Holographic contrast transfer theory
With the advent of reliable cold field emission transmission electron microscopes there is substantial interest in using the amplitude and phase information recorded in electron holograms to optically or numerically correct for the coherent aberrations of transmission electron microscopes. However electron holography cannot compensate for incoherent aberrations. The derivation of the contrast transfer function for off axis electron holography in this paper shows there is no fundamental improvement in resolution for electron holography over conventional transmission electron microscopy.Evaluating the contrast transfer function involves mathematically following an electron beam through a field emission electron microscope set up for off axis electron holography. Due to the high coherence of the field emission electron beam coherent aberrations caused by the pre-specimen beam focusing system must be accounted for. Starting with a spacial frequency distribution, C(v), for the electron beam leaving the gun, the electron beam is limited by the condenser aperture and coherently aberrated by the condenser lens and objective pre-field as it passes to the specimen region: