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

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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.