Inversion of Volume Scattering Function for Estimation of Bubble Size Distribution in Ocean Waters

Angular distribution of the intensity of light scattered by a spherical air bubble in the oceanic medium is distinctive near the critical scattering angle region, when light interacts with a bubble with a refractive index less than its surrounding medium. This study is aimed at presenting theoretical and experimental results for the volume scattering function (VSF) of the bubbles generated under oceanic and laboratory conditions. The effect of bubbles on the VSFs was investigated using Mie calculations for the bubble sizes ranging from 5 to
$200~\mu \text{m}$
and their size distribution slopes ranging from 3.6 to 4.6. Findings revealed that the critical angle scattering patterns (50°-80°) produced by bubbles become well-pronounced, enhanced and dependent on the minimum and maximum bubble sizes and their size distribution slopes (
$r_{min}$
,
$r_{max}$
and
$\alpha$
). A relationship of the volume scattering phase function (
$\tilde {\beta }(\theta, \lambda))$
between an inverse power-law and a normally-distributed bubble population was established based on experimental data. Both experimental results and Mie simulations showed that the angular position of the first critical dark fringe (
$\theta _{1}$
) shifts in the direction of the critical angle as the minimum and mean values of the bubble size increase in accordance with the power law and normally-distributed bubble populations. The new inversion method predicted the light scattering patterns produced by bubbles near the critical angle region in close agreement with results from Mie theory simulations. The inversion method for estimating the bubble size distribution based on the measured VSF data have significant implications for underwater optical communication, imaging and ocean colour remote sensing studies.