Method and system for determining the local position of at least one optical element in a machine for laser processing of a material, using low-coherence optical interferometry techniques

A method for determining local position of an optical element associated with an optical path for transporting a laser beam in a working head of a machine for laser processing a material, includes generating a measurement beam of low coherence optical radiation traveling a measurement optical path, leading the measurement beam towards the optical element and the reflected or diffused measurement beam towards an optical interferometric sensor arrangement, generating a reference beam of low coherence optical radiation traveling a reference optical path and leading the reference beam towards the interferometric optical sensor arrangement, superimposing the measurement and reference beams on a common region of incidence, detecting a position of a pattern of interference fringes between the measurement and reference beams, and determining a difference in optical length between the measurement and reference optical paths as a function of the position of the interference pattern along an illumination axis, or of the frequency of the interference pattern in the frequency domain.