In this article the Fourier transform method is applied to analyze multiple-beam interference Fizeau fringes. The real part of the inverse Fourier transform is used to estimate a theoretical pattern. This pattern coincides with the experimental one. A derivative-sign binary image of the interference pattern is also used in automated determination of the contour line of the fringe pattern, regardless of the quality of this pattern. A correlation between the pixel size and the accuracy of the measured fiber refractive index is presented.