Apparatus and methods for measuring a surface of a sample

In one arrangement, a surface follower 8 is configured to interact with a local portion 10 of a surface 4 of a sample 6 such that a position along a first axis of an interrogation surface of the surface follower depends on a position along the first axis (axis Z) of the local portion of the surface of the sample. A sensing arrangement 14 is configured to measure the position of the interrogation surface 12 along the first axis by detecting electromagnetic radiation (eg. laser, infrared radiation) reflected or scattered from the interrogation surface, thereby measuring the position of the local portion of the surface of the sample along the first axis. A positioner 20 is configured to provide relative movement between the sample and the surface follower in directions perpendicular to the first axis, thereby allowing the sensing arrangement to measure positions along the first axis of a plurality of different local portions of the surface of the sample.