为准确地测量出尾流气泡群的衰减,提高前向光尾流探测的可靠性,研究了气泡数密度对尾流光束衰减测量的影响.基于辐射传输方程的小角度近似解,得到了探测截面上的约化功率和漫射功率的表达式.根据测量条件,引入了有尾流气泡和无尾流气泡时探测截面上接收到的辐射功率之比作为透射函数,并进一步引进了复散射校正因子,它表征了复散射效应的强弱.针对典型的尾流气泡分布,通过数值计算得到了不同测量条件下气泡数密度与复散射校正因子、透射函数的关系.数值计算结果表明：复散射校正因子都随气泡数密度的增大单调的增大,透射函数都随气泡数密度的增大单调的减小；测量条件不同,气泡数密度对光束衰减的影响也不同.研究结果表明,给定测量条件和透射比时,利用小角度辐射方程可以得到气泡群数密度的量化信息.

To measure the beam attenuation in ship wakes accurately and improve the reliability of detecting ship wakes by forward light attenuation,the influence of bubbles′ number density on the measurement of beam attenuation in wakes was investigated.The scattered power and un-scattered power on the detector cross-section were derived based on radiative transfer equation in small angle approximation.According to the measurement condition,transmission function,which is the ratio of the received power by detector in wakes to the received power by detector in non-wakes marine environment,was introduced.Correction coefficient,denoting the extent of multiple scattering,was further introduced.Given a typical bubble distribution in wakes,the numerical results relating the transmission function and correction coefficient to bubbles′ number density under different measuring conditions were presented.The numerical results show that,the correction coefficient increases monotonously but the transmission function decreases monotonously as the bubbles′ number density increases; the influence of bubbles′ number density on beam attenuation is different as the measurement conditions change.The results show that,given a measurement condition and transmission function,the bubbles′ number density can be quantified by means of radiative transfer equation in small angle approximation.