Shadow montage and cone-beam reconstruction in 4D-STEM tomography

Diffraction images in a scanning transmission electron microscope (STEM) provide a real-space projection of the sample at sufficient probe defocus. These so-called shadow images can be acquired patch by patch in a 4D-STEM setup using a pixelated detector and assembled into a shadow montage. Due to parallel acquisition within each illuminated patch, an upscaled bright field (BF) image is rendered efficiently in time and with little additional computational demand compared to other STEM techniques. We show that in this shadow regime described by geometrical optics, the algorithm achieves the result of a tilt-corrected bright field image. Furthermore, the solution is equivalent to cone-beam reconstruction in a particular scenario of a scanning point illumination source in a plane. The contrast transfer is similar to that of conventional wide-field TEM, but like STEM the focus is insensitive to energy loss and objective lens chromatic aberration. By adjusting the overlap between shadow patch images in the diffraction plane, the shadow montage is synchronized to specific layers in the sample, rendering a 3D shadow volume from a single dataset. The method is also amenable to conventional tilt tomography, by adding a shadow montage or shadow volume to each tilt view prior to back-projection. This approach effectively circumvents the basic presumption of parallel-projection tomography that the depth of field must be greater than the specimen thickness.