Effect of a physical phase plate on contrast transfer in an aberration-corrected transmission electron microscope

Abstract

In this theoretical study we analyze contrast transfer of weak-phase objects in a transmission electron microscope, which is equipped with an aberration corrector ( C s-corrector) in the imaging lens system and a physical phase plate in the back focal plane of the objective lens. For a phase shift of π/2 between scattered and unscattered electrons induced by a physical phase plate, the sine-type phase contrast transfer function is converted into a cosine-type function. Optimal imaging conditions could theoretically be achieved if the phase shifts caused by the objective lens defocus and lens aberrations would be equal to zero. In reality this situation is difficult to realize because of residual aberrations and varying, non-zero local defocus values, which in general result from an uneven sample surface topography. We explore the conditions—i.e. range of C s-values and defocus—for most favourable contrast transfer as a function of the information limit, which is only limited by the effect of partial coherence of the electron wave in C s-corrected transmission electron microscopes. Under high-resolution operation conditions we find that a physical phase plate improves strongly low- and medium-resolution object contrast, while improving tolerance to defocus and C s-variations, compared to a microscope without a phase plate.