Calculation approach of bubble scattering properties

To analyze the changes in the polarization characteristics of the ocean surface caused by foam scattering, we propose a novel approach utilizing geometric optics approximation theory and Fraunhofer diffraction theory to characterize the scattering properties of bubbles composing foam. Assuming that the bubbles are spherical particles coated with a uniformly thick layer of material exhibiting absorption-scattering feature. The polarized Monte Carlo method is employed to simulate the propagation of lights carrying Stokes vectors within bubbles. Counting all the lights leaving the outer surface of bubble and calculating the scattering properties of bubble, including scattering/absorption efficiency factors and scattering phase function matrix. Validity of the proposed method in this paper is confirmed through comparison with the results calculated by Mie scattering methods under identical computing conditions. As an application, the method proposed in this paper is utilized to compute the scattering properties of bubbles under various conditions. On this basis, an analysis was conducted to investigate the influence of bubble diameter, void fraction, and wavelength on the scattering properties of bubbles. The results indicate that: when the absorbability of the water film is not considered, the scattering phase function of the bubble is greatly influenced by its internal structure, and as the inner and outer diameter ratio of the bubble gradually increases, the scattering phase function gradually flattens as the scattering angle increases, and the linear polarization ratio also exhibits a similar change rule; when the absorbability of the water film cannot be ignored, the scattering phase function and linear polarization ratio are hardly affected by the internal structure of the bubble. The scattering phase function of the bubble is extremely sensitive to the change of the particle diameter only when the scattering angle is 0°, but under other scattering angle conditions, the scattering phase function and linear polarization ratio are hardly affected by the particle diameter.