Optimized detector configurations for the reconstruction of phase-contrast images in scanning transmission electron microscopy

Using the differential phase contrast mechanism and anti-symmetric detector geometries it is possible to image distributions of electric and magnetic fields in a scanning transmission electron microscope. Different detector geometries can be used for imaging and, due to their efficiency, mainly ring quadrant detectors and pixelated detectors have been used in recent high resolution differential phase contrast experiments. In 4D-Scanning Transmission Electron Microscopy one uses a pixelated (2D) detector to obtain the complete scattering distribution for every (2D) image point. The accuracy of pixelated detectors increases with an increasing number of pixels, which in turn also leads to a larger amount of data that needs to be evaluated. To reduce the required numerical effort, we are looking for alternative detector geometries by further segmenting ring quadrant detectors. To compare the different geometries, their signal-to-noise ratios are calculated for an ideal STEM and several weak phase objects. Images can be obtained by combining the data of different detector pixels using a scheme similar to a reconstruction from a focal series. The procedure can be interpreted as the simplest example of ptychography including only the first-order diffraction disks. Our results show that a 50-segment annular bright-field detector can reach a signal-to-noise ratio close to that of a 128 x 128 pixelated detector, while having a significantly lower number of segments that need to be evaluated.