An apparatus for measurement of the thickness of thin layers by means of X-rays using an X-ray tube which emits X-rays which are directed at a layer to be measured, has at least one aperture apparatus arranged between the X-ray tube and the layer to be measured. The apparatus includes an area absorbing X-rays and an aperture opening. At least one aperture opening in the aperture apparatus has a geometric shape which, seen in the beam direction, projects an area which at least in places is matched to the geometry of the layer to be measured.