Geometric Optics in a Phase-Space-Based Level Set and Eulerian Framework
Geometric Optics in a Phase-Space-Based Level Set and Eulerian Framework
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DOI：
10.1006/jcph.2002.7080
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发表时间：
2002-07
影响因子：
4.1
通讯作者：
S. Osher;Li-Tien Cheng;Myung-joo Kang;H. Shim;Y. Tsai
中科院分区：
文献类型：
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作者：
S. Osher;Li-Tien Cheng;Myung-joo Kang;H. Shim;Y. Tsai
介绍了一种用于光线跟踪和几何光学中波前构造的水平集方法。这在波传播的各种应用中都很重要。我们的方法自动处理出现的多值解，并自动解析波前。这是通过在基于欧拉和偏微分方程式的框架下在简化的相空间中求解双特征条带来实现的，该双特征条带到空间空间的投影给出了波前。双特征带用水平集方法表示，用于处理更高的余维对象，而负责演化的偏微分方程组是Liouville方程的简化形式。给出了折射率为常数和可变的二维情况的结果，并与该领域中其他现有方法的结果进行了比较。文中还介绍了该方法处理反射的能力，并将该方法推广到三维情况。
We introduce a level set approach for ray tracing and the construction of wavefronts in geometric optics. This is important in a wide variety of applications in wave propagation. Our approach automatically handles the multivalued solutions that appear and automatically resolves the wavefronts. This is achieved through solving for the bicharacteristic strips, whose projection to spatial space gives the wavefronts, in a reduced phase space under a Eulerian and partial differential-equation-based framework. The bicharacteristic strips are represented using a level set approach for handling higher codimensional objects and the partial differential equations responsible for the evolution are reduced forms of the Liouville equations. Results for the two-dimensional case for constant and variable indices of refraction are shown and compared to those of other current methods in the field. Results are also introduced to show the ability to handle reflection and to extend the method to the three-dimensional case.