应用有限元模拟方法, 在外推边界条件下研究圆柱介质中的光传输问题, 讨论了不同光学参数条件下圆柱表面空间分辨反射率和穿透深度的规律, 并且与有限元分析、Monte Carlo模拟和解析解方法的结果进行比较.结果表明: 有限元模拟的结果与Monte Carlo模拟的结果吻合度很好, 其空间反射率在光学参数满足漫射近似条件μ′s/μa≥5时误差小于10%, 在非近源区甚至小于5%; 穿透深度的值随μ′s/μa值增大而增大.但比Monte Carlo模拟的穿透深度略小, 误差不超过7%, 且μ′s/μa的值越大时该误差越小.有限元模拟结果比解析解方法的结果误差要更小, 解析解方法在μ′s/μa≥5时, 其误差在非近源区接近10%, 在近源区会超过15%.此外比较了三种方法的计算速度.单次运算有限元模拟用时约385 s, 甚至比通常用于快速计算的解析解方法(单次运算耗时416 s)更快, 而Monte Carlo模拟单次运算耗时8~9 h.考虑到有限元模拟方法的介质模型构建简便, 计算速度快, 且模拟结果有着不错的精度, 该方法对圆柱边界乃至一般具有曲率的复杂介质中光子辐射传输问题具有非常好的应用前景.

In this paper, we used finite element simulation to study the light diffusion in cylinder. The spatial reflectance of different optical methods was discussed in details. The results were in good agreement with that of Monte Carlo simulation. When μ′s/μa≥5, the error was less than 10% and when in the far-source zone, the error was even less than 5%. Besides the light penetration depths obtained from finite element simulation were also very close to the results of Monte Carlo simulation, which was only a little lower due to the diffusion approximation. The error was no more than 7% and decreasing with higher value of μ′s/μa. Moreover, finite element simulation results were more accurate than analytical solution. The error of analytical solution was about 10% in the far-source zone and more than 15% at the near-source zones. The calculation time of the three methods were also compared. For one simulation, it cost about 385 second for finite element simulation, 416 seconds for analytical solution and 8~9 hours for Monte Carlo simulation. The finite element simulation has better accuracy than analytical solution while has much faster calculation speed than Monte Carlo simulation. So it is an effective and promising method to solve light diffusion in cylinder or turbid with curvatures.