Scattering by Large Bubbles: Correction for Debye Coefficient at a Small Number of Sub-Waves

I found that when the Debye theory calculates the far-field scattered light intensity of bubbles, the forward scattered light intensity is quite different from the result calculated by the Mie theory due to the convergence problem, so the expression of the Debye coefficient has been revised. I derived the Debye reflectance and transmittance according to the physical meaning of Debye theory and compared them with Fresnel’s formula. I modified the Debye coefficient expressions for bubbles based on the differences between the Debye reflectance and transmittance from the Fresnel formula. Finally, compared with the far-field scattered light intensity calculated by the original Debye theory, the far-field scattered light intensity calculated based on the modified Debye coefficient can obtain more accurate forward scattered light intensity with fewer sub-waves.