Signal processing in white-light scanning interferometry by Fourier transform and its application to surface profile measurements

A general equation of the interference signal of white-light scanning interferometer (WSI) and its Fourier transform are derived. Based on these equations, simulations and experiments are performed to investigate effects of phase random noise and dispersion phase. In the experiments a new method for elimination of a dispersion effect in WSI is proposed. A dispersion phase caused by the two sides of unequal length in a beam-splitter is detected with a spectrally resolved interferometer (SRI). A spectral distribution is obtained by using Fourier transform from an interference signal detected with a WSI. The spectral phase of the SRI is subtracted from the spectral phase of the WSI to get a dispersion-free spectral phase, which provides an improved complex-valued interference signal whose maximum amplitude and zero phase provide two measurement values. These two measurement values are compared to a measurement value obtained from the linear component in the spectral phase.