Optimal Imaging Parameters in Cs-Corrected Transmission Electron Microscopy with a Physical Phase Plate

Abstract

The double-hexapole Cs-corrector [1] has substantially improved resolution and interpretability of images in transmission electron microscopy. The device allows the adjustment of arbitrary, even negative Cs-values with a precision of ∼ 1 µm. Lentzen et al. [2] derived optimum imaging parameters \( C_{S,Len} = {\raise0.5ex\hbox{$\scriptstyle {64}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {27}$}}(\lambda ^{ - 3} u._{\inf }^{ - 4} ) \) and \( Z_{Len} = - {\raise0.5ex\hbox{$\scriptstyle {16}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 9$}}(\lambda ^{ - 1} u._{\inf }^{ - 2} ) \) (uinf: spatial frequency corresponding the information limit) for imaging weak-phase objects with a Cs-corrected microscope without a physical phase plate. These settings result in high contrast transfer at intermediate and large spatial frequencies and optimized delocalisation but transfer at low spatial frequencies is limited due to the sine shape of the phase contrast transfer function (PCTF). Combining Cs-correction with a physical phase plate in the back focal plane of the objective lens could overcome this problem. Several different concepts for physical phase plates were proposed and realized successfully in the recent past [3–5]. In analogy to Zernike’s λ/4 phase plate in light microscopy, such phase plates generate a phase shift χPP between the scattered and unscattered electrons. The total phase shift of the electrons is then given by \( \chi _{tot} (u) = \pi (z\lambda u^2 + 1/2C_S \lambda ^3 u^4 ) + \chi _{pp} \) resulting in a cosine shape of the PCTF for χpp=π/2.