Image Reconstruction For Fast Non-raster Scanning Atomic Force Microscopy Using Gaussian Process

Atomic force microscopy is a powerful tool that has had a tremendous impact on understanding systems with nanometer-scale features.But the traditional raster scanning pattern cannot meet the requirement of highspeed scanning.In contrast,the non-raster scanning patterns that are based on sinusoidal trajectories provide a novel perspective of the realization of high-speed atomic force microscopy.By designing the trajectories that are suitable for the mechanical systems,these patterns avoid tremendous engineering difficulties.However,there exist several problems for the application of the nonraster scanning patterns.First,the lengths of the non-raster scanning paths are shortened.When the sampling frequency of these scanning patterns equals that of the raster scanning pattern,the number of the sampling points will be reduced.Second,the points sampled by the non-raster scanning trajectories are located in non-raster positions.Thus,the metrological performance of the method largely depends on the posterior data processing techniques which are responsible for recovering measured surfaces from relatively few non-raster data.Firstly,this thesis has analyzed the difficulty of achieving high-speed scanning from the perspective of the imaging process.The non-raster scanning patterns are investigated,including spiral scanning,Lissajous scanning,and sinusoidal scanning.The advantages and disadvantages of existing image reconstruction methods based on non-raster scatter points are analyzed.In this thesis,a new method of imaging is presented,which combines the data collected by the sensor with the reconstruction technology.Secondly,this thesis proposes a Gaussian process regression model to reconstruct images from non-raster sampling points.The reconstruction problem is cast as a regression problem and the spatial correlations of the non-raster data are represented by the covariance functions.The sapling points and the raster positions are treated as the training set and the testing set,respectively.The statistic nature of the Gaussian process regression offers great flexibility in reconstructing various topographies with high accuracy by designing task-specific covariance functions.The experimental study has verified the accuracy and the adaptability of the Gaussian process regression model in reconstructing images and enhancing the performance of non-raster scanning atomic force microscopy.Furthermore,this thesis investigates semi-sparse non-raster scanning patterns to further shorten the scanning time and enable the non-raster scanning atomic force microscopy to observe the dynamic processes that happen within a second or a few seconds.These patterns inevitably entail the challenge of reconstructing accurate images from semi-sparse sampling points.In this thesis,one of the frames is regarded as the reference frame while the others are regarded as the target frames.Instead of reconstructing the target frames independently,a dependent Gaussian process regression model is proposed to make full use of the information provided by the reference frame and the currently processed target frame.Comparisons with the renowned Delaunay triangulation-based interpolation method and the Gaussian process regression method prove that the proposed method has dramatically improved the reconstruction accuracy of multi-frame semisparse video images.The study will lay a solid foundation for the further development of high-speed non-raster scanning atomic force microscopy.