A wafer grooving apparatus (100) for forming an elongate recess (103) in a semiconductor wafer surface, the apparatus comprising:a wafer table (110) for receiving and holding a semiconductor wafer;a radiation device (120) for generating a radiation beam (121);a beam directing device (130) for directing the radiation beam to a top surface (102) of the wafer so as to create a beam spot (142) where the radiation beam ablates wafer material on the wafer surface to form a recess;a wafer table displacement drive (170) for effecting a mutual displacement between the radiation beam and the wafer surface in a radiation beam displacement direction;a recess profile measuring device (180) arranged at a predetermined distance behind the beam directing device in the radiation beam displacement direction effected by the wafer table displacement drive for measuring a depth profile of the recess that has been formed by the radiation beam.