Automated focusing and astigmatism correction in electron microscopy

Nowadays electron microscopy still requires an expert operator in order to manually obtain in-focus and astigmatism-free images. Both the defocus and the twofold astigmatism have to be adjusted regularly during the image recording process. Possible reasons are for instance the instabilities of the environment and the magnetic nature of some samples. For some applications the high level of repetition severely strains the required concentration. Therefore, a robust and reliable autofocus and twofold astigmatism correction algorithm is a necessary tool for electron microscopy automation. Most of the automatic focusing methods are based on a sharpness function, which delivers a real-valued estimate of an image quality. In this thesis we study sharpness functions based on image derivative, image Fourier transform, image variance, autocorrelation and histogram. A new method for rapid automated focusing is developed, based on a quadratic interpolation of the derivative-based sharpness function. This function has been already used before on heuristic grounds. In this thesis we give a more solid mathematical foundation for this function and get a better insight into its analytical properties. Further we consider a focus series method, which could act as an extension for an autofocus technique. The method is meant to obtain the astigmatism information from the focus series of images. The method is based on the moments of the image Fourier transforms. After all the method of simultaneous defocus and astigmatism correction is developed. The method is based on a three-parameter optimization (Nelder-Mead simplex method or interpolation-based trust region method) of a sharpness function. All the three methods are employed for the scanning transmission electron microscopy. To be more specific, we have implemented them in the FEI scanning transmission electron microscope and successfully tested their performance as a part of a real-world application.