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Optical wide-field tomography of sediment resuspension

Adi Vainiger, Yoav Y. Schechner, Tali Treibitz, Aviad Avni, and David S. Timor

Open Access Open Access

Abstract

We present a wide-field imaging approach to optically sense underwater sediment resuspension events. It uses wide-field multi-directional views and diffuse backlight. Our approach algorithmically quantifies the amount of material resuspended and its spatiotemporal distribution. The suspended particles affect the radiation that reaches the cameras, hence the captured images. By measuring the radiance during and prior to resuspension, we extract the optical depth on the line of sight per pixel. Using computed tomography (CT) principles, the optical depths yield estimation of the extinction coefficient of the suspension, per voxel. The suspended density is then derived from the reconstructed extinction coefficient.

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

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Figures (9)
Fig. 1
Fig. 1 The concept of an underwater optical tomography system. The volume includes water and a resuspended sediment cloud. There are n voxels. A line of sight corresponding to pixel p is LOSp.

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Fig. 2
Fig. 2 Simulations. (a) Scenario illustration: the cameras are distributed uniformly on a 125° arch of height of 0.5 [m], and facing the cloud from a 3 [m] distance. Note: for visualization we used an open source 3D camera model [41]. (b) Representative images of several side views (water images IWater, cloud images I, optical depth images τ in the green channel). (c) The reconstructed β ^ Sed of the cloud . (d) Reconstruction errors vs. the number of IDS UI3260xCP-C cameras.

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Fig. 3
Fig. 3 (a) System design. (b) The camera housing is made of polycarbonate resin, sealed using a flat–port, and contains: an ODROID XU-4 computer, an IDS UI3260xCP-C camera with Tamron M112FM12 12 [mm] lens, Li-ion batteries and a nano USB WiFi adapter.

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Fig. 4
Fig. 4 (a) Side view of the system outside of the pool. The nozzle emerges from the middle of the screen, and the cameras’ rig is centered above the screen at a height of 2.5 [m]. (b) Top view of the system submerged in a seawater pool. (c) Submerged screen and active calibration board.

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Fig. 5
Fig. 5 Experiment: (a) Representative images of two cameras. Each camera yields a clear water image IWater, an image having resuspension I; The optical depth τ in the green channel; A pruned optical depth image τmasked. (b) Initial reconstruction β ^ Sed ( 0 ) of the cloud in the green channel. (c) Final reconstruction β ^ Sed of the cloud in the green channel.

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Fig. 6
Fig. 6 (a) The estimated mass of a resuspension event, after each resuspension initiation. Each curve averages two experiment repetitions (shown as ∗ and ◦). (b) Average reconstructed mass of 30 [ mgr cm 3 ] source suspension density ( ≜ μ ^ total , 1 Sed) vs. average reconstructed mass of 22.5 [ mgr cm 3 ] source suspension density ( ≜ μ ^ total , 2 Sed).

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Fig. 7
Fig. 7 (a) An RGB image of the cloud, 46 [sec] after the cloud’s initiation. (b) The estimated optical depth τ in the green channel. The values of τ are presented in a false-color palette manner. Negative values beyond screen borders are due to scattered light contributing to measured radiance.

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Fig. 8
Fig. 8 Calibration results of βSed vs. ρSed for RGB channels. The non-linear domain is due to multiple-scattering [49]. The images demonstrate the intensity attenuation of the transmitted light beam, for increasing particle density.

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Fig. 9
Fig. 9 (a) Light path in a water tank from the entry aperture, through a glass beaker with particle suspension, to the camera side. (b) Top-side view. (c) Front view. (d) Water image IWater .

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Equations (17)

Equations on this page are rendered with MathJax. Learn more.

i p Water ≜ i p ( 0 ) exp [ − ∫ X ∈ LOS p β Water d X ] + i p Ambient [ W m 2 ⋅ sr ] .
β Water ≜ β A Water + β S Water [ m − 1 ] ,
ϖ Water ≜ β S Water β A Water + β S Water .
i p = i p ( 0 ) exp [ − ∫ X ∈ LOS p ( β Water + β Sed ( X ) ) d X ] + i p Ambient [ W m 2 ⋅ sr ] .
τ p ≜ ∫ X ∈ LOS p β Sed ( X ) d X .
τ p = − ln ( i p − i p Ambient i p Water − i p Ambient ) .
τ p ≈ ∑ v a p , v β v Sed ≜ α p ⋅ β Sed .
τ = A β Sed .
β ^ Sed ≜ arg min β Sed ( ‖ A β Sed − τ ‖ 2 2 + α ‖ ℒ β Sed ‖ 2 2 ) s . t β Sed ≥ 0 .
μ v Sed = ρ v Mass ϑ [ gr ] .
β v Sed = σ ρ v # [ m − 1 ] .
β v Sed ≜ b ρ v Mass [ m − 1 ] .
μ ^ v Sed = ϑ b β ^ v Sed [ gr ] ,
μ ^ total Sed = ∑ v μ ^ v Sed [ gr ] .
δ = ‖ β ^ Sed ‖ 1 − ‖ β Sed ‖ 1 ‖ β Sed ‖ 1 ,
∈ 2 = 1 n ‖ β ^ Sed − β Sed ‖ 2 2 max ( β Sed ) .
β Sed = 1 l ⋅ ln ( i rec Water i rec ) ,
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