Analysis of the spectral interferograms using Fourier-transform and recurrence non-linear data processing methods

摘要

Spectral-domain optical interference phenomena for broadband spectra take in the case of a two-beam interference the forms of the spectral interferograms. The group optical path differences (OPDs) between interfering beams that include information about the distance to be measured and about the properties of propagating wavefronts are inscribed in phase functions of the corresponding spectral interferograms. To recover the phase functions, a standard, Fourier-transform method, or a new, recurrence non-linear data processing method can be used. In the former case, the Fourier spectra in the wavelength domain are computed and filtered out to obtain the reference spectrum and the overall phase information using a phase-unwrapping algorithm. In the latter case, interferometric data are assumed to be a series of samples of the interferometric signal defined by a known model. It is predicted the signal value from the previous step of discretization to the next step. The prediction error is used for the signal parameters corrections. Recurrence non-linear processing generally gives the optimal dynamic assessment of the phase function, frequency and visibility maximum position of the interferogram. The method was applied for the spectral interferograms measured in the Michelson interferometer configuration and a low-coherence source to recover the corresponding phase functions. The recovered phase functions and the corresponding group OPDs were compared with those obtained using the Fourier-transform method.