Localization of stationary phase point through centroid shift in spectral interference

Abstract We present a novel method for investigating material dispersion in spectral interferometry by analysing the behaviour of spectral modulations in the vicinity of stationary phase points through centroid shift variations as a function of path delay. The centroid shift distributions of spectral modulations carry distinct signatures that can localize stationary phase points, with the extent of asymmetry in these curves directly linked to the dispersion present in the optical system. A Michelson interferometer employing sources with Gaussian spectral profiles centred at a single wavelength and possessing narrow bandwidths is capable of probing the spectral response while minimizing the adverse effects of chromatic dispersion within the optical system. In addition, the use of a spectrometer combined with automated path-delay scanning ensures reliable data acquisition. This approach represents a narrowband variant of spectrally resolved interferometry, optimized for group refractive index measurement, where full dispersion curves are not required. The method avoids rigorous fitting procedures, complex phase unwrapping, and cumbersome data processing. This simplified spectrally resolved interferometry using centroid shift tracking enables compact, dispersion-free, and accurate group refractive index measurement with minimal computational overhead, outperforming broadband methods for narrowband applications.