Institut fur Lasertechnologien in der Medizin und Messtechnik, Helmholtzstrasse 12, Ulm, D-89081 Germany.
J Biomed Opt. 2010 Mar-Apr;15(2):025003. doi: 10.1117/1.3368685.
We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.
我们研究了 N 层混浊介质中的光扩散。针对具有有限或无限厚的第 N 层的 N 层混浊介质，求解了稳态扩散方程。各层的折射率不同。应用傅立叶变换形式主义推导出了在傅立叶空间中通量率的解析解。通过使用四种不同的方法计算逆傅立叶变换，以测试它们的性能和准确性。此外，为了避免数值误差，还在傅立叶空间中推导出了近似公式。通过使用这些方法，我们找到了计算具有小相对差异（<10(-7))的 N 层混浊介质的空间分辨反射率和透射率的快速解决方案（大约 10 毫秒）。此外，还将扩散方程的解与具有多达 20 层的混浊介质的蒙特卡罗模拟进行了比较。
