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Robust underwater visibility parameter

J. Ronald V. Zaneveld and W. Scott Pegau

Open Access Open Access

Abstract

We review theoretical models to show that contrast reduction at a specific wavelength in the horizontal direction depends directly on the beam attenuation coefficient at that wavelength. If a black target is used, the inherent contrast is always negative unity, so that the visibility of a black target in the horizontal direction depends on a single parameter only. That is not the case for any other target or viewing arrangement. We thus propose the horizontal visibility of a black target to be the standard for underwater visibility. We show that the appropriate attenuation coefficient can readily be measured with existing simple instrumentation. Diver visibility depends on the photopic beam attenuation coefficient, which is the attenuation of the natural light spectrum convolved with the spectral responsivity of the human eye (photopic response function). In practice, it is more common to measure the beam attenuation coefficient at one or more wavelength bands. We show that the relationship: visibility is equal to 4.8 divided by the photopic beam attenuation coefficient; originally derived by Davies-Colley [1], is accurate with an average error of less than 10% in a wide variety of coastal and inland waters and for a wide variety of viewing conditions. We also show that the beam attenuation coefficient measured at 532 nm, or attenuation measured by a WET Labs commercial 20 nm FWHM transmissometer with a peak at 528nm are adequate substitutes for the photopic beam attenuation coefficient, with minor adjustments.

©2003 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. Visibility range at 50m depth versus visibility range at the surface for Jerlov water types I, IA, IB, II, III, 1, 3, 5, 7, and 9. Calculations are for ag(532)=0.33cpg(532), but ag(532)<K(532), γ=1 and S=0.012 (see text).

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Fig. 2.
Fig. 2. Prediction of visibility range using α (blue dots); cpg(532)*0.9+αW(12m) at 532 nm for γ=0, 1, and 2 and for ag/cpg=0 and 0.2 (green dots),similarly for a green LED c *0.9+αW(12m) (red dots). Units are m-1 for attenuation measures and m for visibility range.

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Fig. 3.
Fig. 3. Horizontal visibility of a 200 mm diameter black target. Blue points, Davies-Colley, “green” c-meter; red points, Zaneveld, c(532)*0.9+0.081; black point, Twardowski cpg(532)*0.9+0.081; green points, Pegau, cpg(532)*0.9+0.081;

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Tables (1)

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Table 1. Parameters required to predict visibility range. All situations also require the inherent contrast of the target.

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Equations (23)

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cos ⁡ ( θ ) dL ( θ , ϕ , z ) dz = − c ( z ) L ( θ , ϕ , z ) + ∫ 0 2 π ∫ 0 π β ( θ , ϕ , θ ' , ϕ ' , z ) L ( θ ' , ϕ ' , z ) sin ⁡ θ ' dθ ' dϕ '
cos ⁡ ( θ ) dL ( θ , ϕ , z ) dz = − c ( z ) L ( θ , ϕ , z ) + L * ( θ , ϕ , z ) .
cos ⁡ ( θ ) d L T ( θ , ϕ , z ) dz = − c L T ( θ , ϕ , z ) + L * ( θ , ϕ , z ) .
cos ⁡ ( θ ) d L B ( θ , ϕ , z ) dz = − c L B ( θ , ϕ , z ) + L * ( θ , ϕ , z ) .
cos ⁡ ( θ ) d [ L T ( θ , ϕ , z ) − L B ( θ , ϕ , z ) ] dz = − c [ L T ( θ , ϕ , z ) − L B ( θ , ϕ , z ) ] .
[ L Tr ( θ , ϕ , z ) − L Br ( θ , ϕ , z ) ] = [ L T 0 ( θ , ϕ , z T ) − L B 0 ( θ , ϕ , z T ) ] exp ⁡ ( − cr ) .
C v = L T ( θ , ϕ , z ) − L B ( θ , ϕ , z ) L B ( θ , ϕ , z ) .
C vr ( θ , ϕ , z ) C v 0 ( θ , ϕ , z T ) = exp ⁡ ( − cr ) L B 0 ( θ , ϕ , z T ) L Br ( θ , ϕ , z ) .
K B ( θ , ϕ , z ) = − 1 L B ( θ , ϕ , z ) d L B ( θ , ϕ , z ) dz ,
L B 0 ( θ , ϕ , z T ) L Br ( θ , ϕ , z ) = exp ⁡ [ K B ( θ , ϕ , z ) z ] = exp ⁡ [ K B ( θ , ϕ , z ) r cos ⁡ θ ] ,
C vr ( θ , ϕ , z ) C v 0 ( θ , ϕ , z T ) = exp ⁡ [ − cr + K B ( θ , ϕ , z ) r cos ⁡ θ ]
C vr ( π 2 , ϕ , z T ) C v 0 ( π 2 , ϕ , z T ) = exp ⁡ [ − cr ]
visibility range = − ( 1 c ) ln ⁡ ∣ C L ∣
C vr = N T ( r ) − N B ( r ) N B ( r ) = − exp ⁡ [ − α r ]
visibility range = y = − ( 1 α ) ln ⁡ ∣ C L ∣ .
N T ( r ) = N B [ 1 − exp ⁡ ( − α r ) ]
L T ( λ , r ) = L B ( λ ) [ 1 − exp ⁡ ( − c ( λ ) r ) ]
N T ( r ) = K m ∫ 400 700 L T ( r , λ ) Y ( λ ) dλ
N T ( r ) = K m ∫ 400 700 L T ( r , λ ) Y ( λ ) dλ = K m ∫ 400 700 L B ( λ ) Y ( λ ) [ 1 − exp ⁡ ( − c ( λ ) r ) ] dλ
C vr = N T ( r ) − N B ( r ) N B ( r ) = − exp ⁡ [ − α r ] = ∫ 400 700 L B ( λ ) Y ( λ ) [ − exp ⁡ ( − c ( λ ) r ) ] dλ [ ∫ 400 700 L B ( λ ) Y ( λ ) dλ ] − 1
α U = − ( 1 r ) ln ⁡ { ∫ 400 700 Y ( λ ) [ − exp ⁡ ( − c ( λ ) r ) ] dλ [ ∫ 400 700 Y ( λ ) dλ ] − 1 }
c p ( λ ) c p ( 532 ) = ( λ 532 ) − γ .
a g ( λ ) a g ( 532 ) = exp ⁡ [ − S ( λ − 532 ) ] .
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