Method of measuring a displacement speed of a mobile element, comprising the following steps: - connecting a first mirror to the mobile element so that said first mirror is driven in a first mirror displacement during the displacement of said mobile element; - arranging a source in order to produce a radiation beam having an initial radiation intensity, and means for producing an interference between a first part of said radiation beam reflected by the first mirror and a second part of said radiation beam reflected by a second mirror; and - arranging a detector for simultaneously receiving the first and second parts of the radiation beam after said beam parts have been reflected respectively by the first and second mirrors, for measuring a radiation intensity produced by the interference; so that respective optical paths of the first and second parts of the radiation beam have lengths between the source and the detector which vary differently during the displacement of the mobile element, said displacement of the mobile element thus itself producing a variation in the intensity measured by the detector at a first frequency when the initial intensity (A 0) of the radiation beam produced by the source is constant; said method being characterised in that it further comprises the following steps: /1/ during the displacement of the mobile element: modulating the initial intensity (A 0) of the radiation beam produced by the source at a second frequency (f 0) and simultaneously activating the detector; then /2/ determining the displacement speed of the mobile element from a spectral component of the radiation intensity measured by the detector during said displacement of the mobile element, said spectral component being correlated with a difference between said first frequency and said second frequency, and the second frequency (f 0) with which the initial intensity of the source is modulated corresponds to a target value for the displacement speed of the mobile element, and whereby said displacement speed of the mobile element is automatically controlled as a function of the difference between said first frequency and said second frequency. - connecting a first mirror to the mobile element so that said first mirror is driven in a first mirror displacement during the displacement of said mobile element; - arranging a source in order to produce a radiation beam having an initial radiation intensity, and means for producing an interference between a first part of said radiation beam reflected by the first mirror and a second part of said radiation beam reflected by a second mirror; and - arranging a detector for simultaneously receiving the first and second parts of the radiation beam after said beam parts have been reflected respectively by the first and second mirrors, for measuring a radiation intensity produced by the interference; so that respective optical paths of the first and second parts of the radiation beam have lengths between the source and the detector which vary differently during the displacement of the mobile element, said displacement of the mobile element thus itself producing a variation in the intensity measured by the detector at a first frequency when the initial intensity (A 0) of the radiation beam produced by the source is constant; said method being characterised in that it further comprises the following steps: /1/ during the displacement of the mobile element: modulating the initial intensity (A 0) of the radiation beam produced by the source at a second frequency (f 0) and simultaneously activating the detector; then /2/ determining the displacement speed of the mobile element from a spectral component of the radiation intensity measured by the detector during said displacement of the mobile element, said spectral component being correlated with a difference between said first frequency and said second frequency, /1/ during the displacement of the mobile element: modulating the initial intensity (A 0) of the radiation beam produced by the source at a second frequency (f 0) and simultaneously activating the detector; then /2/ determining the displacement speed of the mobile element from a spectral component of the radiation intensity measured by the detector during said displacement of the mobile element, said spectral component being correlated with a difference between said first frequency and said second frequency,