Unique interpretation of Talbot Bands and Fourier domain white light interferometry

A theoretical model is developed to interpret the output of the diffraction grating spectrometer used to analyze the channelled spectrum produced by a low coherence interferometer set-up. This model leads to an unique interpretation which covers both cases (i) of Talbot bands and (ii) of a Michelson interferometer used in most spectral interferometry set-ups for sensing as well as for Fourier domain optical coherence tomography (FDOCT). Explanation of Talbot bands visibility as well as the decay of sensitivity with depth, characteristic for FDOCT, is explained by considering the extension of the two wavetrains diffracted by the diffraction grating in the spectrometer.