This work focuses on the compensation of motion artefacts that may occur during a line scan acquisition and can be detected with our multi-line scan imaging system [10]. These artefacts are caused by fluctuations of the transport velocity that are not correctly reflected by the camera trigger, and are especially visible at high magnifications. We reduce such artefacts by analyzing the light field acquired with our system. Specifically, we use a variational formulation to design a warping function, such that lines that are acquired too early or too late are stretched or squeezed appropriately. To this end, we exploit the information comprised in the light field, i.e., control the estimation of the warping function by comparing light field views and enforce uniform spacing between line acquisitions. The proposed approach enables our system to perform the multi-line scan light field imaging at virtually any magnification independent from the transport and trigger quality. We demonstrate the capabilities of our approach for various objects by comparing 3D reconstructions from unprocessed acquisitions and our corrected acquisitions. Our approach significantly reduces artefacts in light fields and in 3D reconstructions that are generated from them.