Apparatus (1) for additively manufacturing three-dimensional objects (2) by means of successive layerwise selective irradiation and consolidation of layers of a build material (3) which can be consolidated by means of an energy source (5), wherein a measurement beam source (4, 17) is provided which is adapted to generate a measurement beam (7), wherein a beam guiding unit (20) is provided that is adapted to guide the measurement beam (7) in the build plane (6) in the process chamber, wherein a determination device (8) is adapted to determine at least one parameter relating to the object (2) and/or a build material layer (9) based on interference.