Theoretical background of defocus image modulation processing (DIMP) based on three dimensional optical transfer functions (3D-OTFs)

Defocus-image modulation processing (DIMP), where a bipolar weighted image integration of the observed defocus series is performed, is one of the most promising ap preaches for real-time observation of spherical-aberration-free phase and amplitude images with a transmission electron microscope. DIMP can be extended to hollow-cone illumination (HCI) to improve the resolution of the electron microscope significantly, which has been already confirmed in the experiment using an optical microscope. In this paper, the theoretical background of DIMP is investigated by using 3D-OTFs in 3D-Fourier space. First, 3D-OTFs are derived under coherent illumination and the filtering characteristics of the DIMP are interpreted using the 3D-OTFs. Then the bipolar weighting functions used in DIMP are obtained by inverse Fourier transform of the filter functions in 3D-Fourier space under axial and hollow-cone illuminations.