High-speed 4-dimensional scanning transmission electron microscopy using compressive sensing techniques

Here we show that compressive sensing allows 4-dimensional (4-D) STEM data to be obtained and accurately reconstructed with both high-speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4-D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal-to-noise ratio in the recovered phase using 0.3% of the total data. Lay abstract: Four-dimensional scanning transmission electron microscopy (4-D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2-dimensional signal is acquired at each 2-D probe location, equating to a 4-D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4-D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100-1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4-D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10-100 times. The acquired data is then processed to fill-in or inpaint the missing data, taking advantage of the inherently low-complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4-D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4-D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100-300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.