Image formation in the scanning transmission electron microscope using object-conjugate detectors

This work presents a theoretical analysis of image formation in a scanning transmission electron microscope equipped with electron detectors in a plane conjugate to the specimen. This optical geometry encompasses both the three-dimensional imaging technique of scanning confocal electron microscopy (SCEM) and a recently developed atomic resolution imaging technique coined real-space scanning transmission electron microscopy (R-STEM). Image formation in this geometry is considered from the viewpoints of both wave optics and geometric optics, and the validity of the latter is analysed by means of Wigner distributions. Relevant conditions for the validity of a geometric interpretation of image formation are provided. For R-STEM, where a large detector is used, it is demonstrated that a geometric optics description of image formation provides an accurate approximation to wave optics, and that this description offers distinct advantages for interpretation and numerical implementation. The resulting description of R-STEM is also demonstrated to be in good agreement with experiment. For SCEM, it is emphasized that a geometric optics description of image formation is valid provided that higher-order aberrations can be ignored and the detector size is large enough to average out diffraction from the angle-limiting aperture.