Simulating dynamic image formation in a Transmission Electron Microscope with a proposed electron beam phase plate

Imaging thin organic specimens with Transmission Electron Microscopy (TEM) presents a significant challenge due to their inherently weak contrast. An additional electron optical element, placed in a focal plane of the objective lens, such as a phase plate (PP) can improve the contrast by inducing a relative phase shift between scattered and unscattered electrons. However, any additional optical element can also lead to additional noise due to random and beam-induced variations. To address this problem we have, as a first example, simulated the dynamic image formation of a weak phase object in a TEM equipped with a proposed PP consisting of two electron beams orthogonal to the optical axis of the TEM. The random and beam-induced variation of the PP is simulated with particle dynamics including all pairwise interactions among the electrons of the PP and the TEM electron. The resulting three-dimensional PP potential, which now includes these variations, is then used in a variant of the multislice algorithm to compute the exit wave's interaction with the PP. The quality of the simulation was validated against previous theoretical calculations and the simulated images were quantitatively compared to the projected potential of the specimen using Fourier ring correlation. These simulations indicate that a TEM equipped with this type of PP could produce images with consistent contrast in a resolution band up to about 4 Å. This range could be extended to higher resolutions by a modified CTF-correction including the effect of the PP. The underlying idea of dynamic simulations taking the variation of optical elements and maybe even the specimen into account could be generalized to many other imaging situations.