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Photoelectric Detecting System for measuring the Number density of Ship Optical-wakes' Bubbles

This paper aims to design a detecting system for measuring the number density of ship wake's bubbles based on its optical forward scattering characteristics. The sizes of ship wakes' bubbles are almost in the range from 10~300um, which are far greater than the wavelength of incident blue or green light, so the bubbles' scatterings are predominantly the small angled. The theoretic expression of the received power, coming from the detector placed on the axis of incident direction, is derived from narrow-angle radiative transfer equation. And the transmission function, denoting the ratio of received radiant power to reference power, is introduced, which is a function of bubbles' size and concentration. The reference power, decided by experimental condition, is obtained from the same detector when there are no bubbles in testing region. Since the received power and reference power can be obtained from detectors distinctly, given the detecting system and bubbles size distribution, we can find the bubbles' concentration. Based on this method, we designed a testing system to detect the simulated ship wakes, and obtained the number density of the bubbles. The theoretic analysis and experimental results confirmed that this detecting system and method can be used for measuring the bubbles number density of ship wakes.