Imaging built-in electric fields and light matter by Fourier-precession TEM

We report the precise measurement of electric fields in nanostructures, and high-contrast imaging of soft matter at ultralow electron doses by transmission electron microscopy (TEM). In particular, a versatile method based on the theorem of reciprocity is introduced to enable differential phase contrast imaging and ptychography in conventional, plane-wave illumination TEM. This is realised by a series of TEM images acquired under different tilts, thereby introducing the sampling rate in reciprocal space as a tuneable parameter, in contrast to momentum-resolved scanning techniques. First, the electric field of a p–n junction in GaAs is imaged. Second, low-dose, in-focus ptychographic and DPC characterisation of Kagome pores in weakly scattering covalent organic frameworks is demonstrated by using a precessing electron beam in combination with a direct electron detector. The approach offers utmost flexibility to record relevant spatial frequencies selectively, while acquisition times and dose requirements are significantly reduced compared to the 4D-STEM counterpart.