  The properties of semiconductors and functional dielectrics are defined by
their response in electric fields, which may be perturbed by defects and the
strain they generate. In this work, we demonstrate how diffraction-based X-ray
microscopy techniques may be utilized to image the electric field in insulating
crystalline materials. By analysing a prototypical ferro- and piezoelectric
material, BaTiO$_{3}$, we identify trends that can guide experimental design
towards imaging the electric field using any diffraction-based X-ray microscopy
technique. We explain these trends in the context of dark-field X-ray
microscopy, but the framework is also valid for Bragg scanning probe X-ray
microscopy, Bragg coherent diffraction imaging and Bragg X-ray ptychography.
The ability to quantify electric field distributions alongside the defects and
strain already accessible via these techniques offers a more comprehensive
picture of the often complex structure-property relationships that exist in
many insulating and semiconducting materials.
