Rigorous simulation of speckle fields caused by large area rough surfaces using fast algorithms based on higher order boundary element methods

粗糙表面的光散射有着广泛的实际应用，如遥感、表面检测的光学计量、医学成像中的癌症检测、固体力学中的振动和应变测量。散斑现象几乎可以在任何光学相干成像和测量中观察到。通过分析散斑场可以检索被检测表面的深刻信息。因此，严格的计算是必不可少的理解散斑特性和评估所涉及的表面和结构的属性。虽然严格模拟已经被广泛研究了很长一段时间，许多问题仍然是开放的，由于问题的复杂性和强大的计算挑战。这些包括网格元素的类型如何影响结果，表面应网格化的精细程度，以及不同粗糙度和材料的表面所需的物理尺寸。此外，从测量的散射场导出表面参数的逆方法是强烈期望的，但由于缺乏快速严格的模拟器，尚未得到很好的研究。本项目的目的是提高散斑模拟器的性能（计算速度，感兴趣的区域和表面特性），我们已经开发了高阶边界元法和表面积分方程。在此基础上，我们将在这个项目中实现一个快速多极子方法（FMM）和它的多层版本，即多层快速多极子方法（MLFMM）。这些算法的计算量和内存开销将从O（NxN）减少到O（Nlog（N））。在实验上，我们将制造不同材料的不同粗糙度的表面，并将使用待构建的设置来测量BRDF和散斑场。通过比较模拟结果与测量结果，我们将验证我们的实现，并建立粗糙表面模拟的基准。特别是，我们将提供散斑图作为机器学习过程的训练示例。

Light scattering from rough surfaces are involved in wide-ranging practical applications such as remote sensing, optical metrology for surface inspection, cancer detection in medical imaging, or vibration and strain measurements in solid mechanics. Speckle phenomena can be observed in almost any optical coherent imaging and measurement. Profound information of the surface under inspection can be retrieved via analyzing the speckle fields. Rigorous calculation is therefore indispensable for understanding the speckle properties and for evaluating the properties of the involved surfaces and structures. Although rigorous simulation has been widely studied for a long time, many questions are still open due to the complexity of the problem and the formidable computational challenge. These include how the type of meshing element influences the results, how fine the surface should be meshed, and what a physical size is needed for surfaces with different roughness and materials. In further, inverse approaches to derive surface parameters from measured scattered field are strongly desired, but have not yet been well studied due to the absence of fast rigorous simulators. The objective of this project is to improve the performance of a speckle simulator (calculation speed, area of interest and surface properties), which we have developed using higher order boundary element method and surface integral equations. On this basis, we will in this project implement a fast multipole method (FMM) and its multilevel version, namely, a multilevel fast multipole method (MLFMM). With these algorithms, the computation and memory cost will be reduced from O(NxN) to O(Nlog(N)). Experimentally, we will fabricate surfaces with different roughness of different materials and will measure the BRDF and speckle fields using a setup to be built. Through comparing the simulated results with the measured, we will validate our implementation and build benchmarks for rough surface simulations. In particular, we will provide specklegrams as training examples for a machine learning process.