Abstract
The brightness of an object in a parallel beam with the intensity of light of I0 seen from the position of the light source, can be represented by the following equation:
H=1/π•RI0•e-2σγ+αI0/2σ(1-e-2σγ), (1)
where, R: index of reflection of the object,
σ: coefficient of absorption in water,
α: coefficient of scattering per unit solid angle by unit volume of water againstthe direction of the incident light,
γ: distance from the light source to the object.
In the above equation, the first term is the brightness shown by the object itself, while the second is the contribution to the brightness by the water existing between the object and the position of the eyes.
In Eq. (1) when γ=∞, the brightness shown by the water itself where there exists no object will be obtained. Then, Should it be put as H∞,
H∞=αI0/2 ?? (2)
Consequently,
log(H-H∞)=long(RI0/π-H∞)-2σγ.
Therefore, it is learned that log (H-H∞) and γ are in an linearity. The coefficient of absorption σ can be obtained out of this by measuring H∞ and the brightness of the object in each distance.
Generally speaking, that an object becomes unrecognisable means the contrast between the object and the surrounding brightness becomes below η, or the threshold of the eyes. Therefore, the underwater visibility in a parallel beam is determined out of the following relationship;
H-H∞/H∞=η (3)
(However, H ?? H∞, namely, η ?? 0 against R πα/2σ)* Visibility v, when an object in a parallel beam is seen at the position of light source, can be obtained from Eqs. (1), (2) and (3), as follows;
v=1/2σlog{(2σ/α•π•R-1)•1/η} Therefore, as for a black object that does not perfectly reflect light, putting R=0,
v ?? =1/2σlog1/η. (5)
From Eqs. (4) and (5), the following equation will be obtained as a relative equation between the visibilities of an object of R=0 and an object having an index of reflection R.
v-v ?? =1/2σlog (2σ/απ•R-1). (6)
In other words, it is seen that the visibilities of a black object is affected by coefficient of absorption alone, in the optical nature of water, and is in an inverse proportion. And, as for an object the index of reflection which is not zero, it is affected by a factor σ/α. There-fore, even in water with the same coefficient of absorption, the visibility becomes smaller as the coefficient of scatterieg α becomes larger. Also, by Eq. (6), when σ is known, out of the measurement of visibilities of an object having a fixed index of reflection and a black object, coefficient of scattering a will be obtainable, as is known.
Here, the present authors are desirous to report the coefficients of absorption and scattering that calculated from the results of measurements of the brightness and visibility of the object in a parallel beam. Also, results obtained by measuring the horizontal visibility in sea-water in the bathysphere will be explained.
