Abstract 4D-STEM, in which the 2D diffraction plane is captured for each 2D scan position in the scanning transmission electron microscope (STEM) using a pixelated detector, is complementing, and increasingly replacing existing imaging approaches. However, at present the speed of those detectors, although having drastically improved in the recent years, is still 100 to 1,000 times slower than the current PMT technology operators are used to. Regrettably, this means environmental scanning-distortion often limits the overall performance of the recorded 4D data. Here, we present an extension of existing STEM distortion correction techniques for the treatment of 4D data series. Although applicable to 4D data in general, we use electron ptychography and electric-field mapping as model cases and demonstrate an improvement in spatial fidelity, signal-to-noise ratio (SNR), phase precision, and spatial resolution.