ]	$n$ [ $\times 10^{3}$ ]	$E (l_{h, 1}) [m]$	$E (l_{h, 2}) [m]$	$E (\| l_{h, 1} - l_{h, 2} \|) [m]$
DS1	2536	68 (2.7%)	$2.25 \pm 0.31$	$2.16 \pm 0.54$	$0.50 \pm 0.23$
DS2	1272	48 (3.8%)	$2.64 \pm 0.45$	$2.55 \pm 0.45$	$0.52 \pm 0.20$

Håvard Snefjellå Løvås	https://orcid.org/0000-0002-4887-0860
Martin Kvisvik Larsen	https://orcid.org/0000-0003-3047-084X
Oscar Pizarro	https://orcid.org/0000-0001-6612-2738

Abstract

Data availability

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Figures (12)

Tables (3)

Equations (41)

Applied Optics