The sampling of sound fields involves the measurement of spatially dependent room impulse responses, where the Nyquist-Shannon sampling theorem applies in both the temporal and spatial domain. Therefore, sampling inside a volume of interest requires a huge number of sampling points in space, which comes along with further difficulties such as exact microphone positioning and calibration of multiple microphones. In this paper, we present a method for measuring sound fields using moving microphones whose trajectories are known to the algorithm. At that, the number of microphones is customizable by trading measurement effort against sampling time. Through spatial interpolation of the dynamic measurements, a system of linear equations is set up which allows for the reconstruction of the entire sound field inside the volume of interest.