Precise method for measuring spatial coherence in TEM beams using Airy diffraction patterns

Abstract

Abstract We have developed a method to precisely measure spatial coherence in electron beams. The method does not require an electron biprism and can be implemented in existing analytical transmission electron microscopes equipped with a post-column energy filter. By fitting the Airy diffraction pattern of the selector aperture, various parameters such as geometric aberrations of the lens system and the point-spread function of the diffraction blurring are precisely determined. From the measurements of various beam diameters, components that are attributed to the partial spatial coherence are successfully separated from the point-spread functions. A linear relationship between the spatial coherence length and beam diameter is revealed, thus indicating that a wide range of coherence lengths can be determined by our proposed method as long as the coherence length remains >80% of the aperture diameter. A remarkable feature of this method is its ability to simultaneously determine diffraction blurring and lens aberrations. Possible applications of this method are also discussed.