Cascaded machine learning model for reconstruction of surface topography from light scattering

In this paper, we propose a light scattering method to identify classes of structured surface topographies and estimate their main geometric properties. The method is based on a cascaded machine learning model, designed as a two-layer architecture implemented using neural networks. The first layer consists of a classification model designed to determine which type/class of surface is being observed amongst a set of predefined surfaces The second layer, cascaded to the first one, is designed to infer geometric properties specific to the individual structured surface being measured within each class, for example, pitch and height for a grating-type surface. The training datasets for the cascaded machine learning model, i.e. scattering signals from different surfaces, are generated through rigorous scattering simulation applied to computer-generated surfaces and based on a boundary element method. Once the model is trained, any scattering signal obtained from a real surface belonging to the considered classes can be fed into the model, and both the surface class and specific values for its geometric properties can be quickly estimated. For validation, we developed a prototype experimental apparatus to generate light scattering data from real surface samples. Different grating patterns (classes) were considered, as well as different values for the main geometric properties specific to each class. Validation consisted both in the assessment of classification performance in recognising instances of each specific class and in quantification of estimation accuracy in determining the geometric properties of each instance, by comparison with measurements performed with atomic force microscopy.