Spectrally Resolved White-Light Interferometric Sensor for Absolute Position Measurement Based on Hilbert Transform

A spectrally resolved white-light interferometric sensor for absolute position measurement based on Hilbert transform is presented. In order to avoid the possible singularities in the standard method obtained during the division of the measured spectral fringes and their Hilbert transform, a novel method is developed. The method is based on the simple mathematical apparatus where the division with zero is avoided by the division of the measured channeled spectrum and its Hilbert transform with envelope of both functions. Both of the divided functions are further differentiated, squared, and summed in order to find the optical path difference in the interferometer and thus the absolute position. The proposed sensing system currently provides unambiguous measurement over a range of 200 μm with a mid range error of better than 17 nm.